5,246 research outputs found
A numerical method with properties of consistency in the energy domain for a class of dissipative nonlinear wave equations with applications to a Dirichlet boundary-value problem
In this work, we present a conditionally stable finite-difference scheme that
consistently approximates the solution of a general class of (3+1)-dimensional
nonlinear equations that generalizes in various ways the quantitative model
governing discrete arrays consisting of coupled harmonic oscillators.
Associated with this method, there exists a discrete scheme of energy that
consistently approximates its continuous counterpart. The method has the
properties that the associated rate of change of the discrete energy
consistently approximates its continuous counterpart, and it approximates both
a fully continuous medium and a spatially discretized system. Conditional
stability of the numerical technique is established, and applications are
provided to the existence of the process of nonlinear supratransmission in
generalized Klein-Gordon systems and the propagation of binary signals in
semi-unbounded, three-dimensional arrays of harmonic oscillators coupled
through springs and perturbed harmonically at the boundaries, where the basic
model is a modified sine-Gordon equation; our results show that a perfect
transmission is achieved via the modulation of the driving amplitude at the
boundary. Additionally, we present an example of a nonlinear system with a
forbidden band-gap which does not present supratransmission, thus establishing
that the existence of a forbidden band-gap in the linear dispersion relation of
a nonlinear system is not a sufficient condition for the system to present
supratransmission
Coupled oscillators with power-law interaction and their fractional dynamics analogues
The one-dimensional chain of coupled oscillators with long-range power-law
interaction is considered. The equation of motion in the infrared limit are
mapped onto the continuum equation with the Riesz fractional derivative of
order , when . The evolution of soliton-like and
breather-like structures are obtained numerically and compared for both types
of simulations: using the chain of oscillators and using the continuous medium
equation with the fractional derivative.Comment: 16 pages, 5 figure
Fermion Schwinger's function for the SU(2)-Thirring model
We study the Euclidean two-point function of Fermi fields in the
SU(2)-Thirring model on the whole distance (energy) scale. We perform
perturbative and renormalization group analyses to obtain the short-distance
asymptotics, and numerically evaluate the long-distance behavior by using the
form factor expansion. Our results illustrate the use of bosonization and
conformal perturbation theory in the renormalization group analysis of a
fermionic theory, and numerically confirm the validity of the form factor
expansion in the case of the SU(2)-Thirring model.Comment: 27 pages, harvmac.tex, references added, typos correcte
Structure of the broken phase of the sine-Gordon model using functional renormalization
We study in this paper the sine-Gordon model using functional Renormalization
Group (fRG) at Local Potential Approximation (LPA) using different RG schemes.
In , using Wegner-Houghton RG we demonstrate that the location of the
phase boundary is entirely driven by the relative position to the Coleman fixed
point even for strongly coupled bare theories. We show the existence of a set
of IR fixed points in the broken phase that are reached independently of the
bare coupling. The bad convergence of the Fourier series in the broken phase is
discussed and we demonstrate that these fixed-points can be found only using a
global resolution of the effective potential. We then introduce the methodology
for the use of Average action method where the regulator breaks periodicity and
show that it provides the same conclusions for various regulators. The behavior
of the model is then discussed in and the absence of the previous
fixed points is interpreted.Comment: 43 pages, 32 figures, accepted versio
Noncoaxial multivortices in the complex sine-Gordon theory on the plane
We construct explicit multivortex solutions for the complex sine-Gordon
equation (the Lund-Regge model) in two Euclidean dimensions. Unlike the
previously found (coaxial) multivortices, the new solutions comprise single
vortices placed at arbitrary positions (but confined within a finite part of
the plane.) All multivortices, including the single vortex, have an infinite
number of parameters. We also show that, in contrast to the coaxial complex
sine-Gordon multivortices, the axially-symmetric solutions of the
Ginzburg-Landau model (the stationary Gross-Pitaevskii equation) {\it do not}
belong to a broader family of noncoaxial multivortex configurations.Comment: 40 pages, 7 figures in colou
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