Related papers: Different routes towards oscillatory zoning in the…
Oscillatory Zoning (OZ) is a phenomenon exhibited by many geologically formed crystals. It is characterized by quasi periodic oscillations in the composition of a solid solution, caused by self-organization. We present a new model for OZ.…
We analyzed the stability of the uniform flow solution in the optimal velocity model for traffic and granular flow under the open boundary condition. It was demonstrated that, even within the linearly unstable region, there is a parameter…
We construct families of one-dimensional (1D) stable solitons in two-component $\mathcal{PT}$-symmetric systems with spin-orbit coupling (SOC) and quintic nonlinearity, which plays the critical role in 1D setups. The system models light…
We study nonlinear stability of spatially homogeneous oscillations in reaction-diffusion systems. Assuming absence of unstable linear modes and linear diffusive behavior for the neutral phase, we prove that spatially localized perturbations…
We study theoretically the spatial evolution of optical beams inside a graded-index fiber exhibiting saturable nonlinearity. Utilizing an approach based on the variational principle, we identify the existence of bistable spatial solitons…
We study the oscillations and stability of self-gravitating cylindrically symmetric fluid systems and collisionless systems. This is done by studying small perturbations to the equilibrium system and finding the normal modes, using methods…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
The dynamics of two active nonlinear resonators coupled to a linear resonator is studied theoretically. Possible stationary states and its dynamical stability are considered in detail. The spontaneous symmetry breaking is found and it is…
We consider a dynamical system, possibly infinite dimensional or non-autonomous, with fast and slow time scales which is oscillatory with high frequencies in the fast directions. We first derive and justify the limit system of the slow…
The possibility that extremely long-lived, time-dependent, and localized field configurations (``oscillons'') arise during the collapse of asymmetrical bubbles in 2+1 dimensional phi^4 models is investigated. It is found that oscillons can…
The May-Leonard model for three competing species, symmetric with respect to cyclic permutation of the variables and extended by diffusive terms, is considered. Exact time-periodic solutions of the system have been found, and their…
We consider the stability of a system of equations which are a singular perturbation of the incompressible rigid-plastic flow equations used to model granular flow. A linear stability analysis shows that solutions of these equations are…
We investigate the time-periodic solutions to the nonlinear wave and beam equations and uncover their intricate, fractal-like structure. In particular, we identify a new class of large-energy solutions with complex mode compositions and…
Industrial coating processes create thin liquid films with tight thickness tolerances, and thus models that predict the response to inevitable disturbances are essential. The mathematical modeling complexities are reduced through…
Starting from an ideal crystalline state, we numerically study a nonequilibrium dynamical order- disorder transition promoted by the application of a periodic shearing protocol at low temperatures in model systems in two and three…
Oscillons are spatially stationary, quasi-periodic solutions of nonlinear field theories seen in settings ranging from granular systems, low temperature condensates and early universe cosmology. We describe a new class of oscillon in which…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
Within the framework of the frozen temperature approximation we develop a strongly-nonlinear theory of one-dimensional pattern formation during directional solidification of binary mixture under nonequilibrium segregation. In the case of…
We investigate the presence of static solutions in generalized models described by a real scalar field in four-dimensional space-time. We study models in which the scalar field engenders higher-order derivatives and spontaneous symmetry…
We consider the orientational instabilities, both homogeneous and spatially periodic, developing in a nematic liquid crystal under rectilinear oscillatory Couette flow for director alignment perpendicular to the flow plane. Using numerical…