Related papers: Response Regimes in Equivalent Mechanical Model of…
In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…
In Part I of this paper series, a theoretical and numerical model for a a driven pendulum filled with liquid was developed. The system was analyzed in the framework of tuned liquid dampers (TLD) and hybrid mass liquid dampers (HMLD) theory.…
Nonlinear stochastic modeling is useful for describing complex engineering systems. Meanwhile, neuromorphic (brain-inspired) computing paradigms are developing to tackle tasks that are challenging and resource intensive on digital…
We analyze experimental data obtained from an electrical circuit having components at different temperatures, showing how to predict its response to temperature variations. This illustrates in detail how to utilize a recent linear response…
New-generation space missions require satellites to carry substantial amounts of liquid propellant, making it essential to analyse the coupled control-structure-propellant dynamics in detail. While Computational Fluid Dynamics (CFD) offers…
Long-range interacting systems, while relaxing to equilibrium, often get trapped in long-lived quasistationary states which have lifetimes that diverge with the system size. In this work, we address the question of how a long-range system…
The linear response of non-equilibrium systems with Markovian dynamics satisfies a generalized fluctuation-dissipation relation derived from time symmetry and antisymmetry properties of the fluctuations. The relation involves the sum of two…
We introduce and analyze a natural class of nonlinear dynamics for spin systems such as the Ising model. This class of dynamics is based on the framework of mass action kinetics, which models the evolution of systems of entities under…
The classical theory of linear response applies to statistical mechanics close to equilibrium. Away from equilibrium, one may describe the microscopic time evolution by a general differentiable dynamical system, identify nonequilibrium…
We first review the phenomenology of viscous liquids and the standard models used for explaining the non-Arrhenius average relaxation time. Then the focus is turned to the so-called elastic models, arguing that these models are all…
The non-Markovian stochastic dynamics involving Levy flights and a potential in the form of a harmonic and non-linear oscillator is discussed. The subordination technique is applied and the memory effects, which are nonhomogeneous, are…
We use the semi-classical approach to study the non-equilibrium dynamics of the O(3) non-linear sigma model. For a class of quenches defined in the text, we obtain the order parameter dynamical correlator in the thermodynamic limit. In…
The aim of this paper is to calculate the time dependence of the mean position (and orientation) of a fluid particle when a fluid system at thermodynamic equilibrium is submitted to a mechanical action. The starting point of this novel…
We consider the 3-dimensional nonlinear Schr\"{o}dinger equation (NLS) with average nonlinearity. This is a limiting model of NLS with strong magnetic confinement and a generalized model of the resonant system of NLS with a partial harmonic…
By means of a simple model system, the total volume fluctuations of a tapped granular material in the steady state are studied. In the limit of a system with a large number of particles, they are found to be Gaussian distributed, and…
For nonlinear dispersive systems, the nonlinear Schr\"odinger (NLS) equation can usually be derived as a formal approximation equation describing slow spatial and temporal modulations of the envelope of a spatially and temporally…
The connection between domain relaxations at individual scales and the collective heterogeneous response in non-equilibrium systems is a topic of profound interest in recent times. In a model sys- tem of constantly driven oppositely charged…
The elastic behavior of materials operating in the linear regime is constrained, by definition, to operations that are linear in the imposed deformation. Though the nonlinear regime holds promise for new functionality, the design in this…
We study the free surface response in a cylindrical container undergoing an elliptic periodic orbit. For small forcing amplitudes and deep liquid layers, we quantify the effect of orbit's aspect ratio onto the surface dynamics in the…
A large number of processes in the mesoscopic world occur out of equilibrium, where the time course of a system evolution becomes immensely important since it is driven principally by dissipative effects. Non-equilibrium steady states…