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.
Meshless Point collocation Method For 1D and 2D Groundwater Flow SimulationAshvini Kumar
This document describes the development of a meshless point collocation method (PPCM) for simulating 1D and 2D groundwater flow. PPCM is a numerical technique that can establish algebraic equations over a problem domain without a predefined mesh, using scattered nodes. The document outlines the governing equations for 1D and 2D transient groundwater flow. It then describes how PPCM formulates these equations by defining a trial solution using shape functions and radial basis functions. The document verifies the 1D and 2D PPCM models against analytical and finite element method solutions. It also presents a case study application of the 2D PPCM model to a hypothetical confined aquifer with varying properties.
Thin Film Pressure Estimation of Argon and Water using LAMMPSCSCJournals
In this work, we investigate the pressure and density characteristics of water film when simulated using the emerging technique called many body dissipative particle dynamics method. This work also layout the methodology of estimating local pressure from LAMMPS simulation using Harasima scheme. Using the triangular shaped cloud interpolation function, pressure and density are estimated at local bins and compared with the experimental database. Our results show good agreement for the molecular dynamics results of the argon system, while the many body dissipative particle model fails to simulate the water properties at room temperature. In its current form, the many body dissipative particle method cannot be used for accurate liquid vapor interfacial simulations and heat transfer studies.
Choice of Numerical Integration Method for Wind Time History Analysis of Tall...inventy
Wind tunnel tests are being performed routinely around the world for designing tall buildings but the advent of powerful computational tools will make time-history analysis for wind more common in near future. As the duration of wind storms ranges from tens of minutes to hours while earthquake durations are typically less than a three to four minutes, the choice of a time step size (Δt) for wind studies needs to be much larger both to reduce the computational time and to save disk space. As the error in any numerical solution of the equation of motion is dependent on step size (Δt), careful investigations on the choice of numerical integration methods for wind analyses are necessary. From a wide variety of integration methods available, it was decided to investigate three methods that seem appropriate for 3D-time history analysis of tall buildings for wind. These are modal time history analysis, the Hilber-Hughes-Taylor (HHT) method or α-method with α=- 0.1, and the Newmark method with β=0.25 and γ=0.5 ( i.e., trapezoidal rule). SAP2000, a common structural analysis software tool, and a 64-story structure are used to conduct all the analyses in this paper. A boundary layer wind tunnel (BLWT) pressure time history measured at 120 locations around the building envelope of a similar structure is used for the analyses. Analyses performed with both the HHT and Newmark-method considering P-delta effects show that second order effects have a considerable impact on both displacement and acceleration response. This result shows that it is necessary to account P-delta effect for wind analysis of tall buildings. As the direct integration time history analysis required very large computation times and very large computer physical memory for a wind duration of hours, a modal analysis with reduced stiffness is considered as a good alternative. For that purpose, a non-linear static analysis of the structure with a load combination of 1.0D + 1.0L is performed in SAP2000 and the reduced stiffness of the structure after the analysis is used to conduct an eigenvalue analysis to extract the mode shapes and frequencies of this structure. Then the first 20- modes are used to perform a modal time history analysis for wind load. The result shows that the responses from modal analysis with “20-mode (reduced stiffness)” are comparable with that from the P-Δ analyses of Newmark-method
This document presents a new mathematical model for estimating the compressive strength of Portland cement concrete. The model relies on determining the water-to-cement ratio that provides maximum compressive strength and how this ratio varies with curing time. The model is derived based on existing experimental data. It is shown that the water-to-cement ratio providing maximum strength ranges from 0.18 to 0.23 for plain and latex-modified concretes cured for 28 days. However, the model may have limited applicability for predicting the strength of silica fume blended concretes.
This document summarizes research developing a new isogeometric boundary element method using subdivision surfaces for solving Helmholtz problems. It presents the governing Helmholtz equation and boundary integral formulation for acoustic problems. Subdivision surfaces are introduced as an alternative to NURBS for isogeometric analysis that overcome limitations of tensor-product bases. Results show the subdivision boundary element method achieves higher accuracy than a Lagrangian discretization with the same order basis functions. Future work is outlined on coupling acoustic and structural models and electromagnetic scattering problems.
Comparison of MOC and Lax FDE for simulating transients in Pipe FlowsIRJET Journal
This document compares the method of characteristics (MOC) and Lax finite difference explicit (Lax FDE) methods for simulating transients in pipe flows. It develops numerical models using both MOC and Lax FDE to discretize the governing equations of fluid flow through a pipe. The models are implemented using data from a previous study to simulate pressure and discharge changes after rapid valve closure. The results show that Lax FDE provides more damping of pressure and discharge fluctuations compared to MOC. Therefore, the document concludes that Lax FDE is a better numerical method for calculating hydraulic transients in pipes.
Concurrent Ternary Galois-based Computation using Nano-apex Multiplexing Nibs...VLSICS Design
Novel realizations of concurrent computations utilizing three-dimensional lattice networks and their corresponding carbon-based field emission controlled switching is introduced in this article. The formalistic ternary nano-based implementation utilizes recent findings in field emission and nano applications which include carbon-based nanotubes and nanotips for three-valued lattice computing via field-emission methods. The presented work implements multi-valued Galois functions by utilizing concurrent nano-based lattice systems, which use two-to-one controlled switching via carbon-based field emission devices by using nano-apex carbon fibers and carbon nanotubes that were presented in the first part of the article. The introduced computational extension utilizing many-to-one carbon field-emission devices will be further utilized in implementing congestion-free architectures within the third part of the article. The emerging nano-based technologies form important directions in low-power compact-size regular lattice realizations, in which carbon-based devices switch less-costly and more-reliably using much less power than silicon-based devices. Applications include low-power design of VLSI circuits for signal processing and control of autonomous robots.
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.
Meshless Point collocation Method For 1D and 2D Groundwater Flow SimulationAshvini Kumar
This document describes the development of a meshless point collocation method (PPCM) for simulating 1D and 2D groundwater flow. PPCM is a numerical technique that can establish algebraic equations over a problem domain without a predefined mesh, using scattered nodes. The document outlines the governing equations for 1D and 2D transient groundwater flow. It then describes how PPCM formulates these equations by defining a trial solution using shape functions and radial basis functions. The document verifies the 1D and 2D PPCM models against analytical and finite element method solutions. It also presents a case study application of the 2D PPCM model to a hypothetical confined aquifer with varying properties.
