Related papers: The Interplay Between Symmetries and Impact Effect…
The existence and search for thermodynamic phase transitions is of unfading interest. In this paper, we present numerical evidence of dynamical phase transitions occurring in boundary driven systems with a constrained integrated current. It…
We define double principal bundles (DPBs), for which the frame bundle of a double vector bundle, double Lie groups and double homogeneous spaces are basic examples. It is shown that a double vector bundle can be realized as the associated…
Optimal control problems for underactuated mechanical systems can be seen as a higher-order variational problem subject to higher-order constraints (that is, when the Lagrangian function and the constraints depend on higher-order…
The conditions under which an open quantum mechanical system may be described by mixed quantum-classical dynamics are investigated. Decoherence is studied using influence functional methods in a model composite quantum system comprising two…
We give a derivation for the indirect interaction between two magnetic dipoles induced by the quantized electromagnetic field. It turns out that the interaction between permanent dipoles directly returns to the classical form; the…
The fiber bundle model is essentially an array of elements that break when sufficient load is applied on them. With a local loading mechanism, this can serve as a model for a one-dimensional interface separating the broken and unbroken…
The study of controlled hybrid systems requires practical tools for approximation and comparison of system behaviors. Existing approaches to these problems impose undue restrictions on the system's continuous and discrete dynamics.…
Hydrodynamic interactions (HIs), namely solvent mediated long-range interactions between dispersed particles, play a crucial role in the assembly and dynamics of many active systems, from swimming bacteria to swarms of propelling…
Transitions between steady dynamical regimes in diverse applications are often modelled using discontinuities, but doing so introduces problems of uniqueness. No matter how quickly a transition occurs, its inner workings can affect the…
One may define a complex system as a system in which phenomena emerge as a consequence of multiscale interaction among the system's components and their environments. The field of Complex Systems is the study of such systems--usually…
We give an overview exploring the role of kinetics in multicomponent mixtures. Compared to the most commonly studied binary (single species plus solvent) case, multicomponent fluids show a rich interplay between kinetics and thermodynamics…
In this paper, we analyse the impact of delayed event detection on the stability of a 2-mode planar hybrid automata. We consider hybrid automata with a unique equilibrium point for all the modes, and we find the maximum delay that preserves…
In this paper, we provide a theoretical analysis of strongly interacting quantum systems confined by a time-dependent external potential in one spatial dimension. We show that such systems can be used to simulate spin chains described by…
Invariant manifolds play an important role in organizing global dynamical behaviors. For example, it is found that in multi-well conservative systems where the potential energy wells are connected by index-1 saddles, the motion between…
Multiple time scales in dynamical systems lead to a bundling of trajectories onto slow invariant manifolds (SIMs). Although they are absent in two-dimensional holomorphic dynamical systems, a bundling of orbits is often observed as well.…
Bifurcations of dynamical systems, described by a second order differential equations and by an impact condition are studied. It is shown that the variation of parameters when the number of impacts of a periodic solution increases, leads to…
In this paper we introduce the concept of random time changes in dynamical systems. The subordination principle may be applied to study the long time behavior of the random time systems. We show, under certain assumptions on the class of…
In this work, we study the dynamics of an impact hybrid system. We built applications called ZDM (Zero Discontinuity Mapping) and PDM (Poincar\'e Discontinuity Mapping), for points in a neighbourhood of the 4 order regular grazing point,…
Given a discrete-state continuous-time reactive system, like a digital circuit, the classical approach is to first model it as a state transition system and then prove its properties. Our contribution advocates a different approach: to…
Motivated by recent developments in Hamiltonian variational principles, Hamiltonian variational integrators, and their applications such as to optimization and control, we present a new Type II variational approach for Hamiltonian systems,…