Search results for "Burg"

Dissipative soliton resonance as a guideline for high-energy pulse laser oscillators

2010

Dissipative soliton resonance (DSR) occurs in the close vicinity of a hypersurface in the space of parameters of the equation governing propagation in a dissipative nonlinear medium. Pulsed solutions can acquire virtually unlimited energies as soon as the equation parameters converge toward that specific hypersurface. Here we extend previous studies that have recently unveiled DSRs from the complex cubic-quintic Ginzburg-Landau equation. We clearly confirm the existence of DSR for a wide range of parameters in both regimes of chromatic dispersion, and we establish general features of the ultra-high-energy pulses that can be found close to a DSR. Application to high-energy mode-locked fiber …

Matrix solutions of diffusion equation

2002

Some evolution equations arising in physics

1983

In this paper we consider a new series of evolution equations generalizing the Korteweg-deVries (KdV) and Burgers equations, and we report recent advances on these equations together with the physical phenomena where they arise. In particular we consider a generalized Burgers' equation and we sketch a method for solution in series by using the theory of Sobolevskij and Tanabe. Then we study the KdV equation with nonuniformity terms and we describe various physical interpretation of this equation. We consider various particular cases in which varying solitonic solutions exist. Also we sketch a unicity theorem. Finally modified Burgers-KdV equations are considered.

Wave Modulations in the Nonlinear Biinductance Transmission Line

2001

Adding dissipative elements to a discrete biinductance transmission line which admits both low frequency (LF) and high frequency (HF) modes, dynamics of a weakly nonlinear modulated wave is investi...

Singular behavior of a vortex layer in the zero thickness limit

2017

The aim of this paper is to study the Euler dynamics of a 2D periodic layer of non uniform vorticity. We consider the zero thickness limit and we compare the Euler solution with the vortex sheet evolution predicted by the Birkhoff-Rott equation. The well known process of singularity formation in shape of the vortex sheet correlates with the appearance of several complex singularities in the Euler solution with the vortex layer datum. These singularities approach the real axis and are responsible for the roll-up process in the layer motion.

Surface-directed spinodal decomposition: Lattice model versus Ginzburg-Landau theory

2009

When a binary mixture is quenched into the unstable region of the phase diagram, phase separation starts by spontaneous growth of long-wavelength concentration fluctuations ("spinodal decomposition"). In the presence of surfaces, the latter provide nontrivial boundary conditions for this growth. These boundary conditions can be derived from lattice models by suitable continuum approximations. But the lattice models can also be simulated directly, and thus used to clarify the conditions under which the Ginzburg–Landau type theory is valid. This comparison shows that the latter is accurate only in the immediate vicinity of the bulk critical point, if thermal fluctuations can also be neglecte…

General interpolation scheme for thermal fluctuations in superconductors

2006

We present a general interpolation theory for the phenomenological effects of thermal fluctuations in superconductors. Fluctuations are described by a simple gauge invariant extension of the gaussian effective potential for the Ginzburg-Landau static model. The approach is shown to be a genuine variational method, and to be stationary for infinitesimal gauge variations around the Landau gauge. Correlation and penetration lengths are shown to depart from the mean field behaviour in a more or less wide range of temperature below the critical regime, depending on the class of material considered. The method is quite general and yields a very good interpolation of the experimental data for very…

Simulation of surface-controlled phase separation in slit pores: Diffusive Ginzburg-Landau kinetics versus Molecular Dynamics

2008

The phase separation kinetics of binary fluids in constrained geometry is a challenge for computer simulation, since nontrivial structure formation occurs extending from the atomic scale up to mesoscopic scales, and a very large range of time needs to be considered. One line of attack to this problem is to try nevertheless standard Molecular Dynamics (MD), another approach is to coarse-grain the model to apply a time-dependent nonlinear Ginzburg–Landau equation that is numerically integrated. For a symmetric binary mixture confined between two parallel walls that prefer one species, both approaches are applied and compared to each other. There occurs a nontrivial interplay between the forma…

Notes on the Electroelastic Interaction in Joint Hamiltonian and Stochastic Treatment of Polarization Response

2008

Conventional Landau theory for ferroelectric phase instability is extended by entities accounting for the violation of thermodynamic equilibrium and the impact of thermal fluctuations. The physical content concerns Ginzburg-Landau type model Hamiltonians assigned to the mean field interaction of macroscopically small and microscopically large lattice cells affected by thermal fluctuations. A special topic derived in a systematic way is long range electroelastic interaction formally given by selfconsistent solution of the polarization and strain fields. Test solution for inhomogeneous strain in a slab is presented within the framework of lattice cell picture.

Asymptotic structure factor for the two-component Ginzburg-Landau equation

1992

We derive an analytic form for the asymptotic time-dependent structure factor for the two-component Ginzburg-Landau equation in arbitrary dimensions. This form is in reasonable agreement with results from numerical simulations in two dimensions. A striking feature of our analytic form is the absence of Porod's law in the tail. This is a consequence of the continuous symmetry of the Hamiltonian, which inhibits the formation of sharp domain walls.