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These expository notes address certain stationary and ergodic properties of the equations of fluid dynamics subject to a spatially degenerate (i.e. frequency localized), white in time gaussian forcing. In order to provide an accessible…
It is known that, in the thermodynamic limit, the Chern number of a translationally invariant system cannot change under unitary time evolutions that are smooth in momentum space. Yet a real-space counterpart of the Chern number, the Bott…
Stochastic optimal control problems have a long tradition in applied probability, with the questions addressed being of high relevance in a multitude of fields. Even though theoretical solutions are well understood in many scenarios, their…
Particle flows in spatial networks are susceptible to congestion. In this paper, we analyze the phase transitions of these networks to a state of congested transport and the influence of both topology and spatial dynamics on its emergence.…
We consider a model for substrate-depletion oscillations in genetic systems, based on a stochastic differential equation with a slowly evolving external signal. We show the existence of critical transitions in the system. We apply two…
We consider a general class of stochastic networks and ask which network nodes need to be controlled, and how, to stabilize and switch between desired metastable (target) states in terms of the first and second statistical moments of the…
We study long-range interacting systems driven by external stochastic forces that act collectively on all the particles constituting the system. Such a scenario is frequently encountered in the context of plasmas, self-gravitating systems,…
The steady sliding state of periodic structures such as charge density waves and flux line lattices is numerically studied based on two and three dimensional driven random field XY models. We focus on the dynamical phase transition between…
The stochastic frontier model with heterogeneous technical efficiency explained by exoge-nous variables is augmented with a spatial-temporal component, a generalization relaxing the panel independence assumption in a panel data. The…
We develop a path-based approach to continuous-time random walks on networks with arbitrarily weighted edges. We describe an efficient numerical algorithm for calculating statistical properties of the stochastic path ensemble. After…
Critical transitions (or tipping points) are drastic sudden changes observed in many dynamical systems. Large classes of critical transitions are associated to systems, which drift slowly towards a bifurcation point. In the context of…
Transport currents can alter alter order parameter dynamics and change steady states in superconductors, in ferromagnets, and in hybrid systems. In this article we present a scheme for fully microscopic evaluation of order parameter…
In contrast to conservative systems, in nonlinear media with gain and loss the dynamics of localized topological structures can exhibit unique features that can be controlled externally. We propose a robust mechanism to perform topological…
In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…
The Topological Hypothesis states that phase transitions should be related to changes in the topology of configuration space. The necessity of such changes has already been demonstrated. We characterize exactly the topology of the…
There exist extensive studies on periodic and random perturbations of various continuous maps investigating their dynamics. This paper presents a random piecewise smooth map derived from a simple inductor-less switching circuit. The…
Topological edge states in systems of two (or more) dimensions offer scattering-free transport, exhibiting robustness to inhomogeneities and disorder. In a different domain, time-modulated systems, such as photonic time crystals (PTCs),…
We extend the notion of fragile topology to periodically-driven systems. We demonstrate driving-induced fragile topology in two different models, namely, the Floquet honeycomb model and the Floquet $\pi$-flux square-lattice model. In both…
We consider two-dimensional periodically driven systems of fermions with particle-hole symmetry. Such systems support non-trivial topological phases, including ones that cannot be realized in equilibrium. We show that a space-time defect in…
Recent works have demonstrated that the Floquet-Bloch bands of periodically-driven systems feature a richer topological structure than their non-driven counterparts. The additional structure in the driven case arises from the periodicity of…