scholarly journals NUMERICAL SIMULATION OF CHARGED FULLERENE SPECTRUM

2019 ◽  
Vol 24 (2) ◽  
pp. 263-275
Author(s):  
Rafael Arutyunyan ◽  
Yuri Obukhov ◽  
Petr Vabishchevich
Keyword(s):  
Spectral Problem ◽  
Electron Spectrum ◽  
Computational Algorithm ◽  
Piecewise Linear ◽  
Spherically Symmetric ◽  
Charged Sphere ◽  
One Dimensional ◽  
Spectral Problems ◽  
The One ◽  
The Mathematical Model

The mathematical model of the electron spectrum of a charged fullerene is constructed on the basis of the potential of a charged sphere and the spherically symmetric potential of an uncharged fullerene. The electron spectrum is defined as the solution of the spectral problem for the one-dimensional Schr\"odinger equation. For the numerical solution of the spectral problem, piecewise-linear finite elements are used. The computational algorithm was tested on the analytical solution of the problem of the spectrum of the hydrogen atom. For solution of matrix spectral problems, a free library for solving spectral problems of SLEPc is used. The results of calculations of the electron spectrum of a charged fullerene C60 are presented.

scholarly journals Nonequilibrium Time Reversibility with Maps and Walks

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 78
Author(s):  
William Graham Hoover ◽  
Carol Griswold Hoover ◽  
Edward Ronald Smith
Keyword(s):  
Piecewise Linear ◽  
Second Law Of Thermodynamics ◽  
Model Systems ◽  
Computational Time ◽  
Nonequilibrium Systems ◽  
Time Reversibility ◽  
One Dimensional ◽  
Fractal Properties ◽  
Dynamical Simulations ◽  
The One

Time-reversible dynamical simulations of nonequilibrium systems exemplify both Loschmidt’s and Zermélo’s paradoxes. That is, computational time-reversible simulations invariably produce solutions consistent with the irreversible Second Law of Thermodynamics (Loschmidt’s) as well as periodic in the time (Zermélo’s, illustrating Poincaré recurrence). Understanding these paradoxical aspects of time-reversible systems is enhanced here by studying the simplest pair of such model systems. The first is time-reversible, but nevertheless dissipative and periodic, the piecewise-linear compressible Baker Map. The fractal properties of that two-dimensional map are mirrored by an even simpler example, the one-dimensional random walk, confined to the unit interval. As a further puzzle the two models yield ambiguities in determining the fractals’ information dimensions. These puzzles, including the classical paradoxes, are reviewed and explored here.

scholarly journals A MULTIDIMENSIONAL SUBDIFFUSION MODEL WITH CHEMOTAXIS

2019 ◽  
Vol 11 (2) ◽  
pp. 1
Author(s):  
Bambang Hendriya Guswanto
Keyword(s):  
Mathematical Model ◽  
Probability Measure ◽  
Random Walks ◽  
Unit Ball ◽  
Dimensional Case ◽  
One Dimensional ◽  
The One ◽  
The Mathematical Model

The mathematical model for subdiffusion process with chemotaxis proposed by Langlands and Henry [1] for the one-dimensional case is extended to the multi-dimensional case. The model is derived from random walks process using a probability measure on a n-multidimensional unit ball $S^{n-1}$.

scholarly journals Novel Parameter Estimation Method for a Ballistic Warhead with Micromotion

2020 ◽  
Vol 20 (4) ◽  
pp. 262-269
Author(s):  
Inoh Choi ◽  
Jooho Jung ◽  
Kyungtae Kim ◽  
Sanghong Park
Keyword(s):  
Estimation Method ◽  
Doppler Frequency ◽  
Two Dimensional ◽  
Unknown Parameters ◽  
Swarm Optimization ◽  
One Dimensional ◽  
Time Frequency ◽  
Novel Method ◽  
The One ◽  
The Mathematical Model

This paper proposes a novel method to estimate the parameters of a ballistic warhead with micromotion. First, the independent component analysis decomposes the echo signals received from the ballistic warhead into individual signals corresponding to each scatterer. Second, the one-dimensional micro-Doppler frequency trajectories are extracted from two-dimensional joint time-frequency images of decomposed individual signals. Finally, the adaptive particle swarm optimization is used to estimate the parameters that best match the mathematical model composed of unknown parameters to the one-dimensional micro-Doppler frequency trajectories. In simulations using a conical warhead model, the parameters for a ballistic warhead with micromotion are accurately estimated.

