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Despite major advances in the understanding of the formation and dynamics of nano-clusters in the past decades, theoretical bases for the control of their shape are still lacking. We investigate strategies for driving fluctuating…
This article solves an optimal control problem arising in attitude control of a spacecraft under state and control constraints. We first derive the discrete-time attitude dynamics by employing discrete mechanics. The orientation transfer,…
Clustering provides a common means of identifying structure in complex data, and there is renewed interest in clustering as a tool for the analysis of large data sets in many fields. A natural question is how many clusters are appropriate…
Influence of surrounding matter on the properties of clusters is considered by an approach combining the methods of statistical and quantum mechanics. A cluster is treated as a bound N-particle system and surrounding matter as thermostat.…
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…
The article considers a two-level open quantum system whose dynamics is driven by a combination of coherent and incoherent controls. Coherent control enters into the Hamiltonian part of the dynamics whereas incoherent control enters into…
Optimal control is a central problem in quantum thermodynamics. When minimizing dissipated work and work fluctuations defined via the two-point measurement scheme in open quantum systems, existing approaches largely focus on the rapid- and…
Methods of optimal control are applied to a model system of interacting two-level particles (e.g., spin-half atomic nuclei or electrons or two-level atoms) to produce high-fidelity quantum gates while simultaneously negating the detrimental…
The problem concerning the minimum time for an initial state to evolve up to a target state plays an important role in the Classic Optimal Control theory. In the quantum context, as quantum states are so sensitive to environmental…
In a recent paper ["Cluster Model of Decagonal Tilings" (to be published in Phys. Rev. B)], we have introduced a cluster model for decagonal tilings in two dimensions. This model is now extended to three dimensions. Two-dimensional tilings…
When engineering microscopic machines, increasing efficiency can often come at a price of reduced reliability due to the impact of stochastic fluctuations. Here we develop a general method for performing multi-objective optimisation of…
This paper studies the time optimal control problem for systems of heat equations coupled by a pair of constant matrices. The control constraint is of the ball-type, while the target is the origin of the state space. We obtain an upper…
Two dimensional (2D) classical system of dipole particles confined by a quadratic potential is studied. For clusters of N < 81 particles ground state configurations and appropriate eigenfrequencies and eigenvectors for the normal modes are…
We study stochastic optimal control problems for (possibly degenerate) McKean-Vlasov controlled diffusions and obtain discrete-time as well as finite interacting particle approximations. (i) Under mild assumptions, we first prove the…
We propose a general framework for studying optimal impulse control problem in the presence of uncertainty on the parameters. Given a prior on the distribution of the unknown parameters, we explain how it should evolve according to the…
Using a series of fast cooling protocols we have probed aging effects in the spin glass state as a function of temperature. Analyzing the logarithmic decay found at very long time scales within a simple phenomenological barrier model, leads…
Progress in miniaturized technology allows us to control physical systems at nanoscale with remarkable precision. Experimental advancements have sparked interest in control problems in stochastic thermodynamics, typically concerning a…
We characterize the optimal control for a class of singular stochastic control problems as the unique solution to a related Skorokhod reflection problem. The considered optimization problems concern the minimization of a discounted cost…
Employing Monte-Carlo simulation techniques we investigate the statistical properties of equally charged particles confined in a one-dimensional box trap and detect a crossover from a crystalline to a cluster phase with increasing…
The thermal evolution of the shell correction energy is investigated for deformed nuclei using Strutinsky prescription in a self-consistent relativistic mean-field framework. For temperature independent single-particle states corresponding…