4,022 research outputs found

    Pseudo-High-Order Symplectic Integrators

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    Symplectic N-body integrators are widely used to study problems in celestial mechanics. The most popular algorithms are of 2nd and 4th order, requiring 2 and 6 substeps per timestep, respectively. The number of substeps increases rapidly with order in timestep, rendering higher-order methods impractical. However, symplectic integrators are often applied to systems in which perturbations between bodies are a small factor of the force due to a dominant central mass. In this case, it is possible to create optimized symplectic algorithms that require fewer substeps per timestep. This is achieved by only considering error terms of order epsilon, and neglecting those of order epsilon^2, epsilon^3 etc. Here we devise symplectic algorithms with 4 and 6 substeps per step which effectively behave as 4th and 6th-order integrators when epsilon is small. These algorithms are more efficient than the usual 2nd and 4th-order methods when applied to planetary systems.Comment: 14 pages, 5 figures. Accepted for publication in the Astronomical Journa

    Symplectic integrators for index one constraints

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    We show that symplectic Runge-Kutta methods provide effective symplectic integrators for Hamiltonian systems with index one constraints. These include the Hamiltonian description of variational problems subject to position and velocity constraints nondegenerate in the velocities, such as those arising in sub-Riemannian geometry and control theory.Comment: 13 pages, accepted in SIAM J Sci Compu

    Is the content of patient’s written emotional disclosure associated with improved health outcomes for asthma patients?

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    Written emotional disclosure (WED) is a self-directed, writing intervention. Treatment effects post-WED vary between studies, prompting research into which variables promote the largest improvements. Thus far, research has focused on the frequency of certain linguistic properties of the writing, and subjective stress-related ratings. This study tests the feasibility of using an objective coding framework for stress typology to categorise WED extracts and explores whether any characteristics of the stress described were associated with intervention outcomes. WED extracts from a randomised controlled trial of patients with asthma were coded using an objective stress typology framework. The contents of the WED extracts were reviewed to ascertain whether the experience met the DSM-5 definition for trauma, involved abuse, and was experienced directly or vicariously. Also analysed were the degree of upheaval and upset associated with the event described, together with the time of the event, and number of events written about. Correlational analyses indicated that improvements in asthma-related outcomes were associated with writing about experiences that occurred in childhood, constituted abuse, or caused greater upheaval (all ps <. 05). We found some evidence that the treatment effects of WED may be dependent on what types of stressful experiences participants write about. The use of our objective stress coding scheme was only partially successful as it could not be applied consistently to all WED extracts. Findings require replication using a prospective experimental design

    Nonequilibrium Atom-Dielectric Forces Mediated by a Quantum Field

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    In this paper we give a first principles microphysics derivation of the nonequilibrium forces between an atom, treated as a three dimensional harmonic oscillator, and a bulk dielectric medium modeled as a continuous lattice of oscillators coupled to a reservoir. We assume no direct interaction between the atom and the medium but there exist mutual influences transmitted via a common electromagnetic field. By employing concepts and techniques of open quantum systems we introduce coarse-graining to the physical variables - the medium, the quantum field and the atom's internal degrees of freedom, in that order - to extract their averaged effects from the lowest tier progressively to the top tier. The first tier of coarse-graining provides the averaged effect of the medium upon the field, quantified by a complex permittivity (in the frequency domain) describing the response of the dielectric to the field in addition to its back action on the field through a stochastic forcing term. The last tier of coarse- graining over the atom's internal degrees of freedom results in an equation of motion for the atom's center of mass from which we can derive the force on the atom. Our nonequilibrium formulation provides a fully dynamical description of the atom's motion including back action effects from all other relevant variables concerned. In the long-time limit we recover the known results for the atom-dielectric force when the combined system is in equilibrium or in a nonequilibrium stationary state.Comment: 24 pages, 2 figure

    The Complete Characterization of Fourth-Order Symplectic Integrators with Extended-Linear Coefficients

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    The structure of symplectic integrators up to fourth-order can be completely and analytical understood when the factorization (split) coefficents are related linearly but with a uniform nonlinear proportional factor. The analytic form of these {\it extended-linear} symplectic integrators greatly simplified proofs of their general properties and allowed easy construction of both forward and non-forward fourth-order algorithms with arbitrary number of operators. Most fourth-order forward integrators can now be derived analytically from this extended-linear formulation without the use of symbolic algebra.Comment: 12 pages, 2 figures, submitted to Phys. Rev. E, corrected typo

    Geometric Integration of Hamiltonian Systems Perturbed by Rayleigh Damping

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    Explicit and semi-explicit geometric integration schemes for dissipative perturbations of Hamiltonian systems are analyzed. The dissipation is characterized by a small parameter ϵ\epsilon, and the schemes under study preserve the symplectic structure in the case ϵ=0\epsilon=0. In the case 0<ϵ10<\epsilon\ll 1 the energy dissipation rate is shown to be asymptotically correct by backward error analysis. Theoretical results on monotone decrease of the modified Hamiltonian function for small enough step sizes are given. Further, an analysis proving near conservation of relative equilibria for small enough step sizes is conducted. Numerical examples, verifying the analyses, are given for a planar pendulum and an elastic 3--D pendulum. The results are superior in comparison with a conventional explicit Runge-Kutta method of the same order

    Enhanced dispersion interaction in confined geometry

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    The dispersion interaction between two point-like particles confined in a dielectric slab between two plates of another dielectric medium is studied within a continuum (Lifshitz) theory. The retarded (Casimir-Polder) interaction at large inter-particle distances is found to be strongly enhanced as the mismatch between the dielectric permittivities of the two media is increased. The large-distance interaction is multiplied due to confinement by a factor of (33γ5/2+13γ3/2)/46(33\gamma^{5/2}+13\gamma^{-3/2})/46 at zero temperature, and by (5γ2+γ2)/6(5\gamma^2+\gamma^{-2})/6 at finite temperature, \gamma=\ein(0)/\eout(0) being the ratio between the static dielectric permittivities of the inner and outer media. This confinement-induced amplification of the dispersion interaction can reach several orders of magnitude.Comment: 4 page

    Matter-screened Casimir force and Casimir-Polder force in planar structures

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    Using a recently developed theory of the Casimir force (Raabe C and Welsch D-G 2005 Phys. Rev. A 71 013814), we calculate the force that acts on a plate in front of a planar wall and the force that acts on the plate in the case where the plate is part of matter that fills the space in front of the wall. We show that in the limit of a dielectric plate whose permittivity is close to unity, the force obtained in the former case reduces to the ordinary, i.e., unscreened Casimir-Polder force acting on isolated atoms. In the latter case, the theory yields the Casimir-Polder force that is screened by the surrounding matter.Comment: 11 pages, 1 figure -- published online at J. Opt. B on Nov 16 200

    Ground-state van der Waals forces in planar multilayer magnetodielectrics

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    Within the frame of lowest-order perturbation theory, the van der Waals potential of a ground-state atom placed within an arbitrary dispersing and absorbing magnetodielectric multilayer system is given. Examples of an atom situated in front of a magnetodielectric plate or between two such plates are studied in detail. Special emphasis is placed on the competing attractive and repulsive force components associated with the electric and magnetic matter properties, respectively, and conditions for the formation of repulsive potential walls are given. Both numerical and analytical results are presented.Comment: 16 pages, 8 figures, minor correction

    Dipoles in Graphene Have Infinitely Many Bound States

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    We show that in graphene charge distributions with non-vanishing dipole moment have infinitely many bound states. The corresponding eigenvalues accumulate at the edges of the gap faster than any power
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