Related papers: Pattern Formation with Two Length Scales: Spatiote…
We present measurements of the complete spatio-temporal Fourier spectrum of Faraday waves. The Faraday waves are generated at the interface of two immiscible index matched liquids of different density. By use of a new absorption technique…
Coupling diffusion process of signaling molecules with nonlinear interactions of intracellular processes and cellular growth/transformation leads to a system of reaction-diffusion equations coupled with ordinary differential equations…
Interference between two waves is a well-known concept in physics, and its generalization to more than two waves is straight-forward. The order of interference is defined as the number of paths that interfere in a manner that cannot be…
Using simple kinematics, we propose a general theory of linear wave interactions between the interfacial waves of a two dimensional (2D), inviscid, multi-layered fluid system. The strength of our formalism is that one does not have to…
The spatiotemporal variation in tropical air-sea interaction is investigated by applying a simple model that considers the fundamental dynamics in tropical oceans. The model decomposes sea surface temperature anomaly (SSTA) variation into a…
We present an experimental study of quasiperiodic transitions between a highly ordered square-lattice pattern and a disordered, defect-riddled state, in a circular Faraday system. We show that the transition is driven initially by a…
Pattern formation often occurs in spatially extended physical, biological and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and…
Ocean motions at frequencies of the internal wave band are generally associated with freely propagating waves that are supported by stable vertical stratification in density. Previous analyses of yearlong current observations from the Bay…
Triadic interactions are higher-order interactions that occur when a set of nodes affects the interaction between two other nodes. Examples of triadic interactions are present in the brain when glia modulate the synaptic signals among…
The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…
Waves patterns in the Faraday instability have been studied for decades. Besides the rich dynamics that can be observed on the waves at the interface, Faraday waves hide beneath them an elusive range of flow patterns --or streaming…
Motivated by the modeling of three-dimensional fluid turbulence, we define and study a class of stochastic partial differential equations (SPDEs) that are randomly stirred by a spatially smooth and uncorrelated in time forcing term. To…
The dynamics of hexagon patterns in rotating systems are investigated within the framework of modified Swift-Hohenberg equations that can be considered as simple models for rotating convection with broken up-down symmetry, e.g.…
Pattern formation in parametric surface waves is studied in the limit of weak viscous dissipation. A set of quasi-potential equations (QPEs) is introduced that admits a closed representation in terms of surface variables alone. A multiscale…
We study the structure, stability, and dynamics of dark solitary waves in parabolically trapped, collisionally inhomogeneous Bose-Einstein condensates (BECs) with spatially periodic variations of the scattering length. This collisional…
Large amplitude water waves on deep water has long been known in the sea faring community, and the cause of great concern for, e.g., oil platform constructions. The concept of such freak waves is nowadays, thanks to satellite and radar…
We describe the theory and present numerical evidence for a new type of nonlinear resonant interaction between gravity waves on the surface of deep water. The resonance constitutes a generalisation of the usual 'exact' resonance as we show…
This work is a numerical study of a transitional shock wave boundary layer interaction (SWBLI). The main goal is to improve our understanding of the well known low-frequency SWBLI unsteadiness and especially the suspected role of triadic…
A nonlinear theory of pattern selection in parametric surface waves (Faraday waves) is presented that is not restricted to small viscous dissipation. By using a multiple scale asymptotic expansion near threshold, a standing wave amplitude…
Enhancement of the predictive power and robustness of nonlinear population dynamics models allows ecologists to make more reliable forecasts about species' long term survival. However, the limited availability of detailed ecological data,…