Related papers: Non-equilibrium Pattern Modes Extracted from Exper…
Unlike the power-law model, the Ellis model describes the apparent viscosity of a shear-thinning fluid with no singularity in the limit of a vanishingly small shear stress. In particular, this model matches the Newtonian behaviour when the…
The objective of the present paper is to develop a two-step methodology integrating system identification and numerical continuation for the experimental extraction of nonlinear normal modes (NNMs) under broadband forcing. The first step…
The coupled equations which describe the temporal evolution of the Bose-Einstein condensed system are derived in the framework of nonequilibrium Thermo Field Dynamics. The key element is that they are not the naive assemblages of presumable…
The dynamics of a quantum system coupled to a classical environment and subject to constraints that drive it out of equilibrium is described. The evolution of the system is governed by the quantum-classical Liouville equation. Rather than…
Statistical equilibrium models of coherent structures in two-dimensional and barotropic quasi-geostrophic turbulence are formulated using canonical and microcanonical ensembles, and the equivalence or nonequivalence of ensembles is…
Can far-from-equilibrium material response under arbitrary loading be inferred from equilibrium data and vice versa? Can the effect of element transmutation on mechanical behavior be predicted? Remarkably, such extrapolations are possible…
In an Oberbeck-Boussinesq model, rigorously derived, which includes compressibility, one could expect that the onset of convection for the B\'enard problem occurs at a higher critical Rayleigh number. Since of the difficulties related to…
Fluctuations in systems away from thermal equilibrium have features that have no analog in equilibrium systems. One of such features concerns large rare excursions far from the stable state in the space of dynamical variables. For…
The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…
Nonlinear and non-stationary processes are prevalent in various natural and physical phenomena, where system dynamics can change qualitatively due to bifurcation phenomena. Traditional machine learning methods have advanced our ability to…
We report for the first time the pattern dynamics in the vicinity of an inverse homoclinic bifurcation in an extended dissipative system. We observe, in direct numerical simulations of three dimensional Rayleigh-B\'{e}nard convection, a…
The integrable system is constrained strictly by the conservation law during the time evolution, and the nearly integrable system or nonintegrable system is also constrained by the conserved parameters (like the constants of motion) with…
Spatiotemporal dynamics models are fundamental for various domains, from heat propagation in materials to oceanic and atmospheric flows. However, currently available neural network-based spatiotemporal modeling approaches fall short when…
Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…
Maximum-entropy ensembles are key primitives in statistical mechanics from which thermodynamic properties can be derived. Over the decades, several approaches have been put forward in order to justify from minimal assumptions the use of…
We propose a deep probabilistic-neural-network architecture for learning a minimal and near-orthogonal set of non-linear modes from high-fidelity turbulent-flow-field data useful for flow analysis, reduced-order modeling, and flow control.…
This paper reports on a theoretical analysis of the rich variety of spatio-temporal patterns observed recently in inclined layer convection at medium Prandtl number when varying the inclination angle $\gamma$ and the Rayleigh number $R$.…
Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…
Recently, a framework for controller design of sampled-data nonlinear systems via their approximate discrete-time models has been proposed in the literature. In this paper we develop novel tools that can be used within this framework and…
We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…