In this paper, integration of the power series method and the Padé approximants (PS-Padé) is utilized to study buckling and pull-in instability of multi-walled carbon nanotube (MWCNT) cantilevers in the vicinity of graphite sheets due to intermolecular forces. A hybrid nano-scale continuum model based on the Lennard–Jones potential is used to simulate the Van der Waals forces and evaluate the buckling of MWCNT. A closed form power series, based on the symbolic power series polynomials, is utilized to obtain a series solution for the governing boundary value differential equation of the nanotube. In order to handle the boundary conditions and increasing the accuracy of solution, the symbolic power series are transformed into Padé approximants. The governing differential equation is also solved numerically using the finite difference method. The PS-Padé results are compared with the numerical results and other methods reported in literature. The results obtained by using the PS-Padé approach correspond very well with the numerical results. Furthermore, the detachment length and the minimum gap between MWCNT and the graphite plane as important parameters of engineering designs are computed. It is found that for a fixed gap, the detachment length of a MWCNT can be increased with the increase of the radius, wall thickness and the effective Young modulus of the MWCNT.
A New Two-Dimensional Analytical Model of Small Geometry GaAs MESFETIJMERJOURNAL
ABSTRACT : In this paper, a simple and exact analytical model for Small Geometry GaAs MESFET is developed to determine the potential distribution along the channel of the device. The model is based on the exact solution of two-dimensional Poisson’s equation in the depletion region under the gate. Then the obtained model is used to study the channel potential and threshold voltage of the device. Using the analytical model, the effect of the device parameter and bias conditions on performance of the device is investigated. The obtained results are graphically exhibited and discussed. In order to verification of the analytical results, TCAD device simulator is used and good accordance is observed.
First order shear deformation (FSDT) theory for laminated composite beams is used to study free vibration of
laminated composite beams, and finite element method (FEM) is employed to obtain numerical solution of the
governing differential equations. Free vibration analysis of laminated beams with rectangular cross – section for
various combinations of end conditions is studied. To verify the accuracy of the present method, the frequency
parameters are evaluated and compared with previous work available in the literature. The good agreement with
other available data demonstrates the capability and reliability of the finite element method and the adopted beam
model used.
ON INCREASING OF DENSITY OF ELEMENTS IN A MULTIVIBRATOR ON BIPOLAR TRANSISTORSijcsitcejournal
In this paper we consider an approach to increase density of elements of a multivibrator on bipolar transistors.
The considered approach based on manufacturing a heterostructure with necessity configuration,
doping by diffusion or ion implantation of required areas to manufacture the required type of conductivity
(p or n) in the areas and optimization of annealing of dopant and/or radiation defects to manufacture more
compact distributions of concentrations of dopants. We also introduce an analytical approach to prognosis
technological process.
This document summarizes research on using an immersed boundary method with wall modeling for large-eddy simulation (LES) of complex high Reynolds number flows. The researchers developed a two-layer wall modeling approach to extend the applicability of LES to higher Reynolds numbers by replacing the near-wall region with a simplified model. Preliminary results of simulations of flow over a hydrofoil trailing edge showed improvement over LES without a wall model, though some discrepancies remained compared to experimental data and previous full LES, which could be addressed in future work through grid refinement. The wall modeling approach reduced computational cost compared to fully resolving the boundary layer.
Nonlinear Viscoelastic Analysis of Laminated Composite Plates – A Multi Scale...rtme
Laminated composite plates are widely used in modern structures. Resins of composites are almost made of
polymers which show time dependent and and in some cases stress dependent behaviour. In this paper, a
laminated composite plate is analysed using a multiscale method. At first, material properties of a lamina is
obtained using an analytical micromechanical approach called simplified unit cell method (SUCM) and
then in macromechanical level, Generalized Differential Quadrature Method (GDQM) is used to analyse
laminated composite plate. Schapery's integral is used to model nonlinear viscoelastic behaviour of the
matrix. Prony series is considered to define the compliance of matrix. Micromechanical process includes
obtaining overall properties of the composite by SUCM. Both geometrical and material nonlinearity are
taken into account in order to multiscale analysis of laminated composite plate.
FURTHER RESULTS ON THE DIRAC DELTA APPROXIMATION AND THE MOMENT GENERATING FU...IJCNC
In this article, we employ two distinct methods to derive simple closed-form approximations for the
statistical expectations of the positive integer powers of Gaussian probability integral Eg [Qp ( bWg )]
with
respect to its fading signal-to-noise ratio (SNR) g random variable. In the first approach, we utilize the
shifting property of Dirac delta function on three tight bounds/approximations for Q(.) to circumvent the
need for integration.
The document discusses the chimera grid method for computational fluid dynamics simulations of complex geometries. It has two main elements: (1) decomposition of the computational domain into sub-domains that are each gridded independently, and (2) communication of solution data between sub-domains through interpolation. Overlapping grids allow each sub-domain to be gridded with structured grids while handling interfaces through hole and outer boundaries. The chimera grid method makes it possible to model problems with complex geometries using easier-to-generate body-fitted grids. It has been used successfully for simulations of configurations like the integrated space shuttle.
A Numerical Method for Modelling Discontinuous Mechanics of Asphalt MixtureIDES Editor
In order to simulate discontinuous mechanics for
asphalt mixture pavement, a new numerical scheme—
Meshfree Manifold Method is deduced in this paper by
integrating Numerical Manifold Method and Mesh-free
Method, which is not only appropriate for contact computation
but easy to eliminate the limitation of regular mesh. Some
kernel principles are discussedÿand an example is given to
prove its efficiency in simulating discontinuous deformation
of asphalt mixture.
A New Two-Dimensional Analytical Model of Small Geometry GaAs MESFETIJMERJOURNAL
ABSTRACT : In this paper, a simple and exact analytical model for Small Geometry GaAs MESFET is developed to determine the potential distribution along the channel of the device. The model is based on the exact solution of two-dimensional Poisson’s equation in the depletion region under the gate. Then the obtained model is used to study the channel potential and threshold voltage of the device. Using the analytical model, the effect of the device parameter and bias conditions on performance of the device is investigated. The obtained results are graphically exhibited and discussed. In order to verification of the analytical results, TCAD device simulator is used and good accordance is observed.
First order shear deformation (FSDT) theory for laminated composite beams is used to study free vibration of
laminated composite beams, and finite element method (FEM) is employed to obtain numerical solution of the
governing differential equations. Free vibration analysis of laminated beams with rectangular cross – section for
various combinations of end conditions is studied. To verify the accuracy of the present method, the frequency
parameters are evaluated and compared with previous work available in the literature. The good agreement with
other available data demonstrates the capability and reliability of the finite element method and the adopted beam
model used.
ON INCREASING OF DENSITY OF ELEMENTS IN A MULTIVIBRATOR ON BIPOLAR TRANSISTORSijcsitcejournal
In this paper we consider an approach to increase density of elements of a multivibrator on bipolar transistors.
The considered approach based on manufacturing a heterostructure with necessity configuration,
doping by diffusion or ion implantation of required areas to manufacture the required type of conductivity
(p or n) in the areas and optimization of annealing of dopant and/or radiation defects to manufacture more
compact distributions of concentrations of dopants. We also introduce an analytical approach to prognosis
technological process.
This document summarizes research on using an immersed boundary method with wall modeling for large-eddy simulation (LES) of complex high Reynolds number flows. The researchers developed a two-layer wall modeling approach to extend the applicability of LES to higher Reynolds numbers by replacing the near-wall region with a simplified model. Preliminary results of simulations of flow over a hydrofoil trailing edge showed improvement over LES without a wall model, though some discrepancies remained compared to experimental data and previous full LES, which could be addressed in future work through grid refinement. The wall modeling approach reduced computational cost compared to fully resolving the boundary layer.
Nonlinear Viscoelastic Analysis of Laminated Composite Plates – A Multi Scale...rtme
Laminated composite plates are widely used in modern structures. Resins of composites are almost made of
polymers which show time dependent and and in some cases stress dependent behaviour. In this paper, a
laminated composite plate is analysed using a multiscale method. At first, material properties of a lamina is
obtained using an analytical micromechanical approach called simplified unit cell method (SUCM) and
then in macromechanical level, Generalized Differential Quadrature Method (GDQM) is used to analyse
laminated composite plate. Schapery's integral is used to model nonlinear viscoelastic behaviour of the
matrix. Prony series is considered to define the compliance of matrix. Micromechanical process includes
obtaining overall properties of the composite by SUCM. Both geometrical and material nonlinearity are
taken into account in order to multiscale analysis of laminated composite plate.
FURTHER RESULTS ON THE DIRAC DELTA APPROXIMATION AND THE MOMENT GENERATING FU...IJCNC
In this article, we employ two distinct methods to derive simple closed-form approximations for the
statistical expectations of the positive integer powers of Gaussian probability integral Eg [Qp ( bWg )]
with
respect to its fading signal-to-noise ratio (SNR) g random variable. In the first approach, we utilize the
shifting property of Dirac delta function on three tight bounds/approximations for Q(.) to circumvent the
need for integration.
The document discusses the chimera grid method for computational fluid dynamics simulations of complex geometries. It has two main elements: (1) decomposition of the computational domain into sub-domains that are each gridded independently, and (2) communication of solution data between sub-domains through interpolation. Overlapping grids allow each sub-domain to be gridded with structured grids while handling interfaces through hole and outer boundaries. The chimera grid method makes it possible to model problems with complex geometries using easier-to-generate body-fitted grids. It has been used successfully for simulations of configurations like the integrated space shuttle.
A Numerical Method for Modelling Discontinuous Mechanics of Asphalt MixtureIDES Editor
In order to simulate discontinuous mechanics for
asphalt mixture pavement, a new numerical scheme—
Meshfree Manifold Method is deduced in this paper by
integrating Numerical Manifold Method and Mesh-free
Method, which is not only appropriate for contact computation
but easy to eliminate the limitation of regular mesh. Some
kernel principles are discussedÿand an example is given to
prove its efficiency in simulating discontinuous deformation
of asphalt mixture.
On the solution of incompressible fluid flow equationsAlexander Decker
This document compares the performance of three iterative methods - Gauss-Seidel, Point Successive Over-Relaxation, and Generalized Minimal Residual - for solving large sparse linear systems arising from computations of incompressible Navier-Stokes equations. The methods are applied to solve the lid-driven cavity benchmark problem. It is found that as the mesh size increases, GMRES converges faster and requires less CPU time than the other two methods.
