Related papers: Driven linear modes: Analytical solutions for fini…
We investigate the reduced dynamics of two identical superconducting qubits capacitively coupled through a finite-length transmission line. Starting from circuit quantization, we derive a circuit Hamiltonian that naturally separates the…
A class of models of driven diffusive systems which is shown to exhibit phase separation in $d=1$ dimensions is introduced. Unlike all previously studied models exhibiting similar phenomena, here the phase separated state is fluctuating in…
Finite-state abstractions (a.k.a. symbolic models) present a promising avenue for the formal verification and synthesis of controllers in continuous-space control systems. These abstractions provide simplified models that capture the…
A novel strategy is proposed for the coupling of field and circuit equations when modeling power devices in the low-frequency regime. The resulting systems of differential-algebraic equations have a particular geometric structure which…
The aim of this short note is to give a synthetic presentation of the mathematical elements that are used to solve the elastic wave system of equations in a bounded anisotropic elastic body, in a general framework. In particular, the proof…
The formal analysis and design of control systems is one of recent trends in control theory. In this area, in order to reduce the complexity and scale of control systems, finite abstractions of control systems are introduced and explored.…
Extended systems driven through strong disorder are modeled generically using coarse-grained degrees of freedom that interact elastically in the directions parallel to the driving force and that slip along at least one of the directions…
For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer or estimate their modes from observations in real time. The modes can be real or complex. For…
Two questions related to elastic motions are raised and addressed. First: in which theoretical framework can the equations of motion be written for an elastic half-space put into uniform rotation? It is seen that nonlinear finite elasticity…
We examine - both experimentally and numerically - a two-dimensional nonlinear driven electrical lattice with honeycomb structure. Drives are considered over a range of frequencies both outside (below and above) and inside the band of…
We study one-dimensional systems with random diagonal disorder but off-diagonal short-range correlations imposed by structural constraints. We find that these correlations generate effective conduction channels for finite systems. At a…
We propose a model for frequency-dependent damping in the linear wave equation. After proving well-posedness of the problem, we study qualitative properties of the energy. In the one-dimensional case, we provide an explicit analysis for…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
We consider the differential conductance of a periodically driven system connected to infinite electrodes. We focus on the situation where the dissipation occurs predominantly in these electrodes. Using analytical arguments and a detailed…
Nonlinear waves are a robust phenomenon observed in complex systems ranging from mechanics to ecology. Fronts are fundamental due to their robustness against perturbations and capacity to propagate one state over another. Controlling and…
Embedded solitons are exceptional modes in nonlinear-wave systems with the propagation constant falling in the system's propagation band. An especially challenging topic is seeking for such modes in nonlinear dynamical lattices (discrete…
A mathematical model describing the capture of nonlinear systems into the autoresonance by a combined parametric and external periodic slowly varying perturbation is considered. The autoresonance phenomenon is associated with solutions…
We consider large but finite systems of identical agents on the line with up to next nearest neighbor asymmetric coupling. Each agent is modelled by a linear second order differential equation, linearly coupled to up to four of its…
Standandard Hamiltonian mechanics in its homogeneous formulation is applied to the study of discontinuities representing rapid changes of Hamiltonians. Different formulations of Hamiltonian mechanics are reviewed. An original representation…
Periodically driven systems are a common topic in modern physics. In optical lattices specifically, driving is at the origin of many interesting phenomena. However, energy is not conserved in driven systems, and under periodic driving,…