scholarly journals A BGK model for charge transport in graphene

2019 ◽  
Vol 10 (1) ◽  
pp. 153-161
Author(s):  
Armando Majorana
Keyword(s):  
Boltzmann Equation ◽  
Charge Transport ◽  
Electronic Devices ◽  
Kinetic Equations ◽  
Collision Operator ◽  
Perfect Gas ◽  
Bgk Model ◽  
Temporal Behaviour ◽  
Integral Term ◽  
Classical Boltzmann Equation

Abstract The classical Boltzmann equation describes well temporal behaviour of a rarefied perfect gas. Modified kinetic equations have been proposed for studying the dynamics of different type of gases. An important example is the transport equation, which describes the charged particles flow, in the semi-classical regime, in electronic devices. In order to reduce the difficulties in solving the Boltzmann equation, simple expressions of a collision operator have been proposed to replace the standard Boltzmann integral term. These new equations are called kinetic models. The most popular and widely used kinetic model is the Bhatnagar-Gross-Krook (BGK) model. In this work we propose and analyse a BGK model for charge transport in graphene.

scholarly journals Hydrodynamic limits of kinetic equations for polyatomic and reactive gases

2017 ◽  
Vol 8 (1) ◽  
pp. 23-42 ◽  
Author(s):  
M. Bisi ◽  
G. Spiga
Keyword(s):  
Degrees Of Freedom ◽  
Continuum Limit ◽  
Fluid Dynamic ◽  
Energy Levels ◽  
Kinetic Equations ◽  
Navier Stokes ◽  
Bgk Model ◽  
Hydrodynamic Limits ◽  
Stress Diffusion ◽  
Reactive Gases

Abstract Starting from a kinetic BGK-model for a rarefied polyatomic gas, based on a molecular structure of discrete internal energy levels, an asymptotic Chapman-Enskog procedure is developed in the asymptotic continuum limit in order to derive consistent fluid-dynamic equations for macroscopic fields at Navier-Stokes level. In this way, the model allows to treat the gas as a mixture of mono-atomic species. Explicit expressions are given not only for dynamical pressure, but also for shear stress, diffusion velocities, and heat flux. The analysis is shown to deal properly also with a mixture of reactive gases, endowed for simplicity with translational degrees of freedom only, in which frame analogous results can be achieved.

THE CONTRIBUTION OF THE BHATNAGAR–GROSS–KROOK MODEL TO THE DEVELOPMENT OF RAREFIED GAS DYNAMICS IN THE EARLY YEARS OF THE SPACE AGE

2013 ◽  
Vol 25 (01) ◽  
pp. 1340025
Author(s):  
RODDAM NARASIMHA
Keyword(s):  
Boltzmann Equation ◽  
Gas Dynamics ◽  
Rarefied Gas ◽  
Rarefied Gas Dynamics ◽  
Early Years ◽  
Plane Shock ◽  
Bgk Model ◽  
The Boltzmann Equation ◽  
Nonequilibrium Flows ◽  
Space Age

The advent of the space age in 1957 was accompanied by a sudden surge of interest in rarefied gas dynamics (RGD). The well-known difficulties associated with solving the Boltzmann equation that governs RGD made progress slow but the Bhatnagar–Gross–Krook (BGK) model, proposed three years before Sputnik, turned out to have been an uncannily timely, attractive and fruitful option, both for gaining insights into the Boltzmann equation and for estimating various technologically useful flow parameters. This paper gives a view of how BGK contributed to the growth of RGD during the first decade of the space age. Early efforts intended to probe the limits of the BGK model showed that, in and near both the continuum Euler limit and the collisionless Knudsen limit, BGK could provide useful answers. Attempts were therefore made to tackle more ambitious nonlinear nonequilibrium problems. The most challenging of these was the structure of a plane shock wave. The first exact numerical solutions of the BGK equation for the shock appeared during 1962 to 1964, and yielded deep insights into the character of transitional nonequilibrium flows that had resisted all attempts at solution through the Boltzmann equation. In particular, a BGK weak shock was found to be amenable to an asymptotic analysis. The results highlighted the importance of accounting separately for fast-molecule dynamics, most strikingly manifested as tails in the distribution function, both in velocity and in physical space — tails are strange versions or combinations of collisionless and collision-generated flows. However, by the mid-1960s Monte-Carlo methods of solving the full Boltzmann equation were getting to be mature and reliable and interest in the BGK waned in the following years. Interestingly, it has seen a minor revival in recent years as a tool for developing more effective algorithms in continuum computational fluid dynamics, but the insights derived from the BGK for strongly nonequilibrium flows should be of lasting value.

