1,026 research outputs found
Nonlinear dynamics of self-sustained supersonic reaction waves: Fickett's detonation analogue
The present study investigates the spatio-temporal variability in the
dynamics of self-sustained supersonic reaction waves propagating through an
excitable medium. The model is an extension of Fickett's detonation model with
a state dependent energy addition term. Stable and pulsating supersonic waves
are predicted. With increasing sensitivity of the reaction rate, the reaction
wave transits from steady propagation to stable limit cycles and eventually to
chaos through the classical Feigenbaum route. The physical pulsation mechanism
is explained by the coherence between internal wave motion and energy release.
The results obtained clarify the physical origin of detonation wave instability
in chemical detonations previously observed experimentally.Comment: 4 pages, 3 figure
Achievable Qubit Rates for Quantum Information Wires
Suppose Alice and Bob have access to two separated regions, respectively, of
a system of electrons moving in the presence of a regular one-dimensional
lattice of binding atoms. We consider the problem of communicating as much
quantum information, as measured by the qubit rate, through this quantum
information wire as possible. We describe a protocol whereby Alice and Bob can
achieve a qubit rate for these systems which is proportional to N^(-1/3) qubits
per unit time, where N is the number of lattice sites. Our protocol also
functions equally in the presence of interactions modelled via the t-J and
Hubbard models
The Modulation of Multiple Phases Leading to the Modified KdV Equation
This paper seeks to derive the modified KdV (mKdV) equation using a novel
approach from systems generated from abstract Lagrangians that possess a
two-parameter symmetry group. The method to do uses a modified modulation
approach, which results in the mKdV emerging with coefficients related to the
conservation laws possessed by the original Lagrangian system. Alongside this,
an adaptation of the method of Kuramoto is developed, providing a simpler
mechanism to determine the coefficients of the nonlinear term. The theory is
illustrated using two examples of physical interest, one in stratified
hydrodynamics and another using a coupled Nonlinear Schr\"odinger model, to
illustrate how the criterion for the mKdV equation to emerge may be assessed
and its coefficients generated.Comment: 35 pages, 5 figure
Modeling M-Theory Vacua via Gauged S-Duality
We construct a model of M-theory vacua using gauged S-duality and the
Chan-Paton symmetries by introducing an infinite number of open string charges.
In the Bechi-Rouet-Stora-Tyutin formalism, the local description of the gauged
S-duality on its moduli space of vacua is fully determined by one physical
state condition on the vacua. We introduce the string probe of the spatial
degrees of freedom and define the increment of the cosmic time. The
dimensionality of space-time and the gauge group of the low energy effective
theory originate in the symmetries (with or without their breakdown) in our
model. This modeling leads to the derived category formulation of the quantum
mechanical world including gravity and to the concept of a non-linear potential
of gauged and affinized S-duality which specifies the morphism structure of
this derived category.Comment: 31 pages, version reflecting the erratum. arXiv admin note:
substantial text overlap with arXiv:1102.460
Self-Similar Blowup Solutions to the 2-Component Camassa-Holm Equations
In this article, we study the self-similar solutions of the 2-component
Camassa-Holm equations% \begin{equation} \left\{ \begin{array} [c]{c}%
\rho_{t}+u\rho_{x}+\rho u_{x}=0
m_{t}+2u_{x}m+um_{x}+\sigma\rho\rho_{x}=0 \end{array} \right. \end{equation}
with \begin{equation} m=u-\alpha^{2}u_{xx}. \end{equation} By the separation
method, we can obtain a class of blowup or global solutions for or
. In particular, for the integrable system with , we have the
global solutions:% \begin{equation} \left\{ \begin{array} [c]{c}%
\rho(t,x)=\left\{ \begin{array} [c]{c}% \frac{f\left( \eta\right)
}{a(3t)^{1/3}},\text{ for }\eta^{2}<\frac {\alpha^{2}}{\xi}
0,\text{ for }\eta^{2}\geq\frac{\alpha^{2}}{\xi}% \end{array} \right.
