Breathers in the weakly coupled topological discrete sine-Gordon system

Existence of breather (spatially localized, time periodic, oscillatory) solutions of the topological discrete sine-Gordon (TDSG) system, in the regime of weak coupling, is proved. The novelty of this result is that, unlike the systems previously considered in studies of discrete breathers, the TDSG system does not decouple into independent oscillator units in the weak coupling limit. The results of a systematic numerical study of these breathers are presented, including breather initial profiles and a portrait of their domain of existence in the frequency-coupling parameter space. It is found that the breathers are uniformly qualitatively different from those found in conventional spatially discrete systems.Comment: 19 pages, 4 figures. Section 4 (numerical analysis) completely rewritte

Processing multiple non-adjacent dependencies: evidence from sequence learning

Processing non-adjacent dependencies is considered to be one of the hallmarks of human language. Assuming that sequence-learning tasks provide a useful way to tap natural-language-processing mechanisms, we cross-modally combined serial reaction time and artificial-grammar learning paradigms to investigate the processing of multiple nested (A(1)A(2)A(3)B(3)B(2)B(1)) and crossed dependencies (A(1)A(2)A(3)B(1)B(2)B(3)), containing either three or two dependencies. Both reaction times and prediction errors highlighted problems with processing the middle dependency in nested structures (A(1)A(2)A(3)B(3-)B(1)), reminiscent of the 'missing-verb effect' observed in English and French, but not with crossed structures (A(1)A(2)A(3)B(1-)B(3)). Prior linguistic experience did not play a major role: native speakers of German and Dutch-which permit nested and crossed dependencies, respectively-showed a similar pattern of results for sequences with three dependencies. As for sequences with two dependencies, reaction times and prediction errors were similar for both nested and crossed dependencies. The results suggest that constraints on the processing of multiple non-adjacent dependencies are determined by the specific ordering of the non-adjacent dependencies (i.e. nested or crossed), as well as the number of non-adjacent dependencies to be resolved (i. e. two or three). Furthermore, these constraints may not be specific to language but instead derive from limitations on structured sequence learning.Netherlands Organisation of Scientific Research (NWO) [446-08-014]; Max Planck Institute for Psycholinguistics; Donders Institute for Brain, Cognition and Behaviour; Fundacao para a Ciencia e Tecnologia (IBB/CBME, LA, FEDER/POCI) [PTDC/PSI-PCO/110734/2009]; Stockholm Brain Institute; Vetenskapsradet; Swedish Dyslexia Foundation; Hedlunds Stiftelse; Stockholm County Council (ALF, FoUU)info:eu-repo/semantics/publishedVersio

Static axisymmetric space-times with prescribed multipole moments

In this article we develop a method of finding the static axisymmetric space-time corresponding to any given set of multipole moments. In addition to an implicit algebraic form for the general solution, we also give a power series expression for all finite sets of multipole moments. As conjectured by Geroch we prove in the special case of axisymmetry, that there is a static space-time for any given set of multipole moments subject to a (specified) convergence criterion. We also use this method to confirm a conjecture of Hernandez-Pastora and Martin concerning the monopole-quadropole solution.Comment: 14 page

Lagrange-mesh calculations in momentum space

The Lagrange-mesh method is a powerful method to solve eigenequations written in configuration space. It is very easy to implement and very accurate. Using a Gauss quadrature rule, the method requires only the evaluation of the potential at some mesh points. The eigenfunctions are expanded in terms of regularized Lagrange functions which vanish at all mesh points except one. It is shown that this method can be adapted to solve eigenequations written in momentum space, keeping the convenience and the accuracy of the original technique. In particular, the kinetic operator is a diagonal matrix. Observables in both configuration space and momentum space can also be easily computed with a good accuracy using only eigenfunctions computed in the momentum space. The method is tested with Gaussian and Yukawa potentials, requiring respectively a small or a great mesh to reach convergence.Comment: Extended versio

