The approximate bound state of the nonrelativistic Schrӧdinger equation was
obtained with the modified trigonometric scarf type potential in the framework of
asymptotic iteration method for any arbitrary angular momentum quantum number l
using a suitable approximate scheme to the centrifugal term. The effect of the screening
parameter and potential depth on the eigenvalue was studied numerically. Finally, the
scattering phase shift of the nonrelativistic Schrӧdinger equation with the potential
under consideration was calculated.
EXACT SOLUTIONS OF SCHRÖDINGER EQUATION WITH SOLVABLE POTENTIALS FOR NON PT/P...ijrap
We have obtained explicitly the exact solutions of the Schrodinger equation with Non PT/PT symmetric
Rosen Morse II, Scarf II and Coulomb potentials. Energy eigenvalues and the corresponding
unnormalized wave functions for these systems for both Non PT and PT symmetric are also obtained using
the Nikiforov-Uvarov (NU) method.
The approximate bound state of the nonrelativistic Schrӧdinger equation was
obtained with the modified trigonometric scarf type potential in the framework of
asymptotic iteration method for any arbitrary angular momentum quantum number l
using a suitable approximate scheme to the centrifugal term. The effect of the screening
parameter and potential depth on the eigenvalue was studied numerically. Finally, the
scattering phase shift of the nonrelativistic Schrӧdinger equation with the potential
under consideration was calculated.
EXACT SOLUTIONS OF SCHRÖDINGER EQUATION WITH SOLVABLE POTENTIALS FOR NON PT/P...ijrap
We have obtained explicitly the exact solutions of the Schrodinger equation with Non PT/PT symmetric
Rosen Morse II, Scarf II and Coulomb potentials. Energy eigenvalues and the corresponding
unnormalized wave functions for these systems for both Non PT and PT symmetric are also obtained using
the Nikiforov-Uvarov (NU) method.
optimal solution method of integro-differential equaitions under laplace tran...INFOGAIN PUBLICATION
In this paper, Laplace Transform method is developed to solve partial Integro-differential equations. Partial Integro-differential equations (PIDE) occur naturally in various fields of science. Engineering and Social Science. We propose a max general form of linear PIDE with a convolution Kernal. We convert the proposed PIDE to an ordinary differential equation (ODE) using the LT method. We applying inverse LT as exact solution of the problems obtained. It is observed that the LT is a simple and reliable technique for solving such equations. The proposed model illustrated by numerical examples.
SCHRODINGER'S CAT PARADOX RESOLUTION USING GRW COLLAPSE MODELijrap
Possible solution of the Schrödinger's cat paradox is considered.We pointed out that: the collapsed
state of the cat always shows definite and predictable measurement outcomes even if Schrödinger's
cat consists of a superposition: cat=livecat+
deathcat
MODELING OF REDISTRIBUTION OF INFUSED DOPANT IN A MULTILAYER STRUCTURE DOPANT...mathsjournal
In this paper we used an analytical approach to model nonlinear diffusion of dopant in a multilayer structure with account nonstationary annealing of the dopant. The approach do without crosslinking solutions at
the interface between layers of the multilayer structure. In this paper we analyzed influence of pressure of
vapor of infusing dopant during doping of multilayer structure on values of optimal parameters of technological process to manufacture p-n-junctions. It has been shown, that doping of multilayer structures by
diffusion and optimization of annealing of dopant gives us possibility to increase sharpness of p-n-junctions
(single p-n-junctions and p-n-junctions within transistors) and to increase homogeneity of dopant distribution in doped area.
Eh4 energy harvesting due to random excitations and optimal designUniversity of Glasgow
This lecture is about vibration energy harvesting when both the excitation and the system have uncertainties. Two cases, namely, when the excitation is a random process and when the system parameters are described by random variables are described. Optimal design for both cases is discussed.
JEE Main 2020 Question Paper With Solution 08 Jan 2020 Shift 1 Memory BasedMiso Study
JEE Main 2020 Question Paper With Solution 08 Jan 2020 Shift 1 Memory Based, which helps you to understand the chapter in easy way also downaload sample papers and previous year papers and practice to solve the question on time. Download at www.misostudy.com.
