scholarly journals О подвижности носителей заряда определенной энергии

2018 ◽  
Vol 52 (1) ◽  
pp. 28
Author(s):  
Ю.М. Белоусов ◽  
В.Н. Горелкин ◽  
И.В. Черноусов
Keyword(s):  
Kinetic Equation ◽  
Elastic Scattering ◽  
Physical Meaning ◽  
Source Function ◽  
Collision Integral ◽  
Charge Carriers ◽  
Stationary Case ◽  
Clear Physical Meaning ◽  
Mobility Function ◽  
Isotropic Approximation

AbstractThe quasi-mobility function of charge carriers with a specified energy for describing their dynamics using the kinetic equation is studied in the important case of two-term isotropic approximation. In the stationary case, the quasi-mobility function is independent of the source function of charge carriers and makes it possible to calculate the integral mobility. The correlation between the quasi-mobility and parameters of the system is analyzed. It is proved that this characteristic does not generally describe the contribution of charge carriers with a specified energy to the integral mobility. In the case of almost elastic scattering, the quasi-mobility, as is known, can have a clear physical meaning; however, in the case of the scattering of charge carriers at acoustic phonons in a solid, this quasi-mobility interpretation is found to be incorrect due to the specific features of the collision integral and the form of the quasi-mobility function.

Deep Impurities with Collision Delay

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Wave Function ◽  
Kinetic Equation ◽  
Elastic Scattering ◽  
Response Function ◽  
Plasma Oscillation ◽  
Impurity Scattering ◽  
Fermi Momentum ◽  
Screening Length ◽  
Plasma Mode ◽  
Dissipative Mechanism

The linearised nonlocal kinetic equation is solved analytically for impurity scattering. The resulting response function provides the conductivity, plasma oscillation and Fermi momentum. It is found that virial corrections nearly compensate the wave-function renormalizations rendering the conductivity and plasma mode unchanged. Due to the appearance of the correlated density, the Luttinger theorem does not hold and the screening length is influenced. Explicit results are given for a typical semiconductor. Elastic scattering of electrons by impurities is the simplest but still very interesting dissipative mechanism in semiconductors. Its simplicity follows from the absence of the impurity dynamics, so that individual collisions are described by the motion of an electron in a fixed potential.

scholarly journals Existence of Bounded Solutions to a Modified Version of the Bagley–Torvik Equation

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 289
Author(s):  
Daniel Cao Labora ◽  
José António Tenreiro Machado
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Thin Plate ◽  
Newtonian Fluid ◽  
Physical Meaning ◽  
Source Term ◽  
Vertical Motion ◽  
Bounded Solutions ◽  
Clear Physical Meaning ◽  
Fractional Differential

This manuscript reanalyses the Bagley–Torvik equation (BTE). The Riemann–Liouville fractional differential equation (FDE), formulated by R. L. Bagley and P. J. Torvik in 1984, models the vertical motion of a thin plate immersed in a Newtonian fluid, which is held by a spring. From this model, we can derive an FDE for the particular case of lacking the spring. Here, we find conditions for the source term ensuring that the solutions to the equation of the motion are bounded, which has a clear physical meaning.

Vibration Analysis of Non-Classically Damped Linear Systems

2004 ◽  
Vol 126 (3) ◽  
pp. 456-458 ◽  
Author(s):  
Z. S. Liu, ◽  
D. T. Song, and ◽  
C. Huang ◽  
D. J. Wang ◽  
S. H. Chen
Keyword(s):  
Linear Systems ◽  
Physical Meaning ◽  
Vibration Analysis ◽  
Original System ◽  
New Method ◽  
Order System ◽  
Damping Term ◽  
Clear Physical Meaning ◽  
Damped System

This Technical Brief presents a new method for vibration analysis of a non-classically damped system. The basic idea is to introduce a transformation, which bears clear physical meaning, so that the original non-classical damped system is transformed into a new 2nd-order system that does not have the damping term. The transformed system not only provides an alternative of calculating response, but also reveals more clearly vibration behaviors of the original system.

Limitations of Boltzmann's kinetic equation

2008 ◽  
Vol 464 (2095) ◽  
pp. 1923-1940 ◽  
Author(s):  
L.C Woods
Keyword(s):  
Kinetic Equation ◽  
Transport Theory ◽  
Strong Field ◽  
Fluid Velocity ◽  
Velocity Distribution Function ◽  
Collision Integral ◽  
Ambient Conditions ◽  
Taylor Series Expansions ◽  
Almost All ◽  
And Diffusion

It is often assumed that Boltzmann's kinetic equation (BKE) for the evolution of the velocity distribution function f ( r ,  w ,  t ) in a gas is valid regardless of the magnitude of the Knudsen number defined by ϵ ≡ τ d ln  ϕ /d t , where ϕ is a macroscopic variable like the fluid velocity v or temperature T , and τ is the collision interval. Almost all accounts of transport theory based on BKE are limited to terms in O ( ϵ )≪1, although there are treatments in which terms in O ( ϵ 2 ) are obtained, classic examples being due to Burnett and Grad. The mathematical limitations that arise are discussed, for example, by Kreuzer and Cercignani. However, as we shall show, the physical limitation to BKE is that it is not valid for the terms of order higher than ϵ because the assumption of ‘molecular chaos’, which is the basis of Boltzmann's collision integral, is an approximation that applies only up to first order in ϵ . Another difficulty with Boltzmann's collision integral is that it is defined at a point, so that the varying ambient conditions upon which transport depends must be found by Taylor series expansions along particle trajectories. This fails in a strong-field magnetoplasma where, in a single collision interval, the trajectories are almost infinitely repeating gyrations; we shall illustrate this by deriving a dominant O ( ϵ 2 ) transport equation for a magnetoplasma that cannot be found from Boltzmann's equation. A further problem that sometimes arises in BKE occurs when an external force is present, the equilibrium state being constrained by the stringent Maxwell–Boltzmann conditions. Unless this is removed by a transformation of coordinates, confusion between convection and diffusion is probable. A mathematical theory for transport in tokamaks, termed neoclassical transport , is shown to be invalid, one of several errors being the retention of an electric field component in the drift kinetic equation.

A modified truncation procedure for the BBGKY hierarchy

1969 ◽  
Vol 3 (1) ◽  
pp. 107-118 ◽  
Author(s):  
C. J. Myerscough
Keyword(s):  
Kinetic Equation ◽  
Physical Interpretation ◽  
Coulomb Potential ◽  
Kinetic Equations ◽  
Bbgky Hierarchy ◽  
Collision Integral ◽  
The Other ◽  
Standard Methods ◽  
Particle Separations ◽  
Number Of Authors

The approximations usually made to truncate the BBGKY hierarchy for a plasma are discussed; their failure at small inter-particle separations leads to divergence of the Balescu—Lenard collision integral. A number of authors have obtained convergent kinetic equations, often by rather complicated methods.It is shown here that, if the standard truncation procedure is modified in a way which makes it less obviously inconsistent for close approaches, the standard methods maybe closely followed in deriving a convergent collision integral which agrees to dominant order with the ‘cutoff’ Balescu—Lenard integral and with the other work on the problem. In fact, the kinetic equation obtained is identical with the Balescu—Lenard equation except that the Coulomb potential is replaced by another that is non-singular at the origin. A physical interpretation of this result is suggested.

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