2,960 research outputs found
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
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
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
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
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
Entropic Elasticity of Double-Strand DNA Subject to Simple Spatial Constraints
The aim of the present paper is the study of the entropic elasticity of the
dsDNA molecule, having a cristallographic length L of the order of 10 to 30
persistence lengths A, when it is subject to spatial obstructions. We have not
tried to obtain the single molecule partition function by solving a
Schodringer-like equation. We prefer to stay within a discretized version of
the WLC model with an added one-monomer potential, simulating the spatial
constraints. We derived directly from the discretized Boltzmann formula the
transfer matrix connecting the partition functions relative to adjacent
"effective monomers". We have plugged adequate Dirac delta-functions in the
functional integral to ensure that the monomer coordinate and the tangent
vector are independent variables. The partition function is, then, given by an
iterative process which is both numerically efficient and physically
transparent. As a test of our discretized approach, we have studied two
configurations involving a dsDNA molecule confined between a pair of parallel
plates.Comment: The most formal developments of Section I have been moved into an
appendix and replaced by a direct derivation of the transfer matrix used in
the applications. of Section II. Two paragraphs and two figures have been
added to clarify the physical interpretation of the result
Casimir Forces between Spherical Particles in a Critical Fluid and Conformal Invariance
Mesoscopic particles immersed in a critical fluid experience long-range
Casimir forces due to critical fluctuations. Using field theoretical methods,
we investigate the Casimir interaction between two spherical particles and
between a single particle and a planar boundary of the fluid. We exploit the
conformal symmetry at the critical point to map both cases onto a highly
symmetric geometry where the fluid is bounded by two concentric spheres with
radii R_- and R_+. In this geometry the singular part of the free energy F only
depends upon the ratio R_-/R_+, and the stress tensor, which we use to
calculate F, has a particularly simple form. Different boundary conditions
(surface universality classes) are considered, which either break or preserve
the order-parameter symmetry. We also consider profiles of thermodynamic
densities in the presence of two spheres. Explicit results are presented for an
ordinary critical point to leading order in epsilon=4-d and, in the case of
preserved symmetry, for the Gaussian model in arbitrary spatial dimension d.
Fundamental short-distance properties, such as profile behavior near a surface
or the behavior if a sphere has a `small' radius, are discussed and verified.
The relevance for colloidal solutions is pointed out.Comment: 37 pages, 2 postscript figures, REVTEX 3.0, published in Phys. Rev. B
51, 13717 (1995
Surface Critical Behavior of Binary Alloys and Antiferromagnets: Dependence of the Universality Class on Surface Orientation
The surface critical behavior of semi-infinite
(a) binary alloys with a continuous order-disorder transition and
(b) Ising antiferromagnets in the presence of a magnetic field is considered.
In contrast to ferromagnets, the surface universality class of these systems
depends on the orientation of the surface with respect to the crystal axes.
There is ordinary and extraordinary surface critical behavior for orientations
that preserve and break the two-sublattice symmetry, respectively. This is
confirmed by transfer-matrix calculations for the two-dimensional
antiferromagnet and other evidence.Comment: Final version that appeared in PRL, some minor stylistic changes and
one corrected formula; 4 pp., twocolumn, REVTeX, 3 eps fig
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