8,741 research outputs found
Droplet Fluctuations in the Morphology and Kinetics of Martensites
We derive a coarse grained, free-energy functional which describes droplet
configurations arising on nucleation of a product crystal within a parent. This
involves a new `slow' vacancy mode that lives at the parent-product interface.
A mode-coupling theory suggests that a {\it slow} quench from the parent phase
produces an equilibrium product, while a {\it fast} quench produces a
metastable martensite. In two dimensions, the martensite nuclei grow as
`lens-shaped' strips having alternating twin domains, with well-defined front
velocities. Several empirically known structural and kinetic relations drop out
naturally from our theory.Comment: 4 pages, REVTEX, and 3 .eps figures, compressed and uuencoded,
Submitted to Phys. Rev. Let
Kinematics of Multigrid Monte Carlo
We study the kinematics of multigrid Monte Carlo algorithms by means of
acceptance rates for nonlocal Metropolis update proposals. An approximation
formula for acceptance rates is derived. We present a comparison of different
coarse-to-fine interpolation schemes in free field theory, where the formula is
exact. The predictions of the approximation formula for several interacting
models are well confirmed by Monte Carlo simulations. The following rule is
found: For a critical model with fundamental Hamiltonian H(phi), absence of
critical slowing down can only be expected if the expansion of
in terms of the shift psi contains no relevant (mass) term. We also introduce a
multigrid update procedure for nonabelian lattice gauge theory and study the
acceptance rates for gauge group SU(2) in four dimensions.Comment: 28 pages, 8 ps-figures, DESY 92-09
Evaporation of Sessile Droplets on Slippery Liquid-Infused Porous Surfaces (SLIPS)
Over the past decade, the most common approach to creating liquid shedding surfaces has been to amplify the effects of nonwetting surface chemistry, using micro/nanotexturing to create superhydrophobic and superoleophobic surfaces. Recently, an alternative approach using impregnation of micro/nanotextured surfaces with immiscible lubricating liquids to create slippery liquid-infused porous surfaces (SLIPS) has been developed. These types of surfaces open up new opportunities to study the mechanism of evaporation of sessile droplets in zero contact angle hysteresis situations where the contact line is completely mobile. In this study, we fabricated surfaces consisting of square pillars (10–90 μm) of SU-8 photoresist arranged in square lattice patterns with the center-to-center separation between pillars of 100 μm, on which a hydrophobic coating was deposited and the textures impregnated by a lubricating silicone oil. These surfaces showed generally low sliding angles of 1° or less for small droplets of water. Droplet profiles were more complicated than on nonimpregnated surfaces and displayed a spherical cap shape modified by a wetting ridge close to the contact line due to balancing the interfacial forces at the line of contact between the droplet, the lubricant liquid and air (represented by a Neumann triangle). The wetting ridge leads to the concept of a wetting “skirt” of lubricant around the base of the droplet. For the SLIP surfaces, we found that the evaporation of small sessile droplets (∼2 mm in diameter) followed an ideal constant contact angle mode where the apparent contact angle was defined from the intersection of the substrate profile with the droplet spherical cap profile. A theoretical model based on diffusion controlled evaporation was able to predict a linear dependence in time for the square of the apparent contact radius. The experimental data was in excellent quantitative agreement with the theory and enabled estimates of the diffusion constant to be obtained
Proposal of an extended t-J Hamiltonian for high-Tc cuprates from ab initio calculations on embedded clusters
A series of accurate ab initio calculations on Cu_pO-q finite clusters,
properly embedded on the Madelung potential of the infinite lattice, have been
performed in order to determine the local effective interactions in the CuO_2
planes of La_{2-x}Sr_xCuO_4 compounds. The values of the first-neighbor
interactions, magnetic coupling (J_{NN}=125 meV) and hopping integral
(t_{NN}=-555 meV), have been confirmed. Important additional effects are
evidenced, concerning essentially the second-neighbor hopping integral
t_{NNN}=+110meV, the displacement of a singlet toward an adjacent colinear
hole, h_{SD}^{abc}=-80 meV, a non-negligible hole-hole repulsion
V_{NN}-V_{NNN}=0.8 eV and a strong anisotropic effect of the presence of an
adjacent hole on the values of the first-neighbor interactions. The dependence
of J_{NN} and t_{NN} on the position of neighbor hole(s) has been rationalized
from the two-band model and checked from a series of additional ab initio
calculations. An extended t-J model Hamiltonian has been proposed on the basis
of these results. It is argued that the here-proposed three-body effects may
play a role in the charge/spin separation observed in these compounds, that is,
in the formation and dynamic of stripes.Comment: 24 pages, 4 figures, submitted to Phys. Rev.
