Solitons propagation dynamics in a saturable PT-symmetric fractional medium

2021 ◽  
Author(s):  
Davood Hajitaghi Tehrani ◽  
Mehdi Solaimani ◽  
Mahboubeh Ghalandari ◽  
Bahman Babayar Razlighi
Keyword(s):  
Monte Carlo ◽  
Numerical Methods ◽  
Physical Properties ◽  
Maximum Intensity ◽  
Step Method ◽  
Saturation Parameter ◽  
Potential Depth ◽  
Fractional System ◽  
Nonlinear Fractional Schrödinger Equation ◽  
Good Agreement

Abstract In the current research, the propagation of solitons in a saturable PT-symmetric fractional system is studied by solving nonlinear fractional Schrödinger equation. Three numerical methods are employed for this purpose, namely Monte Carlo based Euler-Lagrange variational schema, split-step method, and extrapolation approach. The results show good agreement and accuracy. The effect of different parameters such as potential depth, Levy indices, and saturation parameter, on the physical properties of the systems such as maximum intensity and soliton width oscillations are considered.

NUMERICAL MODEL TO SIMULATE THE EROSION ON THE SLOPE DUE TO OVERTOPPING

2010 ◽  
Vol 13 (3) ◽  
pp. 78-87
Author(s):  
Hoai Cong Huynh
Keyword(s):  
Numerical Model ◽  
Flow Model ◽  
Bed Load ◽  
Experiment Data ◽  
Step Method ◽  
Morphological Model ◽  
Load Transport ◽  
Bed Load Transport ◽  
The Finite Difference Method ◽  
Good Agreement

The numerical model is developed consisting of a 1D flow model and the morphological model to simulate the erosion due to the water overtopping. The step method is applied to solve the water surface on the slope and the finite difference method of the modified Lax Scheme is applied for bed change equation. The Meyer-Peter and Muller formulae is used to determine the bed load transport rate. The model is calibrated and verified based on the data in experiment. It is found that the computed results and experiment data are good agreement.

Numerical Methods for the Kinetic Theory of Fluids

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Molecular Dynamics ◽  
Monte Carlo ◽  
Numerical Methods ◽  
Kinetic Theory ◽  
Computational Efficiency ◽  
Lattice Boltzmann ◽  
Direct Simulation Monte Carlo ◽  
Particle Methods ◽  
Direct Simulation ◽  
Simulation Monte Carlo

This chapter provides a bird’s eye view of the main numerical particle methods used in the kinetic theory of fluids, the main purpose being of locating Lattice Boltzmann in the broader context of computational kinetic theory. The leading numerical methods for dense and rarified fluids are Molecular Dynamics (MD) and Direct Simulation Monte Carlo (DSMC), respectively. These methods date of the mid 50s and 60s, respectively, and, ever since, they have undergone a series of impressive developments and refinements which have turned them in major tools of investigation, discovery and design. However, they are both very demanding on computational grounds, which motivates a ceaseless demand for new and improved variants aimed at enhancing their computational efficiency without losing physical fidelity and vice versa, enhance their physical fidelity without compromising computational viability.

Vulcanization of Elastomers. 23. The Chemical Kinetics of Vulcanization Reactions and The Physical Properties of The Vulcanizates. I

1960 ◽  
Vol 33 (2) ◽  
pp. 335-341
Author(s):  
Walter Scheele ◽  
Karl-Heinz Hillmer
Keyword(s):  
Activation Energy ◽  
Physical Properties ◽  
Chemical Kinetics ◽  
Kcal Mole ◽  
First Order ◽  
Equilibrium Swelling ◽  
Kinetics Of ◽  
Kinetics Of Vulcanization ◽  
Limiting Value ◽  
Good Agreement

Abstract As a complement to earlier investigations, and in order to examine more closely the connection between the chemical kinetics and the changes with vulcanization time of the physical properties in the case of vulcanization reactions, we used thiuram vulcanizations as an example, and concerned ourselves with the dependence of stress values (moduli) at different degrees of elongation and different vulcanization temperatures. We found: 1. Stress values attain a limiting value, dependent on the degree of elongation, but independent of the vulcanization temperature at constant elongation. 2. The rise in stress values with the vulcanization time is characterized by an initial delay, which, however, is practically nonexistent at higher temperatures. 3. The kinetics of the increase in stress values with vulcanization time are both qualitatively and quantitatively in accord with the dependence of the reciprocal equilibrium swelling on the vulcanization time; both processes, after a retardation, go according to the first order law and at the same rate. 4. From the temperature dependence of the rate constants of reciprocal equilibrium swelling, as well as of the increase in stress, an activation energy of 22 kcal/mole can be calculated, in good agreement with the activation energy of dithiocarbamate formation in thiuram vulcanizations.

Novel use of the Monte-Carlo methods to visualize singularity configurations in serial manipulators

2021 ◽  
Vol 15 (2) ◽  
pp. 7948-7963
Author(s):  
Mohamed Aboelnasr ◽  
Hussein M Bahaa ◽  
Ossama Mokhiamar
Keyword(s):  
Monte Carlo ◽  
Numerical Methods ◽  
Curve Fitting ◽  
Jacobian Matrix ◽  
Forward Kinematics ◽  
Graphical Methods ◽  
Kinematic Singularity ◽  
Serial Manipulators ◽  
Serial Robots ◽  
Contour Plots

This paper analyses the problem of the kinematic singularity of 6 DOF serial robots by extending the use of Monte-Carlo numerical methods to visualize singularity configurations. To achieve this goal, first, forward kinematics and D-H parameters have been derived for the manipulator. Second, the derived equations are used to generate and visualize a workspace that gives a good intuition of the motion shape of the manipulator. Third, the Jacobian matrix is computed using graphical methods, aiming to locate positions that cause singularity. Finally, the data obtained are processed in order to visualize the singularity and to design a trajectory free of singularity. MATLAB robotics toolbox, Symbolic toolbox, and curve fitting toolbox are the MATLAB toolboxes used in the calculations. The results of the surface and contour plots of the determinate of the Jacobian matrix behavior lead to design a manipulator’s trajectory free of singularity and show the parameters that affect the manipulator’s singularity and its behavior in the workspace.

