Vortex Perturbation Dynamics

An initial value approach is used to examine the dynamics of perturbations introduced into a vortex under strain. Both the basic vortex considered and the perturbations are taken as three-dimensional. An explicit solution for the time evolution of the vorticity perturbations is given for arbitrary initial vorticity. Analytical solutions for the resulting velocity components are found when the initial vorticity is assumed to be localized. For more general initial vorticity distributions, the velocity components are determined numerically. It is found that the variation in the radial direction of the initial vorticity disturbance is the most important factor influencing the qualitative behavior of the solutions. Transient growth in the magnitude of the velocity components is found to be directly attributable to the compactness of the initial vorticity.     

Vortex Generation in a Liquid Metal Duct Flow near a Magnetic Dipole

The generation of vortical structures by a strong magnetic dipole field in a liquid metal duct flow is studied by means of three-dimensional direct numerical simulations. The dipole is considered as the paradigm for a magnetic obstacle which will deviate the streamlines due to Lorentz forces which act on the fluid elements. Our model uses the quasi-static approximation applicable in the limit of small magnetic Reynolds numbers. The analysis covers the stationary flow regime at smaller flow Reynolds numbers Re as well as the fully time-dependent regimes at higher values with a turbulent flow in the wake of the magnetic obstacle. We present a systematic study of these two basic flow regimes on Re and the Hartmann number Ha, a measure of the strength of the magnetic dipole field. Furthermore, three orientations of the dipole are compared, the streamwise, spanwise and wall-normal ones. The most efficient generation of turbulence at a fixed distance above the duct occurs for the spanwise orientation in which we can observe the formation of Hartmann layers at the top plate. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Lateral Vortex Dynamics behind Ahmed body

The flow-field in the wake of Ahmed body was studied experimentally. The study is oriented on unsteady behavior of the lateral vortex pair arising in the wake as well as on the wake itself. The time-mean characteristics of the wake flow are presented. The dynamical behavior of the longitudinal vortex pair is studied in details. The Stereo Time-Resolved PIV method was applied in the wake plane perpendicular to the mean flow. Two variants of Ahmed Body with slat angle 25 and 35 degrees are investigated respectively. Comparison shows considerable differences in the vortex pair topology and dynamics of the cases in question. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

YMCS模型局部涡旋解的存在性

对规范场中出现的Yang-Mills-Chern-Simons(简记为YMCS)模型,首先讨论了其数学结构并由此导出了它所对应的非线性常微分方程的两点边值问题;其次,利用直接变分法证明了YMCS模型局部涡旋解的存在性,并利用分析技巧研究了解的性质;最后,利用比较原理建立了解在端点处的渐近估计.     

Effective Computation of the Dynamics Around a Two-Dimensional Torus of a Hamiltonian System

The purpose of this paper is to give an explicit analysis of the nonlinear dynamics around a two-dimensional invariant torus of an analytic Hamiltonian system. The study is based on high-order normal form techniques and the computation of an approximated first integral around the torus. One of the main novel aspects of the current work is the implementation of the symplectic reducibility of the quasi-periodic time-dependent variational equations of the torus. We illustrate the techniques in a particular example that is a quasi-periodic perturbation of the well-known Restricted Three Body Problem. The results are useful for describing the neighborhood of the triangular points of the Sun-Jupiter system.     

The ABCs of Magnetic Monopole Dynamics

We revisit the explicit solution of Newton's equation of motion (mass times acceleration equals force) for a (pointlike, massive) magnetic monopole moving in the Coulomb field of a (fixed, pointlike) electric charge or, equivalently, of a (pointlike, massive) electric charge moving in the magnetic field of a (fixed) magnetic monopole.     

Effective Potential and Quantum Dynamical Correlators

A new approach to the study of the properties of quantum dynamical systems by calculations of classical type is suggested. This approach is based on Mori theory and projection techniques. Bibliography: 14 titles.     