On small-noise equations with degenerate limiting system arising from volatility models
The one-dimensional SDE with non Lipschitz diffusion coefficient is widely
studied in mathematical finance. Several works have proposed asymptotic
analysis of densities and implied volatilities in models involving instances of
this equation, based on a careful implementation of saddle-point methods and
(essentially) the explicit knowledge of Fourier transforms. Recent research on
tail asymptotics for heat kernels [J-D. Deuschel, P.~Friz, A.~Jacquier, and
S.~Violante. Marginal density expansions for diffusions and stochastic
volatility, part II: Applications. 2013, arxiv:1305.6765] suggests to work with
the rescaled variable : while
allowing to turn a space asymptotic problem into a small- problem
with fixed terminal point, the process satisfies a SDE in
Wentzell--Freidlin form (i.e. with driving noise ). We prove a
pathwise large deviation principle for the process as
. As it will become clear, the limiting ODE governing the
large deviations admits infinitely many solutions, a non-standard situation in
the Wentzell--Freidlin theory. As for applications, the -scaling
allows to derive exact log-asymptotics for path functionals of the process:
while on the one hand the resulting formulae are confirmed by the CIR-CEV
benchmarks, on the other hand the large deviation approach (i) applies to
equations with a more general drift term and (ii) potentially opens the way to
heat kernel analysis for higher-dimensional diffusions involving such an SDE as
a component.Comment: 21 pages, 1 figur
Multigrid Monte Carlo Algorithms for SU(2) Lattice Gauge Theory: Two versus Four Dimensions
We study a multigrid method for nonabelian lattice gauge theory, the time
slice blocking, in two and four dimensions. For SU(2) gauge fields in two
dimensions, critical slowing down is almost completely eliminated by this
method. This result is in accordance with theoretical arguments based on the
analysis of the scale dependence of acceptance rates for nonlocal Metropolis
updates. The generalization of the time slice blocking to SU(2) in four
dimensions is investigated analytically and by numerical simulations. Compared
to two dimensions, the local disorder in the four dimensional gauge field leads
to kinematical problems.Comment: 24 pages, PostScript file (compressed and uuencoded), preprint
MS-TPI-94-
Sharp interface limits of phase-field models
The use of continuum phase-field models to describe the motion of
well-defined interfaces is discussed for a class of phenomena, that includes
order/disorder transitions, spinodal decomposition and Ostwald ripening,
dendritic growth, and the solidification of eutectic alloys. The projection
operator method is used to extract the ``sharp interface limit'' from phase
field models which have interfaces that are diffuse on a length scale . In
particular,phase-field equations are mapped onto sharp interface equations in
the limits and , where and are
respectively the interface curvature and velocity and is the diffusion
constant in the bulk. The calculations provide one general set of sharp
interface equations that incorporate the Gibbs-Thomson condition, the
Allen-Cahn equation and the Kardar-Parisi-Zhang equation.Comment: 17 pages, 9 figure
Frictional Coulomb drag in strong magnetic fields
A treatment of frictional Coulomb drag between two 2-dimensional electron
layers in a strong perpendicular magnetic field, within the independent
electron picture, is presented. Assuming fully resolved Landau levels, the
linear response theory expression for the transresistivity is
evaluated using diagrammatic techniques. The transresistivity is given by an
integral over energy and momentum transfer weighted by the product of the
screened interlayer interaction and the phase-space for scattering events. We
demonstrate, by a numerical analysis of the transresistivity, that for
well-resolved Landau levels the interplay between these two factors leads to
characteristic features in both the magnetic field- and the temperature
dependence of . Numerical results are compared with recent
experiments.Comment: RevTeX, 34 pages, 8 figures included in tex
Gas-Kinetic-Based Traffic Model Explaining Observed Hysteretic Phase Transition
Recently, hysteretic transitions to `synchronized traffic' with high values
of both density and traffic flow were observed on German freeways [B. S. Kerner
and H. Rehborn, Phys. Rev. Lett. 79, 4030 (1997)]. We propose a macroscopic
traffic model based on a gas-kinetic approach that can explain this phase
transition. The results suggest a general mechanism for the formation of
probably the most common form of congested traffic.Comment: With corrected formula (3). For related work see
http://www.theo2.physik.uni-stuttgart.de/helbing.htm
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