Related papers: Nonlinear dynamical systems and linearly forced is…
We consider a system of two cubic-quintic non-linear Schr\"odinger equations in two dimensions, coupled by repulsive cubic terms. We analyse situations in which a probe lump of one of the modes is surrounded by a fluid of the other one and…
In this paper, we present an experimental investigation of the turbulent saturation of the flow driven by parametric resonance of inertial waves in a rotating fluid. In our set-up, a half-meter wide ellipsoid filled with water is brought to…
Nonlinear waves in a liquid with gas bubbles are studied. Higher order terms with respect to the small parameter are taken into account in the derivation of the equation for nonlinear waves. A nonlinear differential equation is derived for…
This paper considers the robustness of an uncertain nonlinear system along a finite-horizon trajectory. The uncertain system is modeled as a connection of a nonlinear system and a perturbation. The analysis relies on three ingredients.…
In this paper we study the existence of solutions to an isotropic differential inclusion.
In this paper, we prove the linear damping for the 2-D Euler equations around a class of shear flows under the assumption that the linearized operator has no embedding eigenvalues. For the symmetric flows, we obtain the explicit decay…
We present a new version of the Grobman-Hartman's linearization theorem for random dynamics. Our result holds for infinite dimensional systems whose linear part is not necessarily invertible. In addition, by adding some restrictions on the…
Following our first report (A. Groisman and V. Steinberg, $\sl Nature$ $\bf 405$, 53 (2000)) we present an extended account of experimental observations of elasticity induced turbulence in three different systems: a swirling flow between…
This paper considers the oscillations modeled by a forced Van der Pol generalized oscillator. These oscillations are described by a nonlinear differential equation of the form $…
Lyapunov's indirect method is an attractive method for analyzing stability of non-linear systems since only the stability of the corresponding linearized system needs to be determined. Unfortunately, the proof for finite-dimensional systems…
This paper considers nonlinear dynamics of plasma oscillations modeled by a forced modified Van der Pol-Duffing oscillator. These plasma oscillations are described by a nonlinear differential equation of the form $ \ddot{x}+ \epsilon (1…
We consider the case of finite-size spherical particles which are settling under gravity in a homogeneous turbulent background flow. Turbulence is forced with the aid of the random forcing method of Eswaran and Pope [Comput. Fluids,…
We subject the stationary solutions of inviscid and axially symmetric rotational accretion to a time-dependent radial perturbation, which includes nonlinearity to any arbitrary order. Regardless of the order of nonlinearity, the equation of…
We discuss some important issues arising from computational efforts in dynamical systems and fluid dynamics. Various individuals have misunderstood these issues since the onset of these problem areas; indeed, they have been routinely…
We consider linear parabolic equations on a random non-cylindrical domain. Utilizing the domain mapping method, we write the problem as a partial differential equation with random coefficients on a cylindrical deterministic domain.…
We use a simple model consisting of energy-momentum tensor conservation and a Maxwell-Cattaneo equation for its viscous part to study nonlinear phenomena in a real relativistic fluid. We focus on new types of behavior without…
The modelling of fluid particle accelerations in homogeneous, isotropic turbulence in terms of second-order stochastic models for the Lagrangian velocity is considered. The basis for the Reynolds model (A. M. Reynolds, \textit{Phys. Rev.…
Properties of an infinite system of nonlinearly coupled ordinary differential equations are discussed. This system models some properties present in the equations of motion for an inviscid fluid such as the skew symmetry and the…
The dynamics of a viscous accretion disc subject to a slowly varying warp of large amplitude is considered. Attention is restricted to discs in which self-gravitation is negligible, and to the generic case in which the resonant wave…
We have developed a simulation technique of multiscale Lagrangian fluid dynamics to tackle hierarchical problems relating to historical dependency of polymeric fluid. We investigate flow dynamics of dilute polymeric fluid by using the…