479 research outputs found
Hydrodynamic Model for Conductivity in Graphene
Based on the recently developed picture of an electronic ideal relativistic
fluid at the Dirac point, we present an analytical model for the conductivity
in graphene that is able to describe the linear dependence on the carrier
density and the existence of a minimum conductivity. The model treats
impurities as submerged rigid obstacles, forming a disordered medium through
which graphene electrons flow, in close analogy with classical fluid dynamics.
To describe the minimum conductivity, we take into account the additional
carrier density induced by the impurities in the sample. The model, which
predicts the conductivity as a function of the impurity fraction of the sample,
is supported by extensive simulations for different values of , the
dimensionless strength of the electric field, and provides excellent agreement
with experimental data.Comment: 19 pages, 4 figure
Derivation of the Lattice Boltzmann Model for Relativistic Hydrodynamics
A detailed derivation of the Lattice Boltzmann (LB) scheme for relativistic
fluids recently proposed in Ref. [1], is presented. The method is numerically
validated and applied to the case of two quite different relativistic fluid
dynamic problems, namely shock-wave propagation in quark-gluon plasmas and the
impact of a supernova blast-wave on massive interstellar clouds. Close to
second order convergence with the grid resolution, as well as linear dependence
of computational time on the number of grid points and time-steps, are
reported
Cooling Effect of the Richtmyer-Meshkov Instability
We provide numerical evidence that the Richtmyer-Meshkov (RM) instability
contributes to the cooling of a relativistic fluid. Due to the presence of jet
particles traveling throughout the medium, shock waves are generated in the
form of Mach cones. The interaction of multiple shock waves can trigger the RM
instability, and we have found that this process leads to a down-cooling of the
relativistic fluid. To confirm the cooling effect of the instability, shock
tube Richtmyer-Meshkov instability simulations are performed. Additionally, in
order to provide an experimental observable of the RM instability resulting
from the Mach cone interaction, we measure the two particle correlation
function and highlight the effects of the interaction. The simulations have
been performed with an improved version of the relativistic lattice Boltzmann
model, including general equations of state and external forces.Comment: 10 pages, 6 figure
Quaternionic Madelung Transformation and Non-Abelian Fluid Dynamics
In the 1920's, Madelung noticed that if the complex Schroedinger wavefunction
is expressed in polar form, then its modulus squared and the gradient of its
phase may be interpreted as the hydrodynamic density and velocity,
respectively, of a compressible fluid. In this paper, we generalize Madelung's
transformation to the quaternionic Schroedinger equation. The non-abelian
nature of the full SU(2) gauge group of this equation leads to a richer, more
intricate set of fluid equations than those arising from complex quantum
mechanics. We begin by describing the quaternionic version of Madelung's
transformation, and identifying its ``hydrodynamic'' variables. In order to
find Hamiltonian equations of motion for these, we first develop the canonical
Poisson bracket and Hamiltonian for the quaternionic Schroedinger equation, and
then apply Madelung's transformation to derive non-canonical Poisson brackets
yielding the desired equations of motion. These are a particularly natural set
of equations for a non-abelian fluid, and differ from those obtained by
Bistrovic et al. only by a global gauge transformation. Because we have
obtained these equations by a transformation of the quaternionic Schroedinger
equation, and because many techniques for simulating complex quantum mechanics
generalize straightforwardly to the quaternionic case, our observation leads to
simple algorithms for the computer simulation of non-abelian fluids.Comment: 15 page
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