1,955 research outputs found
Two-timing, variational principles and waves
In this paper, it is shown how the author's general theory of slowly varying wave trains may be derived as the first term in a formal perturbation expansion. In its most effective form, the perturbation procedure is applied directly to the governing variational principle and an averaged variational principle is established directly. This novel use of a perturbation method may have value outside the class of wave problems considered here. Various useful manipulations of the average Lagrangian are shown to be similar to the transformations leading to Hamilton's equations in mechanics. The methods developed here for waves may also be used on the older problems of adiabatic invariants in mechanics, and they provide a different treatment; the typical problem of central orbits is included in the examples
Comments on some recent multisoliton solutions
It is shown that some recently proposed multisoliton solutions for the nonlinear Klein-Gordon equations can be reduced to a simple form which can be obtained immediately from the equation
Exact shock solution of a coupled system of delay differential equations: a car-following model
In this paper, we present exact shock solutions of a coupled system of delay
differential equations, which was introduced as a traffic-flow model called
{\it the car-following model}. We use the Hirota method, originally developed
in order to solve soliton equations. %While, with a periodic boundary
condition, this system has % a traveling-wave solution given by elliptic
functions. The relevant delay differential equations have been known to allow
exact solutions expressed by elliptic functions with a periodic boundary
conditions. In the present work, however, shock solutions are obtained with
open boundary, representing the stationary propagation of a traffic jam.Comment: 6 pages, 2 figure
On the excitation of edge waves on beaches
The excitation of standing edge waves of frequency ½ω by a normally incident wave train of frequency ω has been discussed previously (Guza & Davis 1974; Guza & Inman 1975; Guza & Bowen 1976) on the basis of shallow-water theory. Here the problem is formulated in the full water-wave theory without making the shallow-water approximation and solved for beach angles β = π/2N, where N is an integer. The work confirms the shallow-water results in the limit N » 1, shows the effect of larger beach angles and allows a more complete discussion of some aspects of the problem
Sharp bounds on enstrophy growth in the viscous Burgers equation
We use the Cole--Hopf transformation and the Laplace method for the heat
equation to justify the numerical results on enstrophy growth in the viscous
Burgers equation on the unit circle. We show that the maximum enstrophy
achieved in the time evolution is scaled as , where
is the large initial enstrophy, whereas the time needed for
reaching the maximal enstrophy is scaled as . These bounds
are sharp for sufficiently smooth initial conditions.Comment: 12 page
Gradient Catastrophe and Fermi Edge Resonances in Fermi Gas
A smooth spatial disturbance of the Fermi surface in a Fermi gas inevitably
becomes sharp. This phenomenon, called {\it the gradient catastrophe}, causes
the breakdown of a Fermi sea to disconnected parts with multiple Fermi points.
We study how the gradient catastrophe effects probing the Fermi system via a
Fermi edge singularity measurement. We show that the gradient catastrophe
transforms the single-peaked Fermi-edge singularity of the tunneling (or
absorption) spectrum to a set of multiple asymmetric singular resonances. Also
we gave a mathematical formulation of FES as a matrix Riemann-Hilbert problem
Strongly nonlinear waves in capillary electrophoresis
In capillary electrophoresis, sample ions migrate along a micro-capillary
filled with a background electrolyte under the influence of an applied electric
field. If the sample concentration is sufficiently high, the electrical
conductivity in the sample zone could differ significantly from the
background.Under such conditions, the local migration velocity of sample ions
becomes concentration dependent resulting in a nonlinear wave that exhibits
shock like features. If the nonlinearity is weak, the sample concentration
profile, under certain simplifying assumptions, can be shown to obey Burgers'
equation (S. Ghosal and Z. Chen Bull. Math. Biol. 2010, 72(8), pg. 2047) which
has an exact analytical solution for arbitrary initial condition.In this paper,
we use a numerical method to study the problem in the more general case where
the sample concentration is not small in comparison to the concentration of
background ions. In the case of low concentrations, the numerical results agree
with the weakly nonlinear theory presented earlier, but at high concentrations,
the wave evolves in a way that is qualitatively different.Comment: 7 pages, 5 figures, 1 Appendix, 2 videos (supplementary material
Shock waves in strongly interacting Fermi gas from time-dependent density functional calculations
Motivated by a recent experiment [Phys. Rev. Lett. 106, 150401 (2011)] we
simulate the collision between two clouds of cold Fermi gas at unitarity
conditions by using an extended Thomas-Fermi density functional. At variance
with the current interpretation of the experiments, where the role of viscosity
is emphasized, we find that a quantitative agreement with the experimental
observation of the dynamics of the cloud collisions is obtained within our
superfluid effective hydrodynamics approach, where density variations during
the collision are controlled by a purely dispersive quantum gradient term. We
also suggest different initial conditions where dispersive density ripples can
be detected with the available experimental spatial resolution.Comment: 5 pages, 4 figures, to be published in Phys. Rev.
Diamagnetic susceptibility obtained from the six-vertex model and its implications for the high-temperature diamagnetic state of cuprate superconductors
We study the diamagnetism of the 6-vertex model with the arrows as directed
bond currents. To our knowledge, this is the first study of the diamagnetism of
this model. A special version of this model, called F model, describes the
thermal disordering transition of an orbital antiferromagnet, known as
d-density wave (DDW), a proposed state for the pseudogap phase of the high-Tc
cuprates. We find that the F model is strongly diamagnetic and the
susceptibility may diverge in the high temperature critical phase with power
law arrow correlations. These results may explain the surprising recent
observation of a diverging low-field diamagnetic susceptibility seen in some
optimally doped cuprates within the DDW model of the pseudogap phase.Comment: 4.5 pages, 2 figures, revised version accepted in Phys. Rev. Let
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
- …