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Recent experiments have demonstrated the ability to manipulate nonlinear interactions via time modulation, giving rise to the so-called stroboscopic nonlinearity. To date, however, this phenomenon has not been subjected to a rigorous…
Stochastic extensions of the Schrodinger equation have attracted attention recently as plausible models for state reduction in quantum mechanics. Here we formulate a general approach to stochastic Schrodinger dynamics in the case of a…
It has been known that noise can suppress multistability by dynamically connecting coexisting attractors in the system which are otherwise in separate basins of attraction. The purpose of this mini-review is to argue that quasiperiodic…
Computational feasibility of turbulent reacting flows hinges on the reduction of large chemical kinetics systems to smaller more manageable reaction sets. Recently, several sophisticated reduction techniques have been developed but they…
The weak turbulence model, also known as the quasilinear theory in plasma physics, has been a cornerstone in modeling resonant particle-wave interactions in plasmas. This reduced model stems from the Vlasov-Poisson/Maxwell system under the…
This thesis is devoted to the theoretical study of slow thermodynamic processes in non-equilibrium stochastic systems. Its main result is a physically and mathematically consistent construction of relevant thermodynamic quantities in the…
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…
We consider macroscopic systems in weak contact with boundary reservoirs and under the action of external fields. We present an explicit formula for the Hamiltonian of such systems, from which we deduce the equation of motions, the action…
Quasistationary states are long-lived nonequilibrium states, observed in some systems with long-range interactions under deterministic Hamiltonian evolution. These intriguing non-Boltzmann states relax to equilibrium over times which…
The Quasi Steady-State (QSS) model of long-term dynamics relies on the idea of time-scale decomposition. Assuming that the fast variables are infinitely fast and are stable in the long-term, the QSS model replaces the differential equations…
Exposing a molecule to intense light pulses may bring this molecule to a nonstationary quantum state, thus launching correlated dynamics of electronic and nuclear subsystems. Although much had been achieved in the understanding of…
The appearance of so-called exceptional points in the complex spectra of non-Hermitian systems is often associated with phenomena that contradict our physical intuition. One example of particular interest is the state-exchange process…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
A stochastic system under the influence of a stochastic environment is correlated with both present and future states of the environment. Such a system can be seen as implicitly implementing a predictive model of future environmental…
Periodic approximations of quasicrystals are a powerful tool in analyzing spectra of Schr\"odinger operators arising from quasicrystals, given the known theory for periodic crystals. Namely, we seek periodic operators whose spectra…
The understanding of the emergence of equilibrium statistical mechanics has progressed significantly thanks to developments from typicality, canonical and dynamical, and from the eigenstate thermalization hypothesis. Here we focus on a…
The quasi-stationary nonequilibrium distribution function of an independent electron gas interacting with a medium, which is at local thermal equilibrium, can be obtained by entropy production rate minimization, subject to constraints of…
A theory is developed for the evolution of the non-equilibrium distribution of quasiparticles when the scattering rate decreases due to particle collisions. We propose a "modified one-collision approximation" which is most effective for…
The accuracy of quasilinear theory applied to the electron bump-on-tail instability, a classic model problem, is explored with conservative high-order discontinuous Galerkin methods applied to both the quasilinear equations and to a direct…
In this paper, we quantify the resilience of nonlinear dynamical systems by studying the increased energy used by all inputs of a system that suffers a partial loss of control authority, either through actuator malfunctions or through…