11.on the solution of incompressible fluid flow equationsAlexander Decker
This document summarizes a study comparing the performance of three iterative methods - Gauss-Seidel, Point Successive Over-relaxation, and Generalized Minimal Residual - for solving large sparse linear systems arising from numerical computations of incompressible Navier-Stokes equations. The study finds that as the mesh size increases, the Generalized Minimal Residual method converges faster and requires less CPU time than the other two methods.
TWO DIMENSIONAL MODELING OF NONUNIFORMLY DOPED MESFET UNDER ILLUMINATIONVLSICS Design
A two dimensional numerical model of an optically gated GaAs MESFET with non uniform channel doping has been developed. This is done to characterize the device as a photo detector. First photo induced voltage (Vop) at the Schottky gate is calculated for estimating the channel profile. Then Poisson’s equation for the device is solved numerically under dark and illumination condition. The paper aims at developing the MESFET 2-D model under illumination using Monte Carlo Finite Difference method. The results discuss about the optical potential developed in the device, variation of channel potential under different biasing and illumination and also about electric fields along X and Y directions. The Cgs under different illumination is also calculated. It has been observed from the results that the characteristics of the device are strongly influenced by the incident optical illumination.
The document describes a resistance distance method for determining isomorphism among planar kinematic chains and their derived mechanisms. The method represents kinematic chains as resistance graphs to generate a laplacian matrix and resistance distance matrix. Square sums of resistances in the resistance distance matrix are used as an index for identifying isomorphism. The method is tested on 6, 8, 10-link 1-DOF chains, a 9-link 2-DOF chain, and a 10-link 3-DOF chain, successfully determining the distinct mechanisms derived from each chain.
Optimization of Thin Adhesive Layer Based on Colonial Competitive AlgorithmWaqas Tariq
In this paper a novel evolutionary global search strategy called colonial competitive algorithm (CCA) is utilized to determine an optimal imperfect transmission condition for a thin intermediate layer which reveal between two bonded materials in a dissimilar strip with a temperature-dependent source or sink formulation. Recently introduced CCA has proven its excellent capabilities such as faster convergence and better global optimum achievement. Finally the results of CCA are compared with finite element analysis. Comparison is shown the success of CCA for design of adhesive joints.
A High Order Continuation Based On Time Power Series Expansion And Time Ratio...IJRES Journal
In this paper, we propose a high order continuation based on time power series expansion and time rational representation called Pad´e approximants for solving nonlinear structural dynamic problems. The solution of the discretized nonlinear structural dynamic problems, by finite elements method, is sought in the form of a power series expansion with respect to time. The Pad´e approximants technique is introduced to improve the validity range of power series expansion. The whole solution is built branch by branch using the continuation method. To illustrate the performance of this proposed high order continuation, we give some numerical comparisons on an example of forced nonlinear vibration of an elastic beam.
This document provides a summary of a master's thesis that analyzes smart composite beams using a meshfree method. The objectives of the project are to define shape function construction for meshfree methods, derive the solution for smart composite beams, and compare the meshfree method results to exact solutions for three-layered and four-layered composite beams. The document introduces meshfree methods, describes the moving least squares shape functions used, and presents the analysis of smart composite beams by deriving the governing equations and compatible displacement fields for the substrate beam and piezoelectric layer.
ON APPROACH TO DECREASE DIMENSIONS OF FIELD-EFFECT TRANSISTORS FRAMEWORK ELEM...ijfcstjournal
In this paper we consider manufacturing of elements SRAM with increased density of field-effect transistors
consisting these elements. The approach based on manufacturing of the elements in heterostructure with
specific configuration. We consider doping of several required areas of the heterostructure by diffusion or
by ion implantation. After that dopant and radiation defects have been annealed framework optimized
scheme.
ON DECREASING OF DIMENSIONS OF FIELDEFFECT TRANSISTORS WITH SEVERAL SOURCESmsejjournal
This document analyzes mass and heat transport during manufacturing field-effect heterotransistors with several sources to decrease their dimensions. An analytical approach is introduced to model mass and heat transport during technological processes like doping and annealing. This approach accounts for nonlinearities in mass and heat transport and variations in physical parameters over space and time. The goal is to optimize doping distributions to increase compactness and homogeneity of transistor elements. Equations are developed to model concentration distributions of dopants and point defects over space and time during diffusion and ion implantation doping processes and subsequent annealing.
- The document proposes grey-box models that combine physics-based Morison's equation and data-based Gaussian process models to improve prediction of wave loading on offshore structures.
- Morison's equation is used as the physics component to predict wave loading from assumed wave particle velocities and accelerations. Gaussian process NARX models are used as the data-based components.
- Two approaches are presented for combining the white-box and black-box components: 1) simple summation, and 2) using the white-box prediction as additional input to the black-box. The best approach was found to be a residual modelling GP-NARX.
Numerical computation of eigenenergy and transmission coefficient of symmetri...IAEME Publication
This document summarizes a study on numerically computing the eigenenergy and transmission coefficient of a symmetric quantum double barrier structure with variable effective mass under an applied electric field. The study uses the transfer matrix method to solve Schrodinger's equation for a GaAs/AlxGa1-xAs material system. It finds that eigenenergy decreases nonlinearly with increasing electric field. Transmission coefficient decreases with increasing barrier thickness or height but can occur at lower energies with increasing well thickness. The existence of higher quasi-bound states is also observed.
An approximate solution for plates resting on winkler foundationIAEME Publication
This document presents an approximate finite grid solution method for plates resting on a Winkler foundation. The method represents plates as a grid of intersecting beam elements, with each element using the exact stiffness matrix of a beam on a Winkler foundation. Shape functions are derived for the beam elements that include the effects of the foundation. Some example problems are solved using this finite grid representation and compared to known analytical solutions, showing accurate results. The method provides a computationally efficient way to solve general plate bending problems on an elastic foundation.
Mathematical models for a chemical reactorLuis Rodríguez
This document presents a mathematical model for the concentration of a chemical in a reactor. It examines both steady state and time-dependent models. For steady state, the model is an ordinary differential equation that can be solved analytically. For time dependence, the model is a partial differential equation that requires numerical solution. Two numerical methods are presented: an implicit finite difference method and the finite element method.
1) The document analyzes optimum parameters for a geometric multigrid method for solving a two-dimensional thermoelasticity problem and Laplace equation numerically.
2) It studies the effect of grid size, inner iterations, and number of grids on computational time.
3) The results are compared between the two problems, single-grid methods, and other literature to determine if coupling equations impacts multigrid performance.
Numerical Simulation and Prediction for Steep Water Gravity Waves of Arbitrar...CSCJournals
Nonlinear permanent progressive wave is one of the most important applications in water waves. In this study, analytic formulation of the steep water gravity waves is presented. Abohadima and Isobe [1] showed that Cokelet solution [2] is the most accurate among many other solutions. Due to the nonlinearity of analytic equations, the need to numeric simulation is raised up. In the current paper, consequence numerical models, using one of the artificial intelligence techniques, are designed to simulate and then predict the non linear properties of permanent steep water waves. Artificial Neural Network (ANN), one of the artificial intelligence techniques, is introduced in the current paper to simulate and predict the wave celerity, momentum, energy and other wave integral properties for any permanent waves in water of arbitrary uniform depth. The ANN results presented in the current study showed that ANN technique, with less effort, is very efficiently capable of simulating and predicting the non linear properties of permanent steep water waves.
Numerical Simulation of Gaseous Microflows by Lattice Boltzmann MethodIDES Editor
This work is concerned with application of the
Lattice Boltzmznn Method (LBM) to compute flows in microgeometries.
The choice of using LBM for microflow simulation
is a good one owing to the fact that it is based on the Boltzmann
equation which is valid for the whole range of the Knudsen
number. In this work LBM is applied to simulate the pressure
driven microchannel flows and micro lid-driven cavity flows.
First, the microchannel flow is studied in some details with
the effects of varying the Knudsen number, pressure ratio
and Tangential Momemtum Accomodation Coefficient
(TMAC). The pressure distribution and other parameters are
compared with available experimental and analytical data
with good agreement. After having thus established the
credibility of the code and the method including boundary
conditions, LBM is then used to investigate the micro liddriven
cavity flow. The computations are carried out mainly
for the slip regime and the threshold of the transition regime.
Relevance Vector Machines for Earthquake Response Spectra drboon
This study uses Relevance Vector Machine (RVM) regression to develop a probabilistic model for the average horizontal component of 5%-damped earthquake response spectra. Unlike conventional models, the proposed approach does not require a functional form, and constructs the model based on a set predictive variables and a set of representative ground motion records. The RVM uses Bayesian inference to determine the confidence intervals, instead of estimating them from the mean squared errors on the training set. An example application using three predictive variables (magnitude, distance and fault mechanism) is presented for sites with shear wave velocities ranging from 450 m/s to 900 m/s. The predictions from the proposed model are compared to an existing parametric model. The results demonstrate the validity of the proposed model, and suggest that it can be used as an alternative to the conventional ground motion models. Future studies will investigate the effect of additional predictive variables on the predictive performance of the model.
2011 santiago marchi_souza_araki_cobem_2011CosmoSantiago
This document discusses the performance of the multigrid method for solving the Navier-Stokes equations using two alternative formulations: streamfunction-velocity and streamfunction-vorticity. The study examines the lid-driven cavity flow problem for different grid sizes, Reynolds numbers, numbers of grid levels, and inner iterations to determine optimal parameter values that minimize CPU time. Previous research has found that the multigrid method is less effective for the Navier-Stokes equations at higher Reynolds numbers. The document aims to investigate how formulation choice and multigrid parameters influence efficiency.
The document contains a series of dates from 16/1/2015 with various letters and numbers, as well as Greek letters and words. It also includes a chart with 3 data series showing percentages ranging from 0% to 100%. The final lines contain additional dates from 16/1/2015 and letters/numbers.
Scenario of Rural Electrification in India- Challenges and ImpactIJERA Editor
In this paper, the present scenario of rural electrification in India is taken into account. Basically, the electrification in this country is facing a lot of problem and is a growing matter of concern for all. The development in production is not reaching the one who need them. Also taking into picture the present sources of energy it is difficult to make the electricity available to the people belonging to rural areas who don’t have much source of income. To overcome this drawback we can utilise renewable sources of energy which is easily available and accessible. Also harvesting this will not cost much except the initial cost of setting up the device to utilise this type of energy. Many projects have been initiated by the government of India to provide subsidy and equipments like solar lantern and solar cooker etc. to the rural population but this didn’t turn out to be effective as the follow could not be done by the people to maintain the devices. This can be overcome by implementing off-grid projects which can be initiated at small levels so that people don’t have burden to maintain them and it even don’t have any adverse effect to environment or society.
