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We apply the effective approach to evaluating semiclassical relational dynamics to the closed Friedman--Robertson--Walker cosmological model filled with a minimally coupled massive scalar field. This model is interesting for studying…
We present a general theoretical approach for the quantitative description of parametric excitation of spin-wave modes in confined micromagnetic systems. This type of problem belongs to a broader class of nonlinear modal dynamics that arise…
Spontaneous pattern formation in a variety of spatially extended nonlinear system always occurs through a modulation instability: homogeneous state of the system becomes unstable with respect to growing modulation modes. Therefore, the…
The prescribed-time stabilization problem for a general class of nonlinear systems with unknown input gain and appended dynamics (with unmeasured state) is addressed. Unlike the asymptotic stabilization problem, the prescribed-time…
In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly…
In this article, we present an extension of the formulation recently developed by the authors (A Framework for Data-Driven Computational Mechanics Based on Nonlinear Optimization, arXiv:1910.12736 [math.NA]) to the structural dynamics…
This paper is concerned with the study of continuous-time, non-smooth dynamical systems which arise in the context of time-varying non-convex optimization problems, as for example the feedback-based optimization of power systems. We…
Stability of the zero solution plays an important role in the investigation of positive systems. In this note, we revisit the $\mu$-stability of positive nonlinear systems with unbounded time-varying delays. The system is modelled by…
Time-varying media, characterized by dynamic or spacetime-modulated constitutive parameters such as permittivity and permeability, have recently emerged as a transformative paradigm for advanced wave control, transcending the constraints…
We consider an implementation of the adiabatic spin dynamics approach in a tight-binding description of the electronic structure. The adiabatic approximation for spin-degrees of freedom assumes that the faster electronic degrees of freedom…
The concept of nonlinear modes is useful for the dynamical characterization of nonlinear mechanical systems. While efficient and broadly applicable methods are now available for the computation of nonlinear modes, nonlinear modal testing is…
We show that quantum-interference phenomena can be realized for the dissipative nonlinear systems exhibiting hysteresis-cycle behavior and quantum chaos. Such results are obtained for a driven dissipative nonlinear oscillator with…
This paper presents a novel framework for stabilizing nonlinear systems represented in state-dependent form. We first reformulate the nonlinear dynamics as a state-dependent parameter-varying model and synthesize a stabilizing controller…
In recent years, a new method for experimental nonlinear modal analysis has been developed, which is based on the extended periodic motion concept. The method is well suited to experimentally obtain amplitude-dependent modal properties…
A thermodynamic system is driven into a nonequilibrium condition when a time-dependent force or a nonconservative force represented by a protocol $\lambda(t)$ is applied. Such a system is time irreversible in the sense that the motion under…
The exact dynamics of a system coupled to an environment can be described by an integro-differential stochastic equation of its reduced density. The influence of the environment is incorporated through a mean-field which is both stochastic…
The coherence times achieved with continuous dynamical decoupling techniques are often limited by fluctuations in the driving amplitude. In this work, we use time-dependent phase-modulated continuous driving to increase the robustness…
Turing patterns are a central paradigm for describing spatial patterns in nature. The corresponding theory of reaction-diffusion dynamics combines ideal diffusion with nonlinear reactions, resulting in patterns when species diffuse at…
We present a dynamical framework for modeling the motion of point-like charged particles, with or without mass, in general external electromagnetic fields. A key feature of this formulation is the treatment of time coordinate as a dynamical…
We investigate the Kondo model with time-dependent couplings that are periodically switched on and off. On the Toulouse line we derive exact analytical results for the spin dynamics in the steady state that builds up after an infinite…