Interpolating rational bézier spline curves with local shape controlijcga
The paper presents a technique for construction
of
C
n
interpolating
rational Bézier
spline curves by means
of blending
rational
quadric Bézier curves. A class of polynomials which satisfy special boundary
conditions is used for blending. Properties of the polynomials
are considered
.
The constructed spl
ine
curves have local shape control that make them useful in such geometric applications a
s
real
-
time
trajectory generation and fast curve sketching
.
This talk is about the analysis of nonlinear energy harvesters. A particular example of an inverted beam harvester proposed by our group has been discussed in details.
optimal solution method of integro-differential equaitions under laplace tran...INFOGAIN PUBLICATION
In this paper, Laplace Transform method is developed to solve partial Integro-differential equations. Partial Integro-differential equations (PIDE) occur naturally in various fields of science. Engineering and Social Science. We propose a max general form of linear PIDE with a convolution Kernal. We convert the proposed PIDE to an ordinary differential equation (ODE) using the LT method. We applying inverse LT as exact solution of the problems obtained. It is observed that the LT is a simple and reliable technique for solving such equations. The proposed model illustrated by numerical examples.
SCHRODINGER'S CAT PARADOX RESOLUTION USING GRW COLLAPSE MODELijrap
Possible solution of the Schrödinger's cat paradox is considered.We pointed out that: the collapsed
state of the cat always shows definite and predictable measurement outcomes even if Schrödinger's
cat consists of a superposition: cat=livecat+
deathcat
MODELING OF REDISTRIBUTION OF INFUSED DOPANT IN A MULTILAYER STRUCTURE DOPANT...mathsjournal
In this paper we used an analytical approach to model nonlinear diffusion of dopant in a multilayer structure with account nonstationary annealing of the dopant. The approach do without crosslinking solutions at
the interface between layers of the multilayer structure. In this paper we analyzed influence of pressure of
vapor of infusing dopant during doping of multilayer structure on values of optimal parameters of technological process to manufacture p-n-junctions. It has been shown, that doping of multilayer structures by
diffusion and optimization of annealing of dopant gives us possibility to increase sharpness of p-n-junctions
(single p-n-junctions and p-n-junctions within transistors) and to increase homogeneity of dopant distribution in doped area.
Eh4 energy harvesting due to random excitations and optimal designUniversity of Glasgow
This lecture is about vibration energy harvesting when both the excitation and the system have uncertainties. Two cases, namely, when the excitation is a random process and when the system parameters are described by random variables are described. Optimal design for both cases is discussed.
JEE Main 2020 Question Paper With Solution 08 Jan 2020 Shift 1 Memory BasedMiso Study
JEE Main 2020 Question Paper With Solution 08 Jan 2020 Shift 1 Memory Based, which helps you to understand the chapter in easy way also downaload sample papers and previous year papers and practice to solve the question on time. Download at www.misostudy.com.
Interpolating rational bézier spline curves with local shape controlijcga
The paper presents a technique for construction
of
C
n
interpolating
rational Bézier
spline curves by means
of blending
rational
quadric Bézier curves. A class of polynomials which satisfy special boundary
conditions is used for blending. Properties of the polynomials
are considered
.
The constructed spl
ine
curves have local shape control that make them useful in such geometric applications a
s
real
-
time
trajectory generation and fast curve sketching
.
This talk is about the analysis of nonlinear energy harvesters. A particular example of an inverted beam harvester proposed by our group has been discussed in details.
Utilisation de Neo4j, la base de données graphe, afin de tirer profit de l'Internet of Things.
Challenges Business, développeurs, ...
Le lien vers graphgen pour le graphe : http://graphgen.neoxygen.io/?graph=mwhj6x
Le lien de la vidéo sur l'IoT : https://www.youtube.com/watch?v=nEVatZruJ7k&feature=youtu.be
MODELING OF REDISTRIBUTION OF INFUSED DOPANT IN A MULTILAYER STRUCTURE DOPANT...mathsjournal
In this paper we used an analytical approach to model nonlinear diffusion of dopant in a multilayer structure with account nonstationary annealing of the dopant. The approach do without crosslinking solutions at
the interface between layers of the multilayer structure. In this paper we analyzed influence of pressure of
vapor of infusing dopant during doping of multilayer structure on values of optimal parameters of technological process to manufacture p-n-junctions. It has been shown, that doping of multilayer structures by
diffusion and optimization of annealing of dopant gives us possibility to increase sharpness of p-n-junctions
(single p-n-junctions and p-n-junctions within transistors) and to increase homogeneity of dopant distribution in doped area.
