429 research outputs found
Quasiclassical theory of charge transport in disordered interacting electron systems
We consider the corrections to the Boltzmann theory of electrical transport
arising from the Coulomb interaction in disordered conductors. In this article
the theory is formulated in terms of quasiclassical Green's functions. We
demonstrate that the formalism is equivalent to the conventional diagrammatic
technique by deriving the well-known Altshuler-Aronov corrections to the
conductivity. Compared to the conventional approach, the quasiclassical theory
has the advantage of being closer to the Boltzmann theory, and also allows
description of interaction effects in the transport across interfaces, as well
as non-equilibrium phenomena in the same theoretical framework. As an example,
by applying the Zaitsev boundary conditions which were originally developed for
superconductors, we obtain the -theory of the Coulomb blockade in tunnel
junctions. Furthermore we summarize recent results obtained for the
non-equilibrium transport in thin films, wires and fully coherent conductors.Comment: 46 pages; review articl
Critical dynamics of self-gravitating Langevin particles and bacterial populations
We study the critical dynamics of the generalized Smoluchowski-Poisson system
(for self-gravitating Langevin particles) or generalized Keller-Segel model
(for the chemotaxis of bacterial populations). These models [Chavanis & Sire,
PRE, 69, 016116 (2004)] are based on generalized stochastic processes leading
to the Tsallis statistics. The equilibrium states correspond to polytropic
configurations with index similar to polytropic stars in astrophysics. At
the critical index (where is the dimension of space),
there exists a critical temperature (for a given mass) or a
critical mass (for a given temperature). For or
the system tends to an incomplete polytrope confined by the box (in a
bounded domain) or evaporates (in an unbounded domain). For
or the system collapses and forms, in a finite time, a Dirac peak
containing a finite fraction of the total mass surrounded by a halo. This
study extends the critical dynamics of the ordinary Smoluchowski-Poisson system
and Keller-Segel model in corresponding to isothermal configurations with
. We also stress the analogy between the limiting mass of
white dwarf stars (Chandrasekhar's limit) and the critical mass of bacterial
populations in the generalized Keller-Segel model of chemotaxis
A Comparative Study of an Asymptotic Preserving Scheme and Unified Gas-kinetic Scheme in Continuum Flow Limit
Asymptotic preserving (AP) schemes are targeting to simulate both continuum
and rarefied flows. Many AP schemes have been developed and are capable of
capturing the Euler limit in the continuum regime. However, to get accurate
Navier-Stokes solutions is still challenging for many AP schemes. In order to
distinguish the numerical effects of different AP schemes on the simulation
results in the continuum flow limit, an implicit-explicit (IMEX) AP scheme and
the unified gas kinetic scheme (UGKS) based on Bhatnagar-Gross-Krook (BGk)
kinetic equation will be applied in the flow simulation in both transition and
continuum flow regimes. As a benchmark test case, the lid-driven cavity flow is
used for the comparison of these two AP schemes. The numerical results show
that the UGKS captures the viscous solution accurately. The velocity profiles
are very close to the classical benchmark solutions. However, the IMEX AP
scheme seems have difficulty to get these solutions. Based on the analysis and
the numerical experiments, it is realized that the dissipation of AP schemes in
continuum limit is closely related to the numerical treatment of collision and
transport of the kinetic equation. Numerically it becomes necessary to couple
the convection and collision terms in both flux evaluation at a cell interface
and the collision source term treatment inside each control volume
Ein Gas-Kinetic Scheme Ansatz zur Modellierung und Simulation von Feuer auf massiv paralleler Hardware
This work presents a simulation approach based on a Gas Kinetic Scheme (GKS) for the simulation of fire that is implemented on massively parallel hardware in terms of Graphics Processing Units (GPU) in the framework of General Purpose computing on Graphics Processing Units (GPGPU).
Gas kinetic schemes belong to the class of kinetic methods because their governing equation is the mesoscopic Boltzmann equation, rather than the macroscopic Navier-Stokes equations.
Formally, kinetic methods have the advantage of a linear advection term which simplifies discretization.