Thin Film Pressure Estimation of Argon and Water using LAMMPSCSCJournals
In this work, we investigate the pressure and density characteristics of water film when simulated using the emerging technique called many body dissipative particle dynamics method. This work also layout the methodology of estimating local pressure from LAMMPS simulation using Harasima scheme. Using the triangular shaped cloud interpolation function, pressure and density are estimated at local bins and compared with the experimental database. Our results show good agreement for the molecular dynamics results of the argon system, while the many body dissipative particle model fails to simulate the water properties at room temperature. In its current form, the many body dissipative particle method cannot be used for accurate liquid vapor interfacial simulations and heat transfer studies.
Choice of Numerical Integration Method for Wind Time History Analysis of Tall...inventy
Wind tunnel tests are being performed routinely around the world for designing tall buildings but the advent of powerful computational tools will make time-history analysis for wind more common in near future. As the duration of wind storms ranges from tens of minutes to hours while earthquake durations are typically less than a three to four minutes, the choice of a time step size (Δt) for wind studies needs to be much larger both to reduce the computational time and to save disk space. As the error in any numerical solution of the equation of motion is dependent on step size (Δt), careful investigations on the choice of numerical integration methods for wind analyses are necessary. From a wide variety of integration methods available, it was decided to investigate three methods that seem appropriate for 3D-time history analysis of tall buildings for wind. These are modal time history analysis, the Hilber-Hughes-Taylor (HHT) method or α-method with α=- 0.1, and the Newmark method with β=0.25 and γ=0.5 ( i.e., trapezoidal rule). SAP2000, a common structural analysis software tool, and a 64-story structure are used to conduct all the analyses in this paper. A boundary layer wind tunnel (BLWT) pressure time history measured at 120 locations around the building envelope of a similar structure is used for the analyses. Analyses performed with both the HHT and Newmark-method considering P-delta effects show that second order effects have a considerable impact on both displacement and acceleration response. This result shows that it is necessary to account P-delta effect for wind analysis of tall buildings. As the direct integration time history analysis required very large computation times and very large computer physical memory for a wind duration of hours, a modal analysis with reduced stiffness is considered as a good alternative. For that purpose, a non-linear static analysis of the structure with a load combination of 1.0D + 1.0L is performed in SAP2000 and the reduced stiffness of the structure after the analysis is used to conduct an eigenvalue analysis to extract the mode shapes and frequencies of this structure. Then the first 20- modes are used to perform a modal time history analysis for wind load. The result shows that the responses from modal analysis with “20-mode (reduced stiffness)” are comparable with that from the P-Δ analyses of Newmark-method
This document presents a new mathematical model for estimating the compressive strength of Portland cement concrete. The model relies on determining the water-to-cement ratio that provides maximum compressive strength and how this ratio varies with curing time. The model is derived based on existing experimental data. It is shown that the water-to-cement ratio providing maximum strength ranges from 0.18 to 0.23 for plain and latex-modified concretes cured for 28 days. However, the model may have limited applicability for predicting the strength of silica fume blended concretes.
This document summarizes research developing a new isogeometric boundary element method using subdivision surfaces for solving Helmholtz problems. It presents the governing Helmholtz equation and boundary integral formulation for acoustic problems. Subdivision surfaces are introduced as an alternative to NURBS for isogeometric analysis that overcome limitations of tensor-product bases. Results show the subdivision boundary element method achieves higher accuracy than a Lagrangian discretization with the same order basis functions. Future work is outlined on coupling acoustic and structural models and electromagnetic scattering problems.
Comparison of MOC and Lax FDE for simulating transients in Pipe FlowsIRJET Journal
This document compares the method of characteristics (MOC) and Lax finite difference explicit (Lax FDE) methods for simulating transients in pipe flows. It develops numerical models using both MOC and Lax FDE to discretize the governing equations of fluid flow through a pipe. The models are implemented using data from a previous study to simulate pressure and discharge changes after rapid valve closure. The results show that Lax FDE provides more damping of pressure and discharge fluctuations compared to MOC. Therefore, the document concludes that Lax FDE is a better numerical method for calculating hydraulic transients in pipes.
Concurrent Ternary Galois-based Computation using Nano-apex Multiplexing Nibs...VLSICS Design
Novel realizations of concurrent computations utilizing three-dimensional lattice networks and their corresponding carbon-based field emission controlled switching is introduced in this article. The formalistic ternary nano-based implementation utilizes recent findings in field emission and nano applications which include carbon-based nanotubes and nanotips for three-valued lattice computing via field-emission methods. The presented work implements multi-valued Galois functions by utilizing concurrent nano-based lattice systems, which use two-to-one controlled switching via carbon-based field emission devices by using nano-apex carbon fibers and carbon nanotubes that were presented in the first part of the article. The introduced computational extension utilizing many-to-one carbon field-emission devices will be further utilized in implementing congestion-free architectures within the third part of the article. The emerging nano-based technologies form important directions in low-power compact-size regular lattice realizations, in which carbon-based devices switch less-costly and more-reliably using much less power than silicon-based devices. Applications include low-power design of VLSI circuits for signal processing and control of autonomous robots.
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.
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.
This document summarizes a research paper that was presented at the seventh International Conference on Urban Climate from June 29th to July 3rd, 2009 in Yokohama, Japan. The paper describes the development of a new 1-D Urban Canopy Model to simulate the effects of urban structures on atmospheric flow. Large Eddy Simulations were used to validate the model for different building configurations. The paper also introduces a new method for representing complex urban geometries with a simplified, equivalent representation of regularly spaced buildings that can be used as input for Urban Canopy Models.
GPR Probing of Smoothly Layered Subsurface Medium: 3D Analytical ModelLeonid Krinitsky
An analytical approach to GPR probing of a
horizontally layered subsurface medium is developed, based on the coupled-wave WKB approximation. An empirical model of current in dipole transmitter antenna is used.
1. The document discusses modeling turbidity (TB) in a reservoir using linear regression (LR) and geographically weighted regression (GWR). TB was measured at 10 observation points and estimated from satellite imagery reflectance data.
2. Both LR and GWR were used to model TB, with GWR producing estimates that exactly matched the observed TB values.
3. GWR coefficients were interpolated using inverse distance weighting to produce a continuous TB surface map for the entire reservoir area shown in the satellite image.
Simulation and Experiment Study of Flow Field of Flow channel for Rectangular...IJRESJOURNAL
ABSTRACT: Electrochemical Machining (ECM) is an effective method for machining the parts with the whole structure or special structure. Because the conventional machining methods are not suitable for processing these kinds of structures. In this work, taking electrochemical machining rectangular holes as the research objective, and analyzing the flow field characteristics of machined surface with three kinds of cathode channel structures. First discussing the working state of the ECM process and some equations to be complied with, then numerically simulating the models which have the same characteristics with design and simulation parameters, obtained the pressure contour and velocity contour on the machined surface. The simulation results indicated that the machining effect of long slot structure was not as good as that of arc slot and tilted slot structure, and few differences in machining effects were observed between the arc slot and tilted slot structure. A case study was presented to illustrate the effectiveness of the application of Computational Fluid Dynamics (CFD) in designing the flow field of cathode for ECM.