Handling of Collimated Irradiation on a Plane-Parallel Participating Medium

2000 ◽  
Author(s):  
Christian Proulx ◽  
Daniel R. Rousse ◽  
Rodolphe Vaillon ◽  
Jean-François Sacadura
Keyword(s):  
Heat Flux ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Radiative Heat ◽  
Radiative Heat Flux ◽  
Scattering Media ◽  
One Dimensional ◽  
Plane Parallel ◽  
Collimated Beam ◽  
Good Agreement

Abstract This article presents selected results of a study comparing two procedures for the treatment of collimated irradiation impinging on one boundary of a participating one-dimensional plane-parallel medium. These procedures are implemented in a CVFEM used to calculate the radiative heat flux and source. Both isotropically and anisotropically scattering media are considered. The results presented show that both procedures provide results in good agreement with those obtained using a Monte Carlo method, when the collimated beam impinges normally.

A Simple Statistical Theory for Grain Growth in Materials.

1990 ◽  
Vol 209 ◽  
Author(s):  
P. Mulheran ◽  
J.H. Harding
Keyword(s):  
Growth Rate ◽  
Monte Carlo ◽  
Statistical Theory ◽  
Stochastic Model ◽  
Grain Growth ◽  
Three Dimensional ◽  
Monte Carlo Procedure ◽  
Short Time ◽  
2D And 3D ◽  
Good Agreement

A Monte Carlo procedure has been used to study the ordering of both two and three dimensional (2d and 3d) Potts Hamiltonians, further to the work of Anderson et al. For the 3d lattice, the short time growth rate is found to be much slower than previously reported, though the simulated microstructure is in agreement with the earlier studies. We propose a new stochastic model that gives good agreement with the simulations.

The Free Energy Simulation Approach to Grain Boundary Segregation In Cu-Ni

1990 ◽  
Vol 209 ◽  
Author(s):  
H. Y. Wang ◽  
R. Najafabadi ◽  
D. J. Srolovitz ◽  
R. Lesar
Keyword(s):  
Monte Carlo ◽  
Free Energy ◽  
Grain Boundary ◽  
Chemical Potential ◽  
Boundary Segregation ◽  
Configurational Entropy ◽  
Accurate Method ◽  
Increasing Temperature ◽  
Atomic Coordinates ◽  
Good Agreement

ABSTRACTA new, accurate method for determining equilibrium segregation to defects in solids is employed to examine the segregation of Cu to grain boundaries in Cu-Ni alloys. The results are in very good agreement with the ones given by Monte Carlo. This method is based upon a point approximation for the configurational entropy, an Einstein model for vibrational contributions to the free energy. To achieve the equilibrium state of a defect in an alloy the free energy is minimized with respect to atomic coordinates and composition of each site at constant chemical potential. One of the main advantages this new method enjoys over other methods such as Monte Carlo, is the efficiency with which the atomic structure of a defect, segregation and thermodynamic properties can be determined. The grain boundary free energy can either increase or decrease with increasing temperature due to the competition between energetic and configurational entropy terms. In general, the grain boundary free energy increases with temperature when the segregation is strongest.

Numerical Methods in Coupled Monte Carlo and Thermal-Hydraulic Calculations

2017 ◽  
Vol 185 (1) ◽  
pp. 194-205 ◽  
Author(s):  
Daniel F. Gill ◽  
David P. Griesheimer ◽  
David L. Aumiller
Keyword(s):  
Monte Carlo ◽  
Numerical Methods

MONTE CARLO STUDY OF THE SPIN-1/2 HEISENBERG MODEL IN 1, 2, AND 3 DIMENSIONS

1991 ◽  
Vol 05 (13) ◽  
pp. 907-914 ◽  
Author(s):  
RICHARD J. CRESWICK ◽  
CYNTHIA J. SISSON
Keyword(s):  
Monte Carlo ◽  
High Temperature ◽  
Spin Wave ◽  
Heisenberg Model ◽  
Transition Probability ◽  
Lattice Models ◽  
Wave Theory ◽  
Temperature Expansion ◽  
High Temperature Expansion ◽  
Good Agreement

The properties of the spin-1/2 Heisenberg model on 1, 2, and 3-dimensional lattices are calculated using the Decoupled Cell Method of Homma et al., and these results are compared with high temperature and spin-wave expansions, and with other numerical approaches. The DCM has advantages over other Monte Carlo methods currently in wide use in that the transition probability is positive definite, there is no need to introduce an additional imaginary time, or Trotter, dimension, and the acceptance rate for transitions is comparable to that of classical lattice models. We find very good agreement between the DCM and the high temperature expansion in the temperature region where the high temperature expansion is valid, and reasonably good agreement at low temperatures with spin wave theory. The DCM fails for temperatures T < Tc which decreases with the size of the cell.

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