841 research outputs found
A fractional kinetic process describing the intermediate time behaviour of cellular flows
This paper studies the intermediate time behaviour of a small random perturbation of a periodic cellular flow. Our main result shows that on time scales shorter than the diffusive time scale, the limiting behaviour of trajectories that start close enough to cell boundaries is a fractional kinetic process: A Brownian motion time changed by the local time of an independent Brownian motion. Our proof uses the Freidlin-Wentzell framework, and the key step is to establish an analogous averaging principle on shorter time scales. As a consequence of our main theorem, we obtain a homogenization result for the associated advection-diffusion equation. We show that on intermediate time scales the effective equation is a fractional time PDE that arises in modelling anomalous diffusion
Inverse scattering at fixed energy on surfaces with Euclidean ends
On a fixed Riemann surface with Euclidean ends and genus ,
we show that, under a topological condition, the scattering matrix S_V(\la)
at frequency \la > 0 for the operator determines the potential
if for all
and for some , where denotes the distance
from to a fixed point . The topological condition is given by
for and by if . In \rr^2 this
implies that the operator S_V(\la) determines any potential
such that for all .Comment: 21 page
Universal statistics of non-linear energy transfer in turbulent models
A class of shell models for turbulent energy transfer at varying the
inter-shell separation, , is investigated. Intermittent corrections in
the continuous limit of infinitely close shells () have
been measured. Although the model becomes, in this limit, non-intermittent, we
found universal aspects of the velocity statistics which can be interpreted in
the framework of log-poisson distributions, as proposed by She and Waymire
(1995, Phys. Rev. Lett. 74, 262). We suggest that non-universal aspects of
intermittency can be adsorbed in the parameters describing statistics and
properties of the most singular structure. On the other hand, universal aspects
can be found by looking at corrections to the monofractal scaling of the most
singular structure. Connections with similar results reported in other shell
models investigations and in real turbulent flows are discussed.Comment: 4 pages, 2 figures available upon request to [email protected]
Spatial distribution of local currents of massless Dirac fermions in quantum transport through graphene nanoribbons
We employ the formalism of bond currents, expressed in terms of the
nonequilibrium Green functions, to image the charge flow between two sites of
the honeycomb lattice of graphene ribbons of few nanometers width. In sharp
contrast to nonrelativistic electrons, current density profiles of quantum
transport at energies close to the Dirac point in clean zigzag graphene
nanoribbons (ZGNR) differs markedly from the profiles of charge density peaked
at the edges due to zero-energy localized edge states. For transport through
the lowest propagating mode induced by these edge states, edge vacancies do not
affect current density peaked in the center of ZGNR. The long-range potential
of a single impurity acts to reduce local current around it while concurrently
increasing the current density along the zigzag edge, so that ZGNR conductance
remains perfect .Comment: 5 pages, 5 figure
Supersymmetric Regularization, Two-Loop QCD Amplitudes and Coupling Shifts
We present a definition of the four-dimensional helicity (FDH) regularization
scheme valid for two or more loops. This scheme was previously defined and
utilized at one loop. It amounts to a variation on the standard 't
Hooft-Veltman scheme and is designed to be compatible with the use of helicity
states for "observed" particles. It is similar to dimensional reduction in that
it maintains an equal number of bosonic and fermionic states, as required for
preserving supersymmetry. Supersymmetry Ward identities relate different
helicity amplitudes in supersymmetric theories. As a check that the FDH scheme
preserves supersymmetry, at least through two loops, we explicitly verify a
number of these identities for gluon-gluon scattering (gg to gg) in
supersymmetric QCD. These results also cross-check recent non-trivial two-loop
calculations in ordinary QCD. Finally, we compute the two-loop shift between
the FDH coupling and the standard MS-bar coupling, alpha_s. The FDH shift is
identical to the one for dimensional reduction. The two-loop coupling shifts
are then used to obtain the three-loop QCD beta function in the FDH and
dimensional reduction schemes.Comment: 44 pages, minor corrections and clarifications include
Motion of Three Vortices near Collapse
A system of three point vortices in an unbounded plane has a special family
of self-similarly contracting or expanding solutions: during the motion, vortex
triangle remains similar to the original one, while its area decreases (grows)
at a constant rate. A contracting configuration brings three vortices to a
single point in a finite time; this phenomenon known as vortex collapse is of
principal importance for many-vortex systems. Dynamics of close-to-collapse
vortex configurations depends on the way the collapse conditions are violated.
