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We investigate the stationary states of one-dimensional driven diffusive systems, coupled to boundary reservoirs with fixed particle densities. We argue that the generic phase diagram is governed by an extremal principle for the macroscopic…
The nonlinear rheological properties of dense suspensions are discussed within simplified models, suggested by a recent first principles approach to the model of Brownian particles in a constant-velocity-gradient solvent flow. Shear…
Wave function collapse models are considered as the modified theories of standard quantum mechanics at the macroscopic level. By introducing nonlinear stochastic terms in the Schr\"odinger equation, these models make predictions,…
We numerically analyse solutions of the spherically symmetric gravitational Vlasov-Poisson system close to compactly supported stable steady states. We observe either partially undamped oscillations or macroscopically damped solutions. We…
Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance…
We develop a unified instantaneous-mode description for lasers with dispersive cavities, exploiting the separation of timescales between fast cavity fields and slow carrier dynamics. The resulting reduced rate equations retain the essential…
The dynamics of two two-level dipole-dipole interacting atoms coupled to a common electromagnetic bath and closely located inside a lossy cavity, is reported. Initially injecting only one excitation in the two atoms-cavity system, loss…
The decay of quasi-stable quantum system involves primarily an outgoing probability current density. However, during the transition from exponential to inverse-power-law decay there are time intervals during which this current, although…
The consecutive microscopic solution is presented of the problem of tunneling of a particle through a potential barrier. The method is applied to the alpha and proton decay of compound systems formed in fusion reaction. Appearance of the…
We introduce a model which gives rise to self-trapping of fundamental and higher-order localized states in a one-dimensional nonlinear Schr\"odinger equation with fractional diffraction and the strength of the self-defocusing nonlinearity…
The local field correction to the spontanous dacay rate of an impurity source atom imbedded in a disordered dielectric is calculated to second order in the dielectric density. The result is found to differ from predictions associated with…
We provide a minimal continuum model for mesoscale plasticity, explaining the cellular dislocation structures observed in deformed crystals. Our dislocation density tensor evolves from random, smooth initial conditions to form self-similar…
We study the decay of large amplitude, almost periodic breather-like states in a deformed sine-Gordon model in one spatial dimension. We discover that these objects decay in a staggered fashion via a series of transitions, during which…
In order to investigate the size limit on spatial localized structures in a nonlinear system, we explore the impact of linear nonlocality on their domains of existence and stability. Our system of choice is an optical microresonator…
In the present work, the behavior of vacancy pore inside of spherical particle is investigated. On the assumption of quasistationarity of diffusion fluxes, the nonlinear equation set was obtained analytically, that describes completely pore…
New resonant emission of dispersive waves by oscillating solitary structures is considered analytically and numerically. The resonance condition for the radiation is derived and it is demonstrated that the predicted resonances match the…
The dynamical behavior of a nonlinear micromechanical resonator acting as one of the mirrors in an optical resonance cavity is investigated. The mechanical motion is coupled to the optical power circulating inside the cavity both directly…
Shell structure of the single-particle spectrum for reflection-asymmetric deformed cavity is investigated. Remarkable shell structure emerges for certain combinations of quadrupole and octupole deformations. Semiclassical periodic-orbit…
I review recent results concerning the shape of drifting subpulse patterns, and the relationship to model predictions. While a variety of theoretical models exist for drifting subpulses, observers typically think in terms of a…
Concentrated suspensions may shear-thin when the suspended particles form planar sheets that slide over one another with less friction than if the particles are randomly distributed. In a na\"ive model the suspension is described by a mean…