相关论文: A Hamiltonian approach for point vortices on non-o…

Within the framework of variational modelling we derive a one-phase moving boundary problem describing the motion of a semipermeable membrane enclosing a viscous liquid, driven by osmotic pressure and surface tension of the membrane. For…

We present a novel semiclassical phase-space surface hopping approach that goes beyond the Born-Oppenheimer approximation and all existing surface hopping formalisms. We demonstrate that working with a correct phase-space electronic…

We demonstrate the control of vortical motion of neutral classical particles in driven superlattices. Our superlattice consists of a superposition of individual lattices whose potential depths are modulated periodically in time but with…

We develop a rigorous analytical Hamiltonian formalism adapted to the study of the motion of two planets in co-orbital resonance. By constructing a complex domain of holomorphy for the planetary Hamilto-nian, we estimate the size of the…

We study the motion of a single helical vortex in an unbounded, inviscid, incompressible fluid. The vortex is an infinite tube whose centerline is a helix and whose cross section is a circle of small radius (compared to the radius of…

We prove the existence of at least $cl(M)$ periodic orbits for certain time dependant Hamiltonian systems on the cotangent bundle of an arbitrary compact manifold $M$. These Hamiltonians are not necessarily convex but they satisfy a certain…

A class of Hamiltonian deformations of plane curves is defined and studied. Hamiltonian deformations of conics and cubics are considered as illustrative examples. These deformations are described by systems of hydrodynamical type equations.…

In this paper we extend the standard differential geometric theory of Hamiltonian dynamics to noncommutative spaces, beginning with symplectic forms. Derivations on the algebra are used instead of vector fields, and interior products and…

It is shown that the oscillation method to study liquid viscosity of [1-3,7-34] is based on incorrect consideration of one dimensional forced (constrained) )vibrations of plate in viscous liquid, because additional (apparent) mass of liquid…

We study the effect of time-dependent, non-conservative perturbations on the dynamics along homoclinic orbits to a normally hyperbolic invariant manifold. We assume that the unperturbed system is Hamiltonian, and the normally hyperbolic…

It is shown that the hydrodynamics equations for a thin spherical liquid layer are satisfied by the stream function of a pair of antipodal vortices-APV, in contrast to the stream function of a single point vortex on a sphere with a…

We explore the complex dynamics of a non-coalescing drop of moderate size inside a circular hydraulic jump of the same liquid formed on a horizontal disk. In this situation the drop is moving along the jump and one observes two different…

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…

The quantisation of the reduced first-order dynamics of the nonrelativistic model for Chern-Simons vortices introduced by Manton is studied on a sphere of given radius. We perform geometric quantisation on the moduli space of static…

We study the existence of homoclic solutions for reversible Hamiltonian systems taking the family of differential equations u^4+au^2-u+f(u,b)=0 as a model. Here f is an analytic function and a, b real parameters. These equations are…

We investigate the dynamic behavior of optical vortices, or phase singularities, in random wavefields and demonstrate the direct experimental observation of the anomalous diffusion of optical vortices. The observed subdiffusion of optical…

The motion of a charged particle moving on a flat surface is studied through the constants of motion associated to the system, given the magnetic gauge. The usual Landau' solution and the non separable solution for the Landau's gauge are…

We consider the problem of soliton-mean field interaction for the class of asymptotically integrable equations, where the notion of the asymptotic integrability means that the Hamilton equations for the high-frequency wave packet's…

We prove a sufficient condition for nonlinear stability of relative equilibria in the planar $N$-vortex problem. This result builds on our previous work on the Hamiltonian formulation of its relative dynamics as a Lie--Poisson system. The…

In this paper, we develop a three-dimensional multiple-relaxation-time lattice Boltzmann method (MRT-LBM) based on a set of non-orthogonal basis vectors. Compared with the classical MRT-LBM based on a set of orthogonal basis vectors, the…