2,190 research outputs found
Density of states of a graphene in the presence of strong point defects
The density of states near zero energy in a graphene due to strong point
defects with random positions are computed. Instead of focusing on density of
states directly, we analyze eigenfunctions of inverse T-matrix in the unitary
limit. Based on numerical simulations, we find that the squared magnitudes of
eigenfunctions for the inverse T-matrix show random-walk behavior on defect
positions. As a result, squared magnitudes of eigenfunctions have equal {\it a
priori} probabilities, which further implies that the density of states is
characterized by the well-known Thomas-Porter type distribution. The numerical
findings of Thomas-Porter type distribution is further derived in the
saddle-point limit of the corresponding replica field theory of inverse
T-matrix. Furthermore, the influences of the Thomas-Porter distribution on
magnetic and transport properties of a graphene, due to its divergence near
zero energy, are also examined.Comment: 6 figure
Aspects of the stochastic Burgers equation and their connection with turbulence
We present results for the 1 dimensional stochastically forced Burgers
equation when the spatial range of the forcing varies. As the range of forcing
moves from small scales to large scales, the system goes from a chaotic,
structureless state to a structured state dominated by shocks. This transition
takes place through an intermediate region where the system exhibits rich
multifractal behavior. This is mainly the region of interest to us. We only
mention in passing the hydrodynamic limit of forcing confined to large scales,
where much work has taken place since that of Polyakov.
In order to make the general framework clear, we give an introduction to
aspects of isotropic, homogeneous turbulence, a description of Kolmogorov
scaling, and, with the help of a simple model, an introduction to the language
of multifractality which is used to discuss intermittency corrections to
scaling.
We continue with a general discussion of the Burgers equation and forcing,
and some aspects of three dimensional turbulence where - because of the
mathematical analogy between equations derived from the Navier-Stokes and
Burgers equations - one can gain insight from the study of the simpler
stochastic Burgers equation. These aspects concern the connection of
dissipation rate intermittency exponents with those characterizing the
structure functions of the velocity field, and the dynamical behavior,
characterized by different time constants, of velocity structure functions. We
also show how the exponents characterizing the multifractal behavior of
velocity structure functions in the above mentioned transition region can
effectively be calculated in the case of the stochastic Burgers equation.Comment: 25 pages, 4 figure
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