Using an effective potential representation, a detailed quantitative analysis
of all the different types of near-collapse dynamics is performed when two of
the vortices are identical. We discuss time and length scales, emerging in the
problem, and their behavior as the initial vortex triangle is approaching to an
exact collapse configuration. Different types of critical behaviors, such as
logarithmic or power-law divergences are exhibited, which emphasizes the
importance of the way the collapse is approached. Period asymptotics for all
singular cases are presented as functions of the initial vortices
configurations. Special features of passive particle mixing by a near-collapse
flows are illustrated numerically.Comment: 45 pages, 22 figures Last version of the paper with all update
Numerical Simulation of Vortex Crystals and Merging in N-Point Vortex Systems with Circular Boundary
In two-dimensional (2D) inviscid incompressible flow, low background
vorticity distribution accelerates intense vortices (clumps) to merge each
other and to array in the symmetric pattern which is called ``vortex
crystals''; they are observed in the experiments on pure electron plasma and
the simulations of Euler fluid. Vortex merger is thought to be a result of
negative ``temperature'' introduced by L. Onsager. Slight difference in the
initial distribution from this leads to ``vortex crystals''. We study these
phenomena by examining N-point vortex systems governed by the Hamilton
equations of motion. First, we study a three-point vortex system without
background distribution. It is known that a N-point vortex system with boundary
exhibits chaotic behavior for N\geq 3. In order to investigate the properties
of the phase space structure of this three-point vortex system with circular
boundary, we examine the Poincar\'e plot of this system. Then we show that
topology of the Poincar\'e plot of this system drastically changes when the
parameters, which are concerned with the sign of ``temperature'', are varied.
Next, we introduce a formula for energy spectrum of a N-point vortex system
with circular boundary. Further, carrying out numerical computation, we
reproduce a vortex crystal and a vortex merger in a few hundred point vortices
system. We confirm that the energy of vortices is transferred from the clumps
to the background in the course of vortex crystallization. In the vortex
merging process, we numerically calculate the energy spectrum introduced above
and confirm that it behaves as k^{-\alpha},(\alpha\approx 2.2-2.8) at the
region 10^0<k<10^1 after the merging.Comment: 30 pages, 11 figures. to be published in Journal of Physical Society
of Japan Vol.74 No.
On dissipationless shock waves in a discrete nonlinear Schr\"odinger equation
It is shown that the generalized discrete nonlinear Schr\"odinger equation
can be reduced in a small amplitude approximation to the KdV, mKdV, KdV(2) or
the fifth-order KdV equations, depending on values of the parameters. In
dispersionless limit these equations lead to wave breaking phenomenon for
general enough initial conditions, and, after taking into account small
dispersion effects, result in formation of dissipationless shock waves. The
Whitham theory of modulations of nonlinear waves is used for analytical
description of such waves.Comment: 15 pages, 9 figure
The Minimal Supersymmetric Fat Higgs Model
We present a calculable supersymmetric theory of a composite ``fat'' Higgs
boson. Electroweak symmetry is broken dynamically through a new gauge
interaction that becomes strong at an intermediate scale. The Higgs mass can
easily be 200-450 GeV along with the superpartner masses, solving the
supersymmetric little hierarchy problem. We explicitly verify that the model is
consistent with precision electroweak data without fine-tuning. Gauge coupling
unification can be maintained despite the inherently strong dynamics involved
in electroweak symmetry breaking. Supersymmetrizing the Standard Model
therefore does not imply a light Higgs mass, contrary to the lore in the
literature. The Higgs sector of the minimal Fat Higgs model has a mass spectrum
that is distinctly different from the Minimal Supersymmetric Standard Model.Comment: 13 pages, 5 figures, REVTe
On the relation between effective supersymmetric actions in different dimensions
We make two remarks: (i) Renormalization of the effective charge in a
4--dimensional (supersymmetric) gauge theory is determined by the same graphs
and is rigidly connected to the renormalization of the metric on the moduli
space of the classical vacua of the corresponding reduced quantum mechanical
system. Supersymmetry provides constraints for possible modifications of the
metric, and this gives us a simple proof of nonrenormalization theorems for the
original 4-dimensional theory. (ii) We establish a nontrivial relationship
between the effective (0+1)-dimensional and (1+1)-dimensional Lagrangia (the
latter represent conventional
Kahlerian sigma models).Comment: 15 pages, 2 figure
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