Related papers: Chaos: a bridge from microscopic uncertainty to ma…
The concept of structural invariance previously introduced by the authors is used to argue that the connection between random matrix theory and quantum systems with a chaotic classical counterpart is in fact largely exact in the…
Infinitesimal perturbations in various systems showing spatiotemporal chaos (STC) evolve following the power laws of the Kardar-Parisi-Zhang (KPZ) universality class. While universal properties beyond the power-law exponents, such as…
A Direct Numerical Simulation (DNS) of the incompressible flow around a rectangular cylinder with chord-to-thickness ratio 5:1 (also known as the BARC benchmark) is presented. The work replicates the first DNS of this kind recently…
We investigate the large-scale influence of numerical noises as tiny artificial stochastic disturbances on a sustained turbulence. Using the two-dimensional (2D) turbulent Rayleigh-B\'enard (RB) convection as an example, we numerically…
We observe a crossover from strong to weak chaos in the spatiotemporal evolution of multiple site excitations within disordered chains with cubic nonlinearity. Recent studies have shown that Anderson localization is destroyed, and the wave…
A stochastic model predictive control (SMPC) approach is presented for discrete-time linear systems with arbitrary time-invariant probabilistic uncertainties and additive Gaussian process noise. Closed-loop stability of the SMPC approach is…
Lower bounds on fluctuations of thermodynamic currents depend on the nature of time: discrete or continuous. To understand the physical reason, we compare current fluctuations in discrete-time Markov chains and continuous-time master…
Using the predictor-corrector scheme, the fractional order diffusionless Lorenz system is investigated numerically. The effective chaotic range of the fractional order diffusionless system for variation of the single control parameter is…
How chaos is useful in the brain information processing is greatly unknown. Here, we show that the statistical property of chaos such as invariant measures naturally organized under a great number of iterations of chaotic mappings can be…
Polynomial chaos is a powerful technique for propagating uncertainty through ordinary and partial differential equations. Random variables are expanded in terms of orthogonal polynomials and differential equations are derived for the…
A spline chaos expansion, referred to as SCE, is introduced for uncertainty quantification analysis. The expansion provides a means for representing an output random variable of interest with respect to multivariate orthonormal basis…
Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. It can arise from an external forcing or due to random dynamics internal to the system. It is well established that even weak noise can result in…
The dynamics of one species chemical kinetics is studied. Chemical reactions are modelled by means of continuous time Markov processes whose probability distribution obeys a suitable master equation. A large deviation theory is formally…
In many stochastic dynamical systems, ordinary chaotic behavior is preceded by a full-dimensional phase that exhibits 1/f-type power-spectra and/or scale-free statistics of (anti)instantons such as neuroavalanches, earthquakes, etc. In…
We argue that Gaspard and coworkers do not give evidence for microscopic chaos in the sense in which they use the term. The effectively infinite number of molecules in a fluid can generate the same macroscopic disorder without any intrinsic…
This paper develops a theory of propagation of chaos for a system of weakly interacting particles whose terminal configuration is fixed as opposed to the initial configuration as customary. Such systems are modeled by backward stochastic…
We consider a many-parametric piecewise mapping with discontinuity. That is a one dimensional model of singular dynamic system. The stability boundary are calculated analytically and numerically. New typical features of stable cycle…
Linearly stable shear flows first transition to turbulence in the form of localised patches. At low Reynolds numbers, these turbulent patches tend to suddenly decay, following a memoryless process typical of rare events. How far in advance…
The concept of fundamental dynamic uncertainty (multivaluedness) developed in Parts I-III of this work and used to establish the consistent understanding of genuine chaos in Hamiltonian systems provides also causal description of the…
The practical success of widely used machine learning (ML) and deep learning (DL) algorithms in Artificial Intelligence (AI) community owes to availability of large datasets for training and huge computational resources. Despite the…