This document describes a numerical study using lattice Boltzmann modeling to simulate columnar dendrite growth under forced and natural convection in 3D. The model couples lattice Boltzmann and cellular automaton methods to simulate fluid flow, solute transport, and dendrite growth. Results show that natural convection can influence dendrite morphology by affecting growth rates of different dendrite arms. 3D simulations provide a more accurate representation of dendrite growth kinetics compared to 2D simulations and better satisfy mass conservation. The model enhances understanding of solidification processes influenced by fluid flow.
Prediction of carry over coefficient for fluid flow through teeth on rotor l...Alexander Decker
This document discusses a computational fluid dynamics (CFD) study of fluid flow through teeth on a rotor labyrinth seal. A 2D model of the seal geometry was created in FLUENT software to predict the carry-over coefficient, which represents the portion of fluid kinetic energy that is transferred between seal cavities. The effects of parameters like seal geometry, tooth clearance, Reynolds number, and shaft rotational speed on the carry-over coefficient were investigated. Three CFD models for predicting the carry-over coefficient considering different parameters were developed and validated against experimental data. Correlations for the carry-over coefficient based on the CFD results were proposed.
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.
This document summarizes research on the structure and phase behavior of Cu-Ni nanoalloys. It uses thermodynamic modeling to predict how the phase diagrams and mixing/demixing behavior depend on nanoparticle size, shape, and temperature. The modeling indicates Cu-Ni nanoalloys can form either mixed particles or Janus particles, depending on the synthesis temperature, with nickel preferentially segregating to surfaces. Phase maps are provided to guide experimentalists on controlling particle structure.
This document discusses modeling heat transfer in a tube heat exchanger using analytical and numerical methods. It will use MATLAB and FLUENT software to model the heat transfer process. Governing equations for the heat transfer and fluid flow are presented. Initial and boundary conditions are defined to solve the equations numerically using a 4th order Runge-Kutta method in MATLAB. The goal is to investigate the results from analytical, numerical and simulation approaches to optimize the heat exchanger efficiency.
This study used computational fluid dynamics (CFD) software to analyze airflow patterns in a theoretical city model at two wind velocities. A 3D city model was created in SolidWorks and a grid was generated in Pointwise. Simulations using the Euler equations were run in Cobalt at 4.6 m/s and 30 m/s wind speeds. Results showed increased airflow velocities in streets parallel to wind direction and vortex formation in perpendicular streets. Pressure on building surfaces was highest in windward sides. The study demonstrated CFD's usefulness for urban planning by simulating wind flow effects of building placement and layout. Future work could examine angled wind directions and different building patterns.
This document describes a study that develops expressions for ice particle mass (m) and projected area (A) as a function of maximum dimension (D), for use in atmospheric models and remote sensing. It combines measurements of individual ice particle m and D from ground studies with estimates of m and A from aircraft probe measurements in ice clouds. The resulting m-D and A-D expressions are functions of temperature and cloud type (synoptic vs. anvil), and agree well with other field studies for temperatures between −60 and −20 °C. The expressions allow ice particle properties to be estimated over a wider size range than single power laws, and provide uncertainty estimates for parameterizing the relationships as power laws over limited ranges.
SIMMECHANICS VISUALIZATION OF EXPERIMENTAL MODEL OVERHEAD CRANE, ITS LINEARIZ...ijccmsjournal
Overhead Crane experimental model using Simmechanic Visualization is presented for the robust antisway LQR control. First, 1D translational motion of overhead crane is designed with exact lab model measurements and features. Second, linear least square system identification with 7 past inputs/outputs is applied on collected simulation data to produce more predicted models. Third, minimize root mean square error and identified the best fit model with lowest RMSE. Finally, Linear Quadratic Regulator (LQR) and Reference tracking with pre-compensator have been implemented to minimize load swing and perform fast track on trolley positioning.
This document discusses constructing flow nets to analyze seepage in anisotropic soils where permeability varies in horizontal and vertical directions. It provides the procedure for plotting flow nets in anisotropic soils by transforming the horizontal scale based on the ratio of horizontal to vertical permeability. The steps include: 1) adopting vertical and transformed horizontal scales, 2) plotting the cross-section using these scales, 3) drawing the flow net in the transformed plane, and 4) replotting the flow net in the natural scale. An example problem applies these steps to construct the flow net for a sheet pile structure with a given permeability ratio and calculates the equivalent permeability.
IRJET- Numerical Analysis for Nonlinear Consolidation of Saturated Soil using...IRJET Journal
This document presents a numerical method for analyzing one-dimensional nonlinear consolidation of saturated soil using the lattice Boltzmann method. The lattice Boltzmann-BGK model is used to simulate the nonlinear consolidation equation for saturated soil subjected to time-dependent loading under different boundary conditions. The multiscale Chapman-Enskog expansion is applied to derive the macroscopic nonlinear consolidation equation from the mesoscopic lattice Boltzmann equation. Numerical simulations are performed and found to agree well with available analytical solutions, demonstrating the validity of the proposed lattice Boltzmann method for analyzing nonlinear consolidation problems.
The goal of this project was to characterize a Marcellus shale gas reservoir by determining its Original Gas in Place (OGIP) and CO2 storage capacity. Structural maps, well logs from 12 wells, and Langmuir isotherm data were used. Well logs were analyzed to determine net pay zones and calculate properties like total organic carbon (TOC) and porosity. These were used to calculate OGIP and CO2 storage capacity at each well, which were interpolated over the formation using Matlab. Summing the interpolated values gave the total OGIP of 14.12 TSCF and total CO2 storage capacity of 14.58 TSCF for the formation. Monte Carlo analysis accounted for uncertainty in
Effect of Mobility on (I-V) Characteristics of Gaas MESFET Yayah Zakaria
We present in this paper an analytical model of the current–voltage (I-V) characteristics for submicron GaAs MESFET transistors. This model takes into account the analysis of the charge distribution in the active region and incorporate a field depended electron mobility, velocity saturation and charge
build-up in the channel. We propose in this frame work an algorithm of simulation based on mathematical expressions obtained previously. We propose a new mobility model describing the electric field-dependent. predictions of the simulator are compared with the experimental data [1] and
have been shown to be good.