A New Method and Device for Temperature Measurement Using One-Dimensional Heat Equation

1994 ◽  
Author(s):  
Nicolae A. Damean
Keyword(s):  
Heat Equation ◽  
Temperature Measurement ◽  
Low Temperatures ◽  
Principal Component ◽  
The Other ◽  
New Method ◽  
Gradient Algorithm ◽  
One Dimensional ◽  
The One ◽  
The Mathematical Model

Abstract A new method and device for temperature measurement are presented. The method reduces the measurement of the unknown temperature to the solving of an optimal control problem, using a numerical computer. The device consists of a hardware part including some conventional transducers and a software one. The problem of temperature measurement, according to this method, is mathematically modelled by means of the one-dimensional heat equation, describing the heat transfer through the device. The principal component of the device is a rod. The variation of the temperature which is produced near one end of the rod is determined using some temperature measurements in the other end of the rod, the mathematical model and a type of gradient algorithm. This device works as an attenuator of high temperatures and as an amplifier of low temperatures.

Theoretical modeling of the carbon dioxide injection into the porous medium saturated with methane and water taking into account the CO2 hydrate formation

2018 ◽  
Author(s):  
Gubaidullin A. A. ◽  
Musakaev N. G. ◽  
Duong Ngoc Hai ◽  
Borodin S. L. ◽  
Nguyen Quang Thai ◽  
...  
Keyword(s):  
Carbon Dioxide ◽  
Hydrate Formation ◽  
Carbon Dioxide Injection ◽  
Reservoir Temperature ◽  
One Dimensional ◽  
Porous Reservoir ◽  
Self Similar ◽  
The One ◽  
Similar Solutions ◽  
The Mathematical Model

In this work the mathematical model is constructed and the features of the injection of warm carbon dioxide (with the temperature higher than the initial reservoir temperature) into the porous reservoir initially saturated with methane gas and water are investigated. Self-similar solutions of the one-dimensional problem describing the distributions of the main parameters in the reservoir are constructed. The effect of the parameters of the injected carbon dioxide and the reservoir on the intensity of the CO2 hydrate formation is analyzed

scholarly journals Direct and inverse spectral problems for Dirac systems with nonlocal potentials

2019 ◽  
Vol 39 (5) ◽  
pp. 645-673
Author(s):  
Kamila Dębowska ◽  
Leonid P. Nizhnik
Keyword(s):  
Characteristic Function ◽  
Dirac System ◽  
Inverse Spectral Problems ◽  
One Dimensional ◽  
Spectral Problems ◽  
Dirac Systems ◽  
Inverse Spectral ◽  
The One ◽  
The Given ◽  
Nonlocal Potentials

The main purposes of this paper are to study the direct and inverse spectral problems of the one-dimensional Dirac operators with nonlocal potentials. Based on informations about the spectrum of the operator, we find the potential and recover the form of the Dirac system. The methods used allow us to reduce the situation to the one-dimensional case. In accordance with the given assumptions and conditions we consider problems in a specific way. We describe the spectrum, the resolvent, the characteristic function etc. Illustrative examples are also given.

scholarly journals Developing methods for mathematical modeling of a two-phase dielectric-electrolyte microsystem

2021 ◽  
Vol 2057 (1) ◽  
pp. 012119
Author(s):  
E V Gorbacheva ◽  
E N Kalaidin
Keyword(s):  
Electric Fields ◽  
Stokes Equations ◽  
Constant Electric Field ◽  
Lower Surface ◽  
Short Wave ◽  
Two Phase ◽  
One Dimensional ◽  
Alternating Electric Fields ◽  
The One ◽  
The Mathematical Model

Abstract In this paper, we propose a numerical solution to the problem of stability of a two-phase dielectric / electrolyte system under direct and alternating electric fields. The lower wall adjacent to the electrolyte is assumed to be a charged surface, while the upper one is electrically insulated. The charge on the lower surface is supposed to be stationary, and the surface charge on the free interface between liquids is assumed to be mobile. The model is described by a system of Nernst-Planck-Poisson-Stokes equations. The mathematical model is closed by the corresponding boundary conditions. The linear stability of the one-dimensional flow is investigated. At a constant electric field, and the presence of two types of instabilities is found: short-wave and long-wave.

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