Related papers: Towards a String Formulation of Vortex Dynamics
We study the influence of linear friction on the vortex motion in a non-viscous stratified compressible rotating media. Our method can be applied to describe the complex behavior of a tropical cyclone approaching land. In particular, we…
The fundamental equations of relativistic dynamics are derived from a thought experiment and from the transformation of relativistic velocity avoiding collisions and conservation laws of momentum and energy.
We establish vortex dynamics for the time-dependent Ginzburg-Landau equation for asymptotically large numbers of vortices for the problem without a gauge field and either Dirichlet or Neumann boundary conditions. As our main tool, we…
A general phenomenological reaction-diffusion model for flow-induced phase transitions in complex fluids is presented. The model consists of an equation of motion for a nonconserved composition variable, coupled to a Newtonian stress…
The vorticity plays an important role in aerodynamics and rotational flow. Usually, they are studied with modified Navier-Stokes equation. This research will deduce the motion equation of vorticity from Navier-Stokes equation. To this…
Turbulent fluid flows exhibit a complex small-scale structure with frequently occurring extreme velocity gradients. Particles probing such swirling and straining regions respond with an intricate shape-dependent orientational dynamics,…
We consider a nonlinear model equation, known as the Localized Induction Equation, describing the motion of a vortex filament immersed in an incompressible and inviscid fluid. We prove the unique solvability of an initial-boundary value…
In this paper we study concentrated solutions of the three-dimensional Euler equations in helical symmetry without swirl. We prove that any helical vorticity solution initially concentrated around helices of pairwise distinct radii remains…
The pendulum, in the presence of linear dissipation and a constant torque, is a non-integrable, nonlinear differential equation. In this paper, using the idea of rotated vector fields, derives the relation between the applied force $\beta$…
We investigate the presence of vortex solutions in potentials without vacuum state. The study is conducted considering Maxwell and Chern-Simons dynamics. Also, we use a first order formalism that helps us to find the solutions and their…
The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…
We show how the classical string dynamics in $D$-dimensional curved background can be reduced to the dynamics of a massless particle constrained on a certain surface whenever there exists at least one Killing vector for the background…
We apply the modulation theory to study the vortex and radiation solution in the two-dimensional nonlinear Schr\"{o}dinger equation. The full modulation equations which describe the dynamics of the vortex and radiation separately are…
The normal form and zero dynamics are powerful tools useful in analysis and control of both linear and nonlinear systems. There are no simple closed form solutions to the general zero dynamics problem for nonlinear systems. A few algorithms…
We formulate the string field theory in zero-dimensional target space corresponding to the two-dimensional quantum gravity theory defined through Causal Dynamical Triangulations. This third quantization of the quantum gravity theory allows…
We study the dynamics of vortices in a two-dimensional, non-equilibrium system, described by the compact Kardar-Parisi-Zhang equation, after a sudden quench across the critical region. Our exact numerical solution of the phase-ordering…
The unbinding of vortex-antivortex pairs for the classical two-dimensional XY model in a magnetic field is studied. A single such pair is connected by a string of overturned spins, leading to linear confinement. We show that this system…
The venerable 2D point-vortex model plays an important role as a simplified version of many disparate physical systems, including superfluids, Bose-Einstein condensates, certain plasma configurations, and inviscid turbulence. This system is…
We present the general formulation of the relativistic fluid dynamics with vorticity (including relativistic superfluid) on a manifold with boundary. Making use of the Hodge decomposition, we emphasize that the equations of motion include a…
The formation of vortex loops (global cosmic strings) in an O(2) linear sigma model in three spatial dimensions is analyzed numerically. For over-damped Langevin dynamics we find that defect production is suppressed by an interaction…