On the solution of incompressible fluid flow equationsAlexander Decker
This document compares the performance of three iterative methods - Gauss-Seidel, Point Successive Over-Relaxation, and Generalized Minimal Residual - for solving large sparse linear systems arising from computations of incompressible Navier-Stokes equations. The methods are applied to solve the lid-driven cavity benchmark problem. It is found that as the mesh size increases, GMRES converges faster and requires less CPU time than the other two methods.
11.on the solution of incompressible fluid flow equationsAlexander Decker
This document summarizes a study comparing the performance of three iterative methods - Gauss-Seidel, Point Successive Over-relaxation, and Generalized Minimal Residual - for solving large sparse linear systems arising from numerical computations of incompressible Navier-Stokes equations. The study finds that as the mesh size increases, the Generalized Minimal Residual method converges faster and requires less CPU time than the other two methods.
TWO DIMENSIONAL MODELING OF NONUNIFORMLY DOPED MESFET UNDER ILLUMINATIONVLSICS Design
A two dimensional numerical model of an optically gated GaAs MESFET with non uniform channel doping has been developed. This is done to characterize the device as a photo detector. First photo induced voltage (Vop) at the Schottky gate is calculated for estimating the channel profile. Then Poisson’s equation for the device is solved numerically under dark and illumination condition. The paper aims at developing the MESFET 2-D model under illumination using Monte Carlo Finite Difference method. The results discuss about the optical potential developed in the device, variation of channel potential under different biasing and illumination and also about electric fields along X and Y directions. The Cgs under different illumination is also calculated. It has been observed from the results that the characteristics of the device are strongly influenced by the incident optical illumination.
The document describes a resistance distance method for determining isomorphism among planar kinematic chains and their derived mechanisms. The method represents kinematic chains as resistance graphs to generate a laplacian matrix and resistance distance matrix. Square sums of resistances in the resistance distance matrix are used as an index for identifying isomorphism. The method is tested on 6, 8, 10-link 1-DOF chains, a 9-link 2-DOF chain, and a 10-link 3-DOF chain, successfully determining the distinct mechanisms derived from each chain.
Optimization of Thin Adhesive Layer Based on Colonial Competitive AlgorithmWaqas Tariq
In this paper a novel evolutionary global search strategy called colonial competitive algorithm (CCA) is utilized to determine an optimal imperfect transmission condition for a thin intermediate layer which reveal between two bonded materials in a dissimilar strip with a temperature-dependent source or sink formulation. Recently introduced CCA has proven its excellent capabilities such as faster convergence and better global optimum achievement. Finally the results of CCA are compared with finite element analysis. Comparison is shown the success of CCA for design of adhesive joints.
A High Order Continuation Based On Time Power Series Expansion And Time Ratio...IJRES Journal
In this paper, we propose a high order continuation based on time power series expansion and time rational representation called Pad´e approximants for solving nonlinear structural dynamic problems. The solution of the discretized nonlinear structural dynamic problems, by finite elements method, is sought in the form of a power series expansion with respect to time. The Pad´e approximants technique is introduced to improve the validity range of power series expansion. The whole solution is built branch by branch using the continuation method. To illustrate the performance of this proposed high order continuation, we give some numerical comparisons on an example of forced nonlinear vibration of an elastic beam.
This document provides a summary of a master's thesis that analyzes smart composite beams using a meshfree method. The objectives of the project are to define shape function construction for meshfree methods, derive the solution for smart composite beams, and compare the meshfree method results to exact solutions for three-layered and four-layered composite beams. The document introduces meshfree methods, describes the moving least squares shape functions used, and presents the analysis of smart composite beams by deriving the governing equations and compatible displacement fields for the substrate beam and piezoelectric layer.
ON APPROACH TO DECREASE DIMENSIONS OF FIELD-EFFECT TRANSISTORS FRAMEWORK ELEM...ijfcstjournal
In this paper we consider manufacturing of elements SRAM with increased density of field-effect transistors
consisting these elements. The approach based on manufacturing of the elements in heterostructure with
specific configuration. We consider doping of several required areas of the heterostructure by diffusion or
by ion implantation. After that dopant and radiation defects have been annealed framework optimized
scheme.
ON DECREASING OF DIMENSIONS OF FIELDEFFECT TRANSISTORS WITH SEVERAL SOURCESmsejjournal
This document analyzes mass and heat transport during manufacturing field-effect heterotransistors with several sources to decrease their dimensions. An analytical approach is introduced to model mass and heat transport during technological processes like doping and annealing. This approach accounts for nonlinearities in mass and heat transport and variations in physical parameters over space and time. The goal is to optimize doping distributions to increase compactness and homogeneity of transistor elements. Equations are developed to model concentration distributions of dopants and point defects over space and time during diffusion and ion implantation doping processes and subsequent annealing.
- The document proposes grey-box models that combine physics-based Morison's equation and data-based Gaussian process models to improve prediction of wave loading on offshore structures.
- Morison's equation is used as the physics component to predict wave loading from assumed wave particle velocities and accelerations. Gaussian process NARX models are used as the data-based components.
- Two approaches are presented for combining the white-box and black-box components: 1) simple summation, and 2) using the white-box prediction as additional input to the black-box. The best approach was found to be a residual modelling GP-NARX.
Numerical computation of eigenenergy and transmission coefficient of symmetri...IAEME Publication
This document summarizes a study on numerically computing the eigenenergy and transmission coefficient of a symmetric quantum double barrier structure with variable effective mass under an applied electric field. The study uses the transfer matrix method to solve Schrodinger's equation for a GaAs/AlxGa1-xAs material system. It finds that eigenenergy decreases nonlinearly with increasing electric field. Transmission coefficient decreases with increasing barrier thickness or height but can occur at lower energies with increasing well thickness. The existence of higher quasi-bound states is also observed.
An approximate solution for plates resting on winkler foundationIAEME Publication
This document presents an approximate finite grid solution method for plates resting on a Winkler foundation. The method represents plates as a grid of intersecting beam elements, with each element using the exact stiffness matrix of a beam on a Winkler foundation. Shape functions are derived for the beam elements that include the effects of the foundation. Some example problems are solved using this finite grid representation and compared to known analytical solutions, showing accurate results. The method provides a computationally efficient way to solve general plate bending problems on an elastic foundation.
Mathematical models for a chemical reactorLuis Rodríguez
This document presents a mathematical model for the concentration of a chemical in a reactor. It examines both steady state and time-dependent models. For steady state, the model is an ordinary differential equation that can be solved analytically. For time dependence, the model is a partial differential equation that requires numerical solution. Two numerical methods are presented: an implicit finite difference method and the finite element method.
1) The document analyzes optimum parameters for a geometric multigrid method for solving a two-dimensional thermoelasticity problem and Laplace equation numerically.
2) It studies the effect of grid size, inner iterations, and number of grids on computational time.
3) The results are compared between the two problems, single-grid methods, and other literature to determine if coupling equations impacts multigrid performance.
Numerical Simulation and Prediction for Steep Water Gravity Waves of Arbitrar...CSCJournals
Nonlinear permanent progressive wave is one of the most important applications in water waves. In this study, analytic formulation of the steep water gravity waves is presented. Abohadima and Isobe [1] showed that Cokelet solution [2] is the most accurate among many other solutions. Due to the nonlinearity of analytic equations, the need to numeric simulation is raised up. In the current paper, consequence numerical models, using one of the artificial intelligence techniques, are designed to simulate and then predict the non linear properties of permanent steep water waves. Artificial Neural Network (ANN), one of the artificial intelligence techniques, is introduced in the current paper to simulate and predict the wave celerity, momentum, energy and other wave integral properties for any permanent waves in water of arbitrary uniform depth. The ANN results presented in the current study showed that ANN technique, with less effort, is very efficiently capable of simulating and predicting the non linear properties of permanent steep water waves.
Numerical Simulation of Gaseous Microflows by Lattice Boltzmann MethodIDES Editor
This work is concerned with application of the
Lattice Boltzmznn Method (LBM) to compute flows in microgeometries.
The choice of using LBM for microflow simulation
is a good one owing to the fact that it is based on the Boltzmann
equation which is valid for the whole range of the Knudsen
number. In this work LBM is applied to simulate the pressure
driven microchannel flows and micro lid-driven cavity flows.
First, the microchannel flow is studied in some details with
the effects of varying the Knudsen number, pressure ratio
and Tangential Momemtum Accomodation Coefficient
(TMAC). The pressure distribution and other parameters are
compared with available experimental and analytical data
with good agreement. After having thus established the
credibility of the code and the method including boundary
conditions, LBM is then used to investigate the micro liddriven
cavity flow. The computations are carried out mainly
for the slip regime and the threshold of the transition regime.
Relevance Vector Machines for Earthquake Response Spectra drboon
This study uses Relevance Vector Machine (RVM) regression to develop a probabilistic model for the average horizontal component of 5%-damped earthquake response spectra. Unlike conventional models, the proposed approach does not require a functional form, and constructs the model based on a set predictive variables and a set of representative ground motion records. The RVM uses Bayesian inference to determine the confidence intervals, instead of estimating them from the mean squared errors on the training set. An example application using three predictive variables (magnitude, distance and fault mechanism) is presented for sites with shear wave velocities ranging from 450 m/s to 900 m/s. The predictions from the proposed model are compared to an existing parametric model. The results demonstrate the validity of the proposed model, and suggest that it can be used as an alternative to the conventional ground motion models. Future studies will investigate the effect of additional predictive variables on the predictive performance of the model.
2011 santiago marchi_souza_araki_cobem_2011CosmoSantiago
This document discusses the performance of the multigrid method for solving the Navier-Stokes equations using two alternative formulations: streamfunction-velocity and streamfunction-vorticity. The study examines the lid-driven cavity flow problem for different grid sizes, Reynolds numbers, numbers of grid levels, and inner iterations to determine optimal parameter values that minimize CPU time. Previous research has found that the multigrid method is less effective for the Navier-Stokes equations at higher Reynolds numbers. The document aims to investigate how formulation choice and multigrid parameters influence efficiency.
