9,219 research outputs found
Gaussian approximations for stochastic systems with delay: chemical Langevin equation and application to a Brusselator system
We present a heuristic derivation of Gaussian approximations for stochastic
chemical reaction systems with distributed delay. In particular we derive the
corresponding chemical Langevin equation. Due to the non-Markovian character of
the underlying dynamics these equations are integro-differential equations, and
the noise in the Gaussian approximation is coloured. Following on from the
chemical Langevin equation a further reduction leads to the linear-noise
approximation. We apply the formalism to a delay variant of the celebrated
Brusselator model, and show how it can be used to characterise noise-driven
quasi-cycles, as well as noise-triggered spiking. We find surprisingly
intricate dependence of the typical frequency of quasi-cycles on the delay
period.Comment: 14 pages, 9 figure
Three-level mixing and dark states in transport through quantum dots
We consider theoretically the transport through the double quantum dot
structure of the recent experiment of C. Payette {\it et al.} [Phys. Rev. Lett.
{\bf 102}, 026808 (2009)] and calculate stationary current and shotnoise.
Three-level mixing gives rise to a pronounced current suppression effect, the
character of which charges markedly with bias direction. We discuss these
results in connexion with the dark states of coherent population trapping in
quantum dots.Comment: 6 pages, 5 fig
The Nonlinear Evolution of Instabilities Driven by Magnetic Buoyancy: A New Mechanism for the Formation of Coherent Magnetic Structures
Motivated by the problem of the formation of active regions from a
deep-seated solar magnetic field, we consider the nonlinear three-dimensional
evolution of magnetic buoyancy instabilities resulting from a smoothly
stratified horizontal magnetic field. By exploring the case for which the
instability is continuously driven we have identified a new mechanism for the
formation of concentrations of magnetic flux.Comment: Published in ApJL. Version with colour figure
Noise and Correlations in a Spatial Population Model with Cyclic Competition
Noise and spatial degrees of freedom characterize most ecosystems. Some
aspects of their influence on the coevolution of populations with cyclic
interspecies competition have been demonstrated in recent experiments [e.g. B.
Kerr et al., Nature {\bf 418}, 171 (2002)]. To reach a better theoretical
understanding of these phenomena, we consider a paradigmatic spatial model
where three species exhibit cyclic dominance. Using an individual-based
description, as well as stochastic partial differential and deterministic
reaction-diffusion equations, we account for stochastic fluctuations and
spatial diffusion at different levels, and show how fascinating patterns of
entangled spirals emerge. We rationalize our analysis by computing the
spatio-temporal correlation functions and provide analytical expressions for
the front velocity and the wavelength of the propagating spiral waves.Comment: 4 pages of main text, 3 color figures + 2 pages of supplementary
material (EPAPS Document). Final version for Physical Review Letter
Lower bounds for nodal sets of eigenfunctions
We prove lower bounds for the Hausdorff measure of nodal sets of
eigenfunctions.Comment: To appear in Communications in Mathematical Physics; revised to
include two additional references and update bibliographic informatio
The value of multimodality imaging for detection, characterisation and management of a wall adhering structure in the right atrium
The case presents a wall adherent structure in the right atrium in a young patient with peripheral tcell
lymphoma followed by successful prolonged lysis therapy resulting in the resolution of the
thrombus is presented. This case highlights the utility of multimodality imaging in an accurate
assessment of the right atrium thrombus and the effectiveness of prolonged lysis therapy.peer-reviewe
Fluctuating Elastic Rings: Statics and Dynamics
We study the effects of thermal fluctuations on elastic rings. Analytical
expressions are derived for correlation functions of Euler angles, mean square
distance between points on the ring contour, radius of gyration, and
probability distribution of writhe fluctuations. Since fluctuation amplitudes
diverge in the limit of vanishing twist rigidity, twist elasticity is essential
for the description of fluctuating rings. We find a crossover from a small
scale regime in which the filament behaves as a straight rod, to a large scale
regime in which spontaneous curvature is important and twist rigidity affects
the spatial configurations of the ring. The fluctuation-dissipation relation
between correlation functions of Euler angles and response functions, is used
to study the deformation of the ring by external forces. The effects of inertia
and dissipation on the relaxation of temporal correlations of writhe
fluctuations, are analyzed using Langevin dynamics.Comment: 43 pages, 9 Figure
Weak coupling approximations in non-Markovian Transport
We study the transport properties of the Fano-Anderson model with a
Lorentzian-shaped density of states in one of the electronic reservoirs. We
explicitly show that the energy dependence of the density of states can cause
non-Markovian effects and that the non-Markovian master equation may fail if
these effects are strong. We evaluate the stationary current, the zero
frequency current noise and the occupation dynamics of the resonant level by
means of a quantum master equation approach within different approximation
schemes and compare the results to the exact solution obtained by scattering
theory and Green's functions.Comment: 9 pages, 6 figures; due to suggestions of a referee we have added an
appendix where our kernel is derived in detail; a few typos are correcte
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