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The phenomenon of branched flow, visualized as a chaotic arborescent pattern of propagating particles, waves, or rays, has been identified in disparate physical systems ranging from electrons to tsunamis, with periodic systems only recently…
Drops of active liquid crystal have recently shown the ability to self-propel, which was associated with topological defects in the orientation of active filaments [Sanchez {\em et al.}, Nature {\bf 491}, 431 (2013)]. Here, we study the…
The boundaries of waveguides and nanowires have drastic influence on their coherent scattering properties. Designing the boundary profile is thus a promising approach for transmission and band-gap engineering with many applications. By…
Non-relativistic particles that are effectively confined to two dimensions can in general move on curved surfaces, allowing dynamical phenomena beyond what can be described with scalar potentials or even vector gauge fields. Here we…
The chaotic properties of simple two-dimensional rotation-translation models are explored and simulated. The models are given in difference equation forms, while the corresponding differential equations systems are studied and the resulting…
Structures such as waves, jets, and vortices have a dramatic impact on the transport properties of a flow. Passive tracer transport in incompressible two-dimensional flows is described by Hamiltonian dynamics, and, for idealized structures,…
The propagations of diseases, behaviors and information in real systems are rarely independent of each other, but they are coevolving with strong interactions. To uncover the dynamical mechanisms, the evolving spatiotemporal patterns and…
Spatial patterns are widely observed in numerous nonequilibrium natural systems, often undergoing complex transitions and bifurcations, thereby exhibiting significant importance in many physical and biological systems such as embryonic…
We have adapted classical molecular dynamics to study the structural and dynamical properties of amorphous silica surfaces. Concerning the structure, the density profile exhibits oscillations perpendicularly to the surface as observed in…
Pattern formation often occurs in confined systems, yet how boundaries shape patterning dynamics is unclear. We develop techniques to analyze confinement effects in nonlocal advection-diffusion equations, which generically capture the…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…
A major achievement in the study of complex networks is the observation that diverse systems, from sub-cellular biology to social networks, exhibit universal topological characteristics. Yet this universality does not naturally translate to…
In this paper we consider developable surfaces which are isometric to planar domains and which are piecewise differentiable, exhibiting folds along curves. The paper revolves around the longstanding problem of existence of the so-called…
We study a system whose dynamics are governed by predictions of its future states. A general formalism and concrete examples are presented. We find that the dynamical characteristics depend on how to shape the predictions as well as on how…
Oscillating fields can make domain patterns change into various types of structures. Numerical simulations show that concentric-ring domain patterns centered at a strong defect are observed under a rapidly oscillating field in some cases.…
Numerical and experimental turbulence simulations are nowadays reaching the size of the so-called big data, thus requiring refined investigative tools for appropriate statistical analyses and data mining. We present a new approach based on…
The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the…
Collective dynamics in proliferating anisotropic particle systems arise from an interplay between growth, division, and mechanical interactions, often mediated by particle shape. In classical models of prolate, rod-like growth, flow-induced…
The dynamics of phase-separated interfaces shape the behavior of both passive and active condensates. While surface tension in equilibrium systems minimizes interface length, non-equilibrium fluxes can destabilize flat or constantly curved…
Flow networks are essential for both living organisms and enginneered systems. These networks often present complex dynamics controlled, at least in part, by their topology. Previous works have shown that topologically complex networks…