Search results for "Ginzburg"
showing 10 items of 34 documents
Depolarization Field in Thin Ferroelectric Films With Account of Semiconductor Electrodes
2005
Within the framework of the phenomenological Ginzburg-Landau theory influence of semiconductor electrodes on the properties of thin ferroelectric films is considered. The contribution of the semiconductor electrodes with different Debye screening length of carriers is included in the functional of free energy. The influence of highly doped semiconductor electrodes on the depolarization field and the film properties was shown to be great.
A remark on the radial minimizer of the Ginzburg-Landau functional
2014
Let Omega subset of R-2 be a bounded domain with the same area as the unit disk B-1 and letE-epsilon(u, Omega) = 1/2 integral(Omega) vertical bar del u vertical bar(2) dx + 1/4 epsilon(2) integral(Omega) (vertical bar u vertical bar(2) - 1)(2) dxbe the Ginzburg-Landau functional. Denote by (u) over tilde (epsilon) the radial solution to the Euler equation associated to the problem min {E-epsilon (u, B-1) : u vertical bar(partial derivative B1) = x} and byK = {v = (v(1), v(2)) is an element of H-1 (Omega; R-2) : integral(Omega) v(1) dx = integral(Omega) v(2) dx = 0,integral(Omega) vertical bar v vertical bar(2) dx >= integral(B1) vertical bar(u) over tilde vertical bar(2) dx}.In this note…
WAVE PROPAGATION AND PATTERN FORMATION FOR A REACTION-DIFFUSION SYSTEM WITH NONLINEAR DIFFUSION
2008
We investigate the formation of macroscopic spatio-temporal structures (patterns) for a reaction-diffusion system with nonlinear diffusion. We show that cross-diffusion effects are responsible of pattern initiation. Through a weakly nonlinear analysis we are able to predict the shape and the amplitude of the pattern. In the weakly nonlinear regime we derive the Ginzburg-Landau equation which captures the envelope evolution and the progressing of the pattern as a wave. Numerical simulations, performed using both a particle and a spectral method, are in good agreement with the analytical results.
Influence of semiconducting electrodes on properties of thin ferroelectric films
2005
The influence of semiconducting electrodes on the properties of thin ferroelectric films is considered within the framework of the phenomenological Ginzburg-Landau theory. The contribution of the electric field produced by charges in the electrodes allowing for the screening length of the carriers is included in the functional of the free energy and so in the Euler-Lagrange equation for the film's polarization. Application of the variational method to the solution of this equation allows the transformation of the free energy functional into a conventional type of free energy with renormalized coefficients. The obtained dependence of the coefficients on the film thickness, temperature, elect…
Semiadiabatic High-Field Polarization Response in Ferroelectrics I: Hysteresis and Nonlinear Susceptibility
2004
Ginzburg-Landau theory for ferroelectric phase instability is combined with Langevin, Fokker-Planck and imaginary time Schrodinger equation techniques to model impact of thermal noise in the kinetics of ferroelectric polarization. The proposed real space/real time numerical method allows to efficiently simulating relaxation, dynamic hysteresis and general dielectric response.
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 …
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...
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…