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Using a new cluster Monte Carlo algorithm, we study the phase diagram and critical properties of an interacting pair of resistively shunted Josephson junctions. This system models tunneling between two electrodes through a small…
New necessary and sufficient conditions are proposed for the stability investigation of dynamical systems using the flow and the divergence of the phase vector velocity. The obtained conditions generalize the well-known results of V.P.…
Stationary and nonstationary, in particular, chaotic states in long Josephson junctions are investigated. Bifurcation lines on the parametric bias current-external magnetic field plane are calculated. The chaos strip along the bifurcation…
The entanglement in quantum XY spin chains of arbitrary length is investigated via the geometric (measure of) entanglement. The emergence of entanglement is explained intuitively from the perspective of perturbations. The model is solved…
We investigate a two-dimensional transmission model consisting of a wave equation and a Kirchhoff plate equation with dynamical boundary controls under geometric conditions. The two equations are coupled through transmission conditions…
We study local (also referred to as small-signal) stability of a network of identical DC/AC converters having a rotating degree of freedom. We develop a stability theory for a class of partitioned linear systems with symmetries that has…
Domain walls in soft permalloy strips may exhibit various equilibrium micromagnetic structures depending on the width and thickness of the strip, ranging from the well-known transverse and vortex walls in narrow and thin strips to double…
Young's law fails on soft solid and liquid substrates where there are substantial deformations near the contact line. On liquid substrates, this is captured by Neumann's classic analysis, which provides a geometrical construction for…
Empirical estimation of critical points at which complex systems abruptly flip from one state to another is among the remaining challenges in network science. However, due to the stochastic nature of critical transitions it is widely…
A trajectorial large deviation principle is established in a mean field thermodynamic limit for a multiclass loss network with diminishing rates, which may have several stable equilibria. The large deviation limit is identified as a unique…
We numerically investigate the stability of universal properties at continuous phase transitions against perturbations of the Markov Chain Monte Carlo algorithm used to simulate the system. We consider the three dimensional XY model as test…
We investigate the population dynamics in generalized Rock-Paper-Scissors models with an arbitrary number of species $N$. We show, for the first time, that spiral patterns with $N$-arms may develop both for odd and even $N$, in particular…
According to the May-Wigner stability theorem, increasing the complexity of a network inevitably leads to its destabilization, such that a small perturbation will be able to disrupt the entire system. One of the principal arguments against…
We propose and analyze a generalized two dimensional $XY$ model, whose interaction potential has $n$ weighted wells, describing corresponding symmetries of the system. As the lattice spacing vanishes, we derive by $\Gamma$-convergence the…
We investigate domain walls between topologically ordered phases in two spatial dimensions and present a simple but general framework from which their degrees of freedom can be understood. The approach we present exploits the results on…
Over the past three decades, considerable effort has been devoted to studying the rich and diverse phenomenologies of heterotic strings exhibiting spacetime supersymmetry. Unfortunately, during this same period, there has been relatively…
Understanding which system structure can sustain stable dynamics is a fundamental step in the design and analysis of large scale dynamical systems. Towards this goal, we investigate here the structural stability of systems with a random…
The dynamics of a three-dimensional axisymmetric bluff-body wake are examined at low Reynolds regimes where transitions take place through spatio-temporal symmetry breaking. A linear stability analysis is employed to identify the critical…
In the single-scattering theory of electromagnetic radiation, the {\it fractal regime} is a definite range in the photon momentum-transfer $q$, which is characterized by the scaling-law behavior of the structure factor: $S(q) \propto…
We examine the stability of a 1D electrical transmission line in the simultaneous presence of PT-symmetry and fractionality. The array contains a binary gain/loss distribution $\gamma_{n}$ and a fractional Laplacian characterized by a…