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Consider a linear autonomous Hamiltonian system with a time periodic bound state solution. In this paper we study the structural instability of this bound state ^M relative to time almost periodic perturbations which are small, localized…
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…
At the macroscopic scale, many important models of collective motion fall into the class of kinematic flows for which both velocity and diffusion terms depend only on particle density. When total particle numbers are fixed and finite,…
Consider a partition of $R^n$ into finitely many polyhedral regions $D_i$ and associated drift vectors $\mu_i\in R^n$. We study ``hybrid'' dynamical systems whose trajectories have a constant drift, $\dot x=\mu_i$, whenever $x$ is in the…
We discuss recent work on the static and dynamical properties of the asymmetric exclusion process, generalized to include the effect of disorder. We study in turn: random disorder in the properties of particles; disorder in the spatial…
The aim of this Letter is to characterize the flow regimes of suspensions of finite-size rigid particles in a viscous fluid at finite inertia. We explore the system behavior as function of the particle volume fraction and the Reynolds…
We present a novel method to compute componentwise transient bounds, ultimate bounds, and invariant regions for a class of switching continuous-time linear systems with perturbation bounds that may depend nonlinearly on a delayed state. The…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
In this technical communique we study the maximal robust positively invariant set for state-constrained continuous-time nonlinear systems subjected to a bounded disturbance. Extending results from the theory of barriers, we show that this…
This paper investigates the impact of disturbances on controlling an autonomous vehicle to smooth mixed traffic flow in a ring road setup. By exploiting the ring structure of this system, it is shown that velocity perturbations impacting…
We conjecture that the current fluctuations in one-dimensional driven transport systems obey an upper bound determined by the mean current and the driving force. This inequality originates from repulsive interactions between transporting…
Transition to turbulence is due to the instability of a laminar flow subject to a disturbance. This complicated problem can be explained using a new proposed energy gradient theory in our previous study. This theory is extended to the…
The sequential compactness afforded hybrid systems under mild regularity constraints guarantee outer/upper semicontinuous dependence of solutions on initial conditions and perturbations. For reachable sets of hybrid systems, this property…
In this paper, we seek to understand the behavior of dynamical systems that are perturbed by a parameter that changes discretely in time. If we impose certain conditions, we can study certain embedded systems within a hybrid system as…
There exist some boundary-driven open systems with diffusive dynamics whose particle current fluctuations exhibit universal features that belong to the Edwards-Wilkinson universality class. We achieve this result by establishing a mapping,…
Recent work on stochastic interacting particle systems with two particle species (or single-species systems with kinematic constraints) has demonstrated the existence of spontaneous symmetry breaking, long-range order and phase coexistence…
We study a two-dimensional granular system where external driving force is applied to each particle in the system in such a way that the system is driven into a steady state by balancing the energy input and the dissipation due to inelastic…
A R\"ossler model perturbed with a piecewise constant function is investigated. The perturbation function used in the model is constructed by means of the logistic map. In the absence of the perturbation the system is assumed to possess two…
A recently introduced particle-based model for fluid dynamics with continuous velocities is generalized to model fluids with excluded volume effects. This is achieved through the use of biased stochastic multi-particle collisions which…
We investigate the effect of quenched disorder in the Nagel-Schreckenberg model of traffic flow. Spatial inhomogenities, i.e. lattice sites where the braking probability is enlarged, are considered as well as particle disorder, i.e. cars of…