The document contains a series of dates from 16/1/2015 with various letters and numbers, as well as Greek letters and words. It also includes a chart with 3 data series showing percentages ranging from 0% to 100%. The final lines contain additional dates from 16/1/2015 and letters/numbers.
Scenario of Rural Electrification in India- Challenges and ImpactIJERA Editor
In this paper, the present scenario of rural electrification in India is taken into account. Basically, the electrification in this country is facing a lot of problem and is a growing matter of concern for all. The development in production is not reaching the one who need them. Also taking into picture the present sources of energy it is difficult to make the electricity available to the people belonging to rural areas who don’t have much source of income. To overcome this drawback we can utilise renewable sources of energy which is easily available and accessible. Also harvesting this will not cost much except the initial cost of setting up the device to utilise this type of energy. Many projects have been initiated by the government of India to provide subsidy and equipments like solar lantern and solar cooker etc. to the rural population but this didn’t turn out to be effective as the follow could not be done by the people to maintain the devices. This can be overcome by implementing off-grid projects which can be initiated at small levels so that people don’t have burden to maintain them and it even don’t have any adverse effect to environment or society.
Analysis of Retrofitting Non-Linear Finite Element Of RCC Beam And Column Usi...IJERA Editor
Many of the existing reinforced concrete structures throughout the world are in urgent need of strengthening, repair or reconstruction because of deterioration due to various factors like corrosion, lack of detailing, failure of bonding between beam-column joints, increase in service loads, etc., leading to cracking, spalling, loss of strength, deflection, etc., Direct observation of these damaged structures has shown that damage occurs usually at the beam-column joints, with failure in bending or shear, depending on geometry and reinforcement distribution type.A nonlinear finite element analysis that is a simulation technique is used in this work to evaluate the effectiveness of retrofitting technique called “wrapping technique” for using carbon fibres (FRP) for strengthening of RC beam-column connections damaged due to various reasons. After carrying out a nonlinear finite element analysis of a reinforced concrete frame (Controlled Specimen) and reinforced concrete frame where carbon fibres are attached to the beam column joint portion in different patterns ,the measured response histories of the original and strengthened specimens are then subsequently compared. It is seen that the strengthened specimens exhibit significant increase in strength, stiffness, and stability as compared to controlled specimens. It appears that the proposed simulation technique will have a significant impact in engineering practice in the near future.
The document summarizes some common conventions for magazine front covers and content pages. For front covers, it discusses elements like the masthead, central image, main cover line, pull quotes, and layout considerations. For content pages, it describes how articles are numbered and labeled, how different sections are organized, and how images, headings, and text are structured and presented. Language features on the front cover like questions, alliteration, and quotes are also meant to attract readers.
This portable tea set allows users to enjoy a cup of tea anywhere while being inspired by viewing the moon, as is a tradition in Chinese culture. The set includes a 160ml double-walled glass teapot, two 66ml double-walled glass tea cups, and an EVA carrying bag to hold the set. The portable design lets users experience tea time outside as they view the moon no matter their location.
Modeling the transport of charge carriers in the active devices diode submicr...IJERA Editor
A Monte Carlo simulation program was developed to simulate the movement of electrons in a submicron GaInP diode three dimensional (3D) with 0.1 microns-long active layer. The algorithm couples a standard Monte Carlo particle simulator for the Boltzmann equation with a 3D Poisson solver. Thus a series of hits for a specific MC submicron diode (GaInP), with an active layer (n = 2x1015cm-3) of length 0.1μm surrounded by two regions doped with n = 5x1017cm-3, are presented. The lattice temperature is 300K and the anode voltage Va is 1V. The analysis also showed that the average drift velocity to the electrons in the channel is about 5x106 cm/sec
Studying the factors affecting solar power generation systems performance ( S...IJERA Editor
Solar energy is a huge, clean and renewable source of energy. It is also available everywhere on the earth. However, there are many technical and economic difficulties need to be solved so that solar energy becomes a strong competition against the traditional energy sources. Energy from the sun can be used successfully in electric power generation systems. Depending on the climate conditions and the use of a properly designed, installing and maintained system can meet a large demand in this request. Work plane for this research will include many steps, the first step will include an introduction to solar energy. The second step will be a short review of the solar energy availability, geometry, fields of applications and the largest commercial application of solar energy is the solar thermal power generation. In addition, the most common types of solar thermal power plants, the solar field, heat transfer fluid and the power conversion system types will be explained in detail. The third step, a simple analysis for the solar thermal power plant will be explained in order to predict the optimum conditions leading to maximum performance. Discussions of results will be the fourth step. The last step a conclusion and recommendation for future work will also be included.
Effect of Hand Transmitted Vibration through Tractor during Ploughing FieldIJERA Editor
This document summarizes a study that measured vibration transmission from a tractor steering wheel to an operator's wrist and upper arm during field plowing. Vibration sensors were attached to the steering wheel and the operator's wrist and upper arm to measure vibration levels. Test results found that the highest vibration transmissibility occurred in the frequency intervals of 1-20 Hz and 20-40 Hz. Vibration was highest at the upper arm sensor compared to the wrist sensor. The maximum power spectral densities were observed from 20-40 Hz at the steering wheel and from 1-20 Hz at the upper arm, indicating a risk of harm to operators from vibration in these frequency ranges.
An Intelligent Human Computer Communication with Real Time Hand Gesture for M...IJERA Editor
This document presents a system for controlling a wheelchair using finger gestures. A camera is mounted on the wheelchair to capture images of hand gestures. The images are processed using digital image processing techniques like blurring, color space conversion from RGB to HSV, and thresholding to detect and recognize fingers. The finger positions are used to determine gestures for controlling the wheelchair motors and directing its movement forward, backward, left, right, or stopping. An algorithm is provided to map finger positions to specific motor controls. The system was tested with 5 finger gestures and achieved 100% accuracy in controlling the wheelchair movement as intended by each gesture. The goal of the system is to provide an easier way for disabled people to control a wheelchair through simple hand gestures without
Exergy analysis of inlet water temperature of condenserIJERA Editor
The most of the power plant designed by energetic performance criteria based on first law of thermodynamics. According to First law of thermodynamics energy analysis cannot be justified the losses of energy.The method of exergy analysis is well suited to describe true magnitude of waste and loss to be determined. Such information can be used in the design of new energy efficient system and increasing the efficiency of existing systems.In the present study exergy analysis of the shell and tube condenser is carried out. As the condenser is one of the major components of the power plant, so it is necessary to operate the condenser efficiently under the various operating condition to increase the overall efficiency of the power plant. In the present study inlet temperature of the condenser is optimized using the exergy method. The main aim of paper is to be find out causes of energy destruction that can be helpful to redesign the system and to increase the efficiency
An analytical method with numerical results to be used in the design of optic...nooriasukmaningtyas
This study develops an analytical method with numerical results for the design of optical slab waveguides for optical communication system applications. An optical slab waveguide structure made of silicon on silicon dioxide material is designed and analyzed. The effective index of the mode is studied against variations in the waveguide dimensions. Transmission and reflection coefficients are studied and compared to the wavelength and dimensions of the waveguide. Variations are sketched with the x-axis, in addition to the electric field intensity distribution and effective refractive index. Waveguide bending loss is also studied with waveguide thickness and length variations within three waveguide transmission windows of 850 nm, 1300nm, and 1550nm.
Modelling Optical Waveguide Bends by the Method of LinesTELKOMNIKA JOURNAL
A rigorous analytical and semi analytical method of lines has been used to calculate the
transverse-electric field attenuation coefficient of guided mode as it travels in waveguide bends structure.
Both approaches then were compared to get a better understanding on how the attenuation behaves along
single curve waveguides with constant radius of curvature. The Helmholtz Equation in polar coordinate
was transformed into a curvalinier coordinate to simulate the waveguide bends using the method of line
analysis. The simple absorption boundary conditions are used into the method of lines to demonstrate
evanescent field of the guided mode nature as its travels in waveguide bends structures. The results show
that a reasonable agreement between both theoretical approaches.
Molecular dynamics simulation studies of mechanical properties of different c...Johan Zhi Kang Kok
This document discusses molecular dynamics simulations of the mechanical properties of carbon nanotube systems. It summarizes simulations performed on single-walled carbon nanotubes (SWCNTs) under axial tension, including the effects of varying strain rates and length-diameter ratios on the SWCNT's ultimate tensile strength and critical strain. Simulations were also conducted on double-walled carbon nanotubes (DWCNTs), including extracting the inner tube of a DWCNT and bending tests on DWCNTs with different intertube separations. The results provide insights into the mechanical behavior of carbon nanotubes at the atomic level.
FINITE ELEMENT ANALYSIS OF RIGID PAVEMENT USING EVERFE2.24& COMPARISION OF RE...civej
In this study analysis of plain cement concrete pavement was done with 3-D mechanistic FEM computer
programme EVERFE2.24. This programme was developed by Bill David, University of Maine,USA. Rigid
pavement is modelled as a flat slab with DLC as base course and subgrade beneath it.
Stresses in rigid pavement at critical location was calculated due to combined effect of axle load and
environmental factor.These results are compared with IRC58-2015&2002.The disparity between results
are analysed and plotted on graph.
This study finds that stressesgiven by IRC58-2015 is up to 42% less than that given by IRC58-2002, and
stresses given by EverFE2.24 is nearly same as given by IRC58-2002.italso highlighted some issues related
to new code of design i.e. IRC58-2015.
This document summarizes a research article that analyzes the wavefunctions and energy states of asymmetric double quantum wells (ADQWs) with smoothed interfaces due to interdiffusion or other static disorder effects. The discreet variable representative approach is used to solve the one-dimensional Schrodinger equation and determine the energy eigenvalues and eigenvectors. The behavior of ADQW states is investigated for different well widths, degrees of interface broadening, and under an external electric field. It is shown that interface broadening changes energy levels in a non-monotonic way but does not strongly distort resonant conditions near energy coupling regions. An external electric field may also help achieve resonant conditions for inter-subband emission.
An Efficient Algorithm for Contact Angle Estimation in Molecular Dynamics Sim...CSCJournals
It is important to find contact angle for a liquid to understand its wetting properties, capillarity and surface interaction energy with a surface. The estimation of contact angle from Non Equilibrium Molecular Dynamics (NEMD), where we need to track the changes in contact angle over a period of time is challenging compared to the estimation from a single image from an experimental measurement. Often such molecular simulations involve finite number of molecules above some metallic or non-metallic substrates and coupled to a thermostat. The identification of profile of the droplet formed during this time will be difficult and computationally expensive to process as an image. In this paper a new algorithm is explained which can efficiently calculate time dependent contact angle from a NEMD simulation just by processing the molecular coordinates. The algorithm implements many simple yet accurate mathematical methods available, especially to remove the vapor molecules and noise data and thereby calculating the contact angle with more accuracy. To further demonstrate the capability of the algorithm a simulation study has been reported which compares the contact angle influence with different thermostats in the Molecular Dynamics (MD) simulation of water over platinum surface.
