39,079 research outputs found
Critical Casimir forces and adsorption profiles in the presence of a chemically structured substrate
Motivated by recent experiments with confined binary liquid mixtures near
demixing, we study the universal critical properties of a system, which belongs
to the Ising universality class, in the film geometry. We employ periodic
boundary conditions in the two lateral directions and fixed boundary conditions
on the two confining surfaces, such that one of them has a spatially
homogeneous adsorption preference while the other one exhibits a laterally
alternating adsorption preference, resembling locally a single chemical step.
By means of Monte Carlo simulations of an improved Hamiltonian, so that the
leading scaling corrections are suppressed, numerical integration, and
finite-size scaling analysis we determine the critical Casimir force and its
universal scaling function for various values of the aspect ratio of the film.
In the limit of a vanishing aspect ratio the critical Casimir force of this
system reduces to the mean value of the critical Casimir force for laterally
homogeneous ++ and +- boundary conditions, corresponding to the surface spins
on the two surfaces being fixed to equal and opposite values, respectively. We
show that the universal scaling function of the critical Casimir force for
small but finite aspect ratios displays a linear dependence on the aspect ratio
which is solely due to the presence of the lateral inhomogeneity. We also
analyze the order-parameter profiles at criticality and their universal scaling
function which allows us to probe theoretical predictions and to compare with
experimental data.Comment: revised version, section 5.2 expanded; 53 pages, 12 figures, iopart
clas
The linear tearing instability in three dimensional, toroidal gyrokinetic simulations
Linear gyro-kinetic simulations of the classical tearing mode in
three-dimensional toroidal geometry were performed using the global gyro
kinetic turbulence code, GKW . The results were benchmarked against a
cylindrical ideal MHD and analytical theory calculations. The stability, growth
rate and frequency of the mode were investigated by varying the current
profile, collisionality and the pressure gradients. Both collision-less and
semi-collisional tearing modes were found with a smooth transition between the
two. A residual, finite, rotation frequency of the mode even in the absense of
a pressure gradient is observed which is attributed to toroidal finite
Larmor-radius effects. When a pressure gradient is present at low
collisionality, the mode rotates at the expected electron diamagnetic
frequency. However the island rotation reverses direction at high
collisionality. The growth rate is found to follow a scaling with
collisional resistivity in the semi-collisional regime, closely following the
semi-collisional scaling found by Fitzpatrick. The stability of the mode
closely follows the stability using resistive MHD theory, however a
modification due to toroidal coupling and pressure effects is seen
The Constraints in Spherically Symmetric General Relativity II --- Identifying the Configuration Space: A Moment of Time Symmetry
We continue our investigation of the configuration space of general
relativity begun in I (gr-qc/9411009). Here we examine the Hamiltonian
constraint when the spatial geometry is momentarily static (MS). We show that
MS configurations satisfy both the positive quasi-local mass (QLM) theorem and
its converse. We derive an analytical expression for the spatial metric in the
neighborhood of a generic singularity. The corresponding curvature singularity
shows up in the traceless component of the Ricci tensor. We show that if the
energy density of matter is monotonically decreasing, the geometry cannot be
singular. A supermetric on the configuration space which distinguishes between
singular geometries and non-singular ones is constructed explicitly. Global
necessary and sufficient criteria for the formation of trapped surfaces and
singularities are framed in terms of inequalities which relate appropriate
measures of the material energy content on a given support to a measure of its
volume. The strength of these inequalities is gauged by exploiting the exactly
solvable piece-wise constant density star as a template.Comment: 50 pages, Plain Tex, 1 figure available from the authors
Exact Solutions for the Intrinsic Geometry of Black Hole Coalescence
We describe the null geometry of a multiple black hole event horizon in terms
of a conformal rescaling of a flat space null hypersurface. For the prolate
spheroidal case, we show that the method reproduces the pair-of-pants shaped
horizon found in the numerical simulation of the head-on-collision of black
holes. For the oblate case, it reproduces the initially toroidal event horizon
found in the numerical simulation of collapse of a rotating cluster. The
analytic nature of the approach makes further conclusions possible, such as a
bearing on the hoop conjecture. From a time reversed point of view, the
approach yields a description of the past event horizon of a fissioning white
hole, which can be used as null data for the characteristic evolution of the
exterior space-time.Comment: 21 pages, 6 figures, revtex, to appear in Phys. Rev.
