Related papers: Fake turbulence
Two-dimensional turbulent flows, and to some extent, geophysical flows, are systems with a large number of degrees of freedom, which, albeit fluctuating, exhibit some degree of organization: coherent structures emerge spontaneously at large…
Deterministic many-body systems governed by simple interactions can self-organize into macroscopic patterns, and the determinants of long-time behavior are assumed to be encoded in the initial configuration. Here we show that predictability…
Stochastic dynamics is generated by a matrix of transition probabilities. Certain eigenvectors of this matrix provide observables, and when these are plotted in the appropriate multi-dimensional space the phases (in the sense of phase…
The transition to turbulence is characterized by an abrupt loss of order and predictability, featuring the intermittent proliferation and decay of localized turbulent structures. En-route to becoming fully turbulent, surprisingly order…
Turbulent fluid flows exhibit a complex small-scale structure with frequently occurring extreme velocity gradients. Particles probing such swirling and straining regions respond with an intricate shape-dependent orientational dynamics,…
Viscous flows through pipes and channels are steady and ordered until, with increasing velocity, the laminar motion catastrophically breaks down and gives way to turbulence. How this apparently discontinuous change from low- to…
A novel model of intermittency is presented in which the dynamics of the rates of energy transfer between successive steps in the energy cascade is described by a hierarchy of stochastic differential equations. The probability distribution…
We study data-driven learning of robust stochastic control for infinite-horizon systems with potentially continuous state and action spaces. In many managerial settings--supply chains, finance, manufacturing, services, and dynamic…
We show that nonequilibrium dynamics can play a constructive role in unsupervised machine learning by inducing the spontaneous emergence of latent-state cycles. We introduce a model in which visible and hidden variables interact through two…
We propose a new procedure to monitor and forecast the onset of transitions in high dimensional complex systems. We describe our procedure by an application to the Tangled Nature model of evolutionary ecology. The quasi-stable…
Probabilistic generative models based on measure transport, such as diffusion and flow-based models, are often formulated in the language of Markovian stochastic dynamics, where the choice of the underlying process impacts both algorithmic…
Rate processes are simple and analytically tractable models for many dynamical systems which switch stochastically between a discrete set of quasi stationary states but they may also approximate continuous processes by coarse grained,…
The deterministic dynamics of randomly connected neural networks are studied, where a state of binary neurons evolves according to a discreet-time synchronous update rule. We give a theoretical support that the overlap of systems' states…
A method is developed to estimate the properties of a global hydrodynamic instability in turbulent flows from measurement data of the limit-cycle oscillations. For this purpose, the flow dynamics are separated in deterministic contributions…
A dynamical model is proposed for isotropic turbulence driven by steady forcing that yields a viscosity independent dynamics for the small-scale (inertial) regime. This reproduces the Kolmogorov spectrum for the two-point velocity…
We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…
A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For…
We introduce a general framework for analysing general probabilistic theories, which emphasises the distinction between the dynamical and probabilistic structures of a system. The dynamical structure is the set of pure states together with…
A sequence of large invertible matrices given by a small random perturbation around a fixed diagonal and positive matrix induces a random dynamics on a high-dimensional sphere. For a certain class of rotationally invariant random…
It is shown that the Truncated Euler Equations, i.e. a finite set of ordinary differential equations for the amplitude of the large-scale modes, can correctly describe the complex transitional dynamics that occur within the turbulent regime…