相关论文: Phase Diffusion in Localized Spatio-Temporal Ampli…
A two dimensional model is introduced to study pattern formation, secondary instabilities and the transition to spatiotemporal chaos (weak turbulence) in parametric surface waves. The stability of a periodic standing wave state above onset…
Motivated by the impact of worsening climate conditions on vegetation patches, we study dynamic instabilities in an idealized Ginzburg-Landau model. Our main results predict time instances of sudden drops in wavenumber and the resulting…
We investigate equilibration processes shortly after sudden perturbations are applied to ultracold trapped superfluids. We show the similarity of phase imprinting and localized density depletion perturbations, both of which initially are…
We study the connection between transport phenomenon and escape rate statistics in two-dimensional standard map. For the purpose of having an open phase space, we let the momentum co-ordinate vary freely and restrict only angle with…
In an appropriate moving coordinate frame, source defects are time-periodic solutions to reaction-diffusion equations that are spatially asymptotic to spatially periodic wave trains whose group velocities point away from the core of the…
Species diversity in ecosystems is often accompanied by the self-organisation of the population into fascinating spatio-temporal patterns. Here, we consider a two-dimensional three-species population model and study the spiralling patterns…
The real Ginzburg-Landau equation arises as a universal amplitude equation for the description of pattern-forming systems exhibiting a Turing bifurcation. It possesses spatially periodic roll solutions which are known to be stable against…
We investigate intercellular insulin dynamics in an array of diffusively coupled pancreatic islet \b{eta}-cells. The cells are connected via gap junction coupling, where nearest neighbor interactions are included. Through the multiple scale…
We analyze the Eckhaus instability of plane waves in the one-dimensional complex Ginzburg-Landau equation (CGLE) and describe the nonlinear effects arising in the Eckhaus unstable regime. Modulated amplitude waves (MAWs) are quasi-periodic…
Quantum Phase slips are dual process of particle tunneling in coherent networks. Besides to be of central interest for condensed matter physics, quantum phase slips are resources that are sought to be manipulated in quantum circuits. Here,…
Motivated by the observation of localized traveling-wave states (`pulses') in convection in binary liquid mixtures, the interaction of fronts is investigated in a real Ginzburg-Landau equation which is coupled to a mean field. In that…
Instabilities and pattern formation is the rule in nonequilibrium systems. Selection of a persistent lengthscale, or coarsening (increase of the lengthscale with time) are the two major alternatives. When and under which conditions one…
The general form of the amplitude equations for a hexagonal pattern including spatial terms is discussed. At the lowest order we obtain the phase equation for such patterns. The general expression of the diffusion coefficients is given and…
We study synchronization of locally coupled noisy phase oscillators which move diffusively in a one-dimensional ring. Together with the disordered and the globally synchronized states, the system also exhibits several wave-like states which…
We develop a complete stability theory for two-dimensional periodic traveling waves of reaction-diffusion systems. More precisely, we identify a diffusive spectral stability assumption, prove that it implies nonlinear stability and provide…
Within the Landau-Ginzburg picture of phase transitions, scalar field theories develop phase separation because of a spontaneous symmetry-breaking mechanism. This picture works in thermodynamics but also in the dynamics of phase separation.…
We study a system of phase oscillators with nonlocal coupling in a ring that supports self-organized patterns of coherence and incoherence, called chimera states. Introducing a global feedback loop, connecting the phase lag to the order…
In this work we identify and investigate a novel bifurcation in conserved systems. This secondary bifurcation stops active phase separation in its nonlinear regime. It is then either replaced by an extended, system-filling, spatially…
What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals $\tau$ distributed as a power-law $\sim \tau^{-(1+\alpha)};\alpha>0$? Modeling the stochastic process by diffusion and the…
Spontaneous rhythmic oscillations are widely observed in various real-world systems. In particular, biological rhythms, which typically arise via synchronization of many self-oscillatory cells, often play important functional roles in…