DSpace Collection:
https://dspace.lboro.ac.uk/2134/90
2014-04-18T10:51:28Z
2014-04-18T10:51:28Z
Transcritical flow of a stratified fluid over topography: analysis of the forced Gardner equation
Kamchatnov, A.M.
Kuo, Y.-H.
Lin, T.-C.
Horng, T.-L.
Gou, S.-C.
Clift, R.
El, G.A.
Grimshaw, Roger H.J.
https://dspace.lboro.ac.uk/2134/14279
2014-03-10T12:53:47Z
2013-01-01T00:00:00Z
Title: Transcritical flow of a stratified fluid over topography: analysis of the forced Gardner equation
Authors: Kamchatnov, A.M.; Kuo, Y.-H.; Lin, T.-C.; Horng, T.-L.; Gou, S.-C.; Clift, R.; El, G.A.; Grimshaw, Roger H.J.
Abstract: Transcritical flow of a stratified fluid past a broad localised topographic obstacle is studied
analytically in the framework of the forced extended Korteweg–de Vries (eKdV), or
Gardner, equation. We consider both possible signs for the cubic nonlinear term in the
Gardner equation corresponding to different fluid density stratification profiles. We identify
the range of the input parameters: the oncoming flow speed (the Froude number)
and the topographic amplitude, for which the obstacle supports a stationary localised
hydraulic transition from the subcritical flow upstream to the supercritical flow downstream.
Such a localised transcritical flow is resolved back into the equilibrium flow
state away from the obstacle with the aid of unsteady coherent nonlinear wave structures
propagating upstream and downstream. Along with the regular, cnoidal undular
bores occurring in the analogous problem for the single-layer flow modeled by the forced
KdV equation, the transcritical internal wave flows support a diverse family of upstream
and downstream wave structures, including kinks, rarefaction waves, classical undular
bores, reversed and trigonometric undular bores, which we describe using the recent
development of the nonlinear modulation theory for the (unforced) Gardner equation.
The predictions of the developed analytic construction are confirmed by direct numerical
simulations of the forced Gardner equation for a broad range of input parameters.
Description: This paper was accepted for publication in the Journal of Fluid Mechanics and the definitive version is available at: http://dx.doi.org/10.1017/jfm.2013.556
2013-01-01T00:00:00Z
How big is an outbreak likely to be? Methods for epidemic final-size calculation
House, Thomas
Ross, Joshua V.
Sirl, David
https://dspace.lboro.ac.uk/2134/14271
2014-03-07T15:35:17Z
2013-01-01T00:00:00Z
Title: How big is an outbreak likely to be? Methods for epidemic final-size calculation
Authors: House, Thomas; Ross, Joshua V.; Sirl, David
Abstract: Epidemic models have become a routinely used
tool to inform policy on infectious disease. A
particular interest at the moment is the use of
computationally intensive inference to parametrize
these models. In this context, numerical efﬁciency
is critically important. We consider methods for
evaluating the probability mass function of the total
number of infections over the course of a stochastic
epidemic, with a focus on homogeneous ﬁnite
populations, but also considering heterogeneous and
large populations. Relevant methods are reviewed
critically, with existing and novel extensions also
presented. We provide code in MATLAB and a
systematic comparison of numerical efﬁciency.
Description: © 2012 The Authors. Published by the Royal Society under the terms of the
Creative Commons Attribution License http://creativecommons.org/licenses/
by/3.0/, which permits unrestricted use, provided the original author and
source are credited.
2013-01-01T00:00:00Z
Controlling noise-induced behavior of excitable networks
Patidar, S.
Pototsky, Andrey
Janson, Natalia B.
https://dspace.lboro.ac.uk/2134/12791
2013-07-22T13:56:28Z
2009-01-01T00:00:00Z
Title: Controlling noise-induced behavior of excitable networks
Authors: Patidar, S.; Pototsky, Andrey; Janson, Natalia B.
Abstract: The paper demonstrates the possibility to control the collective behavior of a large network of excitable stochastic units, in which oscillations are induced merely by external random input. Each network element is represented by the FitzHugh–Nagumo system under the influence of noise, and the elements are coupled through the mean field. As known previously, the collective behavior of units in such a network can range from synchronous to non-synchronous spiking with a variety of states in between. We apply the Pyragas delayed feedback to the mean field of the network and demonstrate that this technique is capable of suppressing or weakening the collective synchrony, or of inducing the synchrony where it was absent. On the plane of control parameters we indicate the areas where suppression of synchrony is achieved. To explain the numerical observations on a qualitative level, we use the semi-analytic approach based on the cumulant expansion of the distribution density within Gaussian approximation. We perform bifurcation analysis of the obtained cumulant equations with delay and demonstrate that the regions of stability of its steady state have qualitatively the same structure as the regions of synchrony suppression of the original stochastic equations. We also demonstrate the delay-induced multistability in the stochastic network. These results are relevant to the control of unwanted behavior in neural networks.
2009-01-01T00:00:00Z
Synchronization of a large number of continuous one-dimensional stochastic elements with time delayed mean field coupling
Pototsky, Andrey
Janson, Natalia B.
https://dspace.lboro.ac.uk/2134/12788
2013-07-22T13:39:44Z
2009-01-01T00:00:00Z
Title: Synchronization of a large number of continuous one-dimensional stochastic elements with time delayed mean field coupling
Authors: Pototsky, Andrey; Janson, Natalia B.
Abstract: We study synchronization as a means of control of collective behavior of an ensemble
of coupled stochastic units in which oscillations are induced merely by external noise.
We determine the boundary of the synchronization domain of a large number of onedimensional
continuous stochastic elements with time delayed non-homogeneous
mean-field coupling. Exact location of the synchronization threshold is shown to
be a solution of the boundary value problem (BVP) which was derived from the
linearized Fokker-Planck equation. Here the synchronization threshold is found by
solving this BVP numerically. Approximate analytics is obtained by expanding the
solution of the linearized Fokker-Planck equation into a series of eigenfunctions of
the stationary Fokker-Planck operator. Bistable systems with a polynomial and
piece-wise linear potential are considered as examples. Multistability and hysteresis
is observed in the Langevin equations for finite noise intensity. In the limit of small
noise intensities the critical coupling strength was shown to remain finite.
Description: This article was accepted for publication in the journal Physica D: Nonlinear Phenomena, and the definitive version can be found at: http://dx.doi.org/10.1016/j.physd.2008.09.010
2009-01-01T00:00:00Z