63 research outputs found
Free Energies of Isolated 5- and 7-fold Disclinations in Hexatic Membranes
We examine the shapes and energies of 5- and 7-fold disclinations in
low-temperature hexatic membranes. These defects buckle at different values of
the ratio of the bending rigidity, , to the hexatic stiffness constant,
, suggesting {\em two} distinct Kosterlitz-Thouless defect proliferation
temperatures. Seven-fold disclinations are studied in detail numerically for
arbitrary . We argue that thermal fluctuations always drive
into an ``unbuckled'' regime at long wavelengths, so that
disclinations should, in fact, proliferate at the {\em same} critical
temperature. We show analytically that both types of defects have power law
shapes with continuously variable exponents in the ``unbuckled'' regime.
Thermal fluctuations then lock in specific power laws at long wavelengths,
which we calculate for 5- and 7-fold defects at low temperatures.Comment: LaTeX format. 17 pages. To appear in Phys. Rev.
Statistics and geometry of cosmic voids
We introduce new statistical methods for the study of cosmic voids, focusing
on the statistics of largest size voids. We distinguish three different types
of distributions of voids, namely, Poisson-like, lognormal-like and Pareto-like
distributions. The last two distributions are connected with two types of
fractal geometry of the matter distribution. Scaling voids with Pareto
distribution appear in fractal distributions with box-counting dimension
smaller than three (its maximum value), whereas the lognormal void distribution
corresponds to multifractals with box-counting dimension equal to three.
Moreover, voids of the former type persist in the continuum limit, namely, as
the number density of observable objects grows, giving rise to lacunar
fractals, whereas voids of the latter type disappear in the continuum limit,
giving rise to non-lacunar (multi)fractals. We propose both lacunar and
non-lacunar multifractal models of the cosmic web structure of the Universe. A
non-lacunar multifractal model is supported by current galaxy surveys as well
as cosmological -body simulations. This model suggests, in particular, that
small dark matter halos and, arguably, faint galaxies are present in cosmic
voids.Comment: 39 pages, 8 EPS figures, supersedes arXiv:0802.038
Mutation, selection, and ancestry in branching models: a variational approach
We consider the evolution of populations under the joint action of mutation
and differential reproduction, or selection. The population is modelled as a
finite-type Markov branching process in continuous time, and the associated
genealogical tree is viewed both in the forward and the backward direction of
time. The stationary type distribution of the reversed process, the so-called
ancestral distribution, turns out as a key for the study of mutation-selection
balance. This balance can be expressed in the form of a variational principle
that quantifies the respective roles of reproduction and mutation for any
possible type distribution. It shows that the mean growth rate of the
population results from a competition for a maximal long-term growth rate, as
given by the difference between the current mean reproduction rate, and an
asymptotic decay rate related to the mutation process; this tradeoff is won by
the ancestral distribution.
Our main application is the quasispecies model of sequence evolution with
mutation coupled to reproduction but independent across sites, and a fitness
function that is invariant under permutation of sites. Here, the variational
principle is worked out in detail and yields a simple, explicit result.Comment: 45 pages,8 figure
Cylindrical quantum wires with hydrogen-bonded materials
Properties of cylindrical quantum wires are analysed in this paper. Energies
of elementary excitations as well as one-particle wave functions were found for
mentioned structure. For cylindrical quantum wires the temperature of phase
transition was found. The behaviour of electric susceptibility in paraelectric
phase was investigated.Comment: 10 page
Intrinsic structure and dynamics of the water/nitrobenzene interface
In this paper we present results of a detailed and systematic molecular dynamics study of the water/nitrobenzene interface. Using a simple procedure to eliminate fluctuations of the interface position, we are able to obtain true intrinsic profiles for several properties (density, hydrogen bonds, molecular orientation, etc.) in the direction perpendicular to the interfacial plane. Our results show that both water and organic inter-facial molecules form a tightly packed layer oriented parallel to the interface, with reduced mobility in the perpendicular direction. Beyond this layer, water quickly restores its bulk structure, while nitrobenzene exhibits structural anisotropies that extend further into the bulk region: Water molecules that protrude farthest into the organic phase point one hydrogen atom in the direction perpendicular to the interface, forming a hydrogen bond with a nitrobenzene oxygen. By fitting both the global and the intrinsic density profiles, we obtain estimates for the total and intrinsic interface widths, respectively. These are combined with capillary wave theory to produce a self-consistent method for the calculation of the inter-facial tension. Values calculated using this method are in very good agreement with direct calculations from the components of the pressure tensor
Dependence of Interfacial Tension on the Temperature and Concentration of Stearic Acid in a Waterân-Heptane System
Diffuse X-ray scattering near a two-dimensional solidâliquid phase transition at the n-hexaneâwater interface
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