Related papers: Limiting Phase Trajectories: a new paradigm for th…
We present an adequate analytical approach to the description of nonlinear vibration with strong energy exchange between weakly coupled oscillators and oscillatory chains. The fundamental notion of the limiting phase trajectory (LPT)…
In this paper we fill the gap in understanding the non-stationary resonance dynamics of the weakly coupled pendula model, having significant applications in numerous fields of physics such as super- conducting Josephson junctions,…
We demonstrate that the modulation instability of the zone boundary mode in a finite (periodic) Fermi-Pasta-Ulam chain is the necessary but not sufficient condition for the efficient energy transfer by localized excitations. This transfer…
A set of analytical and computational tools based on transition path theory (TPT) is proposed to analyze flows in complex networks. Specifically, TPT is used to study the statistical properties of the reactive trajectories by which…
We study Lagrangian Perturbation Theory (LPT) and its regularization in the Effective Field Theory (EFT) approach. We evaluate the LPT displacement with the same phases as a corresponding $N$-body simulation, which allows us to compare…
Given two distinct subsets $A,B$ in the state space of some dynamical system, Transition Path Theory (TPT) was successfully used to describe the statistical behavior of transitions from $A$ to $B$ in the ergodic limit of the stationary…
We explore the relationship between the nonlinear matter power spectrum and the various Lagrangian and Standard Perturbation Theories (LPT and SPT). We first look at it in the context of one dimensional (1-d) dynamics, where 1LPT is exact…
Dynamical phase transitions (DPTs) characterize critical changes in system behavior occurring at finite times, providing a lens to study nonequilibrium phenomena beyond conventional equilibrium physics. While extensively studied in quantum…
Logarithmic perturbation theory (LPT) is developed and applied to quasinormal modes (QNMs) in open systems. QNMs often do not form a complete set, so LPT is especially convenient because summation over a complete set of unperturbed states…
In tasks aiming for long-term returns, planning becomes essential. We study generative modeling for planning with datasets repurposed from offline reinforcement learning. Specifically, we identify temporal consistency in the absence of…
Control landscape phase transitions (CLPTs) occur as abrupt changes in the cost function landscape upon varying a control parameter, and can be revealed by non-analytic points in statistical order parameters. A prime example are quantum…
Many chemical reactions can be formulated in terms of particle diffusion in a complex energy landscape. Transition path theory (TPT) is a theoretical framework for describing the direct (reaction) pathways from reactant to product states…
Lagrangian Particle Tracking (LPT) enables practitioners to study various concepts in turbulence by measuring particle positions in flows of interest. This data is subject to measurement errors, and filtering techniques are applied to…
A dynamical system framework is used to describe transport processes in plasmas embedded in a magnetic field. For periodic systems with one degree of freedom the Poincar\'e map provides a splitting of the phase space into regions where…
The stationary and highly non-stationary resonant dynamics of the harmonically forced pendulum are described in the framework of a semi-inverse procedure combined with the Limiting Phase Trajectory concept. This procedure, implying only…
Energy transfer among various spectral components of fluctuating physical parameters in plasma occurs due to the nonlinear interactions, but these effects are typically not captured by the traditional linear spectral methods. Plasma density…
The resonances of forced dynamical systems occur when either the amplitude of the frequency response undergoes a local maximum (amplitude resonance) or phase lag quadrature takes places (phase resonance). This study focuses on the phase…
Over the past two decades, an increasing array of control-theoretic methods have been used to study the brain as a complex dynamical system and better understand its structure-function relationship. This article provides an overview on one…
Transition Path Theory (TPT) provides a rigorous framework to investigate the dynamics of rare thermally activated transitions. In this theory, a central role is played by the forward committor function q^+(x), which provides the ideal…
Driven particle transport in crowded and confining environments is fundamental to diverse phenomena across physics, chemistry, and biology. A main objective in studying such systems is to identify novel emergent states and phases of…