Simulation and Analysis of III V Characteristic and Bandgap Design for Hetero...ijtsrd
This research is the analysis of computer based simulation design for the semiconductor laser diode. The paper is emphasized by analyzing the band structure and voltage current characteristics of AlGaAs GaAs for the laser diode. In this paper, bandgap variation temperature dependence, voltage current V I , band diagram of the p n junction for laser diode are discussed briefly. On the other hand, this paper is emphasized band structure design and voltage current calculation using the mathematical model. The AlGaAs GaAs device technology is used for high speed optical communication. Thu Rein Ye Yint Win | Tin Tin Hla "Simulation and Analysis of III-V Characteristic and Bandgap Design for Heterojunction Laser Diode" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26542.pdfPaper URL: https://www.ijtsrd.com/engineering/electronics-and-communication-engineering/26542/simulation-and-analysis-of-iii-v-characteristic-and-bandgap-design-for-heterojunction-laser-diode/thu-rein-ye-yint-win
This document summarizes research on modeling the effects of adding a rectangular slot to a microstrip patch antenna. The researchers developed an analytical model to predict how the resonant frequency changes based on the slot's length, width, and position. They conducted simulations varying the slot parameters and found that the resonant frequency generally follows a harmonic behavior similar to an antenna without a slot. Experimental antenna prototypes were fabricated and tested, finding good agreement with simulation results. Mathematical functions are presented that can describe how the slot affects specific antenna characteristics.
Total Ionization Cross Sections due to Electron Impact of Ammonia from Thresh...Dr. Amarjeet Singh
In the present paper, we have employed modified Khare-BEB method [Atoms, (2019)] to evaluate total ionization cross sections by the electron impact for ammonia in energy range from the ionization threshold to 10 MeV. The theoretical ionization cross sections have been compared to the available previous theoretical and experimental results. The collision parameters dipole matrix squared M_j^2 and CRP also have been calculated. The present calculations were found in remarkable agreement with the available experimental results.
Effect of mesh grid structure in reducing hot carrier effect of nmos device s...ijcsa
This paper presents the critical effect of mesh grid that should be considered during process and device
simulation using modern TCAD tools in order to develop and optimize their accurate electrical
characteristics. Here, the computational modelling process of developing the NMOS device structure is
performed in Athena and Atlas. The effect of Mesh grid on net doping profile, n++, and LDD sheet
resistance that could link to unwanted “Hot Carrier Effect” were investigated by varying the device grid
resolution in both directions. It is found that y-grid give more profound effect in the doping concentration,
the junction depth formation and the value of threshold voltage during simulation. Optimized mesh grid is
obtained and tested for more accurate and faster simulation. Process parameter (such as oxide thicknesses
and Sheet resistance) as well as Device Parameter (such as linear gain “beta” and SPICE level 3 mobility
roll-off parameter “ Theta”) are extracted and investigated for further different applications.
A New Hybrid Inversion Method For 2D Nuclear Magnetic Resonance Combining TSV...Pedro Craggett
This paper presents a new hybrid method for inverting 2D nuclear magnetic resonance (NMR) data that combines truncated singular value decomposition (TSVD) and Tikhonov regularization. The method computes the exact TSVD of the kernel matrix using its Kronecker product structure, avoiding approximations. It then solves a Tikhonov-like optimization problem using the truncated kernel. The paper also proposes using the Discrete Picard Condition to automatically select both the TSVD truncation index and Tikhonov regularization parameter. The performance of the new hybrid method is evaluated on simulated and real NMR data.
Validation of Polarization angles Based Resonance Modes IJERA Editor
The symmetry, tilt and elongation degrees are figures of merit which can be used to describe the radar target
shape once incorporated with the target resonance modes. Through optimization of the second moments of the
quadrature-polarized residues matrix, the angles are determined by the optimum co-null polarization states. The
approach is tested and validated against low signal-to-noise ratio and also the late-time onset selection when
extracting the mode set. A wire plane model is used and the results show that with ensemble averaging it
possible to have robust polarization angle set, even with small number of sample set
Design modern structure for heterojunction quantum dot solar cells IJECEIAES
This paper proposal new structure for improving the optical, electrical characteristics and efficiency of 3 rd generation heterojunction quantum dot solar cell (HJQDSC) (ITO/CdS/QDPbS/Au) model by using the quantum dot window layer instead of bulk structure layers cell. Also, this paper presents theoretically analysis for the performance of the proposal HJQDSC (ITO/QDCdS/QDPbS/Au) structure. The new design structure was applied on traditional (SnO2/CdS/CdTe/Cu) and (ZnO/CdS/CIGS/Mo) thin film solar cells which based on sub-micro absorber layer thickness models by replacing the bulk CdTe, CIGS absorber layers and CdS window layer with quantum dot size materials to achieve higher efficiency with lesser usage layer material. Also, it has been studied the effect of using semiconductors layers in quantum dots size on electric and optical properties of thin film solar cells and the effect of window and absorber layers quantum dots radii on the performance of solar cells. Finally, a thermal efficiency analysis has been investigated for explaining the importance of new structure HJQD solar cells.
This document summarizes a study investigating the design and characteristics of directional coupler-based optical filters using coupled mode theory. The study examines a directional coupler consisting of two non-identical slab waveguides and analyzes power transfer between the waveguides. It is found that complete power exchange can occur when the waveguide modes are phase matched. The effects of structure parameters on filter response, crosstalk and bandwidth are also analyzed. A novel cascaded coupler structure is introduced to overcome limitations in conventional designs such as decreased coupling efficiency from non-identical waveguides.
A Front Surface Optimization Study for Photovoltaic ApplicationTELKOMNIKA JOURNAL
This document summarizes a study on optimizing the front surface of silicon solar cells to reduce reflectance through antireflection coatings and surface texturing. Silicon nitride films were deposited using plasma-enhanced chemical vapor deposition and hot-wire chemical vapor deposition on silicon substrates, and showed weighted average reflectances of 1.5% and 1.8% respectively. Random pyramid surface textures were formed on silicon using potassium hydroxide etching for 30 minutes, achieving low reflectance. Combining the optimized silicon nitride coatings with the textured surfaces further reduced weighted average reflectances to 1.5% for PECVD and 1.8% for HWCVD coatings.
Studying nanotube-based oscillators and their application as memory cells via...IJERA Editor
A nanoscale continuum model of carbon nanotube-based oscillators is proposed in this paper. In the continuum
model, the nanotube is discretized via the meshfree particle method. The atomistic interlayer interaction between
the outer and inner tubes is approximated by the interlayer interaction between particles. The mechanical
behaviors of oscillators are studied and compared well with molecular dynamics simulation results. The
nanotube-based oscillator can be employed to design a nanoelectromechanical system. In this system, two
electrodes are attached on the top of the outer tube so that the induced electromagnetic force can overcome the
interlayer friction. The mechanisms of such nanoelectromechanical systems as memory cells are also considered.
This paper recommends the use of grasshopper optimization algorithm (GOA), a nature-inspired optimization algorithm, for optimizing switching-angle applied to cascaded H-bridge multilevel inverter (CHBMLI). Switching angles are selected based on the minimum value of the objective function formulated using the concept of selective harmonic minimization pulse width modulation (SHMPWM) technique. MATLAB/Simulink-PSIM dynamic co-simulation conducted on a 3-phase 9-level CHBMLI shows that the CHBMLI controlled using GOA derived switching-angle is able to respond to varying modulation index demand and synthesize an AC staircase output voltage waveform with the desired fundamental harmonic and minimized selected low-order harmonics. Compared to Newton Raphson (NR) technique, GOA is able to find optimum switching-angle solutions over a wider modulation index range. Compared to Genetic Algorithm (GA), GOA is able to find global minima with higher probability. The simulation results validate the performance of GOA for switching-angle calculation based on the concept of SHMPWM.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
ENERGY EFFICIENT FULL ADDER CELL DESIGN WITH USING CARBON NANOTUBE FIELD EFFE...VLSICS Design
Full Adder is one of the critical parts of logical and arithmetic units. So, presenting a low power full adder cell reduces the power consumption of the entire circuit. Also, using Nano-scale transistors, because of their unique characteristics will save energy consumption and decrease the chip area. In this paper we presented a low power full adder cell by using carbon nanotube field effect transistors (CNTFETs). Simulation results were carried out using HSPICE based on the CNTFET model in 32 nanometer technology in Different values of temperature and VDD.
Similar to Buckling and Pull-In Instability of Multi-Walled Carbon Nanotube Probes Near Graphite Sheets Using Power Series and Padé Approximants (20)
For the full video of this presentation, please visit: https://www.edge-ai-vision.com/2024/06/temporal-event-neural-networks-a-more-efficient-alternative-to-the-transformer-a-presentation-from-brainchip/
Chris Jones, Director of Product Management at BrainChip , presents the “Temporal Event Neural Networks: A More Efficient Alternative to the Transformer” tutorial at the May 2024 Embedded Vision Summit.
The expansion of AI services necessitates enhanced computational capabilities on edge devices. Temporal Event Neural Networks (TENNs), developed by BrainChip, represent a novel and highly efficient state-space network. TENNs demonstrate exceptional proficiency in handling multi-dimensional streaming data, facilitating advancements in object detection, action recognition, speech enhancement and language model/sequence generation. Through the utilization of polynomial-based continuous convolutions, TENNs streamline models, expedite training processes and significantly diminish memory requirements, achieving notable reductions of up to 50x in parameters and 5,000x in energy consumption compared to prevailing methodologies like transformers.
Integration with BrainChip’s Akida neuromorphic hardware IP further enhances TENNs’ capabilities, enabling the realization of highly capable, portable and passively cooled edge devices. This presentation delves into the technical innovations underlying TENNs, presents real-world benchmarks, and elucidates how this cutting-edge approach is positioned to revolutionize edge AI across diverse applications.
