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Optimal control of large particle systems with collective dynamics by few agents is a subject of high practical importance (e.g. in evacuation dynamics), but still limited mathematical basis. In particular the transition from discrete…
On the basis of a simple exactly solvable model we discuss the possibilities for state preparation and state control of atoms in a periodic optical potential. In addition to the periodic potential a uniform force with an arbitrary time…
The main objective of this article is to develop a matrix pencil approach for the study of the controllability and reachability of a class of linear singular discrete time systems. The description equation of a practical system may be…
Control theory often takes the mathematical model of the to-be-control-led system for granted. In contrast, port-Hamiltonian systems theory bridges the gap between modelling and control for physical systems. It provides a unified framework…
Networked nonlinear systems present a variety of emergent phenomena as a result of the mutual interactions between their units. An interesting feature of these systems is the presence of stable periodic behavior even when each unit…
The conditions under which stochastic systems of infinitely many interacting particles can maintain sufficient spatial order to move coherently along a time-periodic orbit, thereby breaking the time-translation invariance of the underlying…
A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…
For linear infinite systems the approximate controllability problem by control constraints is considered. Controllability conditions represented via system parameters are obtained. Partial differential control systems and control systems…
In this paper we study the controllability problem for a symmetric-top molecule, both for its classical and quantum rotational dynamics. The molecule is controlled through three orthogonal electric fields interacting with its electric…
The control of chemical reactions is a recurring theme in physics and chemistry. Traditionally, chemical reactions have been investigated by tuning thermodynamic parameters, such as temperature or pressure. More recently, physical methods…
This is a study of localised structures in one-dimensional cellular automata, with the elementary cellular automaton Rule 54 as a guiding example. A formalism for particles on a periodic background is derived, applicable to all…
We study the controllability of the multidimensional wave equation in a bounded domain with Dirichlet boundary condition, in which the support of the control is allowed to change over time. The exact controllability is reduced to the proof…
Given a finite-dimensional time continuous control system and $\varepsilon>0$, we address the question of the existence of controls that maintain the corresponding state trajectories in the $\varepsilon$-neighborhood of any prescribed path…
Natural materials often feature a combination of soft and stiff phases, arranged to achieve excellent mechanical properties, such as high strength and toughness. Many natural materials have even independently evolved to have similar…
We study the dynamics of particles in a multi-component 2d Lennard-Jones (LJ) fluid in the limiting case where {\it all the particles are different} (APD). The equilibrium properties of this APD system were studied in our earlier work…
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…
Positive linear systems on arbitrary time scales are studied. The theory developed in the paper unifies and extends concepts and results known for continuous-time and discrete-time systems. A necessary and sufficient condition for a linear…
The physics of critical phenomena in a many-body system far from thermal equilibrium is an interesting and important issue to be addressed both experimentally and theoretically. The trapped cold atoms have been actively used as a clean and…
The paradigm of layered networks is used to describe many real-world systems -- from biological networks, to social organizations and transportation systems. Recently there has been much progress in understanding the general properties of…
In this paper we are concerned with the approximate controllability of a multidimensional semilinear reaction-diffusion equation governed by a multiplicative control, which is locally distributed in the reaction term. For a given initial…