Dynamo effect in parity-invariant flow with large and moderate separation of scales

It is shown that non-helical (more precisely, parity-invariant) flows capable of sustaining a large-scale dynamo by the negative magnetic eddy diffusivity effect are quite common. This conclusion is based on numerical examination of a large number of randomly selected flows. Few outliers with strongly negative eddy diffusivities are also found, and they are interpreted in terms of the closeness of the control parameter to a critical value for generation of a small-scale magnetic field. Furthermore, it is shown that, for parity-invariant flows, a moderate separation of scales between the basic flow and the magnetic field often significantly reduces the critical magnetic Reynolds number for the onset of dynamo action.Comment: 44 pages,11 figures, significantly revised versio

Fold-Saddle Bifurcation in Non-Smooth Vector Fields on the Plane

This paper presents results concerning bifurcations of 2D piecewise-smooth dynamical systems governed by vector fields. Generic three parameter families of a class of Non-Smooth Vector Fields are studied and its bifurcation diagrams are exhibited. Our main result describes the unfolding of the so called Fold-Saddle singularity

Analytical Study of Certain Magnetohydrodynamic-alpha Models

In this paper we present an analytical study of a subgrid scale turbulence model of the three-dimensional magnetohydrodynamic (MHD) equations, inspired by the Navier-Stokes-alpha (also known as the viscous Camassa-Holm equations or the Lagrangian-averaged Navier-Stokes-alpha model). Specifically, we show the global well-posedness and regularity of solutions of a certain MHD-alpha model (which is a particular case of the Lagrangian averaged magnetohydrodynamic-alpha model without enhancing the dissipation for the magnetic field). We also introduce other subgrid scale turbulence models, inspired by the Leray-alpha and the modified Leray-alpha models of turbulence. Finally, we discuss the relation of the MHD-alpha model to the MHD equations by proving a convergence theorem, that is, as the length scale alpha tends to zero, a subsequence of solutions of the MHD-alpha equations converges to a certain solution (a Leray-Hopf solution) of the three-dimensional MHD equations.Comment: 26 pages, no figures, will appear in Journal of Math Physics; corrected typos, updated reference

SINGULAR PERTURBATIONS AND BOUNDARY LAYER THEORY FOR CONVECTION-DIFFUSION EQUATIONS IN A CIRCLE: THE GENERIC NONCOMPATIBLE CASE

We study the boundary layers and singularities generated by a convection-diffusion equation in a circle with noncompatible data. More precisely, the boundary of the circle has two characteristic points where the boundary conditions and the external data $f$ are not compatible. Very complex singular behaviors are observed, and we analyze them systematically for highly noncompatible data. The problem studied here is a simplified model for problems of major importance in fluid mechanics and thermohydraulics and in physics.open4

Dynamics of Open Bosonic Quantum Systems in Coherent State Representation

We consider the problem of decoherence and relaxation of open bosonic quantum systems from a perspective alternative to the standard master equation or quantum trajectories approaches. Our method is based on the dynamics of expectation values of observables evaluated in a coherent state representation. We examine a model of a quantum nonlinear oscillator with a density-density interaction with a collection of environmental oscillators at finite temperature. We derive the exact solution for dynamics of observables and demonstrate a consistent perturbation approach.Comment: 7 page

Linear instability criteria for ideal fluid flows subject to two subclasses of perturbations

In this paper we examine the linear stability of equilibrium solutions to incompressible Euler's equation in 2- and 3-dimensions. The space of perturbations is split into two classes - those that preserve the topology of vortex lines and those in the corresponding factor space. This classification of perturbations arises naturally from the geometric structure of hydrodynamics; our first class of perturbations is the tangent space to the co-adjoint orbit. Instability criteria for equilibrium solutions are established in the form of lower bounds for the essential spectral radius of the linear evolution operator restricted to each class of perturbation.Comment: 29 page

Generation of small-scale structures in the developed turbulence

The Navier-Stokes equation for incompressible liquid is considered in the limit of infinitely large Reynolds number. It is assumed that the flow instability leads to generation of steady-state large-scale pulsations. The excitation and evolution of the small-scale turbulence is investigated. It is shown that the developed small-scale pulsations are intermittent. The maximal amplitude of the vorticity fluctuations is reached along the vortex filaments. Basing on the obtained solution, the pair correlation function in the limit $r\to 0$ is calculated. It is shown that the function obeys the Kolmogorov law $r^{2/3}$.Comment: 18 page

A momentum-dependent perspective on quasiparticle interference in Bi_{2}Sr_{2}CaCu_{2}O_{8+\delta}

Angle Resolved Photoemission Spectroscopy (ARPES) probes the momentum-space electronic structure of materials, and provides invaluable information about the high-temperature superconducting cuprates. Likewise, the cuprate real-space, inhomogeneous electronic structure is elucidated by Scanning Tunneling Spectroscopy (STS). Recently, STS has exploited quasiparticle interference (QPI) - wave-like electrons scattering off impurities to produce periodic interference patterns - to infer properties of the QP in momentum-space. Surprisingly, some interference peaks in Bi_{2}Sr_{2}CaCu_{2}O_{8+\delta} (Bi-2212) are absent beyond the antiferromagnetic (AF) zone boundary, implying the dominance of particular scattering process. Here, we show that ARPES sees no evidence of quasiparticle (QP) extinction: QP-like peaks are measured everywhere on the Fermi surface, evolving smoothly across the AF zone boundary. This apparent contradiction stems from different natures of single-particle (ARPES) and two-particle (STS) processes underlying these probes. Using a simple model, we demonstrate extinction of QPI without implying the loss of QP beyond the AF zone boundary