相关论文: Collective Coordinate Control of Density Distribut…

We explore quantitative descriptors that herald when a many-particle system in $d$-dimensional Euclidean space $\mathbb{R}^d$ approaches a hyperuniform state as a function of the relevant control parameter. We establish quantitative…

In this work we focus on a recently introduced method [1] to construct the external potential $v$ that, for a given initial state, produces a prescribed time-dependent density in an interacting quantum many-body system. We show how this…

Questions surrounding the spatial disposition of particles in various condensed-matter systems continue to pose many theoretical challenges. This paper explores the geometric availability of amorphous many-particle configurations that…

Efficient coordination for collective spatial distribution is a fundamental challenge in multi-agent systems. Prior research on Density-Driven Optimal Control (D2OC) established a framework to match agent trajectories to a desired spatial…

Hyperuniform many-particle systems are characterized by a structure factor $S({\mathbf{k}})$ that is precisely zero as $|\mathbf{k}|\rightarrow0$; and stealthy hyperuniform systems have $S({\mathbf{k}})=0$ for the finite range $0 <…

Quantum Optimal Control Theory (QOCT) provides the necessary tools to theoretically design driving fields capable of controlling a quantum system towards a given state or along a prescribed path in Hilbert space. This theory must be…

Extracting higher-order structures from multivariate data has become an area of intensive study in complex systems science, as these multipartite interactions can reveal insights into fundamental features of complex systems like emergent…

The trajectories of the pilot-wave formulation of quantum mechanics and hence its empirical predictions may be recovered via the dynamics of a density function on the configuration space of a system, without reference to a physical wave…

A density functional theory for many-body lattice models is considered in which the single-particle density matrix is the basic variable. Eigenvalue equations are derived for solving Levy's constrained search of the interaction energy…

In Stochastic Optimal Control (SOC) one minimizes the average cost-to-go, that consists of the cost-of-control (amount of efforts), cost-of-space (where one wants the system to be) and the target cost (where one wants the system to arrive),…

The phenomenon of solidification of a substance from its liquid phase is of the greatest practical and theoretical importance, and atomistic simulations can provide precious information towards its understanding and control. Unfortunately,…

Particle Swam Optimization is a population-based and gradient-free optimization method developed by mimicking social behaviour observed in nature. Its ability to optimize is not specifically implemented but emerges in the global level from…

A particle filter is introduced to numerically approximate a solution of the global optimization problem. The theoretical significance of this work comes from its variational aspects: (i) the proposed particle filter is a controlled…

We provide numerical constructions of one-dimensional hyperuniform many-particle distributions that exhibit unusual clustering and asymptotic local number density fluctuations growing more slowly than the volume of an observation window but…

This article generalizes the notion of the local density of a many-body system to introduce collective coordinates as explicit degrees of freedom. It is shown that the energy of the system can be expressed as a functional of this object.…

Colloidal fluids can exhibit complex phase behavior and determining phase diagrams via experiments or computer simulations can be laborious. We demonstrate that the dispersion relation $\omega(k)$, obtained from dynamical density functional…

We describe in this paper an optimal control strategy for shaping a large-scale swarm of particles using boundary global actuation. This problem arises as a key challenge in many swarm robotics applications, especially when the robots are…

This paper presents a revolutionary approach to the characterization, forecast, and control of collective systems. Collective systems are an ensemble of conservatively interacting entities. The evolution of the entities are determined by…

We demonstrate how an effective density of states can be derived from the S-matrix describing a coupled-channel system. Besides the locations of poles, the phase of the determinant of the S-matrix encodes essential details in characterizing…

Application of K-Means algorithm is restricted by the fact that the number of clusters should be known beforehand. Previously suggested methods to solve this problem are either ad hoc or require parametric assumptions and complicated…