14,387 research outputs found
Optimal streaks in a Falkner-Skan boundary layer
This paper deals with the optimal streaky perturbations (which maximize the
perturbed energy growth) in a wedge flow boundary layer. These three
dimensional perturbations are governed by a system of linearized boundary layer
equations around the Falkner-Skan base flow. Based on an asymptotic analysis of
this system near the free stream and the leading edge singularity, we show that
for acute wedge semi-angle, all solutions converge after a streamwise transient
to a single streamwise-growing solution of the linearized equations, whose
initial condition near the leading edge is given by an eigenvalue problem first
formulated in this context by Tumin (2001). Such a solution may be regarded as
a streamwise evolving most unstable streaky mode, in analogy with the usual
eigenmodes in strictly parallel flows, and shows an approximate
self-similarity, which was partially known and is completed in this paper. An
important consequence of this result is that the optimization procedure based
on the adjoint equations heretofore used to define optimal streaks is not
necessary. Instead, a simple low-dimensional optimization process is proposed
and used to obtain optimal streaks. Comparison with previous results by Tumin
and Ashpis (2003) shows an excellent agreement. The unstable streaky mode
exhibits transient growth if the wedge semi-angle is smaller than a critical
value that is slightly larger than , and decays otherwise. Thus the
cases of right and obtuse wedge semi-angles exhibit less practical interest,
but they show a qualitatively different behavior, which is briefly described to
complete the analysis
Comment on "Two Phase Transitions in the Fully frustrated XY Model"
The conclusions of a recent paper by Olsson (Phys. Rev. Lett. 75, 2758
(1995), cond-mat/9506082) about the fully frustrated XY model in two dimensions
are questioned. In particular, the evidence presented for having two separate
chiral and U(1) phase transitions are critically considered.Comment: One page one table, to Appear in Physical Review Letter
Charge-Vortex Duality in Double-Layered Josephson Junction Arrays
A system of two parallel Josephson junction arrays coupled by interlayer
capacitances is considered in the situation where one layer is in the
vortex-dominated and the other in the charge-dominated regime. This system
shows a symmetry (duality) of the relevant degrees of freedom, i.e. the
vortices in one layer and the charges in the other. In contrast to single-layer
arrays both contribute to the kinetic energy. The charges feel the magnetic
field created by vortices, and, vice versa, the vortices feel a gauge field
created by charges. For long-range interaction of the charges the system
exhibits two Berezinskii-Kosterlitz-Thouless transitions, one for vortices and
another one for charges. The interlayer capacitance suppresses both transition
temperatures. The charge-unbinding transition is suppressed already for
relatively weak coupling, while the vortex-unbinding transition is more robust.
The shift of the transition temperature for vortices is calculated in the
quasi-classical approximation for arbitrary relations between the capacitances
(both weak and strong coupling).Comment: 12 pages, Revtex 3.
A short proof that the Coulomb-gauge potentials yield the retarded fields
A short demonstration that the potentials in the Coulomb gauge yield the
retarded electric and magnetic fields is presented. This demonstration is
relatively simple and can be presented in an advanced undergraduate curse of
electromagnetic theory
Dissociation of vortex stacks into fractional-flux vortices
We discuss the zero field superconducting phase transition in a finite system
of magnetically coupled superconducting layers. Transverse screening is
modified by the presence of other layers resulting in topological excitations
with fractional flux. Vortex stacks trapping a full flux and present at any
finite temperature undergo an evaporation transition which corresponds to the
depairing of fractional-flux vortices in individual layers. We propose an
experiment with a bi-layer system allowing us to identify the dissociation of
bound vortex molecules.Comment: 4 pages, 1 figure; revised version, to appear in Phys. Rev. Let
Electromagnetic effects of neutrinos in an electron gas
We study the electromagnetic properties of a system that consists of an
electron background and a neutrino gas that may be moving or at rest, as a
whole, relative to the background. The photon self-energy for this system is
characterized by the usual transverse and longitudinal polarization functions,
and two additional ones which are the focus of our calculations, that give rise
to birefringence and anisotropic effects in the photon dispersion relations.
Expressions for them are obtained, which depend on the neutrino number
densities and involve momentum integrals over the electron distribution
functions, and are valid for any value of the photon momentum and general
conditions of the electron gas. Those expressions are evaluated explicitly for
several special cases and approximations which are generally useful in
astrophysical and cosmological settings. Besides studying the photon dispersion
relations, we consider the macroscopic electrodynamic equations for this
system, which involve the standard dielectric and permeability constants plus
two additional ones related to the photon self-energy functions. As an
illustration, the equations are used to discuss the evolution of a magnetic
field perturbation in such a medium. This particular phenomena has also been
considered in a recent work by Semikoz and Sokoloff as a mechanism for the
generation of large-scale magnetic fields in the Early Universe as a
consequence of the neutrino-plasma interactions, and allows us to establish
contact with a specific application in a well defined context, with a broader
scope and from a very different point of view.Comment: Revtex 20 page
Quantum-to-classical crossover for Andreev billiards in a magnetic field
We extend the existing quasiclassical theory for the superconducting
proximity effect in a chaotic quantum dot, to include a time-reversal-symmetry
breaking magnetic field. Random-matrix theory (RMT) breaks down once the
Ehrenfest time becomes longer than the mean time between
Andreev reflections. As a consequence, the critical field at which the
excitation gap closes drops below the RMT prediction as is
increased. Our quasiclassical results are supported by comparison with a fully
quantum mechanical simulation of a stroboscopic model (the Andreev kicked
rotator).Comment: 11 pages, 10 figure
Viscoelasticity and metastability limit in supercooled liquids
A supercooled liquid is said to have a kinetic spinodal if a temperature Tsp
exists below which the liquid relaxation time exceeds the crystal nucleation
time. We revisit classical nucleation theory taking into account the
viscoelastic response of the liquid to the formation of crystal nuclei and find
that the kinetic spinodal is strongly influenced by elastic effects. We
introduce a dimensionless parameter \lambda, which is essentially the ratio
between the infinite frequency shear modulus and the enthalpy of fusion of the
crystal. In systems where \lambda is larger than a critical value \lambda_c the
metastability limit is totally suppressed, independently of the surface
tension. On the other hand, if \lambda < \lambda_c a kinetic spinodal is
present and the time needed to experimentally observe it scales as
exp[\omega/(\lambda_c-\lambda)^2], where \omega is roughly the ratio between
surface tension and enthalpy of fusion
Suppression of Superconductivity in Mesoscopic Superconductors
We propose a new boundary-driven phase transition associated with vortex
nucleation in mesoscopic superconductors (of size of the order of, or larger
than, the penetration depth). We derive the rescaling equations and we show
that boundary effects associated with vortex nucleation lowers the conventional
transition temperature in mesoscopic superconductors by an amount which is a
function of the size of the superconductor. This result explains recent
experiments in small superconductors where it was found that the transition
temperature depends on the size of the system and is lower than the critical
Berezinsk\u{i}-Kosterlitz-Thouless temperature.Comment: To appear in Phys. Rev. Lett. Vol. 86 (15 Jan. 2001
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