Modeling of Redistribution of Infused Dopant in a Multilayer Structure Dopant...mathsjournal
In this paper we used an analytical approach to model nonlinear diffusion of dopant in a multilayer structure with account nonstationary annealing of the dopant. The approach do without crosslinking solutions at the interface between layers of the multilayer structure. In this paper we analyzed influence of pressure of vapor of infusing dopant during doping of multilayer structure on values of optimal parameters of technological process to manufacture p-n-junctions. It has been shown, that doping of multilayer structures by diffusion and optimization of annealing of dopant gives us possibility to increase sharpness of p-n-junctions (single p-n-junctions and p-n-junctions within transistors) and to increase homogeneity of dopant distribution in doped area.
Formulas for Surface Weighted Numbers on Graphijtsrd
The boundary value problem differential operator on the graph of a specific structure is discussed in this article. The graph has degree 1 vertices and edges that are linked at one common vertex. The differential operator expression with real valued potentials, the Dirichlet boundary conditions, and the conventional matching requirements define the boundary value issue. There are a finite number of eig nv lu s in this problem.The residues of the diagonal elements of the Weyl matrix in the eigenvalues are referred to as weight numbers. The ig nv lu s are monomorphic functions with simple poles.The weight numbers under consideration generalize the weight numbers of differential operators on a finite interval, which are equal to the reciprocals of the squared norms of eigenfunctions. These numbers, along with the eig nv lu s, serve as spectral data for unique operator reconstruction. The contour integration is used to obtain formulas for surfacethe weight numbers, as well as formulas for the sums in the case of superficial near ig nv lu s. On the graphs, the formulas can be utilized to analyze inverse spectral problems. Ghulam Hazrat Aimal Rasa "Formulas for Surface Weighted Numbers on Graph" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-6 | Issue-3 , April 2022, URL: https://www.ijtsrd.com/papers/ijtsrd49573.pdf Paper URL: https://www.ijtsrd.com/mathemetics/calculus/49573/formulas-for-surface-weighted-numbers-on-graph/ghulam-hazrat-aimal-rasa
MODELING OF REDISTRIBUTION OF INFUSED DOPANT IN A MULTILAYER STRUCTURE DOPANT...mathsjournal
In this paper we used an analytical approach to model nonlinear diffusion of dopant in a multilayer structure with account nonstationary annealing of the dopant. The approach do without crosslinking solutions at
the interface between layers of the multilayer structure. In this paper we analyzed influence of pressure of
vapor of infusing dopant during doping of multilayer structure on values of optimal parameters of technological process to manufacture p-n-junctions. It has been shown, that doping of multilayer structures by
diffusion and optimization of annealing of dopant gives us possibility to increase sharpness of p-n-junctions
(single p-n-junctions and p-n-junctions within transistors) and to increase homogeneity of dopant distribution in doped area.
Effect of the Thickness of High Tc Superconducting Rectangular Microstrip Pat...IJECEIAES
In recent years, a great interest has been observed in the development and use of new materials in microwave technology. Particularly, a special interest has been observed in the use of superconducting materials in microwave integrated circuits, this is due to their main characteristics. In this paper, the complex resonant frequency problem of a superconductor patch over Ground Plane with Rectangular Aperture is formulated in terms of an integral equation, the kernel of which is the dyadic Green‟s function. Galerkin‟s procedure is used in the resolution of the electric field integral equation. The surface impedance of the superconductor film is modeled using the two fluids model of Gorter and Casimir. Numerical results concerning the effect of the thickness of the superconductor patch on the characteristics of the antenna are presented.