Deformation Calculation for the Existing Tunnel Induced by Undercrossing Shie...IJRES Journal
An analytical solution was presented to calculate the vertical displacement of existing tunnels
based on the elastic foundation beam theory and cavity expansion theory with stress-induced initial anisotropy,
the analytical solution was then degenerated into isotropic results and was verified by an example. Multiple
factor analysis revealed that the maximum deformation of the tunnel is at the quadrature point; larger the
plastic radius a, greater influence on vertical displacement of existing tunnel; and the influence weakens with the
increase of vertical distance; vertical deformation of existing tunnel approximately follows a linear relationship
with lateral pressure coefficient. The analytical solution was a simple relational expression contains several
factors, so it has general applicability to similar problems.
This document summarizes a numerical study on free-surface flow conducted using a computational fluid dynamics (CFD) solver. The study examines the wave profile generated by a submerged hydrofoil through several test cases varying parameters like the turbulence model, grid resolution, and hydrofoil depth. The document provides background on the governing equations solved by the CFD solver and the interface capturing technique used to model the free surface. Five test cases are described that investigate grid convergence, the impact of laminar vs turbulent models, the relationship between hydrofoil depth and wave height, and the effect of discretization schemes.
This document summarizes a numerical study of airflow over an Ahmed body using RANS turbulence models. It finds that the k-ε-v2 model more accurately predicts separation and reattachment compared to other models. The study simulates flow over an Ahmed body with a 35 degree rear angle using various turbulence models and investigates the effects of grid layout and differencing schemes on the results. Numerical results agree well with experimental data on the wake structure and turbulent kinetic energy distribution behind the body.
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.
1) The document compares different simplified models for simulating rivulet flow down a slowly varying substrate to a direct numerical simulation using computational fluid dynamics (CFD).
2) Three simplified models are considered: constant contact angle and varying width, constant width and varying contact angle, and varying both contact angle and width.
3) The CFD simulation uses the lubrication approximation to directly solve the Navier-Stokes equations, while the simplified models make additional assumptions to obtain analytical solutions.
4) Comparison of the results from the different methods show that the model allowing both contact angle and width to vary provides the closest agreement to the CFD simulation.
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.
This document summarizes a research paper that was presented at the seventh International Conference on Urban Climate from June 29th to July 3rd, 2009 in Yokohama, Japan. The paper describes the development of a new 1-D Urban Canopy Model to simulate the effects of urban structures on atmospheric flow. Large Eddy Simulations were used to validate the model for different building configurations. The paper also introduces a new method for representing complex urban geometries with a simplified, equivalent representation of regularly spaced buildings that can be used as input for Urban Canopy Models.
GPR Probing of Smoothly Layered Subsurface Medium: 3D Analytical ModelLeonid Krinitsky
An analytical approach to GPR probing of a
horizontally layered subsurface medium is developed, based on the coupled-wave WKB approximation. An empirical model of current in dipole transmitter antenna is used.
1. The document discusses modeling turbidity (TB) in a reservoir using linear regression (LR) and geographically weighted regression (GWR). TB was measured at 10 observation points and estimated from satellite imagery reflectance data.
2. Both LR and GWR were used to model TB, with GWR producing estimates that exactly matched the observed TB values.
3. GWR coefficients were interpolated using inverse distance weighting to produce a continuous TB surface map for the entire reservoir area shown in the satellite image.
Simulation and Experiment Study of Flow Field of Flow channel for Rectangular...IJRESJOURNAL
ABSTRACT: Electrochemical Machining (ECM) is an effective method for machining the parts with the whole structure or special structure. Because the conventional machining methods are not suitable for processing these kinds of structures. In this work, taking electrochemical machining rectangular holes as the research objective, and analyzing the flow field characteristics of machined surface with three kinds of cathode channel structures. First discussing the working state of the ECM process and some equations to be complied with, then numerically simulating the models which have the same characteristics with design and simulation parameters, obtained the pressure contour and velocity contour on the machined surface. The simulation results indicated that the machining effect of long slot structure was not as good as that of arc slot and tilted slot structure, and few differences in machining effects were observed between the arc slot and tilted slot structure. A case study was presented to illustrate the effectiveness of the application of Computational Fluid Dynamics (CFD) in designing the flow field of cathode for ECM.
This document describes a numerical study using lattice Boltzmann modeling to simulate columnar dendrite growth under forced and natural convection in 3D. The model couples lattice Boltzmann and cellular automaton methods to simulate fluid flow, solute transport, and dendrite growth. Results show that natural convection can influence dendrite morphology by affecting growth rates of different dendrite arms. 3D simulations provide a more accurate representation of dendrite growth kinetics compared to 2D simulations and better satisfy mass conservation. The model enhances understanding of solidification processes influenced by fluid flow.
Prediction of carry over coefficient for fluid flow through teeth on rotor l...Alexander Decker
This document discusses a computational fluid dynamics (CFD) study of fluid flow through teeth on a rotor labyrinth seal. A 2D model of the seal geometry was created in FLUENT software to predict the carry-over coefficient, which represents the portion of fluid kinetic energy that is transferred between seal cavities. The effects of parameters like seal geometry, tooth clearance, Reynolds number, and shaft rotational speed on the carry-over coefficient were investigated. Three CFD models for predicting the carry-over coefficient considering different parameters were developed and validated against experimental data. Correlations for the carry-over coefficient based on the CFD results were proposed.
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.
This document summarizes research on the structure and phase behavior of Cu-Ni nanoalloys. It uses thermodynamic modeling to predict how the phase diagrams and mixing/demixing behavior depend on nanoparticle size, shape, and temperature. The modeling indicates Cu-Ni nanoalloys can form either mixed particles or Janus particles, depending on the synthesis temperature, with nickel preferentially segregating to surfaces. Phase maps are provided to guide experimentalists on controlling particle structure.
This document discusses modeling heat transfer in a tube heat exchanger using analytical and numerical methods. It will use MATLAB and FLUENT software to model the heat transfer process. Governing equations for the heat transfer and fluid flow are presented. Initial and boundary conditions are defined to solve the equations numerically using a 4th order Runge-Kutta method in MATLAB. The goal is to investigate the results from analytical, numerical and simulation approaches to optimize the heat exchanger efficiency.
This study used computational fluid dynamics (CFD) software to analyze airflow patterns in a theoretical city model at two wind velocities. A 3D city model was created in SolidWorks and a grid was generated in Pointwise. Simulations using the Euler equations were run in Cobalt at 4.6 m/s and 30 m/s wind speeds. Results showed increased airflow velocities in streets parallel to wind direction and vortex formation in perpendicular streets. Pressure on building surfaces was highest in windward sides. The study demonstrated CFD's usefulness for urban planning by simulating wind flow effects of building placement and layout. Future work could examine angled wind directions and different building patterns.
