3,623 research outputs found
Casimir interaction of rod-like particles in a two-dimensional critical system
We consider the fluctuation-induced interaction of two thin, rod-like
particles or "needles" immersed in a two-dimensional critical fluid of Ising
symmetry right at the critical point. Conformally mapping the plane containing
the needles onto a simpler geometry in which the stress tensor is known, we
analyze the force and torque between needles of arbitrary length, separation,
and orientation. For infinite and semi-infinite needles we utilize the mapping
of the plane bounded by the needles onto the half plane, and for two needles of
finite length the mapping onto an annulus. For semi-infinite and infinite
needles the force is expressed in terms of elementary functions, and we also
obtain analytical results for the force and torque between needles of finite
length with separation much greater than their length. Evaluating formulas in
our approach numerically for several needle geometries and surface universality
classes, we study the full crossover from small to large values of the
separation to length ratio. In these two limits the numerical results agree
with results for infinitely long needles and with predictions of the
small-particle operator expansion, respectively.Comment: 68 pages, 9 figure
Partial survival and inelastic collapse for a randomly accelerated particle
We present an exact derivation of the survival probability of a randomly
accelerated particle subject to partial absorption at the origin. We determine
the persistence exponent and the amplitude associated to the decay of the
survival probability at large times. For the problem of inelastic reflection at
the origin, with coefficient of restitution , we give a new derivation of
the condition for inelastic collapse, , and determine
the persistence exponent exactly.Comment: 6 page
A nonperturbative Real-Space Renormalization Group scheme
Based on the original idea of the density matrix renormalization group
(DMRG), i.e. to include the missing boundary conditions between adjacent blocks
of the blocked quantum system, we present a rigorous and nonperturbative
mathematical formulation for the real-space renormalization group (RG) idea
invented by L.P. Kadanoff and further developed by K.G. Wilson. This is
achieved by using additional Hilbert spaces called auxiliary spaces in the
construction of each single isolated block, which is then named a superblock
according to the original nomenclature. On this superblock we define two maps
called embedding and truncation for successively integrating out the small
scale structure. Our method overcomes the known difficulties of the numerical
DMRG, i.e. limitation to zero temperature and one space dimension.Comment: 13 pages, 5 figures, late
Simulation of a semiflexible polymer in a narrow cylindrical pore
The probability that a randomly accelerated particle in two dimensions has
not yet left a simply connected domain after a time decays as
for long times. The same quantity also determines the
confinement free energy per unit length of a
semiflexible polymer in a narrow cylindrical pore with cross section . From simulations of a randomly accelerated particle we estimate the
universal amplitude of for both circular and rectangular cross
sections.Comment: 10 pages, 2 eps figure
Effects of pressure, oxygen concentration, and forced convection on flame spread rate of Plexiglas, Nylon and Teflon
Experiments were conducted in which the burning of cylindrical materials in a flowing oxidant stream was studied. Plexiglas, Nylon, and Teflon fuel specimens were oriented such that the flames spread along the surface in a direction opposed to flowing gas. Correlations of flame spread rate were obtained that were power law relations in terms of pressure, oxygen concentration, and gas velocity
Spatial Constraint Corrections to the Elasticity of dsDNA Measured with Magnetic Tweezers
In this paper, we have studied, within a discrete WLC model, the spatial
constraints in magnetic tweezers used in single molecule experiments. Two
elements are involved: first, the fixed plastic slab on which is stuck the
initial strand, second, the magnetic bead which pulls (or twists) the attached
molecule free end. We have shown that the bead surface can be replaced by its
tangent plane at the anchoring point, when it is close to the bead south pole
relative to the force. We are led to a model with two parallel repulsive
plates: the fixed anchoring plate and a fluctuating plate, simulating the bead,
in thermal equilibrium with the system. The bead effect is a slight upper shift
of the elongation, about four times smaller than the similar effect induced by
the fixed plate. This rather unexpected result, has been qualitatively
confirmed within the soluble Gaussian model. A study of the molecule elongation
versus the countour length exhibits a significant non-extensive behaviour. The
curve for short molecules (with less than 2 kbp) is well fitted by a straight
line, with a slope given by the WLC model, but it does not go through the
origin. The non-extensive offset gives a 15% upward shift to the elongation of
a 2 kbp molecule stretched by a 0.3 pN force.Comment: 28 pages, 6 figures An explanatory figure has been added. The
physical interpretation of the results has been made somewhat more
transparen
Pinning by a sparse potential
We consider a directed polymer interacting with a diluted pinning potential
restricted to a line. We characterize explicitely the set of disorder
configurations that give rise to localization of the polymer. We study both
relevant cases of dimension 1+1 and 1+2. We also discuss the case of massless
effective interface models in dimension 2+1.Comment: to appear in Stochastic Processes and their Application
Extraordinary transition in the two-dimensional O(n) model
The extraordinary transition which occurs in the two-dimensional O(n) model
for at sufficiently enhanced surface couplings is studied by conformal
perturbation theory about infinite coupling and by finite-size scaling of the
spectrum of the transfer matrix of a simple lattice model. Unlike the case of
in higher dimensions, the surface critical behaviour differs from that
occurring when fixed boundary conditions are imposed. In fact, all the surface
scaling dimensions are equal to those already found for the ordinary
transition, with, however, an interesting reshuffling of the corresponding
eigenvalues between different sectors of the transfer matrix.Comment: 18 pages, Latex, 12 eps figures; submitted to Nucl. Phys.
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