Critical Casimir Forces in Colloidal Suspensions
Some time ago, Fisher and de Gennes pointed out that long-ranged correlations
in a fluid close to its critical point Tc cause distinct forces between
immersed colloidal particles which can even lead to flocculation [C. R. Acad.
Sc. Paris B 287, 207 (1978)]. Here we calculate such forces between pairs of
spherical particles as function of both relevant thermodynamic variables, i.e.,
the reduced temperature t = (T-Tc)/Tc and the field h conjugate to the order
parameter. This provides the basis for specific predictions concerning the
phase behavior of a suspension of colloidal particles in a near-critical
solvent.Comment: 29 pages, 14 figure
Casimir Forces between Spherical Particles in a Critical Fluid and Conformal Invariance
Mesoscopic particles immersed in a critical fluid experience long-range
Casimir forces due to critical fluctuations. Using field theoretical methods,
we investigate the Casimir interaction between two spherical particles and
between a single particle and a planar boundary of the fluid. We exploit the
conformal symmetry at the critical point to map both cases onto a highly
symmetric geometry where the fluid is bounded by two concentric spheres with
radii R_- and R_+. In this geometry the singular part of the free energy F only
depends upon the ratio R_-/R_+, and the stress tensor, which we use to
calculate F, has a particularly simple form. Different boundary conditions
(surface universality classes) are considered, which either break or preserve
the order-parameter symmetry. We also consider profiles of thermodynamic
densities in the presence of two spheres. Explicit results are presented for an
ordinary critical point to leading order in epsilon=4-d and, in the case of
preserved symmetry, for the Gaussian model in arbitrary spatial dimension d.
Fundamental short-distance properties, such as profile behavior near a surface
or the behavior if a sphere has a `small' radius, are discussed and verified.
The relevance for colloidal solutions is pointed out.Comment: 37 pages, 2 postscript figures, REVTEX 3.0, published in Phys. Rev. B
51, 13717 (1995
Sparse approximations of protein structure from noisy random projections
Single-particle electron microscopy is a modern technique that biophysicists
employ to learn the structure of proteins. It yields data that consist of noisy
random projections of the protein structure in random directions, with the
added complication that the projection angles cannot be observed. In order to
reconstruct a three-dimensional model, the projection directions need to be
estimated by use of an ad-hoc starting estimate of the unknown particle. In
this paper we propose a methodology that does not rely on knowledge of the
projection angles, to construct an objective data-dependent low-resolution
approximation of the unknown structure that can serve as such a starting
estimate. The approach assumes that the protein admits a suitable sparse
representation, and employs discrete -regularization (LASSO) as well as
notions from shape theory to tackle the peculiar challenges involved in the
associated inverse problem. We illustrate the approach by application to the
reconstruction of an E. coli protein component called the Klenow fragment.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS479 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Linear stability analysis of an insoluble surfactant monolayer spreading on a thin liquid film
Recent experiments by several groups have uncovered a novel fingering instability in the spreading of surface active material on a thin liquid film. The mechanism responsible for this instability is yet to be determined. In an effort to understand this phenomenon and isolate a possible mechanism, we have investigated the linear stability of a coupled set of equations describing the Marangoni spreading of a surfactant monolayer on a thin liquid support. The unperturbed flows, which exhibit simple linear behavior in the film thickness and surfactant concentration, are self-similar solutions of the first kind for spreading in a rectilinear geometry. The solution of the disturbance equations determines that the rectilinear base flows are linearly stable. An energy analysis reveals why these base flows can successfully heal perturbations of all wavenumbers. The details of this analysis suggest, however, a mechanism by which the spreading can be destabilized. We propose how the inclusion of additional forces acting on the surfactant coated spreading film might give rise to regions of adverse mobility gradients known to produce fingering instabilities in other fluid flows
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