Related papers: The Global Phase Space of the Three-Vortex Interac…
In this paper, we use rigorous numerics to compute several global smooth branches of steady states for a system of three reaction-diffusion PDEs introduced by Iida et al. [J. Math. Biol., {\bf 53}, 617--641 (2006)] to study the effect of…
Incompressible Navier-Stokes equations in the spherical coordinates are solved using a pseudo-spectral method to simulate the problem of spherical Couette flow. The flow is investigated for a narrow gap ratio with only the inner sphere…
This paper deals with the dynamics of time-reversible Hamiltonian vector fields with 2 and 3 degrees of freedom around an elliptic equilibrium point in presence of symplectic involutions. The main results discuss the existence of…
We consider merger of two parallel toroidal atomic Bose-Einstein condensates with different vorticities in a three-dimensional (3D) trap. In the tunnel-coupling regime, Josephson vortices (rotational fluxons) emerge in the barrier between…
Integrable problem of three vorteces on a plane and sphere are considered. The classification of Poisson structures is carried out. We accomplish the bifurcational analysis using the variables introduced in previous part of the work.
In this paper we use a traveling wave reduction or a so-called spatial approximation to comprehensively investigate the periodic solutions of the complex cubic-quintic Ginzburg-Landau equation. The primary tools used here are Hopf…
In this paper, we study the (1+3) dimensional massive Maxwell-Dirac system in the context of global existence and asymptotic behavior of solutions under the Lorenz gauge condition, as well as the modified and linear scattering phenomena for…
We investigate the process of coarsening via annihilation of vortex-antivortex pairs, following the quench to the condensate phase in a nonresonantly pumped polariton system. We find that the late-time dynamics is an example of universal…
We present a theoretical analysis of the phase diagram of two--component bosons on an optical lattice. A new formalism is developed which treats the effective spin interactions in the Mott and superfluid phases on the same footing. Using…
To facilitate the analysis of pattern formation and of the related phase transitions in Bose-Einstein condensates (BECs) we present an explicit approximate mapping from the nonlocal Gross-Pitaevskii equation with cubic nonlinearity to a…
Symmetry reduction by the method of slices quotients the continuous symmetries of chaotic flows by replacing the original state space by a set of charts, each covering a neighborhood of a dynamically important class of solutions,…
The effect of small forced symmetry breaking on the dynamics near a structurally stable heteroclinic cycle connecting two equilibria and a periodic orbit is investigated. This type of system is known to exhibit complicated, possibly chaotic…
Using Monte Carlo Simulation and fundamental measure theory we study the phase diagram of a two-dimensional lattice gas model with a nearest neighbor hard core exclusion and a next-to-nearest neighbors finite repulsive interaction. The…
The phase diagram of a simple model with two patches of type A and ten patches of type B (2A10B) on the face centred cubic lattice has been calculated by simulations and theory. Assuming that there is no interaction between the B patches…
Josephson junction arrays are ideal model systems where a variety of phenomena, phase transitions, frustration effects, vortex dynamics, chaos, to mention a few of them, can be studied in a controlled way. In this review we focus on the…
The global phase diagram of the spinless Falicov-Kimball model in d = 3 spatial dimensions is obtained by renormalization-group theory. This global phase diagram exhibits five distinct phases. Four of these phases are charge-ordered (CO)…
We examine the phase diagram of a Bose-Einstein condensate of atoms, interacting with an attractive pseudopotential, in a quadratic-plus-quartic potential trap rotating at a given rate. Investigating the behavior of the gas as a function of…
We present a geometric derivation of the quasi-geostrophic equations on the sphere, starting from the rotating shallow water equations. We utilise perturbation series methods in vorticity and divergence variables. The derivation employs…
We present a dimensional reduction argument to derive the classification reduction of fermionic symmetry protected topological phases in the presence of interactions. The dimensional reduction proceeds by relating the topological character…
In this paper, we study the possible bifurcations of periodic orbits by reducing them to graphs. The aforementioned allows to study the genericity of routes to chaos, as well as to analyze their possible complexity. In particular, our…