相关论文: Natural frames and interacting particles in three …
This paper presents a generalization of conventional sliding mode control designs for systems in Euclidean spaces to fully actuated simple mechanical systems whose configuration space is a Lie group for the trajectory-tracking problem. A…
We investigate the kinetics of a nonrelativistic particle interacting with a constant external force on a Lie-algebraic noncommutative space. The structure constants of a Lie algebra, also called noncommutative parameters, are constrained…
We study collective dynamics of interacting deformable self-propelled particles whose migration velocity increases when the local density of particles is increased. Numerical simulations in two dimensions reveal that traveling bands similar…
When particles move at a constant speed and have the tendency to align their directions of motion, ordered large scale movement can emerge despite significant levels of noise. Many variants of this model of self-propelled particles have…
In control theory, researchers need to understand a system's local and global behaviors in relation to its initial conditions. When discussing observability, the main focus is on the ability to analyze the system using an output space…
We propose a new model for the description of complex granular particles and their interaction in molecular dynamics simulations of granular material in two dimensions. The grains are composed of triangles which are connected by deformable…
On the basis of the relativistic kinetic theory the relativistic statistical systems with scalar interaction particles are investigated. The self-consistent system of the equations describing self-gravitating plasma with interpartial scalar…
Aggregation of particles whose interaction potential depends on their mutual orientation is considered. The aggregation dynamics is derived using a version of Darcy's law and a variational principle depending on the geometric nature of the…
An algebraic approach is formulated in the harmonic approximation to describe a dynamics of two-fermion systems, confined in three-dimensional axially symmetric parabolic potential, in an external magnetic field. The fermion interaction is…
We consider left-invariant optimal control problems on connected Lie groups such that generic stabilizer of the coadjoint action is connected and has dimension not more than 1. We introduce a construction for symmetries of the exponential…
We formulate and analyze a three-dimensional model of motion camouflage, a stealth strategy observed in nature. A high-gain feedback law for motion camouflage is formulated in which the pursuer and evader trajectories are described using…
Although rare, collisions of two or more bodies in the N-body problem are apparent obstacles at which Newton's Law of Gravity ceases to make sense. Without understanding the nature of collisions, a complete understanding of the N-body…
The equilibrium statistical mechanics of one-dimensional lattice gases with interactions of arbitrary range and shape between first-neighbor atoms is solved exactly on the basis of statistically interacting vacancy particles. Two sets of…
The quantum properties of localized finite energy solutions to classical Euler-Lagrange equations are investigated using the method of collective coordinates. The perturbation theory in terms of inverse powers of the coupling constant $g$…
We present an overdamped continuum description of oriented active solids in which interactions respect the symmetries of space but do not obey the principle of action and reaction. Taking position and orientation as kinematic variables, we…
The asymptotic analysis of kinetic models describing the behavior of particles interacting through alignment is performed. We will analyze the asymptotic regime corresponding to large alignment frequency where the alignment effects are…
Motivated by the applications, a class of optimal control problems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. Diffusive terms accounting for…
We find and solve a large class of integrable dynamical systems which includes Calogero-Sutherland models and various novel generalizations thereof. In general they describe $N$ interacting particles moving on a circle and coupled to an…
We study an agent-based model of self-propelled particles with a velocity-dependent alignment rule. This interaction is orientation weighted and acts along the line connecting neighboring particles. Tuning the alignment strength produces…
For more than a century Liesegang patterns -- self-organized, quasi-periodic structures occurring in diffusion-limited chemical reactions with two components -- have been attracting scientists. The pattern formation can be described by four…