133 research outputs found
Coarsening scenarios in unstable crystal growth
Crystal surfaces may undergo thermodynamical as well kinetic,
out-of-equilibrium instabilities. We consider the case of mound and pyramid
formation, a common phenomenon in crystal growth and a long-standing problem in
the field of pattern formation and coarsening dynamics. We are finally able to
attack the problem analytically and get rigorous results. Three dynamical
scenarios are possible: perpetual coarsening, interrupted coarsening, and no
coarsening. In the perpetual coarsening scenario, mound size increases in time
as L=t^n, where the coasening exponent is n=1/3 when faceting occurs, otherwise
n=1/4.Comment: Changes in the final part. Accepted for publication in Phys. Rev.
Let
Cryptanalysis of a novel cryptosystem based on chaotic oscillators and feedback inversion
An analysis of a recently proposed cryptosystem based on chaotic oscillators
and feedback inversion is presented. It is shown how the cryptosystem can be
broken when Duffing's oscillator is considered. Some implementation problems of
the system are also discussed.Comment: 9 pages, 3 figures, latex forma
Nonlinear dynamics in one dimension: On a criterion for coarsening and its temporal law
We develop a general criterion about coarsening for a class of nonlinear
evolution equations describing one dimensional pattern-forming systems. This
criterion allows one to discriminate between the situation where a coarsening
process takes place and the one where the wavelength is fixed in the course of
time. An intermediate scenario may occur, namely `interrupted coarsening'. The
power of the criterion lies in the fact that the statement about the occurrence
of coarsening, or selection of a length scale, can be made by only inspecting
the behavior of the branch of steady state periodic solutions. The criterion
states that coarsening occurs if lambda'(A)>0 while a length scale selection
prevails if lambda'(A)<0, where is the wavelength of the pattern and A
is the amplitude of the profile. This criterion is established thanks to the
analysis of the phase diffusion equation of the pattern. We connect the phase
diffusion coefficient D(lambda) (which carries a kinetic information) to
lambda'(A), which refers to a pure steady state property. The relationship
between kinetics and the behavior of the branch of steady state solutions is
established fully analytically for several classes of equations. Another
important and new result which emerges here is that the exploitation of the
phase diffusion coefficient enables us to determine in a rather straightforward
manner the dynamical coarsening exponent. Our calculation, based on the idea
that |D(lambda)|=lambda^2/t, is exemplified on several nonlinear equations,
showing that the exact exponent is captured. Some speculations about the
extension of the present results to higher dimension are outlined.Comment: 16 pages. Only a few minor changes. Accepted for publication in
Physical Review
Effects of disorder on quantum fluctuations and superfluid density of a Bose-Einstein condensate in a two-dimensional optical lattice
We investigate a Bose-Einstein condensate trapped in a 2D optical lattice in
the presence of weak disorder within the framework of the Bogoliubov theory. In
particular, we analyze the combined effects of disorder and an optical lattice
on quantum fluctuations and superfluid density of the BEC system. Accordingly,
the analytical expressions of the ground state energy and quantum depletion of
the system are obtained. Our results show that the lattice still induces a
characteristic 3D to 1D crossover in the behavior of quantum fluctuations,
despite the presence of weak disorder. Furthermore, we use the linear response
theory to calculate the normal fluid density of the condensate induced by
disorder. Our results in the 3D regime show that the combined presence of
disorder and lattice induce a normal fluid density that asymptotically
approaches 4/3 of the corresponding condensate depletion. Conditions for
possible experimental realization of our scenario are also proposed.Comment: 8 pages, 0 figure. To appear in Physical Review
One-parameter Darboux-transformed quantum actions in Thermodynamics
We use nonrelativistic supersymmetry, mainly Darboux transformations of the
general (one-parameter) type, for the quantum oscillator thermodynamic actions.
Interesting Darboux generalizations of the fundamental Planck and pure vacuum
cases are discussed in some detail with relevant plots. It is shown that the
one-parameter Darboux-transformed Thermodynamics refers to superpositions of
boson and fermion excitations of positive and negative absolute temperature,
respectively. Recent results of Arnaud, Chusseau, and Philippe physics/0105048
regarding a single mode oscillator Carnot cycle are extended in the same
Darboux perspective. We also conjecture a Darboux generalization of the
fluctuation-dissipation theoremComment: 14 pages, 13 figures, correction of the formula in the text after Eq.
