1,832 research outputs found
Decrumpling membranes by quantum effects
The phase diagram of an incompressible fluid membrane subject to quantum and
thermal fluctuations is calculated exactly in a large number of dimensions of
configuration space. At zero temperature, a crumpling transition is found at a
critical bending rigidity . For membranes of fixed lateral
size, a crumpling transition occurs at nonzero temperatures in an auxiliary
mean field approximation. As the lateral size L of the membrane becomes large,
the flat regime shrinks with .Comment: 9 pages, 4 figure
Effect of Thermal Undulations on the Bending Elasticity and Spontaneous Curvature of Fluid Membranes
We amplify previous arguments why mean curvature should be used as measure of
integration in calculating the effective bending rigidity of fluid membranes
subjected to a weak background curvature. The stiffening of the membrane by its
fluctuations, recently derived for spherical shapes, is recovered for
cylindrical curvature. Employing curvilinear coordinates, we then discuss
stiffening for arbitrary shapes, confirm that the elastic modulus of Gaussian
curvature is not renormalized in the presence of fluctuations, and show for the
first time that any spontaneous curvature also remains unchanged.Comment: 26 pages, 2 figures, to appear in EPJ
Resonant three-body physics in two spatial dimensions
We discuss the three-body properties of identical bosons exhibiting large
scattering length in two spatial dimensions. Within an effective field theory
for resonant interactions, we calculate the leading non-universal corrections
from the two-body effective range to bound-state and scattering observables. In
particular, we compute the three-body binding energies, the boson-dimer
scattering properties, and the three-body recombination rate for finite
energies. We find significant effective range effects in the vicinity of the
unitary limit. The implications of this result for future experiments are
briefly discussed.Comment: 15 pages, 8 figures, published versio
Three-body problem in heteronuclear mixtures with resonant interspecies interaction
We use the zero-range approximation to study a system of two identical bosons
interacting resonantly with a third particle. The method is derived from
effective field theory. It reduces the three-body problem to an integral
equation which we then solve numerically. We also develop an alternative
approach which gives analytic solutions of the integral equation in coordinate
representation in the limit of vanishing total energy. The atom-dimer
scattering length, the rates of atom-dimer relaxation and three-body
recombination to shallow and to deep molecular states are calculated either
analytically or numerically with a well controlled accuracy for various
energies as functions of the mass ratio, scattering length, and three-body
parameter. We discuss in detail the relative positions of the recombination
loss peaks, which in the universal limit depend only on the mass ratio. Our
results have implications for ongoing and future experiments on Bose-Bose and
Bose-Fermi atomic mixtures.Comment: 13 pages, 8 figures, minor changes, published versio
A novel method for measuring the bending rigidity of model lipid membranes by simulating tethers
The tensile force along a cylindrical lipid bilayer tube is proportional to
the membrane's bending modulus and inversely proportional to the tube radius.
We show that this relation, which is experimentally exploited to measure
bending rigidities, can be applied with even greater ease in computer
simulations. Using a coarse-grained bilayer model we efficiently obtain bending
rigidities that compare very well with complementary measurements based on an
analysis of thermal undulation modes. We furthermore illustrate that no
deviations from simple quadratic continuum theory occur up to a radius of
curvature comparable to the bilayer thickness.Comment: 7 pages, 5 figures, 1 tabl
Quantum Statistical Mechanics of Nonrelativistic Membranes: Crumpling Transition at Finite Temperature
The effect of quantum fluctuations on a nearly flat, nonrelativistic
two-dimensional membrane with extrinsic curvature stiffness and tension is
investigated. The renormalization group analysis is carried out in first-order
perturbative theory. In contrast to thermal fluctuations, which soften the
membrane at large scales and turn it into a crumpled surface, quantum
fluctuations are found to {\em stiffen} the membrane, so that it exhibits a
Hausdorff dimension equal to two. The large-scale behavior of the membrane is
further studied at finite temperature, where a nontrivial fixed point is found,
signaling a crumpling transition.Comment: RevTex, 9 pages, 1 figur
Fluctuation induced interactions between domains in membranes
We study a model lipid bilayer composed of a mixture of two incompatible
lipid types which have a natural tendency to segregate in the absence of
membrane fluctuations. The membrane is mechanically characterized by a local
bending rigidity which varies with the average local lipid
composition . We show, in the case where varies weakly with
, that the effective interaction between lipids of the same type can
either be everywhere attractive or can have a repulsive component at
intermediate distances greater than the typical lipid size. When this
interaction has a repulsive component, it can prevent macro-phase separation
and lead to separation in mesophases with a finite domain size. This effect
could be relevant to certain experimental and numerical observations of
mesoscopic domains in such systems.Comment: 9 pages RevTex, 1 eps figur
Instability and Periodic Deformation in Bilayer Membranes Induced by Freezing
The instability and periodic deformation of bilayer membranes during freezing
processes are studied as a function of the difference of the shape energy
between the high and the low temperature membrane states. It is shown that
there exists a threshold stability condition, bellow which a planar
configuration will be deformed. Among the deformed shapes, the periodic curved
square textures are shown being one kind of the solutions of the associated
shape equation. In consistency with recent expe rimental observations, the
optimal ratio of period and amplitude for such a texture is found to be
approximately equal to (2)^{1/2}\pi.Comment: 8 pages in Latex form, 1 Postscript figure. To be appear in Mod.
Phys. Lett. B. 199
Dynamics of a thin liquid film with surface rigidity and spontaneous curvature
The effect of rigid surfaces on the dynamics of thin liquid films which are
amenable to the lubrication approximation is considered. It is shown that the
Helfrich energy of the layer gives rise to additional terms in the
time-evolution equations of the liquid film. The dynamics is found to depend on
the absolute value of the spontaneous curvature, irrespective of its sign. Due
to the additional terms, a novel finite wavelength instability of flat rigid
interfaces can be observed. Furthermore, the dependence of the shape of a
droplet on the bending rigidity as well as on the spontaneous curvature is
discussed.Comment: 4 pages, 5 figure
Internal solitary wave generation by tidal flow over topography
Author Posting. © The Author(s), 2017. This is the author's version of the work. It is posted here under a nonexclusive, irrevocable, paid-up, worldwide license granted to WHOI. It is made available for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 839 (2018): 387-407, doi:10.1017/jfm.2018.21.Oceanic internal solitary waves are typically generated by barotropic tidal flow over localised topography. Wave generation can be characterised by the Froude number F = U/c(0), where U is the tidal flow amplitude and c(0) is the intrinsic linear long wave phase speed, that is the speed in the absence of the tidal current. For steady tidal flow in the resonant regime, Delta(m) Delta(M) the tidal flow goes through the resonant regime twice, producing undular bores with each passage. The numerical simulations are for both symmetrical topography, and for asymmetric topography representative of Stellwagen Bank and Knight Inlet.RG was supported by the Leverhulme Trust through the award of a Leverhulme Emeritus
Fellowship. KH was supported by grant N00014-11-1-0701 from the Office of Naval
Research
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