This document describes a study that develops expressions for ice particle mass (m) and projected area (A) as a function of maximum dimension (D), for use in atmospheric models and remote sensing. It combines measurements of individual ice particle m and D from ground studies with estimates of m and A from aircraft probe measurements in ice clouds. The resulting m-D and A-D expressions are functions of temperature and cloud type (synoptic vs. anvil), and agree well with other field studies for temperatures between −60 and −20 °C. The expressions allow ice particle properties to be estimated over a wider size range than single power laws, and provide uncertainty estimates for parameterizing the relationships as power laws over limited ranges.
SIMMECHANICS VISUALIZATION OF EXPERIMENTAL MODEL OVERHEAD CRANE, ITS LINEARIZ...ijccmsjournal
Overhead Crane experimental model using Simmechanic Visualization is presented for the robust antisway LQR control. First, 1D translational motion of overhead crane is designed with exact lab model measurements and features. Second, linear least square system identification with 7 past inputs/outputs is applied on collected simulation data to produce more predicted models. Third, minimize root mean square error and identified the best fit model with lowest RMSE. Finally, Linear Quadratic Regulator (LQR) and Reference tracking with pre-compensator have been implemented to minimize load swing and perform fast track on trolley positioning.
This document discusses constructing flow nets to analyze seepage in anisotropic soils where permeability varies in horizontal and vertical directions. It provides the procedure for plotting flow nets in anisotropic soils by transforming the horizontal scale based on the ratio of horizontal to vertical permeability. The steps include: 1) adopting vertical and transformed horizontal scales, 2) plotting the cross-section using these scales, 3) drawing the flow net in the transformed plane, and 4) replotting the flow net in the natural scale. An example problem applies these steps to construct the flow net for a sheet pile structure with a given permeability ratio and calculates the equivalent permeability.
IRJET- Numerical Analysis for Nonlinear Consolidation of Saturated Soil using...IRJET Journal
This document presents a numerical method for analyzing one-dimensional nonlinear consolidation of saturated soil using the lattice Boltzmann method. The lattice Boltzmann-BGK model is used to simulate the nonlinear consolidation equation for saturated soil subjected to time-dependent loading under different boundary conditions. The multiscale Chapman-Enskog expansion is applied to derive the macroscopic nonlinear consolidation equation from the mesoscopic lattice Boltzmann equation. Numerical simulations are performed and found to agree well with available analytical solutions, demonstrating the validity of the proposed lattice Boltzmann method for analyzing nonlinear consolidation problems.
The goal of this project was to characterize a Marcellus shale gas reservoir by determining its Original Gas in Place (OGIP) and CO2 storage capacity. Structural maps, well logs from 12 wells, and Langmuir isotherm data were used. Well logs were analyzed to determine net pay zones and calculate properties like total organic carbon (TOC) and porosity. These were used to calculate OGIP and CO2 storage capacity at each well, which were interpolated over the formation using Matlab. Summing the interpolated values gave the total OGIP of 14.12 TSCF and total CO2 storage capacity of 14.58 TSCF for the formation. Monte Carlo analysis accounted for uncertainty in
Effect of Mobility on (I-V) Characteristics of Gaas MESFET Yayah Zakaria
We present in this paper an analytical model of the current–voltage (I-V) characteristics for submicron GaAs MESFET transistors. This model takes into account the analysis of the charge distribution in the active region and incorporate a field depended electron mobility, velocity saturation and charge
build-up in the channel. We propose in this frame work an algorithm of simulation based on mathematical expressions obtained previously. We propose a new mobility model describing the electric field-dependent. predictions of the simulator are compared with the experimental data [1] and
have been shown to be good.
Deformation Calculation for the Existing Tunnel Induced by Undercrossing Shie...IJRES Journal
An analytical solution was presented to calculate the vertical displacement of existing tunnels
based on the elastic foundation beam theory and cavity expansion theory with stress-induced initial anisotropy,
the analytical solution was then degenerated into isotropic results and was verified by an example. Multiple
factor analysis revealed that the maximum deformation of the tunnel is at the quadrature point; larger the
plastic radius a, greater influence on vertical displacement of existing tunnel; and the influence weakens with the
increase of vertical distance; vertical deformation of existing tunnel approximately follows a linear relationship
with lateral pressure coefficient. The analytical solution was a simple relational expression contains several
factors, so it has general applicability to similar problems.
This document summarizes a numerical study on free-surface flow conducted using a computational fluid dynamics (CFD) solver. The study examines the wave profile generated by a submerged hydrofoil through several test cases varying parameters like the turbulence model, grid resolution, and hydrofoil depth. The document provides background on the governing equations solved by the CFD solver and the interface capturing technique used to model the free surface. Five test cases are described that investigate grid convergence, the impact of laminar vs turbulent models, the relationship between hydrofoil depth and wave height, and the effect of discretization schemes.
This document summarizes a numerical study of airflow over an Ahmed body using RANS turbulence models. It finds that the k-ε-v2 model more accurately predicts separation and reattachment compared to other models. The study simulates flow over an Ahmed body with a 35 degree rear angle using various turbulence models and investigates the effects of grid layout and differencing schemes on the results. Numerical results agree well with experimental data on the wake structure and turbulent kinetic energy distribution behind the body.
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.
1) The document compares different simplified models for simulating rivulet flow down a slowly varying substrate to a direct numerical simulation using computational fluid dynamics (CFD).
2) Three simplified models are considered: constant contact angle and varying width, constant width and varying contact angle, and varying both contact angle and width.
3) The CFD simulation uses the lubrication approximation to directly solve the Navier-Stokes equations, while the simplified models make additional assumptions to obtain analytical solutions.
4) Comparison of the results from the different methods show that the model allowing both contact angle and width to vary provides the closest agreement to the CFD simulation.
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.
2-Dimensional and 3-Dimesional Electromagnetic Fields Using Finite element me...IOSR Journals
This document describes using the finite element method to model 2D and 3D electromagnetic fields. It discusses modeling a quarter section of a rectangular coaxial line with triangular elements. It describes constructing the matrices for each element and combining them to solve the overall matrix equation. The document outlines implementing FEM in MATLAB, including generating meshes, adding sources, and solving the resulting matrices. Several examples are presented of using a graphical user interface created in MATLAB to calculate fields from configurations like straight wires, bent wires, solenoids, and square loops using FEM techniques.
Analysis of Flow in a Convering-Diverging NozzleAlber Douglawi
This document summarizes Alber Douglawi's analysis of air flow through a converging-diverging nozzle using computational fluid dynamics (CFD) software. The project aimed to model the nozzle's flow properties and features like shocks. Douglawi created meshes of varying complexity and ran simulations using inviscid and turbulence models. Initial runs assumed ideal gas and inviscid flow. Later runs added wall functions and turbulence models. Grid convergence was achieved by comparing results from refined meshes. The simulations captured expected flow features like oblique shocks in the diverging section.
