Related papers: Nonlinear Aggregation of Phase Elements on the Uni…
Theoretical studies of synchronization are usually based on models of coupled phase oscillators which, when isolated, have constant angular frequency. Stochastic discrete versions of these uniform oscillators have also appeared in the…
The coupled electron-nuclear spin system in an InGaAs semiconductor as testbed of nonlinear dynamics can develop auto-oscillations, resembling time-crystalline behavior, when continuously excited by a circularly polarized laser. We expose…
Recent advances in the study of synthetic dimensions revealed a possibility to employ the frequency space as an additional degree of freedom which allows for investigating and exploiting higher-dimensional phenomena in a priori…
Directional solidification of water-based solutions has emerged as a versatile technique for templating hierarchical porous materials. However, the underlying mechanisms of pattern formation remain incompletely understood. In this work, we…
This paper is devoted to study the phase space analysis of isotropic and homogenous universe model by taking a noninteracting mixture of electromagnetic and viscous radiating fluids whose viscous pressure satisfies a nonlinear version of…
We consider the one-dimensional Schroedinger equation on a ring, with the cubic term, of either self-attractive or repulsive sign, confined to a narrow segment. This setting can be realized in optics and Bose-Einstein condensates. For the…
We construct a nonlinear $\sigma$ model to describe a system of non-interacting electrons propagating in the presence of random magnetic flux. We find a term describing the long ranged logarithmic interaction between the topological density…
Active colloids belong to a class of non-equilibrium systems where energy uptake, conversion and dissipation occurs at the level of individual colloidal particles, which can lead to particles self-propelled motion and surprising collective…
We provide the detailed asymptotic behavior for first-order aggregation models of heterogeneous oscillators. Due to the dissimilarity of natural frequencies, one could expect that all relative distances converge to definite positive value…
Materials that undergo internal transformations are usually described in solid mechanics by multi-well energy functions that account for both elastic and transformational behavior. In order to separate the two effects, physicists use…
The propagation of stable coherent entities of an electromagnetic field in nonlinear media with parameters varying in space can be described in the framework of iterations of nonlinear integral transformations. It is shown that for a set of…
The aggregation of attractive colloids has been extensively studied from both theoretical and experimental perspectives as the fraction of solid particles is changed, and the range, type and strength of attractive or repulsive forces…
Over the past decades, nonlocal models have been widely used to describe aggregation phenomena in biology, physics, engineering, and the social sciences. These are often derived as mean-field limits of attraction-repulsion agent-based…
This paper addresses the amplitude and phase dynamics of a large system non-linear coupled, non-identical damped harmonic oscillators, which is based on recent research in coupled oscillation in optomechanics. Our goal is to investigate the…
We prove the existence of a compact, finite dimensional, global attractor for a coupled PDE system comprising a nonlinearly damped semilinear wave equation and a nonlinear system of thermoelastic plate equations, without any mechanical…
We present a phase-field model for simulating the solid-state dewetting of anisotropic crystalline films on non-planar substrates. This model exploits two order parameters to trace implicitly the crystal free surface and the substrate…
If a magnetic field normal to the surface of a magnetic fluid is increased beyond a critical value a spontaneous deformation of the surface arises (normal field instability). The instability is subcritical and leads to peaks of a…
Based on Brownian Dynamics computer simulations in two dimensions we investigate aggregation scenarios of colloidal particles with directional interactions induced by multiple external fields. To this end we propose a model which allows…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…
The dynamics of a (nonlinear) Berger plate in the absence of rotational inertia are considered with inhomogenous boundary conditions. In our analysis, we consider boundary damping in two scenarios: (i) free plate boundary conditions, or…