5,947 research outputs found
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
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