COMPARISON OF VOLUME AND DISTANCE CONSTRAINT ON HYPERSPECTRAL UNMIXINGcsandit
The document compares two algorithms for hyperspectral image unmixing - one based on minimum volume constraint and one based on sum of squared distances constraint. It analyzes the performance of the two algorithms under different conditions like flatness of the endmember simplex, effects of initialization, and robustness to noise. The analysis shows that the sum of squared distances constraint performs better than the volume constraint for non-regular simplex shapes and is more robust to random initialization and noise. The comparison provides guidance on which constraint is more suitable for specific hyperspectral unmixing tasks.
Numerical Calculation of Solid-Liquid two-Phase Flow Inside a Small Sewage Pumptheijes
Based on a mixture multiphase flow model,theRNG k–εturbulencemodelandfrozen rotor method were used to perform a numerical simulation of steady flow in the internal flow field of a sewage pump that transports solid and liquid phase flows. Resultsof the study indicate that the degree of wear on the front and the back of the blade suction surface from different densities of solid particles shows a completely opposite influencing trend. With the increase of delivered solid-phase density, the isobaric equilibrium position moves to the leading edge point of the blade, but the solid-phase isoconcentration point on the blade pressure surface and suction surface basically remains unchanged. The difference between hydraulic lift and water lift indelivering solid- and liquid-phase flows shows a rising trend with the increase of working flow
A Drift-Diffusion Model to Simulate Current for Avalanche Photo DetectorIJERA Editor
In this research, a Drift-Diffusion model is carried out to calculate includes impact ionization mechanism and can calculate dark current and photocurrent of avalanche photo diode. Poisson equation, electron and hole density continuity equations and electron and hole current equations have been solved simultaneously using Gummel method. Consideration of impact ionization enables the model to completely simulate the carriers flow in high electrical field. The simulation has been done using MATLAB and the results are compared with other reliable results obtained by researchers. Our results show despite of hydrodynamics and Monte Carlo methods which are very complicated we can get the current characteristics of photo detector easily with acceptable accuracy. In addition we can use this method to calculate currents of device in high fields.
This document describes a methodology for simulating signal propagation on multiconductor transmission lines directly in the time domain using the Transmission Line Modeling (TLM) method combined with Z-transform techniques. The approach models a two-conductor transmission line using telegrapher's equations converted to the TLM format. It defines quantities such as incident and total voltages/currents and applies a bilinear Z-transform to obtain a numerical algorithm to calculate the total line quantities from the incident quantities. As an example, it simulates propagation of a short pulse on a hypothetical two-channel carbon nanotube transmission line.
DWS MODELING OF MULTICONDUCTOR TRANSMISSION LINESPiero Belforte
This document summarizes different methods for simulating multiconductor transmission lines (MTL) using the DWM simulation tool SPRINT. It describes the general modal method, which applies to nonhomogeneous and asymmetrical structures using modal voltages and currents. For homogeneous structures, it presents the Marx method and tridiagonal method. It compares SPRINT's implementation of the modal and Marx methods for a simple 3-conductor line, finding good agreement with SPICE. SPRINT allows more efficient simulation of large MTL networks compared to SPICE.
Intelligent back analysis using data from the instrument (poster)Hamed Zarei
This document presents a model using artificial neural networks for back analysis of tunnel monitoring data from the Chehel Chai water conveyance tunnel in Iran. Input data from 27 parameters across 3 categories were used to train a neural network model on results from 18 convergence stations. The trained model was then able to accurately estimate rock mass elasticity and in situ stress values based on new monitoring data, demonstrating its effectiveness for intelligent back analysis of future tunnel monitoring results.
This project aims at simulating lid driven cavity flow problem using package MATLAB. Steady Incompressible Navier-Stokes equation with continuity equation will be studied at various Reynolds number. The main aim is to obtain the velocity field in steady state using the finite difference formulation on momentum equations and continuity equation. Reynold number is the pertinent parameter of the present study. Taylor’s series expansion has been used to convert the governing equations in the algebraic form using finite difference schemes.
The document describes modeling the 3D geometry of relativistic jets based on 2D projection observations. It presents a mathematical model that uses Bayesian parameter estimation via MCMC to statistically estimate the 3D structural parameters of jet bends from measured 2D projection properties. Figures and equations show how the model accounts for projection effects to determine the intrinsic 3D geometry from observed 2D jet features like bend angles and distances.
This document presents results from a lattice QCD calculation of the proton isovector scalar charge (gs) at two light quark masses. The calculation uses domain-wall fermions and Iwasaki gauge actions on a 323x64 lattice with a spacing of 0.144 fm. Ratios of three-point to two-point correlation functions are formed and fit to a plateau to extract gs. Values of gs are obtained for quark masses of 0.0042 and 0.001, and all-mode averaging is used for the lighter mass. Chiral perturbation theory will be used to extrapolate gs to the physical quark mass. Preliminary results for gs at the unphysical quark masses are reported in lattice units.
CFD and Artificial Neural Networks Analysis of Plane Sudden Expansion FlowsCSCJournals
It has been clearly established that the reattachment length for laminar flow depends on two non-dimensional parameters, the Reynolds number and the expansion ratio, therefore in this work, an ANN model that predict reattachment positions for the expansion ratios of 2, 3 and 5 based on the above two parameters has been developed. The R2 values of the testing set output Xr1, Xr2, Xr3, and Xr4 were 0.9383, 0.8577, 0.997 and 0.999 respectively. These results indicate that the network model produced reattachment positions that were in close agreement with the actual values. When considering the reattachment length of plane sudden-expansions the judicious combination of CFD calculated solutions with ANN will result in a considerable saving in computing and turnaround time. Thus CFD can be used in the first instance to obtain reattachment lengths for a limited choice of Reynolds numbers and ANN will be used subsequently to predict the reattachment lengths for other intermediate Reynolds number values. The CFD calculations concern unsteady laminar flow through a plane sudden expansion and are performed using a commercial CFD code STAR-CD while the training process of the corresponding ANN model was performed using the NeuroShellTM simulator.
DIGITAL WAVE FORMULATION OF THE PEEC METHODPiero Belforte
This document presents a digital wave formulation (DWF) method for solving the quasi-static partial element equivalent circuit (PEEC) method in the time domain. The standard PEEC model is transformed into a wave digital network by using wave variables and defining wave digital circuit elements corresponding to inductors, capacitors, resistors, sources, and connections. This allows the PEEC model to be solved as a wave digital network using a digital wave simulator (DWS). A numerical example compares the proposed DWF-PEEC solver to a standard SPICE solver, showing the DWF-PEEC method provides accurate results with significant speed-up in computation time.
