Related papers: From Phase Space Representation to Amplitude Equat…
Many nonlinear systems are described by eigenmodes with amplitude-dependent frequencies, interacting strongly whenever the frequencies become commensurate at internal resonances. Fast energy exchange via the resonances holds the key to rich…
Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences…
We describe in detail a recently proposed lattice-Boltzmann model for simulating flows with multiple phases and components. In particular, the focus is on the modeling of one-component fluid systems which obey non-ideal gas equations of…
Low-frequency simulations of a one-layer model with lateral buoyancy variations (i.e., thermodynamically active) have revealed circulatory motions resembling quite closely submesoscale observations in the surface ocean rather than…
The Rosensweig instability is the phenomenon that above a certain threshold of a vertical magnetic field peaks appear on the free surface of a horizontal layer of magnetic fluid. In contrast to almost all classical hydrodynamical systems,…
We analyze the dynamics of dissipation and relaxation in the unbroken and broken symmetry phases of scalar theory in the nonlinear regime for large initial energy densities, and after linear unstabilities (parametric or spinodal) are…
We calculate the mean square amplitude of the shape fluctuation -- an equal-time correlation -- of an almost planar fluid membrane immersed in a near-critical binary fluid mixture. One fluid component is usually preferentially attracted by…
We define a nonlinear thermodynamical formalism which translates into dynamical system theory the statistical mechanics of generalized mean-field models, extending investigation of the quadratic case by Leplaideur and Watbled. Under…
This paper is devoted to study the phase space analysis of isotropic and homogenous universe model by taking a noninteracting mixture of electromagnetic and viscous radiating fluids whose viscous pressure satisfies a nonlinear version of…
Pattern formation in uniaxial polymeric liquid crystals is studied for different dynamic closure approximations. Using the principles of mesoscopic non-equilibrium thermodynamics in a mean-field approach, we derive a Fokker-Planck equation…
Identifying quantum phase transitions poses a significant challenge in condensed matter physics, as this requires methods that both provide accurate results and scale well with system size. In this work, we demonstrate how relaxation…
This paper considers the dynamic response of a single degree of freedom system with nonlinear stiffness and nonlinear damping that is subjected to both resonant direct excitation and resonant parametric excitation, with a general phase…
We revisit the issue of relaxation to thermal equilibrium in the so-called "sheet model", i.e., particles in one dimension interacting by attractive forces independent of their separation. We show that this relaxation may be very clearly…
We demonstrate the emergence of self-organized structures in the course of the relaxation of an initially excited, dissipative and finite chain of interacting particles in a periodic potential towards its many particle equilibrium…
We derive the nonlinear fractional surface wave equation that governs compression waves at an interface that is coupled to a viscous bulk medium. The fractional character of the differential equation comes from the fact that the effective…
We present our study on the emergent states of two interacting nonlinear systems with differing dynamical time scales. We find that the inability of the interacting systems to fall in step leads to difference in phase as well as change in…
We propose a new approach to describe the effective microscopic dynamics of (power-law) nonlinear Fokker-Planck equations. Our formalism is based on a nonextensive generalization of the Wiener process. This allow us to obtain, in addition…
To understand the non-equilibrium relaxation dynamics of a liquid droplet on a switchable substrate the interplay of different length- and time-scales needs to be understood. We present a method to map the microscopic information, resulting…
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…
Within the framework of diffuse interface methods, we derive a pressure-based Baer-Nunziato type model well-suited to weakly compressible multiphase flows. The model can easily deal with different equation of states and it includes…