Skybuffer AI: Advanced Conversational and Generative AI Solution on SAP Busin...Tatiana Kojar
Skybuffer AI, built on the robust SAP Business Technology Platform (SAP BTP), is the latest and most advanced version of our AI development, reaffirming our commitment to delivering top-tier AI solutions. Skybuffer AI harnesses all the innovative capabilities of the SAP BTP in the AI domain, from Conversational AI to cutting-edge Generative AI and Retrieval-Augmented Generation (RAG). It also helps SAP customers safeguard their investments into SAP Conversational AI and ensure a seamless, one-click transition to SAP Business AI.
With Skybuffer AI, various AI models can be integrated into a single communication channel such as Microsoft Teams. This integration empowers business users with insights drawn from SAP backend systems, enterprise documents, and the expansive knowledge of Generative AI. And the best part of it is that it is all managed through our intuitive no-code Action Server interface, requiring no extensive coding knowledge and making the advanced AI accessible to more users.
Salesforce Integration for Bonterra Impact Management (fka Social Solutions A...Jeffrey Haguewood
Sidekick Solutions uses Bonterra Impact Management (fka Social Solutions Apricot) and automation solutions to integrate data for business workflows.
We believe integration and automation are essential to user experience and the promise of efficient work through technology. Automation is the critical ingredient to realizing that full vision. We develop integration products and services for Bonterra Case Management software to support the deployment of automations for a variety of use cases.
This video focuses on integration of Salesforce with Bonterra Impact Management.
Interested in deploying an integration with Salesforce for Bonterra Impact Management? Contact us at sales@sidekicksolutionsllc.com to discuss next steps.
FREE A4 Cyber Security Awareness Posters-Social Engineering part 3Data Hops
Free A4 downloadable and printable Cyber Security, Social Engineering Safety and security Training Posters . Promote security awareness in the home or workplace. Lock them Out From training providers datahops.com
Main news related to the CCS TSI 2023 (2023/1695)Jakub Marek
An English 🇬🇧 translation of a presentation to the speech I gave about the main changes brought by CCS TSI 2023 at the biggest Czech conference on Communications and signalling systems on Railways, which was held in Clarion Hotel Olomouc from 7th to 9th November 2023 (konferenceszt.cz). Attended by around 500 participants and 200 on-line followers.
The original Czech 🇨🇿 version of the presentation can be found here: https://www.slideshare.net/slideshow/hlavni-novinky-souvisejici-s-ccs-tsi-2023-2023-1695/269688092 .
The videorecording (in Czech) from the presentation is available here: https://youtu.be/WzjJWm4IyPk?si=SImb06tuXGb30BEH .
HCL Notes and Domino License Cost Reduction in the World of DLAUpanagenda
Webinar Recording: https://www.panagenda.com/webinars/hcl-notes-and-domino-license-cost-reduction-in-the-world-of-dlau/
The introduction of DLAU and the CCB & CCX licensing model caused quite a stir in the HCL community. As a Notes and Domino customer, you may have faced challenges with unexpected user counts and license costs. You probably have questions on how this new licensing approach works and how to benefit from it. Most importantly, you likely have budget constraints and want to save money where possible. Don’t worry, we can help with all of this!
We’ll show you how to fix common misconfigurations that cause higher-than-expected user counts, and how to identify accounts which you can deactivate to save money. There are also frequent patterns that can cause unnecessary cost, like using a person document instead of a mail-in for shared mailboxes. We’ll provide examples and solutions for those as well. And naturally we’ll explain the new licensing model.
Join HCL Ambassador Marc Thomas in this webinar with a special guest appearance from Franz Walder. It will give you the tools and know-how to stay on top of what is going on with Domino licensing. You will be able lower your cost through an optimized configuration and keep it low going forward.
These topics will be covered
- Reducing license cost by finding and fixing misconfigurations and superfluous accounts
- How do CCB and CCX licenses really work?
- Understanding the DLAU tool and how to best utilize it
- Tips for common problem areas, like team mailboxes, functional/test users, etc
- Practical examples and best practices to implement right away
Digital Marketing Trends in 2024 | Guide for Staying AheadWask
https://www.wask.co/ebooks/digital-marketing-trends-in-2024
Feeling lost in the digital marketing whirlwind of 2024? Technology is changing, consumer habits are evolving, and staying ahead of the curve feels like a never-ending pursuit. This e-book is your compass. Dive into actionable insights to handle the complexities of modern marketing. From hyper-personalization to the power of user-generated content, learn how to build long-term relationships with your audience and unlock the secrets to success in the ever-shifting digital landscape.
Introduction of Cybersecurity with OSS at Code Europe 2024Hiroshi SHIBATA
I develop the Ruby programming language, RubyGems, and Bundler, which are package managers for Ruby. Today, I will introduce how to enhance the security of your application using open-source software (OSS) examples from Ruby and RubyGems.
The first topic is CVE (Common Vulnerabilities and Exposures). I have published CVEs many times. But what exactly is a CVE? I'll provide a basic understanding of CVEs and explain how to detect and handle vulnerabilities in OSS.
Next, let's discuss package managers. Package managers play a critical role in the OSS ecosystem. I'll explain how to manage library dependencies in your application.
I'll share insights into how the Ruby and RubyGems core team works to keep our ecosystem safe. By the end of this talk, you'll have a better understanding of how to safeguard your code.
zkStudyClub - LatticeFold: A Lattice-based Folding Scheme and its Application...Alex Pruden
Folding is a recent technique for building efficient recursive SNARKs. Several elegant folding protocols have been proposed, such as Nova, Supernova, Hypernova, Protostar, and others. However, all of them rely on an additively homomorphic commitment scheme based on discrete log, and are therefore not post-quantum secure. In this work we present LatticeFold, the first lattice-based folding protocol based on the Module SIS problem. This folding protocol naturally leads to an efficient recursive lattice-based SNARK and an efficient PCD scheme. LatticeFold supports folding low-degree relations, such as R1CS, as well as high-degree relations, such as CCS. The key challenge is to construct a secure folding protocol that works with the Ajtai commitment scheme. The difficulty, is ensuring that extracted witnesses are low norm through many rounds of folding. We present a novel technique using the sumcheck protocol to ensure that extracted witnesses are always low norm no matter how many rounds of folding are used. Our evaluation of the final proof system suggests that it is as performant as Hypernova, while providing post-quantum security.
Paper Link: https://eprint.iacr.org/2024/257
TrustArc Webinar - 2024 Global Privacy SurveyTrustArc
How does your privacy program stack up against your peers? What challenges are privacy teams tackling and prioritizing in 2024?
In the fifth annual Global Privacy Benchmarks Survey, we asked over 1,800 global privacy professionals and business executives to share their perspectives on the current state of privacy inside and outside of their organizations. This year’s report focused on emerging areas of importance for privacy and compliance professionals, including considerations and implications of Artificial Intelligence (AI) technologies, building brand trust, and different approaches for achieving higher privacy competence scores.
See how organizational priorities and strategic approaches to data security and privacy are evolving around the globe.
This webinar will review:
- The top 10 privacy insights from the fifth annual Global Privacy Benchmarks Survey
- The top challenges for privacy leaders, practitioners, and organizations in 2024
- Key themes to consider in developing and maintaining your privacy program
Have you ever been confused by the myriad of choices offered by AWS for hosting a website or an API?
Lambda, Elastic Beanstalk, Lightsail, Amplify, S3 (and more!) can each host websites + APIs. But which one should we choose?
Which one is cheapest? Which one is fastest? Which one will scale to meet our needs?
Join me in this session as we dive into each AWS hosting service to determine which one is best for your scenario and explain why!
Building Production Ready Search Pipelines with Spark and MilvusZilliz
Spark is the widely used ETL tool for processing, indexing and ingesting data to serving stack for search. Milvus is the production-ready open-source vector database. In this talk we will show how to use Spark to process unstructured data to extract vector representations, and push the vectors to Milvus vector database for search serving.
Programming Foundation Models with DSPy - Meetup SlidesZilliz
Prompting language models is hard, while programming language models is easy. In this talk, I will discuss the state-of-the-art framework DSPy for programming foundation models with its powerful optimizers and runtime constraint system.
Fueling AI with Great Data with Airbyte WebinarZilliz
This talk will focus on how to collect data from a variety of sources, leveraging this data for RAG and other GenAI use cases, and finally charting your course to productionalization.
Dandelion Hashtable: beyond billion requests per second on a commodity serverAntonios Katsarakis
This slide deck presents DLHT, a concurrent in-memory hashtable. Despite efforts to optimize hashtables, that go as far as sacrificing core functionality, state-of-the-art designs still incur multiple memory accesses per request and block request processing in three cases. First, most hashtables block while waiting for data to be retrieved from memory. Second, open-addressing designs, which represent the current state-of-the-art, either cannot free index slots on deletes or must block all requests to do so. Third, index resizes block every request until all objects are copied to the new index. Defying folklore wisdom, DLHT forgoes open-addressing and adopts a fully-featured and memory-aware closed-addressing design based on bounded cache-line-chaining. This design offers lock-free index operations and deletes that free slots instantly, (2) completes most requests with a single memory access, (3) utilizes software prefetching to hide memory latencies, and (4) employs a novel non-blocking and parallel resizing. In a commodity server and a memory-resident workload, DLHT surpasses 1.6B requests per second and provides 3.5x (12x) the throughput of the state-of-the-art closed-addressing (open-addressing) resizable hashtable on Gets (Deletes).
In the realm of cybersecurity, offensive security practices act as a critical shield. By simulating real-world attacks in a controlled environment, these techniques expose vulnerabilities before malicious actors can exploit them. This proactive approach allows manufacturers to identify and fix weaknesses, significantly enhancing system security.
This presentation delves into the development of a system designed to mimic Galileo's Open Service signal using software-defined radio (SDR) technology. We'll begin with a foundational overview of both Global Navigation Satellite Systems (GNSS) and the intricacies of digital signal processing.
The presentation culminates in a live demonstration. We'll showcase the manipulation of Galileo's Open Service pilot signal, simulating an attack on various software and hardware systems. This practical demonstration serves to highlight the potential consequences of unaddressed vulnerabilities, emphasizing the importance of offensive security practices in safeguarding critical infrastructure.