Mathematical Model for Dynamic Damage Probability of the Repetition Pulse Rat...IJERA Editor
Aimed at the high-energy laser system, under the assumption that the tracking error is the normal stochastic
process of mean square differentiability and ergodicity, the Series Expression of the dynamic damage probability
was given. The example demonstrate some characteristics of the dynamic damage probability as follow. The
system proposed indicates the quantitative relationship between dynamic damage probability and transfer function
of the tracking error system, which offers theoretical and technological support on proofing, designing and testing
the dynamic damage probability of laser system.
Computation of electromagnetic_fields_scattered_from_dielectric_objects_of_un...Alexander Litvinenko
Tools for electromagnetic scattering from objects with uncertain shapes are needed in various applications.
We develop numerical methods for predicting radar and scattering cross sections (RCS and SCS) of complex targets.
To reduce cost of Monte Carlo (MC) we offer modified multilevel MC (CMLMC) method.
Numerical simulation of marangoni driven boundary layer flow over a flat plat...eSAT Journals
Abstract
A numerical algorithm is presented for studying Marangoni convection flow over a flat plate with an imposed temperature
distribution. Plate temperature varies with x in the following prescribed manner: where A and k are constants.
By means of similarity transformation, the original nonlinear partial differential equations of flow are transformed to a pair of
nonlinear ordinary differential equations. Subsequently they are reduced to a first order system and integrated using Newton
Raphson and adaptive Runge-Kutta methods. The computer codes are developed for this numerical analysis in Matlab
environment. Velocity profiles for various values of k, and temperature profiles for various Prandtl number and k are illustrated
graphically. The results of the present simulation are then compared with the previous works available in literature with good
agreement.
Keywords: Matlab, Marangoni Convection, Numerical Simulation, Surface Tension, Flat Plate.
A.G. A. Abdelkawy, A.M.K. Shaltout, M.M. Beheary and A. Bakry
Department of Astronomy and Meteorology, Faculty of Science, Al-Azhar University, Cairo, Egypt. Postal Code 11884.
Cables are invaluable structural elements. They have been used in guyed towers, bridges marine vehicles, offshore structures, transmission lines and tensioning applications etc. Briefly, cables are necessary elements for long spans. As known, cables are tension elements; they cannot carry any compression load due to its unique geometry. This tangential convoluted geometry makes them hard to analyze. Engineers solve cables assuming them as linear elements even now, because cables cannot be solved by classical finite element methods. Having almost zero bending rigidity makes it vulnerable to drastic vertical movements. Hence, engineers either define a bending rigidity or apply a checker for drastic movements in each nonlinear iteration to solve cable by classical FEM. Therefore, engineers propose a different iterative finite element method to solve cables more stabilized way. In this research, a 3D static solution method is presented for a cable supported at its ends. This method first makes the cable determinant by releasing one cusp of the cable. Then playing with the reaction at the other cusp changes the position of the released cusp. Thus, one can determine the correct reactions at the first cusp, which makes the second cusp position same with the released support’s. Cable equilibrium equations and stiffness matrix is derived accordingly and some sample cables are solved.
ON ESTIMATION OF TIME SCALES OF MASS TRANSPORT IN INHOMOGENOUS MATERIALZac Darcy
In this paper we generalized recently introduced approach of estimation of time scales of mass transport in inhomogenous materials under influence of inhomogenous potential field. Some examples of using of the approach were considered.
Computation of electromagnetic fields scattered from dielectric objects of un...Alexander Litvinenko
Computational tools for characterizing electromagnetic scattering from objects with uncertain shapes are needed in various applications ranging from remote sensing at microwave frequencies to Raman spectroscopy at optical frequencies. Often, such computational tools use the Monte Carlo (MC) method to sample a parametric space describing geometric uncertainties. For each sample, which corresponds to a realization of the geometry, a deterministic electromagnetic solver computes the scattered fields. However, for an accurate statistical characterization the number of MC samples has to be large. In this work, to address this challenge, the continuation multilevel Monte Carlo (\CMLMC) method is used together with a surface integral equation solver.
The \CMLMC method optimally balances statistical errors due to sampling of
the parametric space, and numerical errors due to the discretization of the geometry using a hierarchy of discretizations, from coarse to fine.
The number of realizations of finer discretizations can be kept low, with most samples
computed on coarser discretizations to minimize computational cost.
Consequently, the total execution time is significantly reduced, in comparison to the standard MC scheme.
