Related papers: Condensation of Classical Nonlinear Waves in a Two…
Intracellular protein patterns are described by (nearly) mass-conserving reaction-diffusion systems. While these patterns initially form out of a homogeneous steady state due to the well-understood Turing instability, no general theory…
We show that spontaneous density segregation in dense systems of aligning circle swimmers is a condensation phenomenon at odds with the phase separation scenarios usually observed in two-dimensional active matter. The condensates, which…
Here we study how coherence appears in a system driven by noise at small scales. In the wave turbulence modeled by the Gross-Pitaevskii / nonlinear Schr\"odinger equation, we observe states with correlation scales less than the system size…
Coherent states play an important role in quantum mechanics because of their unique properties under time evolution. Here we explore this concept for one-dimensional repulsive nonlinear Schr\"odinger equations, which describe weakly…
We measure spectra, spatial correlation functions and probability density functions (PDFs) for waves amplitudes for generalized one-dimensional nonlinear Schrodinger (NLS) equation of focusing type with saturated nonlinearity. All…
In this paper we give a general account of Wave Interaction Theory which by now consists of two parts: kinetic wave turbulence theory (WTT), using a statistical description of wave interactions, and the D-model recently introduced in…
For nonlinear hyperbolic systems of conservation laws in one space variable, we establish the existence of nonclassical entropy solutions exhibiting nonlinear interactions between shock waves with strong strength. The proposed theory is…
The classical dynamics of collisionless cold dark matter, commonly described by fluid variables or a phase-space distribution, can be captured in a single semiclassical wavefunction. We illustrate how classical multi-streaming creates wave…
We study the behavior of perturbations in a compressible one-dimensional inviscid gas with an ambient state consisting of constant pressure and periodically-varying density. We show through asymptotic analysis that long-wavelength…
The occurrence of system-scale coherent structures, so-called condensates, is a well-known phenomenon in two-dimensional turbulence. Here, the transition to condensate formation is investigated as a function of the magnitude of the force…
We analyse the Bose-Einstein condensation process and the Berezinskii-Kosterlitz-Thouless phase transition within the Gross-Pitaevskii model and their interplay with wave turbulence theory. By using numerical experiments we study how the…
We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear dispersion relation.…
The turbulent flow of a fluid carrying trace amounts of a condensable species through a differentially cooled vertical channel geometry is simulated using single-phase direct numerical simulations. The release of latent heat during…
We discuss the response of both moving and trapped solitary wave solutions of a nonlinear two-component nonlinear Schr\"odinger system in 1+1 dimensions to an anti-$\mathcal{PT}$ external periodic complex potential. The dynamical behavior…
In classical fluids, the Weber number is a dimensionless parameter that characterises the flow of a multi-phase fluid. The superfluid analogy of a classical multi-phase fluid can be realised in a system of two or more immiscible…
In the work of Colliander et al. (2010), a minimal lattice model was constructed describing the transfer of energy to high frequencies in the defocusing nonlinear Schr\"odinger equation. In the present work, we present a systematic study of…
We investigate schemes to dynamically create many particle entangled states of a two component Bose-Einstein condensate in a very short time proportional to 1/N where $N$ is the number of condensate particles. For small $N$ we compare exact…
We study the dynamics of weakly coupled non-abelian plasmas within the frameworks of classical-statistical lattice gauge-theory and kinetic theory. We focus on a class of systems which are highly occupied, isotropic at all times and…
We study the statistical properties of an ensemble of weak gravitational waves interacting nonlinearly in a flat space-time. We show that the resonant three-wave interactions are absent and develop a theory for four-wave interactions in a…
The relative phase of the order parameters in the collision of two condensates can influence the outcome of their collision in the case of weak coupling. With increasing interaction strength however, the initially independent phases of the…