Local Simulation Algorithms for Coulombic Interactions

We consider dynamically constrained Monte-Carlo dynamics and show that this leads to the generation of long ranged effective interactions. This allows us to construct a local algorithm for the simulation of charged systems without ever having to evaluate pair potentials or solve the Poisson equation. We discuss a simple implementation of a charged lattice gas as well as more elaborate off-lattice versions of the algorithm. There are analogies between our formulation of electrostatics and the bosonic Hubbard model in the phase approximation. Cluster methods developed for this model further improve the efficiency of the electrostatics algorithm.Comment: Proceedings Statphys22 10 page

Modifications of turbulence and turbulent transport associated with a bias-induced confinement transition in LAPD

Azimuthal flow is driven in the edge of the Large Plasma Device (LAPD) [W. Gekelman, {\itshape et. al}, Rev. Sci. Instr. {\bfseries 62}, 2875 (1991)] through biasing a section of the vacuum vessel relative to the plasma source cathode. As the applied bias exceeds a threshold, a transition in radial particle confinement is observed, evidenced by a dramatic steepening in the density profile, similar to the L- to H-mode transition in toroidal confinement devices. The threshold behavior and dynamic behavior of radial transport is related to flow penetration and the degree of spatial overlap between the flow shear and density gradient profiles. An investigation of the changes in turbulence and turbulent particle transport associated with the confinement transition is presented. Two-dimensional cross-correlation measurements show that the spatial coherence of edge turbulence in LAPD changes significantly with biasing. The azimuthal correlation in the turbulence increases dramatically, while the radial correlation length is little altered. Turbulent amplitude is reduced at the transition, particularly in electric field fluctuations, but the dominant change observed is in the cross-phase between density and electric field fluctuations. The changes in cross-phase lead to a suppression and then apparent reversal of turbulent particle flux as the threshold is exceeded.Comment: 11 pages, 13 figures, accepted for publication in Physics of Plasmas (to appear Jan 2009 issue

Comment on "Elasticity Model of a Supercoiled DNA Molecule"

We perform simulations to numerically study the writhe distribution of a stiff polymer. We compare with analytic results of Bouchiat and Mezard (PRL 80 1556- (1998); cond-mat/9706050).Comment: 1 page, 1 figure revtex

Modification of turbulent transport with continuous variation of flow shear in the Large Plasma Device

Continuous control over azimuthal flow and shear in the edge of the Large Plasma Device (LAPD) has been achieved using a biasable limiter which has allowed a careful study of the effect of flow shear on pressure-gradient-driven turbulence and transport in LAPD. LAPD rotates spontaneously in the ion diamagnetic direction (IDD); positive limiter bias first reduces, then minimizes (producing a near-zero shear state), and finally reverses the flow into the electron diamagnetic direction (EDD). Degradation of particle confinement is observed in the minimum shearing state and reduction in turbulent particle flux is observed with increasing shearing in both flow directions. Near-complete suppression of turbulent particle flux is observed for shearing rates comparable to the turbulent autocorrelation rate measured in the minimum shear state. Turbulent flux suppression is dominated by amplitude reduction in low-frequency ($<10$kHz) density fluctuations. An increase in fluctuations for the highest shearing states is observed with the emergence of a coherent mode which does not lead to net particle transport. The variations of density fluctuations are fit well with power-laws and compare favorably to simple models of shear suppression of transport.Comment: 10 pages, 5 figures; Submitted to Phys. Rev. Let

Energy gaps in quantum first-order mean-field-like transitions: The problems that quantum annealing cannot solve

We study first-order quantum phase transitions in models where the mean-field traitment is exact, and the exponentially fast closure of the energy gap with the system size at the transition. We consider exactly solvable ferromagnetic models, and show that they reduce to the Grover problem in a particular limit. We compute the coefficient in the exponential closure of the gap using an instantonic approach, and discuss the (dire) consequences for quantum annealing.Comment: 6 pages, 3 figure

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 ${\cal A}$ after a time $t$ decays as $e^{-E_0t}$ for long times. The same quantity $E_0$ also determines the confinement free energy per unit length $\Delta f=k_BT\thinspace E_0$ of a semiflexible polymer in a narrow cylindrical pore with cross section ${\cal A}$. From simulations of a randomly accelerated particle we estimate the universal amplitude of $\Delta f$ for both circular and rectangular cross sections.Comment: 10 pages, 2 eps figure

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

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

Two-point microrheology and the electrostatic analogy

The recent experiments of Crocker et al. suggest that microrheological measurements obtained from the correlated fluctuations of widely-separatedprobe particles determine the rheological properties of soft, complex materials more accurately than do the more traditional particle autocorrelations. This presents an interesting problem in viscoelastic dynamics. We develop an important, simplifing analogy between the present viscoelastic problem and classical electrostatics. Using this analogy and direct calculation we analyze both the one and two particle correlations in a viscoelastic medium in order to explain this observation

Local Simulation Algorithms for Coulomb Interaction

Long ranged electrostatic interactions are time consuming to calculate in molecular dynamics and Monte-Carlo simulations. We introduce an algorithmic framework for simulating charged particles which modifies the dynamics so as to allow equilibration using a local Hamiltonian. The method introduces an auxiliary field with constrained dynamics so that the equilibrium distribution is determined by the Coulomb interaction. We demonstrate the efficiency of the method by simulating a simple, charged lattice gas.Comment: Last figure changed to improve demonstration of numerical efficienc