Related papers: On the Divergence and Vorticity of Vector Ambit Fi…

We study convexity properties of R\'{e}nyi entropy as function of $\alpha>0$ on finite alphabets. We also describe robustness of the R\'{e}nyi entropy on finite alphabets, and it turns out that the rate of respective convergence depends on…

We study graphs whose vertex degree tends and which are, therefore, called rapidly branching. We prove spectral estimates, discreteness of spectrum, first order eigenvalue and Weyl asymptotics solely in terms of the vertex degree growth.…

We study wave-current interactions in two-dimensional water flows of constant vorticity over a flat bed. For large-amplitude periodic traveling waves that propagate at the water surface in the same direction as the underlying current…

We consider the evolution of a family of 2D dispersive turbulence models. The members of this family involve the nonlinear advection of a dynamically active scalar field, the locality of the streamfunction-scalar relation is denoted by…

We construct, within the framework of classical statistical mechanics, a mean field theory of dilute flux line liquids which goes beyond linear hydrodynamics. Within our approach, we find that interactions between vortices produce a massive…

We introduce a family of stochastic models motivated by the study of nonequilibrium steady states of fluid equations. These models decompose the deterministic dynamics of interest into fundamental building blocks, i.e., minimal vector…

Fine scales of turbulent velocity fields, beyond the inertial range and well into the dissipative range, are highly intermittent. It has been hypothesized that complex plane singularities are the principal mechanism behind fine scale…

The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…

We investigate the linear instability of flows that are stable according to Rayleigh's criterion for rotating fluids. Using Taylor-Couette flow as a primary test case, we develop large Reynolds number matched asymptotic expansion theories.…

A new mechanism has been identified that explains the generation of Langmuir circulations. A wind-driven current in the presence of surface waves gives rise to an instability where the emerging circulations redistribute the turbulence in…

Linear stability of solid body rotating flows with axisymmetric density variations is addressed analytically. Considering inviscid disturbances, a non trivial dispersion relation is obtained and it is shown that the instability is of…

We consider the motion of incompressible viscous fluid in a rectangle, imposing the periodicity condition in one direction and the no-slip boundary condition in the other. Assuming that the flow is subject to an external random force, white…

We explore the dynamics of driven magnetic flux lines in disordered type-II superconductors in the presence of twin boundaries oriented parallel to the direction of the applied magnetic field, using a three-dimensional elastic line model…

Transmission through a complex network of nonlinear one-dimensional leads is discussed by extending the stationary scattering theory on quantum graphs to the nonlinear regime. We show that the existence of cycles inside the graph leads to a…

We consider a model of axisymmetric flows for a free boundary vortex embedded in a statically stable fluid at rest. We identify the boundary of the vortex by solving a variational problem. Then, we reduce the analysis of the dynamics of the…

We prove real analyticity of all the streamlines, including the free surface, of a gravity- or capillary-gravity-driven steady flow of water over a flat bed, with a H\"{o}lder continuous vorticity function, provided that the propagating…

In this paper, we study the vortex patch problem in an ideal fluid in a planar bounded domain. By solving a certain minimization problem and studying the limiting behavior of the minimizer, we prove that for any harmonic function $q$…

Viscous flow past a finite plate which is impulsively started in direction normal to itself is studied numerically using a high order mixed finite difference and semi-Lagrangian scheme. The goal is to resolve details of the vorticity…

The paper is devoted to vector fields on the spaces R^2 and R^3, their flow and invariants. Attention is plaid on the tensor representations of the group GL(2,R) and on fundamental vector fields. The rotation group on R^3 is generalized to…

We study the relation between flow structure and fluid deformation in steady two-dimensional random flows. Beyond the linear (shear flow) and exponential (chaotic flow) elongation paradigms, we find a broad spectrum of stretching behaviors,…