Buckling and Pull-In Instability of Multi-Walled Carbon Nanotube Probes Near ...IJERA Editor
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.
This document summarizes a proposed assembly-free simulation method for additive manufacturing processes.
Current additive manufacturing simulation methods either use a "quiet" approach where all elements are assembled into a global stiffness matrix from the start, or an "inactive" approach where only deposited elements are assembled. Both have disadvantages like ill-conditioning or remeshing requirements.
The proposed method uses a voxel-based discretization where the workspace is meshed once into identical hexahedral elements. Material deposition is modeled by modifying element properties without reassembling matrices. This avoids remeshing and assembly, reducing memory needs. The method was demonstrated by simulating transient non-linear thermal behavior during laser deposition.
Similar to An Efficient Algorithm for Contact Angle Estimation in Molecular Dynamics Simulations (20)
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
How to Setup Warehouse & Location in Odoo 17 InventoryCeline George
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
An Efficient Algorithm for Contact Angle Estimation in Molecular Dynamics Simulations
1. Sumith YD
International Journal of Engineering (IJE), Volume (9) : Issue (1) : 2015 1
An Efficient Algorithm for Contact Angle Estimation in Molecular
Dynamics Simulations
Sumith YD ydsumith@gmail.com
Research Assistant/Mechanical & Aerospace Engineering Department
Syracuse University
Syracuse, NY, USA
Abstract
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.
Keywords: Molecular Dynamics, Contact Angle, Algorithms, Mahalanobis Technique.
1. INTRODUCTION
It is quite common in the literature to use Berendsen or Nose-Hoover thermostat for liquid
molecular dynamic simulations to study different thermodynamic properties of water. In this paper
I have investigated the effect of such thermostats on the contact angle of water above platinum
substrate.
In the past, Bo Shi et al [1] have simulated the contact angle of water on top of Platinum surface
with FCC 111. Their work involved simulating columbic attraction with P3M method and keeping
the temperature constant using Berendsen thermostat [2]. Maruyama and et al [3] have also done
contact angle studies of water on platinum with truncated potential. Both researchers have used
Zhu Philpott (ZP) potential [4] for water platinum interaction. There exists a wide range of
literature on contact angle estimation for sessile drops over metallic and non-metallic substrates.
However they are not mentioned here since the main focus of the paper is on contact angle
estimation method for molecular simulations.
The paper is divided into two main sections, first explaining the MD simulation details and models
used; second the new algorithm for contact angle estimation.
2. MD SIMULATION OF WATER ABOVE PLATINUM
A 6 nm3 water droplet (7221 molecules) is kept on top of FCC 111 platinum plate as shown in
FIGURE 1. The slab geometry made of water in between platinum walls is applied with periodic
boundary condition (PBC) laterally and wall boundary vertically. The platinum walls are of 20 nm
2
square and kept apart at a distance of 14 nm.
2. Sumith YD
International Journal of Engineering (IJE), Volume (9) : Issue (1) : 2015 2
FIGURE 1: Simulation model for contact angle estimation.
The equations of motions are solved using Velocity Verlet [5] scheme. A shifted truncation
scheme is used instead of Ewald summation methods or P3M. The feature of this scheme is that
both potential and force goes smoothly to zero at the cut off radius.
=
�
[ −
�
+
�
−
�
]
The water molecules are modeled using Simple point charge extended (SPCE) model introduced
by Berendsen et al [6]. The intra molecular bonds are kept rigid throughout the simulation using
the SHAKE algorithm [7].
Since we are not modeling a contiguous array of droplets we can safely ignore the long range
effects of the single water droplet. Simulation of droplet and films with SPME method will be
studied extensively and will be published in another work.
Three cases of simulations with different thermostats are considered here. Berendsen [2], Nose-
Hoover [8] and Velocity rescaling [9]. All the cases are run from 0ps to 1000ps using 2fs time
integration steps. Gromacs [10] is the software package used for simulation.
At the end of simulation the trajectory files are processed and using the algorithm mentioned in
the next section contact angles is determined. The time evolution of contact angle is shown in
FIGURE 2. (a) and (b). The results indicate a transient behavior for contact angle.
FIGURE 2: (a) Contact angle vs. time in XZ plane (b) Contact angle vs. time in YZ plane.
3. Sumith YD
International Journal of Engineering (IJE), Volume (9) : Issue (1) : 2015 3
The contact angles seem to be fluctuating and never reaching a steady state. This is because of
the nature of the potential function that we used for wall- water interaction (LJ potential). However
this can be accounted by using ZP potential for water platinum interaction.
With the enormous amount of result data estimation of contact angle using visual or manual
methods becomes a tedious process. There are not much algorithms which suit well for the direct
post processing of molecular simulations. Hence the need for such algorithm raised and I have
explained it in the next section.
FIGURE 3: (a) Droplet particles (in black) and detected boundary (in red) (b) water molecules on top of
platinum, black line shows the fitted circle from liquid vapor interface.
FIGURE 3. (a) shows a screenshot of molecular centroid after 300 ps simulation using case1
(Berendsen). The red dots show the location of liquid vapor interface detected using the new
algorithm.
3. ALGORITHM DETAILS
Once obtaining the coordinate data (center of mass in case of water molecule) from the molecular
simulations another challenge is to process the data to get a quality sample. Here a new method
is explained to systematically find the boundary or edge of water droplet using simple
mathematical methods and without using any image processing algorithms. For the convenience
of the reader the whole process is divided into 5 steps.
We can process the data by projecting it normal to X-Z plane and also normal to Y-Z plane. (x, y)
represents (X,Z) and (Y,Z) coordinates respectively for the data processing. FIGURE 4 shows
screenshot of water above platinum surface after 500ps simulation.
FIGURE 4: Water on top of Platinum [Berendsen 500ps].
4. Sumith YD
International Journal of Engineering (IJE), Volume (9) : Issue (1) : 2015 4
3.1. Step 1: Preparing the Sample for Processing
The unwanted vapor molecules (outliers) in the data can be removed effectively using
Mahalanobis Distance [11] technique.
If �is the × column centered vector consisting of − ̅, − ̅ data of n points then variance-
covariance matrix � is defined as:
� =
− �
�
�
Then the Mahalanobis Distance (MD) is calculated as:
� = √ �
− �
Where is the mean centered data of i
th
data point. From this list of MD we can neglect those
data points with considerably high MD values. For current study I have neglected all values above
4. Again this can be changed and fine-tuned according to the data.
The effectiveness of MD technique can be visualized from FIGURE 5. (a) and (b). The two vapor
molecules which would have been a hindrance to estimate the contact angle accurately was
removed easily with MD method.