GKS inherently contains the full energy equation which is required for compressible flows.
GKS provides a flux formulation derived from kinetic theory and is usually implemented as a finite volume method on cell-centered grids.
In this work, we consider an implementation on nested Cartesian grids.
To that end, a coupling algorithm for uniform grids with varying resolution was developed and is presented in this work.
The limitation to local uniform Cartesian grids allows an efficient implementation on GPUs, which belong to the class of many core processors, i.e. massively parallel hardware.
Multi-GPU support is also implemented and efficiency is enhanced by communication hiding.
The fluid solver is validated for several two- and three-dimensional test cases including natural convection, turbulent natural convection and turbulent decay.
It is subsequently applied to a study of boundary layer stability of natural convection in a cavity with differentially heated walls and large temperature differences.
The fluid solver is further augmented by a simple combustion model for non-premixed flames.
It is validated by comparison to experimental data for two different fire plumes.
The results are further compared to the industry standard for fire simulation, i.e. the Fire Dynamics Simulator (FDS).
While the accuracy of GKS appears slightly reduced as compared to FDS, a substantial speedup in terms of time to solution is found.
Finally, GKS is applied to the simulation of a compartment fire.
This work shows that the GKS has a large potential for efficient high performance fire simulations.Diese Arbeit prĂ€sentiert einen Simulationsansatz basierend auf einer gaskinetischen Methode (eng. Gas Kinetic Scheme, GKS) zur Simulation von BrĂ€nden, welcher fĂŒr massiv parallel Hardware im Sinne von Grafikprozessoren (eng. Graphics Processing Units, GPUs) implementiert wurde.
GKS gehört zur Klasse der kinetischen Methoden, die nicht die makroskopischen Navier-Stokes Gleichungen, sondern die mesoskopische Boltzmann Gleichung lösen.
Formal haben kinetische Methoden den Vorteil, dass der Advektionsterms linear ist.
Dies vereinfacht die Diskretisierung.
In GKS ist die vollstÀndige Energiegleichung, die zur Lösung kompressibler Strömungen benötigt wird, enthalten.
GKS formuliert den Fluss von ErhaltungsgröĂen basierend auf der gaskinetischen Theorie und wird meistens im Rahmen der Finiten Volumen Methode umgesetzt.
In dieser Arbeit betrachten wir eine Implementierung auf gleichmĂ€Ăigen Kartesischen Gittern.
Dazu wurde ein Kopplungsalgorithmus fĂŒr die Kombination von Gittern unterschiedlicher Auflösung entwickelt.
Die EinschrĂ€nkung auf lokal gleichmĂ€Ăige Gitter erlaubt eine effiziente Implementierung auf GPUs, welche zur Klasse der massiv parallelen Hardware gehören.
Des Weiteren umfasst die Implementierung eine UnterstĂŒtzung fĂŒr Multi-GPU mit versteckter Kommunikation.
Der Strömungslöser ist fĂŒr zwei und dreidimensionale TestfĂ€lle validiert.
Dabei reichen die Tests von natĂŒrlicher Konvektion ĂŒber turbulente Konvektion bis hin zu turbulentem Zerfall.
AnschlieĂend wird der Löser genutzt um die GrenzschichtstabilitĂ€t in natĂŒrlicher Konvektion bei groĂen Temperaturunterschieden zu untersuchen.
DarĂŒber hinaus umfasst der Löser ein einfaches Verbrennungsmodell fĂŒr Diffusionsflammen.
Dieses wird durch Vergleich mit experimentellen Feuern validiert.
AuĂerdem werden die Ergebnisse mit dem gĂ€ngigen Brandsimulationsprogramm FDS (eng. Fire Dynamics Simulator) verglichen.
Die QualitÀt der Ergebnisse ist dabei vergleichbar, allerdings ist der in dieser Arbeit entwickelte Löser deutlich schneller.
AnschlieĂend wird das GKS noch fĂŒr die Simulation eines Raumbrandes angewendet.
Diese Arbeit zeigt, dass GKS ein groĂes Potential fĂŒr die Hochleistungssimulation von Feuer hat
- âŠ