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We discuss deep inelastic scattering at high energies as a critical phenomenon in 2+1 space - time dimensions. In the limit of Bjorken $x \to 0$, $QCD$ SU(3) with quark fields becomes a critical theory with a diverging correlation length…
In this paper we prove the breakdown of an heteroclinic connection in the analytic versal unfoldings of the generic Hopf-Zero singularity in an open set of the parameter space. This heteroclinic orbit appears at any order if one performs…
An rf superconducting quantum interference device (SQUID) consists of a superconducting ring interrupted by a Josephson junction (JJ). When driven by an alternating magnetic field, the induced supercurrents around the ring are determined by…
We study the Cauchy problem for the sine-Gordon equation in the semiclassical limit with pure-impulse initial data of sufficient strength to generate both high-frequency rotational motion near the peak of the impulse profile and also…
We consider a prototypical model in which a nonlinear field (continuum or discrete) evolves on a flexible substrate which feeds back to the evolution of the main field. We identify the underlying physics and potential applications of such a…
In this contribution we study the Klein-Gordon oscillator on the curved background within the Kaluza-Klein theory. The problem of interaction between particles coupled harmonically with a topological defects in Kaluza-Klein theory is…
Spatiotemporal chaos arising from the competition between sine-Gordon-breather and kink-antikink-pair solitons by reshaping an ac force is demonstrated. After introducing soliton collective coordinates, Melnikov's method is applied to the…
Following Part~I, we consider a class of reversible systems and study bifurcations of homoclinic orbits to hyperbolic saddle equilibria. Here we concentrate on the case in which homoclinic orbits are symmetric, so that only one control…
Directed motion of topological solitons (kinks or antikinks) in the damped and AC-driven discrete sine-Gordon system is investigated. We show that if the driving field breaks certain time-space symmetries, the soliton can perform…
Recent experimental and theoretical developments have motivated interest in a more detailed exploration of heavy ion collisions in the range sqrt(sNN)=5-15 GeV. In contrast to interactions at the full RHIC energy of sqrt(sNN)=200 GeV, such…
Starting from the classical Saltzman 2D convection equations, we derive via a severe spectral truncation a minimal 10 ODE system which includes the thermal effect of viscous dissipation. Neglecting this process leads to a dynamical system…
We study quantum dynamics of the rotationally driven Dicke model where the collective spin is rotated around the z axis with a finite velocity. In the absence of the rotating wave approximation we observe that for several physically…
Collapse, or a gravitational-like phase transition is studied in a microcanonical ensemble of particles with an attractive $1/r^{\alpha}$ potential. A mean field continuous integral equation is used to determine a saddle-point density…
The QCD phase diagram may feature a critical end point at a temperature T and baryon chemical potential $\mu$ which is accessible in heavy ion collisions. The universal long wavelength fluctuations which develop near this Ising critical…
The limiting slow dynamics of slow-fast, piecewise-linear, continuous systems of ODEs occurs on critical manifolds that are piecewise-linear. At points of non-differentiability, such manifolds are not normally hyperbolic and so the…
The main goal of this paper is to understand finer properties of the effective burning velocity from a combustion model introduced by Majda and Souganidis [19]. Motivated by results in [4] and applications in turbulent combustion, we show…
One possible framework to interpret the irreversibility transition observed in periodically driven colloidal suspensions is that of a non-equilibrium phase transition towards an absorbing reversible state at low amplitude of the driving…
We study the dynamics and symplectic topology of energy hypersurfaces of mechanical Hamiltonians on twisted cotangent bundles. We pay particular attention to periodic orbits, displaceability, stability and the contact type property, and the…
We study the orbits of two interacting particles described by a fully relativistic classical mechanical Hamiltonian. We use two sets of initial conditions. In the first set (dynamics 1) the system's center of mass is at rest. In the second…
We review the non-relativistic Green's-function approach to the kinetic equations for Fermi liquids far from equilibrium. The emphasis is on the consistent treatment of the off-shell motion between collisions and on the non-instant and…