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Under disturbances, superconductors may experience sudden, most undesirable phase transitions (quench) from superconducting to normal conducting state. Quench may lead to damage or even to catastrophic conductor failure. A superconductor is…
PDEs with periodic boundary conditions are frequently used to model processes in large spatial environments, assuming solutions to extend periodically beyond some bounded interval. However, solutions to these PDEs often do not converge to a…
Critical points and phase transitions are characterized by diverging susceptibilities, reflecting the tendency of the system toward spontaneous symmetry breaking. Equilibrium statistical mechanics bounds these instabilities to occur at zero…
We investigate the finite temperature charge density wave (CDW) transition of lattice Bose gases within optical cavities in the deep Mott-insulator limit. We find a new critical regime emerges at a temperature around one-half of the on-site…
This paper introduces a framework based on Large Deviation Theory (LDT) to accurately and efficiently compute the rare probabilities of voltage collapse. We formulate the problem as finding the most probable failure point (the instanton) on…
The main objective of this article is to develop a matrix pencil approach for the study of the controllability and reachability of a class of linear singular discrete time systems. The description equation of a practical system may be…
In this paper, we propose an AC power flow based cascading failure model that explicitly considers external weather conditions, extreme temperatures in particular, and evaluates the impact of extreme temperature on the initiation and…
The small-signal stability is an integral part of the power system security analysis. The introduction of renewable source related uncertainties is making the stability assessment difficult as the equilibrium point is varying rapidly. This…
Quantum criticality is the intriguing possibility offered by the laws of quantum mechanics when the wave function of a many-particle physical system is forced to evolve continuously between two distinct, competing ground states. This…
We construct a one-parameter family of exact time-dependent solutions to 2+1 gravity with a negative cosmological constant and a massless minimally coupled scalar field as source. These solutions present a continuously self-similar (CSS)…
Phase transitions correspond to the singular behavior of physical systems in response to continuous control parameters like temperature or external fields. Near continuous phase transitions, associated with the divergence of a correlation…
Extreme events represent a challenge to natural as well as man-made systems. For critical infrastructure like power grids, we need to understand their resilience against large disturbances. Recently, new measures of the resilience of…
A direct numerical simulation of the three-dimensional elektrokinetic instability near a charge selective surface (electric membrane, electrode, or system of micro-/nanochannels) is carried out and analyzed. A special finite-difference…
For a power system operating in the vicinity of the power transfer limit of its transmission system, effect of stochastic fluctuations of power loads can become critical as a sufficiently strong such fluctuation may activate voltage…
Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the systems parameters abruptly shift the system to an alternative state with a contrasting dynamical…
We study the critical point (CP) phenomenon through the increase of fluctuations related to characteristic critical mode. CP would also be identified through the production of primary photons induced by conformal anomaly of strong and…
Recently, adaptive control systems with relaxed persistent excitation (PE) conditions have been proposed to guarantee true parameter convergence and improve the transient response. However, in some cases, sufficient control performance and…
Effects of a coupling between the mechanical vibrations of a quantum dot placed between the two leads of a single electron transistor and coherent tunneling of electrons through a single level in the dot has been studied. We have found that…
This paper studies the contraction property of time-varying differential-algebraic equation (DAE) systems by embedding them to higher-dimension ordinary differential equation (ODE) systems. The first result pertains to the equivalence of…
VSG control has emerged as a crucial technology for integrating renewable energy sources. However, renewable energy have limited tolerance to overcurrent, necessitating the implementation of current limiting (CL)strategies to mitigate the…