Related papers: Transverse modulational dynamics of quenched patte…
Gathering together some existing results, we show that the solutions to the one-dimensional Burgers equation converge for long times towards the stationary solutions to the steady Burgers equation, whose Fourier spectrum is not integrable.…
In this work, modulation of periodic interfacial waves on a conduit of viscous liquid is explored utilizing Whitham theory and Nonlinear Schr\"odinger (NLS) theory. Large amplitude periodic wave modulation theory does not require…
A Bayesian multivariate model with a structured covariance matrix for multi-way nested data is proposed. This flexible modeling framework allows for positive and for negative associations among clustered observations, and generalizes the…
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…
We study numerically and analytically the dynamics of defect formation during a finite-time quench of the two dimensional Swift-Hohenberg (SH) model of Rayleigh-Benard convection. We find that the Kibble-Zurek picture of defect formation…
A mesoscopic continuum model is employed to analyse the transport mechanisms and structure formation during the redistribution stage of deposition experiments where organic molecules are deposited on a solid substrate with periodic…
This study investigates transient wave dynamics in Turing pattern formation, focusing on waves emerging from localised disturbances. While the traditional focus of diffusion-driven instability has primarily centred on stationary solutions,…
Dynamic response of the one-dimensional viscoelastic rod of finite length, that has one end fixed and the other subject to prescribed either displacement or stress, is analyzed by the analytical means of Laplace transform, yielding the…
We investigate the stability of traveling front solutions to nonlinear diffusive-dispersive equations of Burgers type, with a primary focus on the Korteweg-de Vries-Burgers (KdVB) equation, although our analytical findings extend more…
A mesoscopic model of a diblock copolymer is used to study the stability of a uniform lamellar phase under a reciprocating shear flow. Approximate viscosity contrast between the microphases is allowed through a linear dependence of the…
We recently developed a tensorial constitutive model for dense, shear-thickening particle suspensions that combines rate-independent microstructural evolution with a stress-dependent jamming threshold. This gives a good qualitative account…
When polydisperse granular systems are sheared, the transverse dynamics is characterized by the interplay of size segregation and diffusion. Segregation in nonuniform and confined shearing flows is studied using annular shear cell…
According to the Kibble-Zurek mechanism, there is a universal power-law relationship between the defect density and the quench rate during a slow linear quench through a critical point. It is generally accepted that a fast quench results in…
We study theoretically nonlinear dynamics induced by shear-flow instability in segregated two-component Bose-Einstein condensates in terms of the Weber number, defined by extending the past theory on the Kelvin-Helmholtz instability in…
The propagation speed of a circumstellar pattern revealed in the plane of the sky is often assumed to represent the expansion speed of the wind matter ejected from a post-main-sequence star at the center. We point out that the often-adopted…
Stationary periodic patterns are widespread in natural sciences, ranging from nano-scale electrochemical and amphiphilic systems to mesoscale fluid, chemical and biological media and to macro-scale vegetation and cloud patterns. Their…
Using the time-dependent Ginzburg-Landau equations we study the propagation of planar fronts in superconductors, which would appear after a quench to zero applied magnetic field. Our numerical solutions show that the fronts propagate at a…
Dense granular flows are often unstable and form inhomogeneous structures. Although significant advances have been recently made in understanding simple flows, instabilities of such flows are often not understood. We present experimental…
We explore the dynamics of driven magnetic flux lines in disordered type-II superconductors in the presence of twin boundaries oriented parallel to the direction of the applied magnetic field, using a three-dimensional elastic line model…
The formation of regular precipitate stripes in the wake of moving chemical reaction-diffusion fronts is investigated. Experiments on the $NaOH+CuCl_2$ reaction in PVA hydrogel yield stripes parallel or slightly oblique to the front that…