Similar to 24 infinite 3 d cubic lattices of identical resistors (20)
Observation of Io’s Resurfacing via Plume Deposition Using Ground-based Adapt...Sérgio Sacani
Since volcanic activity was first discovered on Io from Voyager images in 1979, changes
on Io’s surface have been monitored from both spacecraft and ground-based telescopes.
Here, we present the highest spatial resolution images of Io ever obtained from a groundbased telescope. These images, acquired by the SHARK-VIS instrument on the Large
Binocular Telescope, show evidence of a major resurfacing event on Io’s trailing hemisphere. When compared to the most recent spacecraft images, the SHARK-VIS images
show that a plume deposit from a powerful eruption at Pillan Patera has covered part
of the long-lived Pele plume deposit. Although this type of resurfacing event may be common on Io, few have been detected due to the rarity of spacecraft visits and the previously low spatial resolution available from Earth-based telescopes. The SHARK-VIS instrument ushers in a new era of high resolution imaging of Io’s surface using adaptive
optics at visible wavelengths.
Richard's aventures in two entangled wonderlandsRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
Earliest Galaxies in the JADES Origins Field: Luminosity Function and Cosmic ...Sérgio Sacani
We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest
imaging field observed with JWST. We make use of the ancillary Hubble optical images (5 filters
spanning 0.4−0.9µm) and novel JWST images with 14 filters spanning 0.8−5µm, including 7 mediumband filters, and reaching total exposure times of up to 46 hours per filter. We combine all our data
at > 2.3µm to construct an ultradeep image, reaching as deep as ≈ 31.4 AB mag in the stack and
30.3-31.0 AB mag (5σ, r = 0.1” circular aperture) in individual filters. We measure photometric
redshifts and use robust selection criteria to identify a sample of eight galaxy candidates at redshifts
z = 11.5 − 15. These objects show compact half-light radii of R1/2 ∼ 50 − 200pc, stellar masses of
M⋆ ∼ 107−108M⊙, and star-formation rates of SFR ∼ 0.1−1 M⊙ yr−1
. Our search finds no candidates
at 15 < z < 20, placing upper limits at these redshifts. We develop a forward modeling approach to
infer the properties of the evolving luminosity function without binning in redshift or luminosity that
marginalizes over the photometric redshift uncertainty of our candidate galaxies and incorporates the
impact of non-detections. We find a z = 12 luminosity function in good agreement with prior results,
and that the luminosity function normalization and UV luminosity density decline by a factor of ∼ 2.5
from z = 12 to z = 14. We discuss the possible implications of our results in the context of theoretical
models for evolution of the dark matter halo mass function.
Slide 1: Title Slide
Extrachromosomal Inheritance
Slide 2: Introduction to Extrachromosomal Inheritance
Definition: Extrachromosomal inheritance refers to the transmission of genetic material that is not found within the nucleus.
Key Components: Involves genes located in mitochondria, chloroplasts, and plasmids.
Slide 3: Mitochondrial Inheritance
Mitochondria: Organelles responsible for energy production.
Mitochondrial DNA (mtDNA): Circular DNA molecule found in mitochondria.
Inheritance Pattern: Maternally inherited, meaning it is passed from mothers to all their offspring.
Diseases: Examples include Leber’s hereditary optic neuropathy (LHON) and mitochondrial myopathy.
Slide 4: Chloroplast Inheritance
Chloroplasts: Organelles responsible for photosynthesis in plants.
Chloroplast DNA (cpDNA): Circular DNA molecule found in chloroplasts.
Inheritance Pattern: Often maternally inherited in most plants, but can vary in some species.
Examples: Variegation in plants, where leaf color patterns are determined by chloroplast DNA.
Slide 5: Plasmid Inheritance
Plasmids: Small, circular DNA molecules found in bacteria and some eukaryotes.
Features: Can carry antibiotic resistance genes and can be transferred between cells through processes like conjugation.
Significance: Important in biotechnology for gene cloning and genetic engineering.
Slide 6: Mechanisms of Extrachromosomal Inheritance
Non-Mendelian Patterns: Do not follow Mendel’s laws of inheritance.
