Electromagnetically driven relativistic jets - A class of self-consistent numerical solutions

1993 ◽  
Vol 415 ◽  
pp. 118 ◽  
Author(s):  
Zhi-Yun Li
Keyword(s):  
Numerical Solutions ◽  
Relativistic Jets ◽  
Self Consistent

scholarly journals Numerical Boundary Conditions for Solar Magnetic Hydrodynamic Flows Using the Method of Characteristics

1996 ◽  
Vol 154 ◽  
pp. 149-153
Author(s):  
S. T. Wu ◽  
A. H. Wang ◽  
W. P. Guo
Keyword(s):  
Boundary Conditions ◽  
Method Of Characteristics ◽  
Numerical Solutions ◽  
The Self ◽  
Time Dependent ◽  
Solar Plasma ◽  
The Method Of Characteristics ◽  
Mhd Simulations ◽  
Self Consistent ◽  
Dynamic Structures

AbstractWe discuss the self-consistent time-dependent numerical boundary conditions on the basis of theory of characteristics for magnetohydrodynamics (MHD) simulations of solar plasma flows. The importance of using self-consistent boundary conditions is demonstrated by using an example of modeling coronal dynamic structures. This example demonstrates that the self-consistent boundary conditions assure the correctness of the numerical solutions. Otherwise, erroneous numerical solutions will appear.

scholarly journals A self-consistent hybrid model of kinetic striations in low-current Argon discharges

2022 ◽  
Author(s):  
Vladimir Kolobov ◽  
Juan Alonso Guzmán ◽  
R R Arslanbekov
Keyword(s):  
Kinetic Equation ◽  
Hybrid Model ◽  
Noble Gases ◽  
Numerical Solutions ◽  
Penning Ionization ◽  
Poisson Solver ◽  
Glow Discharges ◽  
Self Consistent ◽  
Ionization Model ◽  
Positive Column Plasma

Abstract A self-consistent hybrid model of standing and moving striations was developed for low-current DC discharges in noble gases. We introduced the concept of surface diffusion in phase space (r,u) (where u denotes the electron kinetic energy) described by a tensor diffusion in the nonlocal Fokker-Planck kinetic equation for electrons in the collisional plasma. Electrons diffuse along surfaces of constant total energy ε=u-eφ(r) between energy jumps in inelastic collisions with atoms. Numerical solutions of the 1d1u kinetic equation for electrons were obtained by two methods and coupled to ion transport and Poisson solver. We studied the dynamics of striation formation in Townsend and glow discharges in Argon gas at low discharge currents using a two-level excitation-ionization model and a “full-chemistry” model, which includes stepwise and Penning ionization. Standing striations appeared in Townsend and glow discharges at low currents, and moving striations were obtained for the discharge currents exceeding a critical value. These waves originate at the anode and propagate towards the cathode. We have seen two types of moving striations with the 2-level and full-chemistry models, which resemble the s and p striations previously observed in the experiments. Simulations indicate that processes in the anode region could control moving striations in the positive column plasma. The developed model helps clarify the nature of standing and moving striations in DC discharges of noble gases at low discharge currents and low gas pressures.

Self-consistent estimates for the viscoelastic creep compliances of composite materials

1978 ◽  
Vol 359 (1697) ◽  
pp. 251-273 ◽  
Keyword(s):  
Composite Materials ◽  
Numerical Solutions ◽  
The Self ◽  
Inclusion Problem ◽  
Inclusion Problems ◽  
Viscoelastic Creep ◽  
Self Consistent ◽  
Title Problem ◽  
Consistent Method ◽  
Selection Of

In this paper the viscoelastic creep compliances of various composites are estimated by the self-consistent method. The phases may be arbitrarily anisotropic and in any concentrations but we demand that one of the phases be a matrix and the remaining phases consist of ellipsoidal inclusions. The theory is succinctly formulated with the help of Stieltjes convolutions. In order to solve the title problem, we first solve the misfitting viscoelastic inclusion problem. Numerical solutions are given for a selection of inclusion problems and for two common composite materials, namely an isotropic dispersion of spheres, and a uni-directional fibre reinforced material.

A SELF-CONSISTENT ANALYTIC THEORY OF THE SPIN BIPOLARON IN THE t–J MODEL

2000 ◽  
Vol 14 (08) ◽  
pp. 809-835
Author(s):  
HEINZ BARENTZEN ◽  
VIKTOR OUDOVENKO
Keyword(s):  
Integral Equation ◽  
Eigenvalue Problem ◽  
Bound States ◽  
Numerical Solutions ◽  
P Wave ◽  
Linear Integral Equation ◽  
Soluble Form ◽  
Coupled Equations ◽  
Self Consistent ◽  
D Wave

The spin bipolaron in the t–J model, i.e., two holes interacting with an antiferromagnetic spin background, is treated by an extension of the self-consistent Born approximation (SCBA), which has proved to be very accurate in the single-hole (spin polaron) problem. One of the main ingredients of our approach is the exact form of the bipolaron eigenstates in terms of a complete set of two-hole basis vectors. This enables us to eliminate the hole operators and to obtain the eigenvalue problem solely in terms of the boson (magnon) operators. The eigenvalue equation is then solved by a procedure similar to Reiter's construction of the single-polaron wave function in the SCBA. As in the latter case, the eigenvalue problem comprises a hierarchy of infinitely many coupled equations. These are brought into a soluble form by means of the SCBA and an additional decoupling approximation, whereupon the eigenvalue problem reduces to a linear integral equation involving the bipolaron self-energy. The numerical solutions of the integral equation are in quantitative agreement with the results of previous numerical studies of the problem. The d-wave bound state is found to have the lowest energy with a critical value J/t| c ≈ 0.4. In contrast to recent claims, we find no indication for a crossover between the d-wave and p-wave bound states.

