13,276 research outputs found
Steady free-surface flow over spatially periodic topography
Two-dimensional free-surface flow over a spatially periodic channel bed topography is examined using a steady periodically forced Korteweg-de Vries equation. The existence of new forced solitary-type waves with periodic tails is demonstrated using recently developed non-autonomous dynamical-systems theory. Bound states with two or more co-existing solitary waves are also identified. The solution space for varying amplitude of forcing is explored using a numerical method. A rich bifurcation structure is uncovered and shown to be consistent with an asymptotic theory based on small forcing amplitude..J. Binder, M.G. Blyth and S. Balasuriy
Kinetics of Phase Separation in Thin Films: Simulations for the Diffusive Case
We study the diffusion-driven kinetics of phase separation of a symmetric
binary mixture (AB), confined in a thin-film geometry between two parallel
walls. We consider cases where (a) both walls preferentially attract the same
component (A), and (b) one wall attracts A and the other wall attracts B (with
the same strength). We focus on the interplay of phase separation and wetting
at the walls, which is referred to as {\it surface-directed spinodal
decomposition} (SDSD). The formation of SDSD waves at the two surfaces, with
wave-vectors oriented perpendicular to them, often results in a metastable
layered state (also referred to as ``stratified morphology''). This state is
reminiscent of the situation where the thin film is still in the one-phase
region but the surfaces are completely wet, and hence coated with thick wetting
layers. This metastable state decays by spinodal fluctuations and crosses over
to an asymptotic growth regime characterized by the lateral coarsening of
pancake-like domains. These pancakes may or may not be coated by precursors of
wetting layers. We use Langevin simulations to study this crossover and the
growth kinetics in the asymptotic coarsening regime.Comment: 39 pages, 19 figures, submitted to Phys.Rev.
Electron-spin beat susceptibility of excitons in semiconductor quantum wells
Recent time-resolved differential transmission and Faraday rotation
measurements of long-lived electron spin coherence in quantum wells displayed
intriguing parametric dependencies. For their understanding we formulate a
microscopic theory of the optical response of a gas of optically incoherent
excitons whose constituent electrons retain spin coherence, under a weak
magnetic field applied in the quantum well's plane. We define a spin beat
susceptibility and evaluate it in linear order of the exciton density. Our
results explain the many-body physics underlying the basic features observed in
the experimental measurements
Spinodal Decomposition in Thin Films: Molecular Dynamics Simulations of a Binary Lennard-Jones Fluid Mixture
We use molecular dynamics (MD) to simulate an unstable homogeneous mixture of
binary fluids (AB), confined in a slit pore of width . The pore walls are
assumed to be flat and structureless, and attract one component of the mixture
(A) with the same strength. The pair-wise interactions between the particles is
modeled by the Lennard-Jones potential, with symmetric parameters that lead to
a miscibility gap in the bulk. In the thin-film geometry, an interesting
interplay occurs between surface enrichment and phase separation.
We study the evolution of a mixture with equal amounts of A and B, which is
rendered unstable by a temperature quench. We find that A-rich surface
enrichment layers form quickly during the early stages of the evolution,
causing a depletion of A in the inner regions of the film. These
surface-directed concentration profiles propagate from the walls towards the
center of the film, resulting in a transient layered structure. This layered
state breaks up into a columnar state, which is characterized by the lateral
coarsening of cylindrical domains. The qualitative features of this process
resemble results from previous studies of diffusive Ginzburg-Landau-type models
[S.~K. Das, S. Puri, J. Horbach, and K. Binder, Phys. Rev. E {\bf 72}, 061603
(2005)], but quantitative aspects differ markedly. The relation to spinodal
decomposition in a strictly 2- geometry is also discussed.Comment: 37 pages, 11 figures, to appear in Phys. Rev.
Multiple time scales hidden in heterogeneous dynamics of glass-forming liquids
A multi-time probing of density fluctuations is introduced to investigate
hidden time scales of heterogeneous dynamics in glass-forming liquids.
Molecular dynamics simulations for simple glass-forming liquids are performed,
and a three-time correlation function is numerically calculated for general
time intervals. It is demonstrated that the three-time correlation function is
sensitive to the heterogeneous dynamics and that it reveals couplings of
correlated motions over a wide range of time scales. Furthermore, the time
scale of the heterogeneous dynamics is determined by the
change in the second time interval in the three-time correlation function. The
present results show that the time scale of the heterogeneous dynamics
becomes larger than the -relaxation time at low
temperatures and large wavelengths. We also find a dynamical scaling relation
between the time scale and the length scale of
dynamical heterogeneity as with .Comment: 4 pages, 5 figures, to appear in Phys. Rev. E (Rapid Communications
Star Polymers Confined in a Nanoslit: A Simulation Test of Scaling and Self-Consistent Field Theories
The free energy cost of confining a star polymer where flexible polymer
chains containing monomeric units are tethered to a central unit in a slit
with two parallel repulsive walls a distance apart is considered, for good
solvent conditions. Also the parallel and perpendicular components of the
gyration radius of the star polymer, and the monomer density profile across the
slit are obtained. Theoretical descriptions via Flory theory and scaling
treatments are outlined, and compared to numerical self-consistent field
calculations (applying the Scheutjens-Fleer lattice theory) and to Molecular
Dynamics results for a bead-spring model. It is shown that Flory theory and
self-consistent field (SCF) theory yield the correct scaling of the parallel
linear dimension of the star with , and , but cannot be used for
estimating the free energy cost reliably. We demonstrate that the same problem
occurs already for the confinement of chains in cylindrical tubes. We also
briefly discuss the problem of a free or grafted star polymer interacting with
a single wall, and show that the dependence of confining force on the
functionality of the star is different for a star confined in a nanoslit and a
star interacting with a single wall, which is due to the absence of a symmetry
plane in the latter case.Comment: 15 pages, 9 figures, LaTeX, to appear in Soft Matte
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