Cytoplasmic Segregation: During cell division, organelles like mitochondria and chloroplasts are randomly distributed to daughter cells.
Heteroplasmy: Presence of more than one type of organellar genome within a cell, leading to variation in expression.
Slide 7: Examples of Extrachromosomal Inheritance
Four O’clock Plant (Mirabilis jalapa): Shows variegated leaves due to different cpDNA in leaf cells.
Petite Mutants in Yeast: Result from mutations in mitochondrial DNA affecting respiration.
Slide 8: Importance of Extrachromosomal Inheritance
Evolution: Provides insight into the evolution of eukaryotic cells.
Medicine: Understanding mitochondrial inheritance helps in diagnosing and treating mitochondrial diseases.
Agriculture: Chloroplast inheritance can be used in plant breeding and genetic modification.
Slide 9: Recent Research and Advances
Gene Editing: Techniques like CRISPR-Cas9 are being used to edit mitochondrial and chloroplast DNA.
Therapies: Development of mitochondrial replacement therapy (MRT) for preventing mitochondrial diseases.
Slide 10: Conclusion
Summary: Extrachromosomal inheritance involves the transmission of genetic material outside the nucleus and plays a crucial role in genetics, medicine, and biotechnology.
Future Directions: Continued research and technological advancements hold promise for new treatments and applications.
Slide 11: Questions and Discussion
Invite Audience: Open the floor for any questions or further discussion on the topic.
This presentation explores a brief idea about the structural and functional attributes of nucleotides, the structure and function of genetic materials along with the impact of UV rays and pH upon them.
THE IMPORTANCE OF MARTIAN ATMOSPHERE SAMPLE RETURN.Sérgio Sacani
The return of a sample of near-surface atmosphere from Mars would facilitate answers to several first-order science questions surrounding the formation and evolution of the planet. One of the important aspects of terrestrial planet formation in general is the role that primary atmospheres played in influencing the chemistry and structure of the planets and their antecedents. Studies of the martian atmosphere can be used to investigate the role of a primary atmosphere in its history. Atmosphere samples would also inform our understanding of the near-surface chemistry of the planet, and ultimately the prospects for life. High-precision isotopic analyses of constituent gases are needed to address these questions, requiring that the analyses are made on returned samples rather than in situ.
DERIVATION OF MODIFIED BERNOULLI EQUATION WITH VISCOUS EFFECTS AND TERMINAL V...Wasswaderrick3
In this book, we use conservation of energy techniques on a fluid element to derive the Modified Bernoulli equation of flow with viscous or friction effects. We derive the general equation of flow/ velocity and then from this we derive the Pouiselle flow equation, the transition flow equation and the turbulent flow equation. In the situations where there are no viscous effects , the equation reduces to the Bernoulli equation. From experimental results, we are able to include other terms in the Bernoulli equation. We also look at cases where pressure gradients exist. We use the Modified Bernoulli equation to derive equations of flow rate for pipes of different cross sectional areas connected together. We also extend our techniques of energy conservation to a sphere falling in a viscous medium under the effect of gravity. We demonstrate Stokes equation of terminal velocity and turbulent flow equation. We look at a way of calculating the time taken for a body to fall in a viscous medium. We also look at the general equation of terminal velocity.
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...University of Maribor
Slides from:
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Track: Artificial Intelligence
https://www.etran.rs/2024/en/home-english/
Seminar of U.V. Spectroscopy by SAMIR PANDASAMIR PANDA
Spectroscopy is a branch of science dealing the study of interaction of electromagnetic radiation with matter.
Ultraviolet-visible spectroscopy refers to absorption spectroscopy or reflect spectroscopy in the UV-VIS spectral region.
Ultraviolet-visible spectroscopy is an analytical method that can measure the amount of light received by the analyte.
Professional air quality monitoring systems provide immediate, on-site data for analysis, compliance, and decision-making.
Monitor common gases, weather parameters, particulates.
