2,230 research outputs found
Non-analytic curvature contributions to solvation free energies: influence of drying
We investigate the solvation of a hard spherical cavity, of radius ,
immersed in a fluid for which the interparticle forces are short ranged. For
thermodynamic states lying close to the liquid binodal, where the chemical
potential deviation is very small and
positive, complete wetting by gas (drying) occurs and two regimes of
interfacial behavior can be identified. These are characterized by the length
scale , where
is the planar gas-liquid surface tension and
is the difference in coexisting densities at temperature . For , the
interfacial free energy and the density profile of the fluid near the hard wall
can be expanded in powers of the curvature , in keeping with the
analysis of Stillinger and Cotter, J. Chem. Phys. {\bf 55}, 3449 (1971). In the
other regime, , the interfacial free energy and its derivatives acquire
terms depending on . Since can be made arbitrarily small this
implies non-analytic behavior, as , of the work of formation of a
hard spherical cavity and of the Gibbs adsorption and the fluid density at
contact with the wall. Our analysis, which is based on an effective interfacial
Hamiltonian combined with exact statistical mechanical sum rules, is confirmed
fully by the results of microscopic density functional calculations for a
square-well fluid.Comment: 17 pages, 3 figures; accepted for publication in J. Chem. Phy
Reduced Persistence Length and Fluctuation-Induced Interactions of Directed Semiflexible Polymers on Fluctuating surfaces
We consider directed semiflexible polymers embedded in a fluctuating surface
which is governed by either surface tension or bending rigidity. The attractive
interactions induced by the fluctuations of the surface reduce the rigidity of
the polymers. In particular, it is shown that for arbitrarily stiff parallel
polymers, there is a characteristic separation below which they prefer to bend
rather than stay linear. The out-of plane fluctuations of the polymer, screen
out the long-range fluctuation-induced forces, resulting in only a short-ranged
effective attraction.Comment: REVTEX, one postscript figur
The unbinding transition of mixed fluid membranes
A phenomenological model for the unbinding transition of multi-component
fluid membranes is proposed, where the unbinding transition is described using
a theory analogous to Flory-Huggins theory for polymers. The coupling between
the lateral phase separation of inclusion molecules and the membrane-substrate
distance explains the phase coexistence between two unbound phases as observed
in recent experiments by Marx et al. [Phys. Rev. Lett. 88, 138102 (2002)].
Bellow a critical end-point temperature, we find that the unbinding transition
becomes first-order for multi-component membranes.Comment: 7 pages, 3 eps figure
Interaction of Conical Membrane Inclusions: Effect of Lateral Tension
Considering two rigid conical inclusions embedded in a membrane subject to
lateral tension, we study the membrane-mediated interaction between these
inclusions that originates from the hat-shaped membrane deformations associated
with the cones. At non-vanishing lateral tensions, the interaction is found to
depend on the orientation of the cones with respect to the membrane plane. The
interaction of inclusions of equal orientation is repulsive at all distances
between them, while the inclusions of opposite orientation repel each other at
small separations, but attract each other at larger ones. Both the repulsive
and attractive forces become stronger with increasing lateral tension. This is
different from what has been predicted on the basis of the same static model
for the case of vanishing lateral tension. Without tension, the inclusions
repel each other at all distances independently of their relative orientation.
We conclude that lateral tension may induce the aggregation of conical membrane
inclusions.Comment: 10 pages (revtech), 5 figures (postscript
Optimal transient growth in thin-interface internal solitary waves
The dynamics of perturbations to large-amplitude Internal Solitary Waves
(ISW) in two-layered flows with thin interfaces is analyzed by means of linear
optimal transient growth methods. Optimal perturbations are computed through
direct-adjoint iterations of the Navier-Stokes equations linearized around
inviscid, steady ISWs obtained from the Dubreil-Jacotin-Long (DJL) equation.