Dynamics of Domain Walls in a Cylindrical Amorphous Ferromagnetic Microwire with Magnetic Inhomogeneities

Theoretical and Mathematical Physics - We study the dynamics of a domain wall (DW) in the magnetic core of thin amorphous glass-coated bistable microwires with a circular cross section containing...     

Dynamics of a Local Perturbation in the X-Y Model II—Excitations

Excitations of a single spin embedded in the X Y chain are studied. We find that the magnetization does not approach equilibrium, even if the external magnetic field approaches a non-zero limit, and that oscillatory excitation resonates with the edge of the one-particle spectrum band.     

Dynamics of Local Automorphisms of Embedded CR-Manifolds

Mathematical Notes -     

Topological Dynamics and Local Product Structure

Topological properties of dynamical systems admitting a localproduct structure are studied. The results obtained are appliedto hyperbolic systems on covers. The main theorem characterizestransitivity on solvable covers in terms of Frobenius elementsof periodic orbits.     

Dynamics of Local Search Trajectory in Traveling Salesman Problem

This paper investigates dynamics of a local search trajectory generated by running the Or-opt heuristic on the traveling salesman problem. This study evaluates the dynamics of the local search heuristic by estimating the correlation dimension for the search trajectory, and finds that the local heuristic search process exhibits the transition from high-dimensional stochastic to low-dimensional chaotic behavior. The detection of dynamical complexity for a heuristic search process has both practical as well as theoretical relevance. The revealed dynamics may cast new light on design and analysis of heuristics and result in the potential for improved search process.     

On Tzitzéica Vortex Streets and Their Reciprocals in Subsonic Gas Dynamics

Hydrodynamic vortex street solutions are generated based on an elliptic Tzitzéica model. A multiparameter class of reciprocal transformations is coupled with the action of a Bäcklund transformation to construct compressible vortex solutions of breather type valid in subsonic flow régimes of a generalized Kármán–Tsien gas.     

Local Entropy Conditions in Transonic Potential Flow Problems

The transonic potential flow problem is handled as a variational problem over a closed convex set which is given by a bound for the gas velocity and by a local entropy condition. It can be shown that the minimum problem has a solution though the functional need not be convex and the given set is not compact. Furthermore, the convergence of an approximation method (KATCHANOV'S method) for the solution to the corresponding variational inequality is proved.     

Boundedness of the Riesz Potential in Local Morrey-Type Spaces

The problem of boundedness of the Riesz potential in local Morrey-type spaces is reduced to the problem of boundedness of the Hardy operator in weighted L _p -spaces on the cone of non-negative non-increasing functions. This allows obtaining sharp sufficient conditions for boundedness for all admissible values of the parameters, which, for a certain range of the parameters wider than known before, coincide with the necessary ones.     

Local Dynamics of a Singularly Perturbed Second Order Equation with State-Dependent Delay

Mathematical Notes -     

The Effect of Surface Tension on the Moore Singularity of Vortex Sheet Dynamics

We investigate the regularization of Moore’s singularities by surface tension in the evolution of vortex sheets and its dependence on the Weber number (which is inversely proportional to surface tension coefficient). The curvature of the vortex sheet, instead of blowing up at finite time t ₀, grows exponentially fast up to a O(We) limiting value close to t ₀. We describe the analytic structure of the solutions and their self-similar features and characteristic scales in terms of the Weber number in a O(We⁻¹) neighborhood of the time at which, in absence of surface tension effects, Moore’s singularity would appear. Our arguments rely on asymptotic techniques and are supported by full numerical simulations of the PDEs describing the evolution of vortex sheets.     

Application of Potential and Vortex Fields to the Description of Gravitation and Electromagnetism

We propose a system of differential equations in the tensor general-covariant form whose solutions are called gravitational and charged particles. For free fields, solutions are found in the form of Newton and Coulomb potentials.For a particle that rotates with constant velocity around another particle with large mass, a solution is obtained in the form if the particle is uncharged, and in the form if it is charged.