6,435 research outputs found
Localised states in an extended Swift-Hohenberg equation
Recent work on the behaviour of localised states in pattern forming partial
differential equations has focused on the traditional model Swift-Hohenberg
equation which, as a result of its simplicity, has additional structure --- it
is variational in time and conservative in space. In this paper we investigate
an extended Swift-Hohenberg equation in which non-variational and
non-conservative effects play a key role. Our work concentrates on aspects of
this much more complicated problem. Firstly we carry out the normal form
analysis of the initial pattern forming instability that leads to
small-amplitude localised states. Next we examine the bifurcation structure of
the large-amplitude localised states. Finally we investigate the temporal
stability of one-peak localised states. Throughout, we compare the localised
states in the extended Swift-Hohenberg equation with the analogous solutions to
the usual Swift-Hohenberg equation
Upper critical field in {BaKBiO}: magnetotransport versus magnetotunneling
Elastic tunneling is used as a powerful direct tool to determine the upper
critical field in the high- oxide BaKBiO. The
temperature dependence of inferred from the tunneling follows the
Werthamer-Helfand-Hohenberg prediction for type-II superconductors. A
comparison will be made with resistively determined critical field data.Comment: 4 pages incl. 5 figure
Existence of a Density Functional for an Intrinsic State
A generalization of the Hohenberg-Kohn theorem proves the existence of a
density functional for an intrinsic state, symmetry violating, out of which a
physical state with good quantum numbers can be projected.Comment: 6 page
The Swift-Hohenberg equation with a nonlocal nonlinearity
It is well known that aspects of the formation of localised states in a
one-dimensional Swift--Hohenberg equation can be described by
Ginzburg--Landau-type envelope equations. This paper extends these multiple
scales analyses to cases where an additional nonlinear integral term, in the
form of a convolution, is present. The presence of a kernel function introduces
a new lengthscale into the problem, and this results in additional complexity
in both the derivation of envelope equations and in the bifurcation structure.
When the kernel is short-range, weakly nonlinear analysis results in envelope
equations of standard type but whose coefficients are modified in complicated
ways by the nonlinear nonlocal term. Nevertheless, these computations can be
formulated quite generally in terms of properties of the Fourier transform of
the kernel function. When the lengthscale associated with the kernel is longer,
our method leads naturally to the derivation of two different, novel, envelope
equations that describe aspects of the dynamics in these new regimes. The first
of these contains additional bifurcations, and unexpected loops in the
bifurcation diagram. The second of these captures the stretched-out nature of
the homoclinic snaking curves that arises due to the nonlocal term.Comment: 28 pages, 14 figures. To appear in Physica
On the thermodynamics of the SwiftâHohenberg theory
We present the microbalance including the microforces, the first- and second-order microstresses for the SwiftâHohenberg equation concomitantly with their constitutive equations, which are consistent with the free-energy imbalance. We provide an explicit form for the microstress structure for a free-energy functional endowed with second-order spatial derivatives. Additionally, we generalize the SwiftâHohenberg theory via a proper constitutive process. Finally, we present one highly resolved three-dimensional numerical simulation to demonstrate the particular form of the resulting microstresses and their interactions in the evolution of the SwiftâHohenberg equation
Grain boundary dynamics in stripe phases of non potential systems
We describe numerical solutions of two non potential models of pattern
formation in nonequilibrium systems to address the motion and decay of grain
boundaries separating domains of stripe configurations of different
orientations. We first address wavenumber selection because of the boundary,
and possible decay modes when the periodicity of the stripe phases is different
from the selected wavenumber for a stationary boundary. We discuss several
decay modes including long wavelength undulations of the moving boundary as
well as the formation of localized defects and their subsequent motion. We find
three different regimes as a function of the distance to the stripe phase
threshold and initial wavenumber, and then correlate these findings with domain
morphology during domain coarsening in a large aspect ratio configuration.Comment: 8 pages, 8 figure
Pattern stabilization through parameter alternation in a nonlinear optical system
We report the first experimental realization of pattern formation in a
spatially extended nonlinear system when the system is alternated between two
states, neither of which exhibits patterning. Dynamical equations modeling the
system are used for both numerical simulations and a weakly nonlinear analysis
of the patterned states. The simulations show excellent agreement with the
experiment. The nonlinear analysis provides an explanation of the patterning
under alternation and accurately predicts both the observed dependence of the
patterning on the frequency of alternation, and the measured spatial
frequencies of the patterns.Comment: 12 pages, 5 figures. To appear in PR
Intrinsic-Density Functionals
The Hohenberg-Kohn theorem and Kohn-Sham procedure are extended to
functionals of the localized intrinsic density of a self-bound system such as a
nucleus. After defining the intrinsic-density functional, we modify the usual
Kohn-Sham procedure slightly to evaluate the mean-field approximation to the
functional, and carefully describe the construction of the leading corrections
for a system of fermions in one dimension with a spin-degeneracy equal to the
number of particles N. Despite the fact that the corrections are complicated
and nonlocal, we are able to construct a local Skyrme-like intrinsic-density
functional that, while different from the exact functional, shares with it a
minimum value equal to the exact ground-state energy at the exact ground-state
intrinsic density, to next-to-leading order in 1/N. We briefly discuss
implications for real Skyrme functionals.Comment: 15 page
Time-Dependent Density-Functional Theory for Superfluids
A density-functional theory is established for inhomogeneous superfluids at
finite temperature, subject to time-dependent external fields in isothermal
conditions. After outlining parallelisms between a neutral superfluid and a
charged superconductor, Hohenberg-Kohn-Sham-type theorems are proved for
gauge-invariant densities and a set of Bogolubov-Popov equations including
exchange and correlation is set up. Earlier results applying in the linear
response regime are recovered.Comment: 12 pages. Europhysics Letters, in pres
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