1,024 research outputs found
Shape Fluctuations of a Droplet Containing a Polymer
We consider the problem of an ideal polymer confined in a droplet. When the
droplet radius is smaller than the (unconfined) polymer radius of gyration, the
polymer entropy will depend on the droplet shape. We compute the resulting
surface free energy. Using parameters appropriate for polymers confined in
microemulsions, we find that the polymer and bending surface energies are
comparable for the lowest modes. Finally, we argue that chain self-avoidance
will decrease the strength of the polymer contribution to the surface energy.Comment: Revtex, 12 pages, one figur
Fluctuation-Induced Interactions between Rods on Membranes and Interfaces
We consider the interaction between two rods embedded in a fluctuating
surface which is governed by either surface tension or rigidity. The
modification of fluctuations by the rods leads to an attractive long-range
interaction that falls off as with their separation. The orientational
dependence of the resulting interaction is non-trivial and may lead to
interesting patterns of rod-like objects on such surfaces.Comment: Revtex, 10 pages, one figur
The Conformal Properties of Liouville Field Theory on Z_N-Riemann Surfaces
The Liouville field theory on Z_N-Riemann surfaces is studied and it is shown
that it decomposes into a Liouville field theory on the sphere and N-1 free
boson theories. Also, the partition function of the Liouville field theory on
the Z_N-Riemann surfaces is expressed as a product of the correlation function
for the Liouville vertex operators on the sphere and a number of twisted
fields.Comment: Version to appear in Phys. Lett. B; LaTeX file, 8 pages, no figure
Duality in Quantum Liouville Theory
The quantisation of the two-dimensional Liouville field theory is
investigated using the path integral, on the sphere, in the large radius limit.
The general form of the -point functions of vertex operators is found and
the three-point function is derived explicitly. In previous work it was
inferred that the three-point function should possess a two-dimensional lattice
of poles in the parameter space (as opposed to a one-dimensional lattice one
would expect from the standard Liouville potential). Here we argue that the
two-dimensionality of the lattice has its origin in the duality of the quantum
mechanical Liouville states and we incorporate this duality into the path
integral by using a two-exponential potential. Contrary to what one might
expect, this does not violate conformal invariance; and has the great advantage
of producing the two-dimensional lattice in a natural way.Comment: Plain TeX File; 36 page
Budding and vesiculation induced by conical membrane inclusions
Conical inclusions in a lipid bilayer generate an overall spontaneous
curvature of the membrane that depends on concentration and geometry of the
inclusions. Examples are integral and attached membrane proteins, viruses, and
lipid domains. We propose an analytical model to study budding and vesiculation
of the lipid bilayer membrane, which is based on the membrane bending energy
and the translational entropy of the inclusions. If the inclusions are placed
on a membrane with similar curvature radius, their repulsive membrane-mediated
interaction is screened. Therefore, for high inclusion density the inclusions
aggregate, induce bud formation, and finally vesiculation. Already with the
bending energy alone our model allows the prediction of bud radii. However, in
case the inclusions induce a single large vesicle to split into two smaller
vesicles, bending energy alone predicts that the smaller vesicles have
different sizes whereas the translational entropy favors the formation of
equal-sized vesicles. Our results agree well with those of recent computer
simulations.Comment: 11 pages, 12 figure
On the Liouville coupling constants
For the general operator product algebra coefficients derived by Cremmer
Roussel Schnittger and the present author with (positive integer) screening
numbers, the coupling constants determine the factors additional to the quantum
group 6j symbols.
They are given by path independent products over a two dimensional lattice in
the zero mode space. It is shown that the ansatz for the three point function
of Dorn-Otto and Zamolodchikov-Zamolodchikov precisely defines the
corresponding flat lattice connection, so that it does give a natural
generalization of these coupling constants to continuous screening numbers. The
consistency of the restriction to integer screening charges is reviewed, and
shown to be linked with the orthogonality of the (generalized) 6j symbols. Thus
extending this last relation is the key to general screening numbers.Comment: Final version to be published in Phys. Lett.
Numerical simulation of the stochastic dynamics of inclusions in biomembranes in presence of surface tension
The stochastic dynamics of inclusions in a randomly fluctuating biomembrane
is simulated. These inclusions can represent the embedded proteins and the
external particles arriving at a cell membrane. The energetics of the
biomembrane is modelled via the Canham-Helfrich Hamiltonian. The contributions
of both the bending elastic-curvature energy and the surface tension of the
biomembrane are taken into account. The biomembrane is treated as a
two-dimensional sheet whose height variations from a reference frame is treated
as a stochastic Wiener process. The lateral diffusion parameter associated with
this Wiener process coupled with the longitudinal diffusion parameter obtained
from the standard Einsteinian diffusion theory completely determine the
stochastic motion of the inclusions. It is shown that the presence of surface
tension significantly affects the overall dynamics of the inclusions,
particularly the rate of capture of the external inclusions, such as drug
particles, at the site of the embedded inclusions, such as the embedded
proteins.Comment: 17 pages, 4 figures, to appear in physica
Attaching Translations to Proper Lexical Senses in DBnary
International audienceThe DBnary project aims at providing high quality Lexical Linked Data extracted from different Wiktionary language editions. Data from 10 different languages is currently extracted for a total of over 3.16M translation links that connect lexical entries from the 10 extracted languages, to entries in more than one thousand languages. In Wiktionary, glosses are often associated with translations to help users understand to what sense they refer to, whether through a textual definition or a target sense number. In this article we aim at the extraction of as much of this information as possible and then the disambiguation of the corresponding translations for all languages available. We use an adaptation of various textual and semantic similarity techniques based on partial or fuzzy gloss overlaps to disambiguate the translation relations (To account for the lack of normalization, e.g. lemmatization and PoS tagging) and then extract some of the sense number information present to build a gold standard so as to evaluate our disambiguation as well as tune and optimize the parameters of the similarity measures. We obtain F-measures of the order of 80\% (on par with similar work on English only), across the three languages where we could generate a gold standard (French, Portuguese, Finnish) and show that most of the disambiguation errors are due to inconsistencies in Wiktionary itself that cannot be detected at the generation of DBnary (shifted sense numbers, inconsistent glosses, etc.)
Liouville theory without an action
We show that the crossing symmetry of the four-point function in the
Liouville conformal field theory on the sphere contains more information than
what was hitherto considered. Under certain assumptions, it provides the
special structure constants that were previously computed perturbatively and
allows to solve the theory without using the Liouville interaction.Comment: 9 page
- …