scholarly journals Electrical conductivity and magnetic bistability in metal–organic frameworks and coordination polymers: charge transport and spin crossover at the nanoscale

2020 ◽  
Vol 49 (15) ◽  
pp. 5601-5638 ◽  
Author(s):  
Víctor Rubio-Giménez ◽  
Sergio Tatay ◽  
Carlos Martí-Gastaldo
Keyword(s):  
Electrical Conductivity ◽  
Charge Transport ◽  
Coordination Polymers ◽  
Spin Crossover ◽  
Electronic Devices ◽  
Metal Organic Frameworks ◽  
Active Components ◽  
Metal Organic

This review aims to reassess the progress, issues and opportunities in the path towards integrating conductive and magnetically bistable coordination polymers and metal–organic frameworks as active components in electronic devices.

scholarly journals Incompressible hydrodynamic approximation with viscous heating to the Boltzmann equation

2017 ◽  
Vol 27 (12) ◽  
pp. 2261-2296 ◽  
Author(s):  
Yan Guo ◽  
Shuangqian Liu
Keyword(s):  
Boltzmann Equation ◽  
Initial Data ◽  
Kinetic Equations ◽  
Navier Stokes ◽  
Viscous Heating ◽  
Text Setting ◽  
Hydrodynamic Approximation ◽  
Energy Conversation ◽  
The Boltzmann Equation

The incompressible Navier–Stokes–Fourier (INSF) system with viscous heating was first derived from the Boltzmann equation in the form of the diffusive scaling by Bardos–Levermore–Ukai–Yang [Kinetic equations: Fluid dynamical limits and viscous heating, Bull. Inst. Math. Acad. Sin.[Formula: see text] 3 (2008) 1–49]. The purpose of this paper is to justify such an incompressible hydrodynamic approximation to the Boltzmann equation in [Formula: see text] setting in a periodic box. Based on an odd–even expansion of the solution with respect to the microscopic velocity, the diffusive coefficients are determined by the INSF system with viscous heating and the super-Burnett functions. More importantly, the remainder of the expansion is proven to decay exponentially in time via an [Formula: see text] approach on the condition that the initial data satisfies the mass, momentum and energy conversation laws.

scholarly journals Boltzmann Equation Theory of Charged Particle Transport in Neutral Gases: Perturbation Treatment

1999 ◽  
Vol 52 (6) ◽  
pp. 999 ◽  
Author(s):  
Slobodan B. Vrhovac ◽  
Zoran Lj. Petrovic
Keyword(s):  
Distribution Function ◽  
Perturbation Theory ◽  
Charged Particle ◽  
Boltzmann Equation ◽  
Particle Transport ◽  
Kinetic Equations ◽  
Initial Distribution ◽  
Formal Structure ◽  
Time Dependent ◽  
Charged Particle Transport

This paper examines the formal structure of the Boltzmann equation (BE) theory of charged particle transport in neutral gases. The initial value problem of the BE is studied by using perturbation theory generalised to non-Hermitian operators. The method developed by R�sibois was generalised in order to be applied for the derivation of the transport coecients of swarms of charged particles in gases. We reveal which intrinsic properties of the operators occurring in the kinetic equation are sucient for the generalised diffusion equation (GDE) and the density gradient expansion to be valid. Explicit expressions for transport coecients from the (asymmetric) eigenvalue problem are also deduced. We demonstrate the equivalence between these microscopic expressions and the hierarchy of kinetic equations. The establishment of the hydrodynamic regime is further analysed by using the time-dependent perturbation theory. We prove that for times t ? τ0 (τ0 is the relaxation time), the one-particle distribution function of swarm particles can be transformed into hydrodynamic form. Introducing time-dependent transport coecients ? *(p) (?q,t), which can be related to various Fourier components of the initial distribution function, we also show that for the long-time limit all ? *(p) (?q,t) become time and ?q independent in the same characteristic time and achieve their hydrodynamic values.

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