FIGURE 5: (a) Before removing the outliers (b) After removing the outliers and monolayer.
3.2. Step 2: Mesh based Contour Conversion using B-Splines
In this step a 2D mesh is generated and the entire droplet data is smeared into the grids using 4
th
order B-spline function. This makes it easier to find a smooth transition between the liquid core
and the vacuum or vapor.
The Nearest Grid Point (NGP) method is a traditional first order method used to assign data to
the grid points. Inspired from Hockney and Eastwood [12] the density of the molecules at every
grid point can be calculated by the below equation.
= ∑
| − �|
∗
| − �|
�=
Where the weight function is defined as
= {
, <
, ℎ �
5. Sumith YD
International Journal of Engineering (IJE), Volume (9) : Issue (1) : 2015 5
The B-spline method is inspired from Smooth Particle Mesh Ewald [13]. Reproducing the
definition gives, for any real number u, let � denote the linear hat function given by � =
− | − | for ≤ ≤ and � = for < or > . For n greater than 2, define �� by
the recursion
�� =
−
��− +
−
−
��− −
For our case n = 4 and u is in fractional coordinates.
FIGURE 6: a) NGP assignment, b) B-spline assignment.
FIGURE 6. (a) and (b) shows the graphical representation of 2D density using NGP method and
B-spline method. It can be seen easily that B-spline assignment scheme provides a smooth
transition between liquid and vapor. Hence it is the recommended method for smearing.
3.3. Step 3: Filter Out the High and Low Density Data
As the next step towards the identification of the droplet boundary the grid points with high
densities which resemble the liquid region and low densities that resemble the noise is eliminated
based on the threshold densities defined as below.
ℎ ℎ � �� = ∗ � �
ℎ ℎ � � = ∗ � �
and are weights which can be fine-tuned according to the data. For present analysis I
have taken them as 2 and 0.5 respectively. Now all the data which meets the below criteria will be
used for further analysis.
ℎ ℎ � � ≤ � � . �� ≤ ℎ ℎ � ��
FIGURE 7: Filtered data (not to scale).
6. Sumith YD
International Journal of Engineering (IJE), Volume (9) : Issue (1) : 2015 6
FIGURE 7 shows the data points obtained after applying the filter based on threshold density
values. We can see that the interior liquid and exterior vapors have been eliminated.
3.4. Step 4: Finding the Ideal Location for Droplet Boundary
In this step we will find the centroid of the data obtained from the Step 3. If centroid lies below y-
axis then set the y coordinate as the top of the platinum plate. This is to ensure that we prevent
the erroneous semicircle shape which will lead to incorrect contact angle estimation. Then we
radially move outwards from that point until we reach the boundary of data as shown in FIGURE
8. (a). This procedure is repeated for ≤ θ ≤ π. If the centroid is above in the positive y-axis then
the procedure is repeated for ≤ � ≤ .
FIGURE 8: (a) Radial rays from centroid to find the extremities (b) Location of the droplet boundary.
At the end we will be left with a collection of points which forms the exterior of the droplet.
FIGURE 8. (b) shows the final data points obtained using the algorithm.
3.5. Step 5: Finalizing the Droplet Boundary
These data points from step 4 are suitable candidates for final droplet boundary. Hence we fit
them with Landau method [14] and find the circle which represents the droplet boundary. Once
we get the equation of circle we can solve it for the angle made by the tangent at the platinum-
water interface.
FIGURE 9: Final boundary of the droplet and fitted circle.
7. Sumith YD
International Journal of Engineering (IJE), Volume (9) : Issue (1) : 2015 7
� = tan−
[
−
−
]
Where � is the contact angle, , is the centroid of the fitted circle.
=
= − √� − −
Where cutoff is the distance above the platinum plate where we want to ignore the data points
related to monolayer (high dense) region. R is the radius of the fitted circle. FIGURE 9 shows a
typical droplet snapshot and also its detected boundary (in red) using the algorithm. The droplet is
shown as single particles since their center of mass is only considered for analysis.
4. CONCLUSION
A new algorithm to accurately estimate the contact angle of the liquid from the molecular
simulation results was presented in the paper. The algorithm is computationally efficient and
accurate. Different parameters used in the identification procedure makes it easier to implement
to new and different data sets. The different thermostat schemes and its effect on contact angle
of water have also been discussed in this work. A MATLAB version of the algorithm will be
provided upon request to author.
5. ACKNOWLEDGEMENT
The author would like to thank Prof. Maroo, Department of Mechanical Engineering, Syracuse
University, for his helpful support for performing the Molecular Dynamics Simulations.
6. REFERENCES
[1] B. Shi, S. Sinha, and V. K. Dhir, in ASME 2005 International Mechanical Engineering
Congress and Exposition (American Society of Mechanical Engineers, 2005), pp. 93.
[2] H. J. Berendsen, J. P. M. Postma, W. F. van Gunsteren, A. DiNola, and J. Haak, The
Journal of chemical physics 81, 3684 (1984).
[3] T. Kimura and S. Maruyama, Heat Transfer 1, 537 (2002).
[4] S.-B. Zhu and M. R. Philpott, Interaction of water with metal surfaces, 1994.
[5] W. C. Swope, H. C. Andersen, P. H. Berens, and K. R. Wilson, The Journal of Chemical
Physics 76, 637 (1982).
[6] H. Berendsen, J. Grigera, and T. Straatsma, Journal of Physical Chemistry 91, 6269
(1987).
[7] B. J. Leimkuhler and R. D. Skeel, Journal of Computational Physics 112, 117 (1994).
[8] W. G. Hoover, Physical Review A 31, 1695 (1985).
[9] G. Bussi, D. Donadio, and M. Parrinello, The Journal of chemical physics 126, 014101
(2007).
[10] B. Hess, C. Kutzner, D. Van Der Spoel, and E. Lindahl, Journal of chemical theory and
computation 4, 435 (2008).
[11] R. De Maesschalck, D. Jouan-Rimbaud, and D. L. Massart, Chemometrics and intelligent
laboratory systems 50, 1 (2000).
8. Sumith YD
International Journal of Engineering (IJE), Volume (9) : Issue (1) : 2015 8
[12] R. W. Hockney and J. W. Eastwood, Computer simulation using particles (CRC Press,
2010).
[13] U. Essmann, L. Perera, M. L. Berkowitz, T. Darden, H. Lee, and L. G. Pedersen, The
Journal of chemical physics 103, 8577 (1995).
[14] S. M. Thomas and Y. Chan, Computer Vision, Graphics, and Image Processing 45, 362
(1989).