2,960 research outputs found

    Partial survival and inelastic collapse for a randomly accelerated particle

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    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 rr, we give a new derivation of the condition for inelastic collapse, r<rc=eπ/3r<r_c=e^{-\pi/\sqrt{3}}, 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

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    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

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    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

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    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

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    The probability that a randomly accelerated particle in two dimensions has not yet left a simply connected domain A{\cal A} after a time tt decays as eE0te^{-E_0t} for long times. The same quantity E0E_0 also determines the confinement free energy per unit length Δf=kBTE0\Delta f=k_BT\thinspace E_0 of a semiflexible polymer in a narrow cylindrical pore with cross section A{\cal A}. From simulations of a randomly accelerated particle we estimate the universal amplitude of Δf\Delta f for both circular and rectangular cross sections.Comment: 10 pages, 2 eps figure

    Entropic Elasticity of Double-Strand DNA Subject to Simple Spatial Constraints

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    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

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    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

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    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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