Quantum limited particle sensing in optical tweezers

Particle sensing in optical tweezers systems provides information on the position, velocity and force of the specimen particles. The conventional quadrant detection scheme is applied ubiquitously in optical tweezers experiments to quantify these parameters. In this paper we show that quadrant detection is non-optimal for particle sensing in optical tweezers and propose an alternative optimal particle sensing scheme based on spatial homodyne detection. A formalism for particle sensing in terms of transverse spatial modes is developed and numerical simulations of the efficacy of both quadrant and spatial homodyne detection are shown. We demonstrate that an order of magnitude improvement in particle sensing sensitivity can be achieved using spatial homodyne over quadrant detection.Comment: Submitted to Biophys

Modelling microelectrode biosensors : free-flow calibration can substantially underestimate tissue concentrations

Microelectrode amperometric biosensors are widely used to measure concentrations of analytes in solution and tissue including acetylcholine, adenosine, glucose and glutamate. A great deal of experimental and modelling effort has been directed at quantifying the response of the biosensors themselves; however, the influence that the macroscopic tissue environment has on biosensor response has not been subjected to the same level of scrutiny. Here we identify an important issue in the way microelectrode biosensors are calibrated that is likely to have led to underestimations of analyte tissue concentrations. Concentration in tissue is typically determined by comparing the biosensor signal to that measured in free-flow calibration conditions. In a free-flow environment the concentration of the analyte at the outer surface of the biosensor can be considered constant. However, in tissue the analyte reaches the biosensor surface by diffusion through the extracellular space. Because the enzymes in the biosensor break down the analyte, a density gradient is set up resulting in a significantly lower concentration of analyte near the biosensor surface. This effect is compounded by the diminished volume fraction (porosity) and reduction in the diffusion coefficient due to obstructions (tortuosity) in tissue. We demonstrate this effect through modelling and experimentally verify our predictions in diffusive environments

Solitary wave dynamics in time-dependent potentials

We rigorously study the long time dynamics of solitary wave solutions of the nonlinear Schr\"odinger equation in {\it time-dependent} external potentials. To set the stage, we first establish the well-posedness of the Cauchy problem for a generalized nonautonomous nonlinear Schr\"odinger equation. We then show that in the {\it space-adiabatic} regime where the external potential varies slowly in space compared to the size of the soliton, the dynamics of the center of the soliton is described by Hamilton's equations, plus terms due to radiation damping. We finally remark on two physical applications of our analysis. The first is adiabatic transportation of solitons, and the second is Mathieu instability of trapped solitons due to time-periodic perturbations.Comment: 38 pages, some typos corrected, one reference added, one remark adde

The double torus as a 2D cosmos: groups, geometry and closed geodesics

The double torus provides a relativistic model for a closed 2D cosmos with topology of genus 2 and constant negative curvature. Its unfolding into an octagon extends to an octagonal tessellation of its universal covering, the hyperbolic space H^2. The tessellation is analysed with tools from hyperbolic crystallography. Actions on H^2 of groups/subgroups are identified for SU(1, 1), for a hyperbolic Coxeter group acting also on SU(1, 1), and for the homotopy group \Phi_2 whose extension is normal in the Coxeter group. Closed geodesics arise from links on H^2 between octagon centres. The direction and length of the shortest closed geodesics is computed.Comment: Latex, 27 pages, 5 figures (late submission to arxiv.org

Taming the Yukawa potential singularity: improved evaluation of bound states and resonance energies

Using the tools of the J-matrix method, we absorb the 1/r singularity of the Yukawa potential in the reference Hamiltonian, which is handled analytically. The remaining part, which is bound and regular everywhere, is treated by an efficient numerical scheme in a suitable basis using Gauss quadrature approximation. Analysis of resonance energies and bound states spectrum is performed using the complex scaling method, where we show their trajectories in the complex energy plane and demonstrate the remarkable fact that bound states cross over into resonance states by varying the potential parameters.Comment: 8 pages, 2 tables, 1 figure. 2 mpg videos and 1 pdf table file are available upon request from the corresponding Autho

Leptonic decays of the eta meson with the WASA detector at CELSIUS

Decay channels of the eta meson with at least one lepton pair in the final state are discussed. Preliminary results on electron-positron pair production from the pd->He eta reaction from the WASA experiment at CELSIUS are presented.Comment: 8 pages, 7 figures, prepared for Symposium on Meson Physics at COSY-11 and WASA-at-COSY, Cracow, 17-22 June 200