2. Applied Mechanics and Materials Vols. 313-314 325
Various values for 1 2 3 ρ ,ρ ,ρ can be obtained directly from Glasser et. al 19 where he presented
different values for 1 2 3 r , r , r ranging from(0,0,0) − (5,5,5) lattice sites. In this work, we calculated
different values for 1 2 3 r , r , r (i.e., 1 2 3 ρ ,ρ ,ρ ) beyond the site (5,5,5) , where we have used the
following relation 22
G (l +1,m,n) + G (l −1,m,n) + G (l,m +1,n) + G (l,m −1, n) = G (l,m, n +1) + G (l,m,n −1) = o o o o o o
2 2 ( , , ) 0 0 0 EG l m n l m n o = − δ δ δ + . (3)
where E = 3.
Our calculated values are presented in Table 1 below.
The value (0,0,0) o G was first evaluated by Watson in his famous paper 23 , where he found that
) (18 12 2 10 3 7 6)[ ( )] 0.505462.
2
(0,0,0) ( = 2 + − − 2 = o o G K k
π
where = (2 − 3)( 3 − 2) o k
= ∫ is the complete elliptic integral of the first kind.
θ
θ
π
2 2
2
0 1
1
( )
k Sin
K k d
−
A similar result was obtained by Glasser and Zucker 24 in terms of gamma function.
Finally, To study the asymptotic behavior of the resistance in a SC network, since
G (l,m,n) →0 o as any of l,m,n goes to infinity then, one can showed that
( , , ) → = o
(0,0,0) 0.505462
R l m n
o G
R
. (4)
III- Results and Discussion
Using the calculated values for 1 2 3 ρ ,ρ ,ρ , and Eq. (1) then we can easily obtained the equivalent
resistance between the origin and any lattice site ( l,m,n ). Our calculated values are presented in
Table 1 above.
Fig. 1. shows the resistance against the site ( l,m,n ) along the [100] direction for a perfect
infinite SC network. It is seen from the figure that the resistance is symmetric (i.e.
R (l,0,0) R ( l,0,0) o o = − ) for the perfect case due to the inversion symmetry of the lattice. As
( l,m,n ) goes away from the origin the resistance approaches its finite value for both cases 8 .
Fig. 2. shows the resistance against the site ( l,m,n ) along the [111] direction for a perfect SC
network. The resistance is symmetric along [111]direction for the perfect network.
Figure Captions
Fig. 1 The resistance of the perfect SC network between the origin and the lattice site (l,0,0) along
the [100] direction as a function of l
Fig. 4 The resistance of the perfect SC network between the origin and the lattice site (l,m,n) along
the [111] direction as a function of (l,m,n)
3. 326 Machinery Electronics and Control Engineering II
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
0.60
0.55
0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
R(l,m,n)/R
The site (l,m,n)
Fig. 1 The resistance of the perfect SC network between the origin and the lattice site (l,0,0) along
the [100] direction as a function of l
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
0.55
0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
R(l,m,n)/R
The Site (l,m,n)
Fig. 2 The resistance of the perfect SC network between the origin and the lattice site (l,m,n) along
the [111] direction as a function of (l,m,n)
4. Applied Mechanics and Materials Vols. 313-314 327
Table Captions
Table 1: Values of the resistance in a perfect infinite SC lattice for arbitrary sites.
