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Exciton condensation, characterized by uniform phase coherence across macroscopic length scales, has enabled the discovery of a variety of excitonic states, greatly enriching our understanding of correlated many-body physics. More exotic…
The dynamics of a one-degree of freedom oscillator with arbitrary polynomial non-linearity subjected to an external periodic excitation is studied. The sequences (cascades) of harmonic and subharmonic stationary solutions to the equation of…
Theories of localised pattern formation are important to understand a broad range of natural patterns, but are less well-understood than more established mechanisms of domain-filling pattern formation. Here, we extend recent work on pattern…
Unconventional d-wave superconductors with pair-breaking edges are predicted to have ground states with spontaneously broken time-reversal and translational symmetries. We use the quasiclassical theory of superconductivity to demonstrate…
We study an emergent semiclassical time crystal composed of two interacting driven-dissipative bosonic modes. The system has a discrete $\mathbb Z_2$ spatial symmetry which, depending on the strength of the drive, can be broken in the…
We study the emergence and the stability of temporal localized structures in the output of a semiconductor laser passively mode-locked by a saturable absorber in the long cavity regime. For large yet realistic values of the linewidth…
A dynamical system of equations describing parametric sound generation (PSG) in a dispersive large aspect ratio resonator is derived. The model generalizes previously proposed descriptions of PSG by including diffraction effects, and is…
A model of superconductivity is proposed taking into account repulsive particle interaction, mesoscopic phase separation and softening of crystalline lattice. These features are typical of many high-temperature superconductors. The main…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
The response of a model micro-electrochemical system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochemistry, colloidal science, and microfluidics. The model problem…
Time crystals, as temporal analogs of space crystals, manifest as stable and periodic behavior that breaks time translation symmetry. In an open quantum system, many-body interaction subjected to dissipation allows one to develop the time…
Supersonic turbulence is a large reservoir of suprathermal energy in the interstellar medium. Its dissipation, because it is intermittent in space and time, can deeply modify the chemistry of the gas. We further explore a hybrid method to…
We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of individual nodes, communities, or the entire graph. Given this…
It is well known that the classical energetically consistent micropolar model has limits in simulating the frequency band structure of packed granular materials (see Merkel et al., 2011). It is here shown that if a standard continualization…
Much work has been devoted to analysing thermodynamic models for solid dispersions with a view to identifying regions in the phase diagram where amorphous phase separation or drug recrystallization can occur. However, detailed partial…
We consider a model problem of the scattering of linear acoustic waves in free homogeneous space by an elastic solid. The stress tensor in the solid combines the effect of a linear dependence of strains with the influence of an existing…
We study the nonlinear behaviors of mass-spring systems damped by dry friction using simulation by a nonlinear LC circuit damped by anti-parallel diodes. We show that the differential equation for the electric oscillator is equivalent to…
Spontaneous pattern formation is a phenomenon ubiquitous in nature, examples ranging from Rayleigh-Benard convection to the emergence of complex organisms from a single cell. In physical systems, pattern formation is generally associated…
Spatio-temporal signals arising from event-driven biological processes, such as surface electromyography (sEMG), exhibit asynchronous and highly structured activation patterns that are challenging to model using conventional discrete or…
Reaction-diffusion-advection media on semi-infinite domains are important in chemical, biological and ecological applications, yet remain a challenge for pattern formation theory. To demonstrate the rich emergence of nonlinear traveling…