Related papers: Pattern selection as a nonlinear eigenvalue proble…
A model-based description of the scaling and radial location of turbulent fluctuations in turbulent pipe flow is presented and used to illuminate the scaling behaviour of the very large scale motions. The model is derived by treating the…
We consider a coarse-grained description of a system of self-propelled particles given by hydrodynamic equations for the density and polarization fields. We find that the ordered moving or flocking state of the system is unstable to spatial…
We present a new energy-stable open boundary condition, and an associated numerical algorithm, for simulating incompressible flows with outflow/open boundaries. This open boundary condition ensures the energy stability of the system, even…
We investigate the stability, nonlinear development and equilibrium structure of vortices in a background shearing Keplerian flow. We make use of high-resolution global two-dimensional compressible hydrodynamic simulations. We introduce the…
Subcritical transition to turbulence in Keplerian accretion disks is still a controversial issue and some theoretical progress is required in order to determine whether or not this scenario provides a plausible explanation for the origin of…
Infinitesimal and finite amplitude error propagation in spatially extended systems are numerically and theoretically investigated. The information transport in these systems can be characterized in terms of the propagation velocity of…
We study non-perturbatively and from first principles the thermodynamics of vortices in 3d U(1) gauge+Higgs theory, or the Ginzburg-Landau model, which has frequently been used as a model for cosmological topological defect formation. We…
The combined effect of mean flow and rotation on hexagonal patterns is investigated using Ginzburg-Landau equations that include nonlinear gradient terms as well as the nonlocal coupling provided by the mean flow. Long-wave and short-wave…
We survey recent results on reaction-diffusion equations with discontinuous hysteretic nonlinearities. We connect these equations with free boundary problems and introduce a related notion of spatial transversality for initial data and…
Contraction-driven self-propulsion of a large class of living cells can be modeled by a Keller-Segel system with free boundaries. The ensuing "active" system, exhibiting both dissipation and anti-dissipation, features stationary and…
The initial value problem for the Ginzburg-Landau-Schr\"odinger equation is examined in the $\epsilon \rightarrow 0$ limit under two main assumptions on the initial data $\phi^\epsilon$. The first assumption is that $\phi^\epsilon$ exhibits…
We study the stability of patterns arising in rotating convection in weakly anisotropic systems using a modified Swift-Hohenberg equation. The anisotropy, either an endogenous characteristic of the system or induced by external forcing, can…
This paper provides a pedagogical introduction to the classical nonlinear stability analysis of the plane Poiseuille and Couette flows. The whole procedure is kept as simple as possible by presenting all the logical steps involved in the…
In our previous papers we proposed a continuum model for the dynamics of the systems of self-propelling particles with conservative kinematic constraints on the velocities. We have determined a class of stationary solutions of this…
The spiral core instability, observed in large aspect ratio Rayleigh-Benard convection, is studied numerically in the framework of the Swift-Hohenberg equation coupled to a large-scale flow. It is shown that the instability leads to…
We have generalized the semi-analytic approach of special flow to the description of flows of passive particles taking into account internal noise. The model is represented by a series of recurrence relations. The recurrence relations are…
This study examines the stability of a flexible material interface between two fluids of the same viscosity in interaction with a free surface. When the layers are motionless, we provide evidence for the onset of a novel instability by…
For the purpose of uncertainty propagation a new quadrature rule technique is proposed that has positive weights, has high degree, and is constructed using only samples that describe the probability distribution of the uncertain parameters.…
We study the excitation of spatial patterns by resonant, multi-frequency forcing in systems undergoing a Hopf bifurcation to spatially homogeneous oscillations. Using weakly nonlinear analysis we show that for small amplitudes only stripe…
In this paper we consider a nonlinear Fokker-Planck equation with asymptotically small parameters. It describes the diffusion of finite-size particles in the presence of a fixed distribution of obstacles in the limit of low-volume fraction.…