Site
lmn 1 ρ 2 ρ 3 ρ
ρ
R l m n
0 ( , , ) ρ
3
= ρ + +
0
2
2
1 0
π
g
g
R
000 0 0 0 0
100 0 0 1/3 0.333333
110 7/12 1/2 0 0.395079
111 9/8 -3/4 0 0.418305
200 -7/3 -2 2 0.419683
210 5/8 9/4 -1/3 0.433598
211 5/3 -2 0 0.441531
222 3/8 27/20 0 0.460159
300 -33/2 -21 13 0.450371
310 115/36 85/6 -4 0.454415
311 15/4 -21/2 2/3 0.457396
320 -271/48 119/8 1/3 0.461311
321 161/36 -269/30 0 0.463146
332 -26/9 1012/105 0 0.471757
333 51/16 -1587/280 0 0.475023
400 -985/9 -542/3 92 0.464885
410 531/16 879/8 -115/3 0.466418
441 4197/32 -919353/2800 0 0.477814
442 -2927/48 31231/200 0 0.479027
443 571/32 -119271/2800 0 0.480700
444 -69/8 186003/7700 0 0.482570
500 -9275/12 -3005/2 2077/3 0.473263
510 11653/36 138331/150 -348 0.473986
511 -271/4 -5751/10 150 0.474646
5620 -2881/16 15123/200 229/3 0.475807
521 949/12 -27059/350 -24 0.476341
522 -501/8 4209/28 2 0.477766
530 -3571/18 1993883/3675 -8 0.478166
531 1337/8 -297981/700 4/3 0.478565
532 -2519/36 187777/1050 0 0.479693
533 2281/48 -164399/1400 0 0.481253
540 -18439/32 28493109/19600 1/3 0.480653
554 -24251/312 -1527851/7700 0 0.485921
555 9459/208 -12099711/107800 0 0.487123
600 -34937/6 -313079/25 5454 0.478749
610 71939/24 160009/20 -9355/3 0.479137
633 18552/72 -747654/1155 0 0.483209
644 -388051/1872 23950043/46200 0 0.486209
655 13157/78 -5698667/13475 0 0.488325
700 -553847/12 5281913/50 44505 0.482685
References
[1] P. G. Doyle and J. L. Snell, Random walks and Electric Networks, (The Carus Mathematical
Monograph, series 22, The Mathematical Association of America, USA, 1984) pp. 83.
[2] Venezian, G. 1994. Am. J. Phys. 62, 1000.
[3] Atkinson, D. and Van Steenwijk, F. J. 1999. Am. J. Phys. 67, 486.
[4] R. E. Aitchison. 1964. Am. J. Phys. 32, 566.
5. 328 Machinery Electronics and Control Engineering II
[5] F. J. Bartis. 1967. Am. J. Phys. 35, 354.
[6] Monwhea Jeng. 2000. Am. J. Phys. 68(1), 37.
[7] Cserti, J. 2000. Am.J.Phys.68, 896-906.
[8] Cserti, J. Gyula, D. and Attila P. 2002. Am. J. Phys, 70, 153.
[9] Asad J.H, Hijjawi R. S, Sakaji A. J, and Khalifeh J. M. 2004.Int. J. Theo. Phys., (43) 11: 2223.
[10] Asad J. H, Hijjawi R. S, Sakaji A. J, and Khalifeh J. M. 2005. Int. J. Theo. Phys., (44) 4: 471.
[11] Asad J. H, Sakaji A. J, Hijjawi R. S, and Khalifeh J. M. 2006. Eur. Phys. J. B, (52) 2: 365.
[12] Hijjawi R. S, Asad J. H, Sakaji A. J, and Khalifeh J. M. 2008. Eur. Phys. J.- Appl. Phys., (41)
2: 111.
[13] Asad J. H. 2009. ICSPS 2009 International Conference on Signal Processing System. 1007-
1009. Digital Object Identifier : 10.1109/ICSPS.2009.169
[14] Morita, T. and Horiguchi, T. 1975. J. phys. C 8, L232.
[15] Joyce, G. S. 1971. J. Math. Phys. 12, 1390.
[16] Morita, T. and Horigucih, T. 1971. J. of Math. Phys. 12(6), 986.
[17] Hijjawi R. S, Sakaji A. J, Asad J. H, and Khalifeh J. M. 2004. Int. J. Theo. Phys., (43) 11:
2299.
[18] Asad J. H. 2007. Mod. Phys. Letters B., (21) 2-3: 139.
[19] Glasser, M. L. and Boersma, J. 2000. J. Phys. A: Math. Gen. 33, No. 28, 5017.
[20] Economou, E. N. Green’s Function in Quantum Physics. 1983. Spriger-Verlag, Berlin.
[21] Duffin, R. J and Shelly, E. P. 1958. Duke Math. J. 25, 209.
[22] Horiguchi, T. 1971. J. Phys. Soc. Japan 30, 1261.
[23] Watson, G. N. 1939. Quart. J. Math. (Oxford) 10, 266.
[24] Glasser, M. L. and Zuker, I. J. 1977. Proc. Natl. Acad. Sci. USA, 74, 1800.
6. Machinery Electronics and Control Engineering II
10.4028/www.scientific.net/AMM.313-314
Infinite 3D Cubic Lattices of Identical Resistors
10.4028/www.scientific.net/AMM.313-314.324