7, accepted at Physica Script
Control and Dynamic Competition of Bright and Dark Lasing States in Active Nanoplasmonic Metamaterials
Active nanoplasmonic metamaterials support bright and dark modes that compete
for gain. Using a Maxwell-Bloch approach incorporating Langevin noise we study
the lasing dynamics in an active nano-fishnet structure. We report that lasing
of the bright negative-index mode is possible if the higher-Q dark mode is
discriminated by gain, spatially or spectrally. The nonlinear competition
during the transient phase is followed by steady-state emission where bright
and dark modes can coexist. We analyze the influence of pump intensity and
polarization and explore methods for mode control.Comment: 5 pages, 4 figure
Similarity solutions of Fokker-Planck equation with time-dependent coefficients
In this work, we consider the solvability of the Fokker-Planck equation with
both time-dependent drift and diffusion coefficients by means of the similarity
method. By the introduction of the similarity variable, the Fokker-Planck
equation is reduced to an ordinary differential equation. Adopting the natural
requirement that the probability current density vanishes at the boundary, the
resulted ordinary differential equation turns out to be integrable, and the
probability density function can be given in closed form. New examples of
exactly solvable Fokker-Planck equations are presented, and their properties
analyzed.Comment: 13 pages, 8 figures. Version to appear in Ann. Phys. Presentation
improved. Discussions and figures of easy examples remove
Singular forces and point-like colloids in lattice Boltzmann hydrodynamics
We present a second-order accurate method to include arbitrary distributions
of force densities in the lattice Boltzmann formulation of hydrodynamics. Our
method may be used to represent singular force densities arising either from
momentum-conserving internal forces or from external forces which do not
conserve momentum. We validate our method with several examples involving point
forces and find excellent agreement with analytical results. A minimal model
for dilute sedimenting particles is presented using the method which promises a
substantial gain in computational efficiency.Comment: 22 pages, 9 figures. Submitted to Phys. Rev.
Exact Analytic Solution for the Rotation of a Rigid Body having Spherical Ellipsoid of Inertia and Subjected to a Constant Torque
The exact analytic solution is introduced for the rotational motion of a
rigid body having three equal principal moments of inertia and subjected to an
external torque vector which is constant for an observer fixed with the body,
and to arbitrary initial angular velocity. In the paper a parametrization of
the rotation by three complex numbers is used. In particular, the rows of the
rotation matrix are seen as elements of the unit sphere and projected, by
stereographic projection, onto points on the complex plane. In this
representation, the kinematic differential equation reduces to an equation of
Riccati type, which is solved through appropriate choices of substitutions,
thereby yielding an analytic solution in terms of confluent hypergeometric
functions. The rotation matrix is recovered from the three complex rotation
variables by inverse stereographic map. The results of a numerical experiment
confirming the exactness of the analytic solution are reported. The newly found
analytic solution is valid for any motion time length and rotation amplitude.
The present paper adds a further element to the small set of special cases for
which an exact solution of the rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" In particular: typos present in Eq. 28 of
the Journal version are HERE correcte
The Totally Asymmetric Simple Exclusion Process with Langmuir Kinetics
We discuss a new class of driven lattice gas obtained by coupling the
one-dimensional totally asymmetric simple exclusion process to Langmuir
kinetics. In the limit where these dynamics are competing, the resulting
non-conserved flow of particles on the lattice leads to stationary regimes for
large but finite systems. We observe unexpected properties such as localized
boundaries (domain walls) that separate coexisting regions of low and high
density of particles (phase coexistence). A rich phase diagram, with high an
low density phases, two and three phase coexistence regions and a boundary
independent ``Meissner'' phase is found. We rationalize the average density and
current profiles obtained from simulations within a mean-field approach in the
continuum limit. The ensuing analytic solution is expressed in terms of Lambert
-functions. It allows to fully describe the phase diagram and extract
unusual mean-field exponents that characterize critical properties of the
domain wall. Based on the same approach, we provide an explanation of the
localization phenomenon. Finally, we elucidate phenomena that go beyond
mean-field such as the scaling properties of the domain wall.Comment: 22 pages, 23 figures. Accepted for publication on Phys. Rev.
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