,u(t,x)=\frac{\overset{\cdot}{a}(3t)}{a(3t)}x
\overset{\cdot\cdot}{a}(s)-\frac{\xi}{3a(s)^{1/3}}=0,\text{ }a(0)=a_{0}%
>0,\text{ }\overset{\cdot}{a}(0)=a_{1}
f(\eta)=\xi\sqrt{-\frac{1}{\xi}\eta^{2}+\left( \frac{\alpha}{\xi}\right)
^{2}}% \end{array} \right. \end{equation}
where with and are
arbitrary constants.\newline Our analytical solutions could provide concrete
examples for testing the validation and stabilities of numerical methods for
the systems.Comment: 5 more figures can be found in the corresponding journal paper (J.
Math. Phys. 51, 093524 (2010) ). Key Words: 2-Component Camassa-Holm
Equations, Shallow Water System, Analytical Solutions, Blowup, Global,
Self-Similar, Separation Method, Construction of Solutions, Moving Boundar
Resonant nonlinearity management for nonlinear-Schr\"{o}dinger solitons
We consider effects of a periodic modulation of the nonlinearity coefficient
on fundamental and higher-order solitons in the one-dimensional NLS equation,
which is an issue of direct interest to Bose-Einstein condensates in the
context of the Feshbach-resonance control, and fiber-optic telecommunications
as concerns periodic compensation of the nonlinearity. We find from
simulations, and explain by means of a straightforward analysis, that the
response of a fundamental soliton to the weak perturbation is resonant, if the
modulation frequency is close to the intrinsic frequency of the
soliton. For higher-order -solitons with and 3, the response to an
extremely weak perturbation is also resonant, if is close to the
corresponding intrinsic frequency. More importantly, a slightly stronger drive
splits the 2- or 3-soliton, respectively, into a set of two or three moving
fundamental solitons. The dependence of the threshold perturbation amplitude,
necessary for the splitting, on has a resonant character too.
Amplitudes and velocities of the emerging fundamental solitons are accurately
predicted, using exact and approximate conservation laws of the perturbed NLS
equation.Comment: 14 pages, 6 figure
Exact Scattering States of Dirac-Born-Infeld Equation with Constant Background Fields
Exact solutions to the Dirac-Born-Infeld equation, which describes
scatterings of localized wave packets in the presence of constant background
fields, are derived in this paper.Comment: 18 pages, latex, no figure
Higher-order splitting algorithms for solving the nonlinear Schr\"odinger equation and their instabilities
Since the kinetic and the potential energy term of the real time nonlinear
Schr\"odinger equation can each be solved exactly, the entire equation can be
solved to any order via splitting algorithms. We verified the fourth-order
convergence of some well known algorithms by solving the Gross-Pitaevskii
equation numerically. All such splitting algorithms suffer from a latent
numerical instability even when the total energy is very well conserved. A
detail error analysis reveals that the noise, or elementary excitations of the
nonlinear Schr\"odinger, obeys the Bogoliubov spectrum and the instability is
due to the exponential growth of high wave number noises caused by the
splitting process. For a continuum wave function, this instability is
unavoidable no matter how small the time step. For a discrete wave function,
the instability can be avoided only for \dt k_{max}^2{<\atop\sim}2 \pi, where
.Comment: 10 pages, 8 figures, submitted to Phys. Rev.
Anomalous Scaling and Solitary Waves in Systems with Non-Linear Diffusion
We study a non-linear convective-diffusive equation, local in space and time,
which has its background in the dynamics of the thickness of a wetting film.
The presence of a non-linear diffusion predicts the existence of fronts as well
as shock fronts. Despite the absence of memory effects, solutions in the case
of pure non-linear diffusion exhibit an anomalous sub-diffusive scaling. Due to
a balance between non-linear diffusion and convection we, in particular, show
that solitary waves appear. For large times they merge into a single solitary
wave exhibiting a topological stability. Even though our results concern a
specific equation, numerical simulations supports the view that anomalous
diffusion and the solitary waves disclosed will be general features in such
non-linear convective-diffusive dynamics.Comment: Corrected typos, added 3 references and 2 figure
Bogoliubov-Cerenkov radiation in a Bose-Einstein condensate flowing against an obstacle
We study the density modulation that appears in a Bose-Einstein condensate
flowing with supersonic velocity against an obstacle. The experimental density
profiles observed at JILA are reproduced by a numerical integration of the
Gross-Pitaevskii equation and then interpreted in terms of Cerenkov emission of
Bogoliubov excitations by the defect. The phonon and the single-particle
regions of the Bogoliubov spectrum are respectively responsible for a conical
wavefront and a fan-shaped series of precursors
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