Energy Efficient Video Encoding for Cloud and Edge Computing Instances
Buckling and Pull-In Instability of Multi-Walled Carbon Nanotube Probes Near Graphite Sheets Using Power Series and Padé Approximants
1. Jalal Alsarraf et al. Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 4, Issue 12( Part 1), December 2014, pp.22-28
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Buckling and Pull-In Instability of Multi-Walled Carbon
Nanotube Probes Near Graphite Sheets Using Power Series and
Padé Approximants
Jalal Alsarraf*, Majed A. Alwatheeqi**, Esam A.M. Husain*, Khaled
Alawadhi*
*(Automotive and Marine Engineering Technology Department, Public Authority for Applied Education and
Training, Shuwaikh 70654)
**(Industrial Training Institute – Shuwaikh, Public Authority for Applied Education and Training, Shuwaikh
70654)
ABSTRACT
In this paper, integration of the power series method and the Padé approximants (PS-Padé) is utilized to study
buckling and pull-in instability of multi-walled carbon nanotube (MWCNT) cantilevers in the vicinity of
graphite sheets due to intermolecular forces. A hybrid nano-scale continuum model based on the Lennard–Jones
potential is used to simulate the Van der Waals forces and evaluate the buckling of MWCNT. A closed form
power series, based on the symbolic power series polynomials, is utilized to obtain a series solution for the
governing boundary value differential equation of the nanotube. In order to handle the boundary conditions and
increasing the accuracy of solution, the symbolic power series are transformed into Padé approximants. The
governing differential equation is also solved numerically using the finite difference method. The PS-Padé
results are compared with the numerical results and other methods reported in literature. The results obtained by
using the PS-Padé approach correspond very well with the numerical results. Furthermore, the detachment length
and the minimum gap between MWCNT and the graphite plane as important parameters of engineering designs
are computed. It is found that for a fixed gap, the detachment length of a MWCNT can be increased with the
increase of the radius, wall thickness and the effective Young modulus of the MWCNT.
Keywords - Cantilever, MWCNT, Padé, Pull-in instability, Symbolic power series.
I. Introduction
Multi-walled Carbon Nanotubes (MWCNTs)
are types of nano-materials with outstanding
mechanical properties. Nowadays, MWCNTs have
attracted considerable attention because of their
unique mechanical and chemical properties. These
novel materials can be visualized in the form of
nano-scale concentric cylinders rolled up by
graphene sheets. There are numerous reports on the
fabrication of single-walled carbon nanotubes
(SWCNT) and MWCNT probes [1]-[3]. MWCNTs
can be synthesized by different techniques, including
laccase-mediator [4], situ oxidative polymerization
method [5]-[7]. Single-walled and multi-walled
carbon nanotubes have been utilized as
electrochemical sensors [8], catalysts [9], [10],
structures [11], and Atomic force microscopes
(AFM) [12]. Electrically induced static and dynamic
mechanical buckling and pull-in instability of
MWCNT cantilevers have many applications, such
as nanotube based electromechanical system
(NEMS) switches [12]-[14].
Consider a typical MWCNT cantilever
probe/switch suspended above a graphite surface
with a small gap between them. When the size of the
gap decreases to nanometers, the Van der Waals
interaction buckles the MWCNT to the substrate. In
a recent piece of work [15], the authors utilized a
hybrid continuum model to consider the molecular
force-induced buckling of the cantilever freestanding
MWCNT probes/actuators suspended over graphite
sheets. They carried out the governing equation of
the deflection of MWCNT cantilever
probes/actuators in the vicinity of thin and thick
graphite layers. The governing equation of the
hybrid distributed model leads to a fourth-order
nonlinear, ordinary differential equation. Because of
the nonlinearity of the governing equation of the
distributed model, an exact solution does not yet
exist.
Reference [15] used the Green’s function method
with a simple second order polynomial as the shape
function to obtain deflection and pull-in parameters
of MWCNT cantilevers. They have also used the
Adomian decomposition method (ADM) to obtain
pull-in instability of MWCNT cantilevers. However,
the accuracy of the results of the Green’s method
and the Adomian decomposition method [15] for
calculating deflection of MWCNT cantilevers near
RESEARCH ARTICLE OPEN ACCESS
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the pull-in instability is not perfect. Reference [16]
examined a monotone positive solution to obtain a
resolution for the buckling of MWCNTs. The
monotone solution is a comparatively accurate
solution for low values of intermolecular forces, but
it fails to evaluate the pull-in instability of MWCNT
cantilevers.
The combination of any series solutions with the
Padé approximants provides a powerful tool for
increasing the accuracy of boundary value problems
[17]-[19]. Hence, the accuracy of the series methods
can be enhanced by using Padé approximants.
In this study, in order to obtain an accurate
analytical solution for pull-in instability of
MWCNTs in the vicinity of graphite sheets,
integration of symbolic power series with Padé
approximants (PS-Padé) is used as a new approach
to study the buckling and pull-in instability of
MWCNT cantilever actuators. A fair comparison is
made between the method presented and numerical
results as well as between the Adomian
decomposition method and monotone solution
reported in literature.
II. Mathematical Model
Fig. 1 shows a physical schematic of a typical
MWCNT cantilever near a surface consisting of N
graphene layers, with interlayer distance d. The
length of MWCNT is L, the mean radius value is RW,
the number of walls of nanotube is NW, and the gap
between MWCNT and the graphite surface is D.
Fig. 1 Schematic of a MWCNT cantilever in the
vicinity of graphite sheets
Based on continuum mechanics, a MWCNT is
modeled by concentric cylindrical tubes. E is the
Young’s modulus of MWCNT which typically is in
the range of 0.9 to 1.2 TPa, and the cross-sectional
moment of inertia I is equal to π (Ro
4
- Ri
4
)/4 [15].
By neglecting the effect of large displacement (finite
kinematics) for L/De>10 and applying the Euler
theory [20], [21], the governing equation of a
MWCNT cantilever can be written as the following
boundary value ordinary differential equation [15]:
UDq
dX
Ud
IE vdWeff 4
4
(1-a)
subject to the following geometrical boundary
conditions at fixed end:
000
dX
dU
U (1-b)
and, natural boundary conditions at free end, as
follows:
03
3
2
2
L
dX
Ud
L
dX
Ud (1-c)
where X is the position along MWCNT measured
from the bending side, U is the deflection of
MWCNT cantilever and qWdv is the intermolecular
force per unit length of MWCNT. According to the
work of [15], qWdv can be represented as follows:
2 2
6
4
2 2
6
4
For large number of layers
4
Forsmall number of layers
2
W W
Wdv
W W
C N R
d D U
q
C NN R
d D U Nd
(2)
In (2), σ≈38nm-2
[22] is the graphene surface
density and C6 = 15.2 eV Å6
is the attractive
constants for the carbon–carbon interaction [23]. By
substituting (2) in (1) and using the following
substitutions:
5
2
4
,
n
NdD
U
n
D
U
u
L
X
x
(3-a)
and:
5
2
4
4
6
422
6
5
422
6
n
NdDIE
LRNNC
n
DIEd
LRNC
f
eff
WW
eff
WW
n
(3-b)
the dimensionless form of (1) can be obtained as
follows:
n
n
xu
f
dx
ud
1
4
4
(4-a)
0 0 , 0,u u at x (4-b)
1 1 0, 1u u at x (4-c)
In the following text, n = 4 and n = 5 correspond
to the large number and small number of graphene
layers, accordingly. In the equations, prime denotes
differentiation with respect to non-dimensional
length of x.
III. Analytical Solution
Equation (4-a) subject to (4-b) and (4-c) can be
solved using a symbolic power series enhanced with
Padé approximants. The basic idea of the symbolic
power series method and Padé approximants are
explained in the works of [17], [18] and also [24],
[25].
III.1 Symbolic Power Series Method
Based on the symbolic power series method, the
fourth-order differential equation of (4-a) can be
written as a system of four first order differential
equation, as follows:
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1
2
2
3
3
4
4
11
n
n
du x
u x
dx
du x
u x
dx
du x
u x
dx
du x f
dx u x
(5)
subject to the following boundary conditions:
1 2
3 4
0 0, 0 0,
0 , 0
u u
u P u Q
(6)
and to the constraints which come from (4-c):
3 41 0, 0 0u u , (7)
Here, P and Q are constants which later will be
computed from the boundary conditions, (4-c) or (7).
Based on the method of symbolic power series
introduced by [17], [18], the solution procedure is
started as follows:
1 1
2 2
3 3
4 4
0
0
n
u x e
u x e
u x P e
u x f e
(8)
Substituting (8) in (5) and neglecting higher order
terms yields:
1
2
3
4
0 0,
0,
0,
0,n
e
e P
e Q
e f
(9)
Solving (9) for e1 to e4 and substituting the
obtained values into (8) and considering a higher
term gives the first approximation of the solution as:
2
1 1
2
2 2
2
3 3
2
4 4
0
n
u x e x
u x Px e x
u x P Qx e x
u x Q f x e x
(10)
Again, substituting (10) in (5) and neglecting
higher order terms yields:
1
2
3
4
2 0,
2 0,
2 0,
2 0,
n
P e
Q e
e f
e
(11)
Substituting the new values of e1 to e4 into (10)
and considering a higher term results in:
2 3
1 1
2 3
2 2
2 3
3 3
3
4 4
2
,
2
2
n
n
P
u x x e x
Q
u x x Px e x
f
u x x Qx P e x
u x Q f x e x
(12)
By substituting e1 to e4 in (5) and repeating this
procedure, the following power series for u1 is
obtained after eight iterations:
2 2
2 3 4 6 7 8 9
1
1
( )
2 6 24 720 5040 13440 40320
nn n n n
n n f Pf nf P nf Q nfP Q
u x x x x x x x O x
(13)
Continuing this procedure results in a symbolic
power series with higher terms. Here, undetermined
coefficients, P and Q, correspond to the second and
third derivatives of beam deflection with respect to x
at x = 0, accordingly. These coefficients can be
evaluated using natural boundary conditions at free
end (i.e. u2 (1) = 0 and u3 (1) = 0).
The combination of any series solutions with the
Padé approximation provides a powerful tool for
handling initial or boundary value problems on
infinite or semi-infinite domains [24]-[26]. In order
to increase the accuracy of solution, the power series
in the symbolic form and before computation of the
unknown values of P and Q, can be converted to
Padé approximation.
III.2 Padé Approximants
Any power series can be represented as a function f
(x), in the form of:
0i
i
i xaxf
(14)
where, the expansion of (14) is the fundamental
starting point of any analysis using Padé
approximants. The objective of the Padé
approximants is to seek a rational function for the
series. The Padé approximants converge on the
entire real axis if the series solution is free of
singularities on the real axis [24]. A Padé
approximant is a rational fraction which provides us
with more stable expression than the original power
series. The notation for such a Padé approximant can
be defined as per [26]:
2
2 0 1 2
0 1 2 2
1 21
M
M
L
L
p p p p
a a a
q q q
(15)
Both sides of (14) are multiplied by the
denominator of the right-hand side of (15):
32 3
0 1 0 1 2 1 1 0 2 3 1 1
2
0 1 21
... ...