scholarly journals Simulations of cosmic ray propagation

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Michał Hanasz ◽  
Andrew W. Strong ◽  
Philipp Girichidis
Keyword(s):  
Interstellar Medium ◽  
Momentum Space ◽  
Large Scale ◽  
Numerical Solutions ◽  
Numerical Models ◽  
Planck Equation ◽  
Cosmic Ray ◽  
Mhd Equations ◽  
Radiative Loss ◽  
Self Consistent

AbstractWe review numerical methods for simulations of cosmic ray (CR) propagation on galactic and larger scales. We present the development of algorithms designed for phenomenological and self-consistent models of CR propagation in kinetic description based on numerical solutions of the Fokker–Planck equation. The phenomenological models assume a stationary structure of the galactic interstellar medium and incorporate diffusion of particles in physical and momentum space together with advection, spallation, production of secondaries and various radiation mechanisms. The self-consistent propagation models of CRs include the dynamical coupling of the CR population to the thermal plasma. The CR transport equation is discretized and solved numerically together with the set of MHD equations in various approaches treating the CR population as a separate relativistic fluid within the two-fluid approach or as a spectrally resolved population of particles evolving in physical and momentum space. The relevant processes incorporated in self-consistent models include advection, diffusion and streaming propagation as well as adiabatic compression and several radiative loss mechanisms. We discuss, applications of the numerical models for the interpretation of CR data collected by various instruments. We present example models of astrophysical processes influencing galactic evolution such as galactic winds, the amplification of large-scale magnetic fields and instabilities of the interstellar medium.

BOGOLUBOV’S HIERARCHIES AND VLASOV’S EQUATIONS IN POPULATION ECOLOGY

1991 ◽  
Vol 05 (15) ◽  
pp. 2499-2513
Author(s):  
I.P. PAVLOTSKY ◽  
V.M. SUSLIN
Keyword(s):  
Cauchy Problem ◽  
Numerical Calculation ◽  
Differential Equations ◽  
Population Ecology ◽  
Numerical Solutions ◽  
Biological Species ◽  
Density Functions ◽  
Mathematical Properties ◽  
Self Consistent ◽  
The Cauchy Problem

Following Bogolubov’s ideas a system of pseudo-differential equations for the density functions of interacting biological species is constructed in self-consistent Vlasov’s approximation. Some mathematical properties of these equations including the Cauchy problem are obtained in the particular case of Volterra’s dynamics. For this case we propose a method of numerical calculation of the evolution of the density functions. Some examples of the numerical solutions are given.

NUMERICAL SOLUTION FOR HYDRODYNAMICAL MODELS OF SEMICONDUCTORS

2000 ◽  
Vol 10 (07) ◽  
pp. 1099-1120 ◽  
Author(s):  
VITTORIO ROMANO ◽  
GIOVANNI RUSSO
Keyword(s):  
Numerical Scheme ◽  
Space Dimension ◽  
Numerical Solutions ◽  
Type System ◽  
Splitting Scheme ◽  
Diffusion Type ◽  
Hydrodynamical Models ◽  
Convection Diffusion ◽  
Relaxation Effects ◽  
Self Consistent

Numerical solutions of recent hydrodynamical models of semiconductors are computed in one-space dimension. Such models describe charge transport in semiconductor devices. Two models are taken into consideration. The first one has been developed by Blotekjaer, Baccarani et al., and the second one by Anile et al. In both cases the system of equations can be written as a convection-diffusion type system, with a right-hand side describing relaxation effects and interaction with a self-consistent electric field. The numerical scheme is a splitting scheme based on the Nessyahu–Tadmor scheme for the hyperbolic step, and a semi-implicit scheme for the relaxation step. The numerical results are compared to detailed Monte-Carlo simulation.

scholarly journals Numerical Counterexamples of Lorenz System in Implicit Time Scheme

2018 ◽  
Author(s):  
Xuan Chen
Keyword(s):  
Lorenz System ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Explicit Scheme ◽  
Implicit Time ◽  
Lorenz Equations ◽  
Consistent System ◽  
Runge Kutta Method ◽  
Self Consistent ◽  
The One

In nonlinear self-consistent system, Lorenz system (Lorenz equations) is a classic case with chaos solutions which are sensitively dependent on the initial conditions. As it is difficult to get the analytical solution, the numerical methods and qualitative analytical methods are widely used in many studies. In these papers, Runge-Kutta method is the one most often used to solve these differential equations. However, this method is still a method based on explicit time scheme, which would be the main reason for the chaotic solutions to Lorenz system. In this work, numerical experiments based on implicit time scheme and explicit scheme are setup for comparison, the results show that: in implicit time scheme, the numerical solutions (counterexamples) are without chaos; for an original volume, the volume shrinks exponentially fast to 0 in common.

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