Optimal perturbations are found as a function of the ISW phase velocity
(alternatively amplitude) for one representative stratification. These
disturbances are found to be localized wave-like packets that originate just
upstream of the ISW self-induced zone (for large enough ) of potentially
unstable Richardson number, . They propagate through the base wave
as coherent packets whose total energy gain increases rapidly with . The
optimal disturbances are also shown to be relevant to DJL solitary waves that
have been modified by viscosity representative of laboratory experiments. The
optimal disturbances are compared to the local WKB approximation for spatially
growing Kelvin-Helmholtz (K-H) waves through the zone. The WKB
approach is able to capture properties (e.g., carrier frequency, wavenumber and
energy gain) of the optimal disturbances except for an initial phase of
non-normal growth due to the Orr mechanism. The non-normal growth can be a
substantial portion of the total gain, especially for ISWs that are weakly
unstable to K-H waves. The linear evolution of Gaussian packets of linear free
waves with the same carrier frequency as the optimal disturbances is shown to
result in less energy gain than found for either the optimal perturbations or
the WKB approximation due to non-normal effects that cause absorption of
disturbance energy into the leading face of the wave.Comment: 33 pages, 22 figure
Solvent free model for self-assembling fluid bilayer membranes: Stabilization of the fluid phase based on broad attractive tail potentials
We present a simple and highly adaptable method for simulating coarse-grained
lipid membranes without explicit solvent. Lipids are represented by one
head-bead and two tail-beads, with the interaction between tails being of key
importance in stabilizing the fluid phase. Two such tail-tail potentials were
tested, with the important feature in both cases being a variable range of
attraction. We examined phase diagrams of this range versus temperature for
both functional forms of the tail-tail attraction and found that a certain
threshold attractive width was required to stabilize the fluid phase. Within
the fluid phase region we find that material properties such as area per lipid,
orientational order, diffusion constant, inter-leaflet flip-flop rate and
bilayer stiffness all depend strongly and monotonically on the attractive
width. For three particular values of the potential width we investigate the
transition between gel and fluid phases via heating or cooling and find that
this transition is discontinuous with considerable hysteresis. We also
investigated the stretching of a bilayer to eventually form a pore and found
excellent agreement with a recently published analytic theory.Comment: 14 pages 12 figure
Continuously stratified nonlinear low-mode internal tides
Author Posting. © Sears Foundation for Marine Research, 2008. This article is posted here by permission of Sears Foundation for Marine Research for personal use, not for redistribution. The definitive version was published in Journal of Marine Research 66 (2008): 299-323, doi:10.1357/002224008786176025.A model for hydrostatic, fully nonlinear, low-mode internal tides is extended to continuously stratified conditions. Periodic inertia-gravity solutions of permanent form are shown to exist only for a limited range of amplitudes for a given stratification and frequency. As found in an earlier two-layer model, the solutions fall into two classes. In one, the waves take on a corner-shape as the limiting amplitude is approached. In the other, the waves remain continuous at the limiting amplitude, but have a lobate shape. Numerical investigation using the Euler equations shows that both classes of nonlinear solutions are robust to weak nonhydrostatic effects representative of oceanic conditions. The numerical solutions are also used to explore the evolution of an initial sinusoidal internal tide. It is demonstrated that the presence of the nonlinear solutions may limit the disintegration of the initial tide into shorter solitary-like waves. The nonlinear tide solutions and the disintegration process are briefly explored for conditions of the northeastern South China Sea where large internal tides and solitary waves are observed.This work was supported by ONR Grant N000140610798
Crumpling transition of the triangular lattice without open edges: effect of a modified folding rule
Folding of the triangular lattice in a discrete three-dimensional space is
investigated by means of the transfer-matrix method. This model was introduced
by Bowick and co-workers as a discretized version of the polymerized membrane
in thermal equilibrium. The folding rule (constraint) is incompatible with the
periodic-boundary condition, and the simulation has been made under the
open-boundary condition. In this paper, we propose a modified constraint, which