... 0
M M
l k k M l k kk k
L M L M
M L l k k Mk
a a a q a a q a q a a q a a q
a a q p p p p
(16)
By comparing the coefficients of both sides of
(16), one can find that:
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1
, 0, ,
M
l l k k lk
a a q p l M
(17)
1
0, 1, ,
L
l l k kk
a a q l M M L
(18)
M and L are the degrees of numerator and
denominator in the Padé series, respectively. By
solving the linear equation, (18), the qk (k=1,…,L) is
determined. After that, by substituting qk in (17), pl
(l=0,…,M) will be determined. For instance, by
following this procedure, the Padé series of (13)
with the size of {2, 2} for u1, can be obtained as
follows.
From (18) with L=2 and M=2:
3 2 1 1 2
4 3 1 2 2
0
0
a a q a q
a a q a q
(19)
Solving for q1 and q2:
2
2 3 1 4 2 4 3
1 22 2
1 3 2 1 3 2
,
a a a a a a a
q q
a a a a a a
(20)
From (17) with M=2:
0 0
1 1 0 1
2 2 1 1 0 2
p a
p a a q
p a a q a q
(21)
After substituting the obtained coefficients and
simplification, the Padé series of u1 with the size of
{2, 2} is as follows:
3 2
1
2 2 2
3
1 12
3
4 3
n
P x
u x
P QPx f P Q x
(22)
If the order of Padé approximation increases, the
accuracy of the solution increases [25], [26].
IV. Results and Discussion
In order to verify the convergence of Padé
approximants, deflection of a typical nanotube-
actuator, which is used in the work of [15], is
computed analytically using the symbolic power
series method. Then the power series are converted
to Padé approximants. The solution results are
compared with the numerical results as well as the
monotone method [16], the Green’s method and
Adomian decomposition method [15]. Numerical
results are obtained using the finite difference
method based on collocation points and Newton’s
method [27], [28]. A highly accurate solution with a
relative tolerance of 10-8
is achieved. Table 1 and
Table 2 compare MWCNT cantilever tip deflection
(utip), computed using different terms of symbolic
power series and different sizes of Padé
approximants, respectively. These tables ensure the
convergence and accuracy of the power series and
Padé approximants. Table 2 reveals that higher
accuracy can be obtained by evaluating more terms
of the Padé approximants.
The relative error is computed from:
Numerical
NumericalAnalytical
u
uu
Error
(23)
where, uAnalytical and uNumerical are the MWCNT
cantilever tip deflection, computed from the
analytical method (i.e. PS or PS-Padé) and the tip
deflection computed using numerical method,
respectively. The Error represents the relative error.
Table 1
The Evaluated Tip Deflection of a Typical
MWCNT Cantilever Using Different
Terms of PS Method for fn=0.5
Series
Size
Tip
Deflection
PS, n=4
Error
n=4
Tip
Deflection
PS, n=5
Error
n=5
4 0.06250 1.903E-01 0.06250 2.491E-01
5 0.06250 1.903E-01 0.06250 2.491E-01
6 0.08657 1.215E-01 0.09533 1.453E-01
7 0.07215 6.525E-02 0.07516 9.700E-02
8 0.08228 6.592E-02 0.09350 1.233E-01
9 0.07396 4.190E-02 0.07737 7.046E-02
10 0.07946 2.945E-02 0.08842 6.228E-02
11 0.07564 2.015E-02 0.07983 4.087E-02
12 0.07833 1.476E-02 0.08613 3.479E-02
13 0.07646 9.511E-03 0.08137 2.236E-02
14 0.07772 6.816E-03 0.08475 1.826E-02
15 0.07684 4.494E-03 0.08223 1.211E-02
16 0.07743 3.087E-03 0.08400 9.263E-03
Numerical 0.077192 0.083233676
Table 2
The Evaluated Tip Deflection of a Typical
MWCNT Cantilever Using Different
Terms of PS-Padé for fn=0.5
Padé
Size
Tip
Deflection
PS-Padé,
(n=4)
Error
(n=4)
Tip
Deflection
PS-Padé,
(n=5)
Error
(n=5)
{2,2} 0.07368 4.544E-02 0.07405 1.103E-01
{3,3} 0.07525 2.519E-02 0.08009 3.777E-02
{4,4] 0.07724 5.716E-04 0.08344 2.449E-03
{5,5} 0.07710 1.148E-03 0.08353 3.504E-03
{6,6} 0.07719 1.795E-05 0.08323 3.415E-05
{7,7} 0.07719 2.054E-06 0.08323 4.200E-06
{8,8} 0.07719 9.067E-07 0.08324 2.537E-05
{9,9} 0.07719 1.460E-08 0.08323 5.240E-08
Numerical 0.0771924 0.0832336
The results in Table 2 show the relative error
between analytical and numerical results is less than
0.0034% by selecting PS- Padé size of {6,6}. It is
worth noticing that the Padé approximants with size
{6,6} are obtained from 15 terms of power series
(i.e. O(x16
)). Comparing this error with the same
series size of the PS method (i.e. 15 terms and
relative error of 1.2%), shows the PS- Padé method
could compute deflection of MWCNT cantilever
with more accuracy than the PS method. The results
of PS- Padé with size of {6, 6} with 0.0034% error
are very similar to the numerical results. Therefore,
the Padé size of {6, 6} is selected, for convenience.
IV.1 Instability Study
In order to study pull-in instability of multi-wall
carbon nanotube cantilevers, (4) is solved
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numerically simulated and the results are compared
with the results of the PS-Padé method. The results
show that for fn greater than critical value of
intermolecular force (f *
), a numerical solution does
not exist and the MWCNT collapses on to the sheets.
The pull-in value of MWCNT-graphite attraction
and the MWCNT pull-in tip deflection can also be
evaluated using the PS-Padé technique by setting
du(1)/dfn→∞ in the solution.
The relationship between fn and utip are presented
in Figs. 2 and 3 for large and small numbers of
graphene layers. Fig. 3 depicts the non-dimensional
tip deflection of MWCNT which it increases from
zero to pull-in instability as fn raises from zero to f *
n.
Table 3 compares the obtained values of f *
n using
different methods for large and small numbers of
graphene layers. When intermolecular attraction
exceeds the critical value of f *
n, no solution exists
and the instability occurs.
Fig. 2 Relation between fn and MWCNT cantilever tip
deflection in the vicinity of large number of graphene
layers (n=4)
Fig. 3 Relation between fn and MWCNT cantilever tip
deflection in the vicinity of small number of graphene
layers (n=5)
Table 3
Comparison of f *
n obtained by different methods
Model f *
n (n=4)
error
(n=4)
f *
n
(n=5)
error
(n=5)
Numerical
Solution
0.939 - 0.769 -
Monotone - - - -
Green’s Function 1.025 9.2 0.841 9.4
Adomian method 0.814 13.3 0.661 14
PS 15 terms of
series
0.810 13.7 0.670 12.9
PS Padé {6,6} 0.939 0 0.769 0
The results in Figs. 2 and 3 and Table 3 reveal
that the PS-Padé method is more accurate than other
methods in comparison with the numerical results.
The centerline deflection of a typical MWCNT
under intermolecular force for a large number of
graphene layers and a small number of graphene
layers are shown in Fig. 4 and Fig. 5, respectively.
Fig. 4 Center line buckling of MWCNT for different
values of fn when n=4
Fig. 5 Center line buckling of MWCNT for different
values of fn when n=5
These figures compare the PS-Padé results with
the numerical results as well as with Green’s
function method and the Adomian method [15]. The
obtained PS-Padé solution at the onset of pull-in
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instability for the large number of graphene layers
(i.e. n=4) is as follows:
2 3 4 5 6
2 3 4 5 6
5322605345000x +1658444884000x -2348055234000x +69078875300x +290980676200x
10901369930000+9353512630000x-571657749500x -920411794500x +25098037920x +16516697530x +4129243874x
u x
(24)
The PS-Padé solution at the onset of instability
for the small number of graphene layers is:
2 3 4 5 6
2 3 4 5 6
4449476518000x +1100463496000x -1906546258000x +151168135800x +208062912800x
10976849700000+8699010750000x-828753282000x -766502257000x +43693697980x +18891227440x +4867875469x
u x
(25)
When the gap between the plane and the
suspended nanotube is small enough, the nanotube
may collapse on to the graphite sheets without
applying voltage due to the intermolecular
attractions. The stable length is an important
parameter for design of nano-switches or AFM
probes and some other engineering applications
[12]-[14]. By substituting the obtained value of f *
n
at the onset of instability in definition of fn (i.e. (3-
b)), then solving for corresponding minimum gap
(Dmin) and detachment length (Lmax) of freestanding
MWCNT, the following relations are obtained:
5
2192.0
4
939.0
4
2
6
62
4
2
6
52
max
nfor
NNC
NdDEtR
nfor
NC
DdEtR
L
W
W
W
W
(26)
5
2
201.5
4
065.1
6
2
42
6
5
2
42
6
max
nfor
Nd
EtR
LNNC
nfor
dEtR
LNC
D
W
W
W
W
(27)
Equation (26) shows the detachment length of a
MWCNT would increase with an increase of the
radius, wall thickness or effective Young modulus of
the MWCNT.
V. Conclusions
A mathematical model based on a nano-scale
continuum model and the Lennard–Jones potential is
used to study buckling of MWCNT cantilevers near
the graphite sheets. The governing equation leads to
a fourth-order ordinary differential equation. Then,
integration of the Adomian decomposition method
and the Padé approximants is used as a new accurate
technique to obtain a solution for buckling of
MWCNT cantilevers. The ADM-Padé solution is
compared with the numerical method, Green’s
function, the Adomian solution and a symbolic
power series in figures and tables. Comparison
between the Adomian results and ADM-Padé results
show that Padé approximants enhanced the
convergence of Adomian decomposition
polynomials to handling the governing boundary
value problem near the pull-in area. Finally, by using
the ADM-Padé technique, the critical value of Van
der Waals attraction (f *
n) and detachment length of
MWCNT as basic parameters for design and
selecting components of nano-electro mechanical
systems has been determined.
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