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A new approach to the stochastic theory of turbulence is suggested. The coloured noise that is present in the stochastic Navier-Stokes equation is generated from the delta-correlated noise allowing us to avoid the nonlocal field theory as…
We show a noise-induced transition in Josephson junction with fundamental as well as second harmonic. A periodically modulated multiplicative colored noise can stabilize an unstable configuration in such a system. The stabilization of the…
The mobility of an overdamped particle, in a periodic potential tilted by a constant external field and moving in a medium with periodic friction coefficient is examined. When the potential and the friction coefficient have the same…
We review the mathematical formalism underlying the modelling of stochasticity in biological systems. Beginning with a description of the system in terms of its basic constituents, we derive the mesoscopic equations governing the dynamics…
A mechanism of formation of small-scale inhomogeneities in spatial distributions of aerosols and droplets associated with clustering instability in the atmospheric turbulent flow is discussed. The particle clustering is a consequence of a…
The discrete self-trapping equation (DST) represents an useful model for several properties of one-dimensional nonlinear molecular crystals. The modulational instability of DST equation is discussed from a statistical point of view,…
We consider the noise-induced transitions in the randomly perturbed discrete logistic map from a linearly stable periodic orbit consisting of T periodic points. The traditional large deviation theory and asymptotic analysis for small noise…
Understanding the phase behavior of mixtures with many components is important in many contexts, including as a key step toward a physics-based description of intracellular compartmentalization. Here, we study the instabilities of a mixture…
This is a review of the theory of the modulational instability in idealised fluid models of strongly magnetised plasmas and reduced models of geophysical fluid dynamics, particularly the role it plays in the formation of zonal flows. The…
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…
Quasigeostrophic flows are induced by spatial variations in interior potential vorticity and boundary buoyancy. We begin by developing the geostrophic turbulence theory of boundary buoyancy anomalies in a fluid with vanishing potential…
We study the instability of a dusty simple shear flow where the dust particles are distributed non-uniformly. A simple shear flow is modally stable to infinitesimal perturbations. Also, a band of particles remains unaffected in the absence…
We consider stochastic partial differential equations (SPDEs) on the one-dimensional torus, driven by space-time white noise, and with a time-periodic drift term, which vanishes on two stable and one unstable equilibrium branches. Each of…
Planetary turbulence is observed to self-organize into large-scale structures such as zonal jets and coherent vortices. One of the simplest models that retains the relevant dynamics of turbulent self-organization is a barotropic flow in a…
The motion of oscillatory-like nonlinear Hamiltonian systems, driven by a weak noise, is considered. A general method to find regions of stability in the phase space of a randomly-driven system, based on a specific Poincar\'e map, is…
A remarkable phenomenon in turbulent flows is the spontaneous emergence of coherent large spatial scale zonal jets. Geophysical examples of this phenomenon include the Jovian banded winds and the Earth's polar front jet. In this work a…
Randomly-forced fluid flow in the presence of scale-unselective dissipation develops mean currents following topographic contours. Known mechanisms based on the scale-selective action of damping processes are not at work in this situation.…
The linear instability of the electron temperature gradient (ETG) driven modes in the presence of zonal flows is investigated. Random and deterministic $cos$ - like profiles of the zonal flow are considered. It is shown that the presence of…
We discovered an oscillatory instability in a system of inelastically colliding hard spheres, driven by two opposite "thermal" walls at zero gravity. The instability, predicted by a linear stability analysis of the equations of granular…
We investigate the stability of stratified fluid layers undergoing homogeneous and periodic tidal deformation. We first introduce a local model which allows to study velocity and buoyancy fluctuations in a Lagrangian domain periodically…