scholarly journals Kinetic Description of Propagation of Quasiparticles Fluxes in Solid-state Structure

Author(s):  
M. B. Kerimi

Within the framework of the kinetic theory, the interaction of systems of quasiparticles and the exchange of quasiparticles of different types between layers of a plane-parallel solid structure are taken into account. The reasons influencing the propagation of differential fluxes of quasiparticles near each boundary of the structure are indicated. These include not only the appearance of a force field, in particular, electric е∇φ(х) and thermal ∇Т(х), fields near the boundary in equilibrium and its modification when equilibrium is disturbed, but also a change in the coordinate and angular dependence of the relaxation length of fluxes le(x, k, Ω) in the same region. Some modification of the distribution of characteristic thermodynamic quantities in the inhomogeneous region of the layer in comparison with the homogeneous layer also affects the propagation of fluxes. The necessity of a self-consistent solution of the kinetic boundary value problem of the joint propagation of differential fluxes of quasiparticles-a system of equations and integral boundary conditions-is substantiated. Near the boundary and in another inhomogeneous region of the layer thickness, as well as in the thin layer as a whole, in quasiparticles systems, it is proposed to use a specific coordinate distribution of the flux density of thermodynamic quantities over the structure thickness, which is mutually self-consistent with the propagation of the corresponding quasiparticles fluxes. The main conclusion of this work: when developing modern multilayer solid-state structures, especially with thin layers, it is necessary to use the kinetic theory, which adequately takes into account the physical picture that occurs not only in homogeneous and inhomogeneous regions of the thickness of each layer, but also at all boundaries of the structure.

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 174
Author(s):  
Chanakarn Kiataramkul ◽  
Weera Yukunthorn ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon

In this paper, we initiate the study of existence of solutions for a fractional differential system which contains mixed Riemann–Liouville and Hadamard–Caputo fractional derivatives, complemented with nonlocal coupled fractional integral boundary conditions. We derive necessary conditions for the existence and uniqueness of solutions of the considered system, by using standard fixed point theorems, such as Banach contraction mapping principle and Leray–Schauder alternative. Numerical examples illustrating the obtained results are also presented.


2021 ◽  
Vol 5 (1) ◽  
pp. 15
Author(s):  
Misir J. Mardanov ◽  
Yagub A. Sharifov ◽  
Yusif S. Gasimov ◽  
Carlo Cattani

This paper considers boundary value problem (BVP) for nonlinear first-order differential problems with multipoint and integral boundary conditions. A suitable Green function was constructed for the first time in order to reduce this problem into a corresponding integral equation. So that by using the Banach contraction mapping principle (BCMP) and Schaefer’s fixed point theorem (SFPT) on the integral equation, we can show that the solution of the multipoint problem exists and it is unique.


Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 130
Author(s):  
Suphawat Asawasamrit ◽  
Yasintorn Thadang ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon

In the present article we study existence and uniqueness results for a new class of boundary value problems consisting by non-instantaneous impulses and Caputo fractional derivative of a function with respect to another function, supplemented with Riemann–Stieltjes fractional integral boundary conditions. The existence of a unique solution is obtained via Banach’s contraction mapping principle, while an existence result is established by using Leray–Schauder nonlinear alternative. Examples illustrating the main results are also constructed.


2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Xiaoyou Liu ◽  
Zhenhai Liu

This paper is concerned with a class of fractional differential inclusions whose multivalued term depends on lower-order fractional derivative with fractional (non)separated boundary conditions. The cases of convex-valued and non-convex-valued right-hand sides are considered. Some existence results are obtained by using standard fixed point theorems. A possible generalization for the inclusion problem with integral boundary conditions is also discussed. Examples are given to illustrate the results.


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