451 research outputs found
Changes in the dynamical behavior of nonlinear systems induced by noise.
Weak noise acting upon a nonlinear dynamical system can have far-reaching consequences. The fundamental underlying problem - that of large deviations of a nonlinear system away from a stable or metastable state, sometimes resulting in a transition to a new stationary state, in response to weak additive or multiplicative noise - has long attracted the attention of physicists. This is partly because of its wide applicability, and partly because it bears on the origins of temporal irreversibility in physical processes. During the last few years it has become apparent that, in a system far from thermal equilibrium, even small noise can also result in qualitative change in the system's properties, e.g., the transformation of an unstable equilibrium state into a stable one, and vice versa, the occurrence of multistability and multimodality, the appearance of a mean field, the excitation of noise-induced oscillations, and noise-induced transport (stochastic ratchets). A representative selection of such phenomena is discussed and analyzed, and recent progress made towards their understanding is reviewed
On beta-time fractional biological population model with abundant solitary wave structures
Abstract The ongoing study deals with various forms of solutions for the biological population model with a novel beta-time derivative operators. This model is very conducive to explain the enlargement of viruses, parasites and diseases. This configuration of the aforesaid classical scheme is scouted for its new solutions especially in soliton shape via two of the well known analytical strategies, namely: the extended Sinh-Gordon equation expansion method (EShGEEM) and the Expa function method. These soliton solutions suggest that these methods have widened the scope for generating solitary waves and other solutions of fractional differential equations. Different types of soliton solutions will be gained such as dark, bright and singular solitons solutions with certain conditions. Furthermore, the obtained results can also be used in describing the biological population model in some better way. The numerical solution for the model is obtained using the finite difference method. The numerical simulations of some selected results are also given through their physical explanations. To the best of our knowledge, No previous literature discussed this model through the application of the EShGEEM and the Expa function method and supported their new obtained results by numerical analysis
Conservative stochastic Cahn--Hilliard equation with reflection
We consider a stochastic partial differential equation with reflection at 0
and with the constraint of conservation of the space average. The equation is
driven by the derivative in space of a space--time white noise and contains a
double Laplacian in the drift. Due to the lack of the maximum principle for the
double Laplacian, the standard techniques based on the penalization method do
not yield existence of a solution. We propose a method based on infinite
dimensional integration by parts formulae, obtaining existence and uniqueness
of a strong solution for all continuous nonnegative initial conditions and
detailed information on the associated invariant measure and Dirichlet form.Comment: Published in at http://dx.doi.org/10.1214/009117906000000773 the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Scaling properties of the gravitational clustering in the nonlinear regime
The growth of density perturbations in an expanding universe in the
non-linear regime is investigated. The underlying equations of motion are cast
in a suggestive form, and motivate a conjecture that the scaled pair velocity,
depends on the expansion factor and comoving
coordinate only through the density contrast . This leads to
the result that the true, non-linear, density contrast
is a universal function of the
density contrast , computed in the linear theory and evaluated
at a scale where . This universality is supported by
existing numerical simulations with scale-invariant initial conditions having
different power laws. We discuss a physically motivated ansatz
and use it to compute the non-linear density contrast
at any given scale analytically. This provides a promising method for analysing
the non-linear evolution of density perturbations in the universe and for
interpreting numerical simulations.Comment: 14 pages 2 figures available on request, TeX, IUCAA-12/9
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