Related papers: Behavior of a Model Dynamical System with Applicat…
The energy-based stochastic extension of the Schrodinger equation is perhaps the simplest mathematically rigourous and physically plausible model for the reduction of the wave function. In this article we apply a new simulation methodology…
A linear dynamical model for the development of the turbulent energy cascade was introduced in Apolin\'ario \emph{et al} (J. Stat. Phys. \textbf{186}, 15 (2022)). This partial differential equation, randomly stirred by a forcing term which…
In this work we present the results of a numerical and semiclassical analysis of high lying states in a Hamiltonian system, whose classical mechanics is of a generic, mixed type, where the energy surface is split into regions of regular and…
According to theorems of Shnirelman and followers, in the semiclassical limit the quantum wavefunctions of classically ergodic systems tend to the microcanonical density on the energy shell. We here develop a semiclassical theory that…
We propose a new application of random tensor theory to studies of non-linear random flows in many variables. Our focus is on non-linear resonant systems which often emerge as weakly non-linear approximations to problems whose linearized…
We present an elementary approach to observe frequency cascade on forced nonlinear Schr{\"o}dinger equations. The forcing term (which may also appear as a potential term instead) consists of a constant term, perturbed by a modulated…
In this paper we study long time stability of a class of nontrivial, quasi-periodic solutions depending on one spacial variable of the cubic defocusing non-linear Schr\"odinger equation on the two dimensional torus. We prove that these…
We study the behavior of shallow water waves over periodically-varying bathymetry, based on the first-order hyperbolic Saint-Venant equations. Although solutions of this system are known to generally exhibit wave breaking, numerical…
The emergence of hydrodynamics is one of the deepest phenomena in many-body systems. Arguably, the hydrodynamic equations are also the most important tools for predicting large-scale behaviour. Understanding how such equations emerge from…
We establish quantum dynamical lower bounds for discrete one-dimensional Schr\"odinger operators in situations where, in addition to power-law upper bounds on solutions corresponding to energies in the spectrum, one also has lower bounds…
The conventional approach to the turbulent energy cascade, based on Richardson-Kolmogorov phenomenology, ignores the topology of emerging vortices, which is related to the helicity of the turbulent flow. It is generally believed that…
Motivated by the modeling of three-dimensional fluid turbulence, we define and study a class of stochastic partial differential equations (SPDEs) that are randomly stirred by a spatially smooth and uncorrelated in time forcing term. To…
This work is motivated by a desire to understand transitions between stable equilibria observed in Stommel's 1961 thermohaline circulation model. We adapt the model, including a forcing parameter as a dynamic slow variable. The resulting…
We consider the hydrodynamics of an incompressible fluid on a 2D periodic domain. There exists a family of stationary solutions with vorticity given by $\Omega^*=\alpha\cos (\mathbf{p} \cdot \mathbf{x} )+\beta \sin (\mathbf{p} \cdot…
Described is n-level quantum system realized in the n-dimensional ''Hilbert'' space H with the scalar product G taken as a dynamical variable. The most general Lagrangian for the wave function and G is considered. Equations of motion and…
Navier-Stokes turbulence subject to solid-body rotation is studied by high-resolution direct numerical simulations (DNS) of freely decaying and stationary flows. Setups characterized by different Rossby numbers are considered. In agreement…
We use a simple model consisting of energy-momentum tensor conservation and a Maxwell-Cattaneo equation for its viscous part to study nonlinear phenomena in a real relativistic fluid. We focus on new types of behavior without…
It is shown that the distributed chaos in the simple Hamiltonian (conservative) dynamical systems, such as the Nose-Hoover oscillator and double oscillator, can mimic the distributed chaos in the isotropic homogeneous turbulence. Direct…
We study the scaling behaviors in the wind velocity time series collected at the atmospheric surface layer and compare them with two commonly used cascade models, the truncated stable distribution and the log-normal model. Results show that…
The nonlinear Schr\"odinger equation in the weakly nonlinear regime with random Gaussian fields as initial data is considered. The problem is set on the torus in any dimension greater than two. A conjecture in statistical physics is that…