is compatible with the periodic-boundary condition; technically, the
restoration of translational invariance leads to a substantial reduction of the
transfer-matrix size. Treating the cluster sizes L \le 7, we analyze the
singularities of the crumpling transitions for a wide range of the bending
rigidity K. We observe a series of the crumpling transitions at K=0.206(2),
-0.32(1), and -0.76(10). At each transition point, we estimate the latent heat
as Q=0.356(30), 0.08(3), and 0.05(5), respectively
Laboratory study of localized boundary mixing in a rotating stratified fluid
Author Posting. © Cambridge University Press, 2004. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 516 (2004): 83-113, doi:10.1017/S0022112004000473.Oceanic observations indicate that abyssal mixing tends to be localized to regions of rough topography. How localized mixing interacts with the ambient fluid in a stratified, rotating system is an open question. To gain insight into this complicated process laboratory experiments are used to explore the interaction of mechanically induced boundary mixing and an interior body of linearly stratified rotating fluid. Turbulence is generated by a single vertically oscillating horizontal bar of finite horizontal extent, located at mid-depth along the tank wall. The turbulence forms a region of mixed fluid which quickly reaches a steady-state height and collapses into the interior. The mixed-layer thickness, , is spatially uniform and independent of the Coriolis frequency . is the initial buoyancy frequency, is the bar oscillation frequency, and cm is an empirical constant determined by the bar geometry. Surprisingly, the export of mixed fluid does not occur as a boundary current along the tank perimeter. Rather, mixed fluid intrudes directly into the interior as a radial front of uniform height, advancing with a speed comparable to a gravity current. The volume of mixed fluid grows linearly with time, , and is independent of the lateral extent of the mixing bar. Entrainment into the turbulent zone occurs principally through horizontal flows at the level of the mixing that appear to eliminate export by a geostrophic boundary flow. The circulation patterns suggest a model of unmixed fluid laterally entrained at velocity into the open sides of a turbulent zone with height and a length, perpendicular to the boundary, proportional to . Here is an equilibrium length scale associated with rotational control of bar-generated turbulence. The model flux of exported mixed fluid is constant and in agreement with the experiments.This work was supported by the Ocean Ventures Fund, the Westcott Fund and
the WHOI Academic Programs Office. Financial support was also provided by the
National Science Foundation through grant OCE-9616949
Circulation around a thin zonal island
Author Posting. © Cambridge University Press, 2001. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 437 (2001): 301-323, doi:10.1017/S0022112001004402.Laboratory and numerical experiments are used to study flow of a uniform-density fluid on the [beta]-plane around a thin zonally elongated island (or ridge segment in the abyss). This orientation is chosen specifically to highlight the roles of the zonal boundary layer dynamics in controlling the circulation around the island. There are examples of deep ocean topography that fall into this category which make the work directly applicable to oceanic flows. Linear theory for the transport around the island and the flow structure is based on a modification of the Island Rule (Pedlosky et al. 1997; Pratt & Pedlosky 1999). The linear solution gives a north–south symmetric flow around the island with novel features, including stagnation points which divide the zonal boundary layers into eastward and westward flowing zones, and a western boundary layer of vanishing length, and zonal jets. Laboratory experiments agree with the linear theory for small degrees of nonlinearity, as measured by the ratio of the inertial to Munk boundary layer scales. With increasing nonlinearity the north–south symmetry is broken. The southern stagnation point (for anticyclonic forcing) moves to the eastern tip of the island. The flow rounding the eastern tip from the northern side of the island now separates from the island. Time-dependence emerges and recirculation cells develop on the northern side of the island. Mean transport around the island is relatively unaffected by nonlinearity and given to within 20% by the modified Island Rule. Numerical solutions of the shallow water equations are in close agreement with the laboratory results. The transition from zonal to meridional island orientation occurs for island inclinations from zonal greater than about 20°.This work was supported by the National Science Foundation
(Grant Number OCE96-16949)
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