Fluctuation-induced interactions between dielectrics in general geometries

We study thermal Casimir and quantum non-retarded Lifshitz interactions between dielectrics in general geometries. We map the calculation of the classical partition function onto a determinant which we discretize and evaluate with the help of Cholesky factorization. The quantum partition function is treated by path integral quantization of a set of interacting dipoles and reduces to a product of determinants. We compare the approximations of pairwise additivity and proximity force with our numerical methods. We propose a ``factorization approximation'' which gives rather good numerical results in the geometries that we study

Numerical methods for fluctuation driven interactions between dielectrics

We develop a discretized theory of thermal Casimir interactions to numerically calculate the interactions between fluctuating dielectrics. From a constrained partition function we derive a surface free energy, while handling divergences that depend on system size and discretization. We derive analytic results for parallel plate geometry in order to check the convergence of the numerical methods. We use the method to calculate vertical and lateral Casimir forces for a set of grooves.Comment: revtex, 20 page

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

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

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

Coulomb Interactions via Local Dynamics: A Molecular--Dynamics Algorithm

We derive and describe in detail a recently proposed method for obtaining Coulomb interactions as the potential of mean force between charges which are dynamically coupled to a local electromagnetic field. We focus on the Molecular Dynamics version of the method and show that it is intimately related to the Car--Parrinello approach, while being equivalent to solving Maxwell's equations with freely adjustable speed of light. Unphysical self--energies arise as a result of the lattice interpolation of charges, and are corrected by a subtraction scheme based on the exact lattice Green's function. The method can be straightforwardly parallelized using standard domain decomposition. Some preliminary benchmark results are presented.Comment: 8 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

Genetic analysis of the Linnaean Ulva lactuca (Ulvales, Chlorophyta) holotype and related type specimens reveals name misapplications, unexpected origins, and new synonymies.

Current usage of the name Ulva lactuca, the generitype of Ulva, remains uncertain. Genetic analyses were performed on the U. lactuca Linnaean holotype, the U. fasciata epitype, the U. fenestrata holotype, the U. lobata lectotype, and the U. stipitata lectotype. The U. lactuca holotype is nearly identical in rbcL sequence to the U. fasciata epitype, a warm temperate to tropical species, rather than the cold temperate species to which the name U. lactuca has generally been applied. We hypothesize that the holotype specimen of U. lactuca came from the Indo-Pacific rather than northern Europe. Our analyses indicate that U. fasciata and U. lobata are heterotypic synonyms of U. lactuca. Ulva fenestrata is the earliest name for northern hemisphere, cold temperate Atlantic and Pacific species, with U. stipitata a junior synonym. DNA sequences from type specimens provide an unequivocal method for applying names to Ulva species. This article is protected by copyright. All rights reserved

Writhing Photons and Berry Phases in Diffusive Wave Scattering

We study theoretically the polarization state of light in multiple scattering media in the limit of weak gradients in refractive index. Linearly polarized photons are randomly rotated due to the Berry phase associated with the scattering path. For circularly polarized light independent speckle patterns are found for the two helical states. The statistics of the geometric phase is related to the writhe distribution of semiflexible polymers such as DNA.Comment: 4 pages, 1 figur

A pragmatic randomised controlled trial of hydrotherapy and land exercises on overall well being and quality of life in rheumatoid arthritis

Background \ud Hydrotherapy is highly valued by people with rheumatoid arthritis yet few studies have compared the benefits of exercises in heated water against exercises on land. In particular, data on quality of life is rarely reported. This is especially important because patients treated with hydrotherapy often report an enhanced sense of well-being. We report a randomised controlled trial in which we compared the effects of hydrotherapy with exercises on land on overall response to treatment, physical function and quality of life in patients with rheumatoid arthritis. \ud \ud Methods \ud One hundred and fifteen patients with RA were randomised to receive a weekly 30-minute session of hydrotherapy or similar exercises on land for 6 weeks. Our primary outcome was a self-rated global impression of change – a measure of treatment effect on a 7-point scale ranging from 1(very much worse) to 7 (very much better) assessed immediately on completion of treatment. Secondary outcomes including EuroQol health related quality of life, EuroQol health status valuation, HAQ, 10 metre walk time and pain scores were collected at baseline, after treatment and 3 months later. Binary outcomes were analysed by Fisher's exact test and continuous variables by Wilcoxon or Mann-Whitney tests. \ud \ud Results \ud Baseline characteristics of the two groups were comparable. Significantly more patients treated with hydrotherapy (40/46, 87%) were much better or very much better than the patients treated with land exercise (19/40, 47.5%), p < 0.001 Fisher's exact test. Eleven patients allocated land exercise failed to complete treatment compared with 4 patients allocated hydrotherapy (p = 0.09). Sensitivity analyses confirmed an advantage for hydrotherapy if we assumed non-completers would all not have responded (response rates 70% versus 38%; p < 0.001) or if we assumed that non-completers would have had the same response as completers (response rates 82% versus 55% p = 0.002). Ten metre walk time improved after treatment in both cases (median pre-treatment time for both groups combined 10.9 seconds, post-treatment 9.1 s, and 3 months later 9.6 s). There was however no difference between treatment groups. Similarly there were no significant differences between groups in terms of changes to HAQ, EQ-5D utility score, EQ VAS and pain VAS. \ud \ud Conclusion \ud Patients with RA treated with hydrotherapy are more likely to report feeling much better or very much better than those treated with land exercises immediately on completion of the treatment programme. This perceived benefit was not reflected by differences between groups in 10-metre walk times, functional scores, quality of life measures and pain scores