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[en] Most existing flocking algorithms assume one single virtual leader and rely on information on both relative positions and relative velocities among neighboring agents. In this paper, the problem of controlling a flock of mobile autonomous agents to follow multiple virtual leaders is investigated by using only position information in the sense that agents with the same virtual leader asymptotically attain the same velocity and track the corresponding virtual leader based on only position measurements. A flocking algorithm is proposed under which every agent asymptotically attains its desired velocity, collision between agents can be avoided, and the final tight formation minimizes all agents' global potentials. A simulation example is presented to verify and illustrate the theoretical results. (general)
[en] Theoretical ideas on the formation and evolution of charged particle tracks in a condensed medium are discussed. The historical development of the field is briefly reviewed. The distribution of charged particle energies over quantum states and the volume of the absorbing medium are considered, and conditions for the formation of various track structures (entities) are discussed. The structures of extended heavy-ion tracks are compared for some ion parameters and track characteristics under equal conditions. Relaxation processes in the tracks of multiply charged ions are analyzed. Track effects are considered and possible mechanisms for the formation of chemically active defects in a latent track are described. (reviews of topical problems)
[en] Characterizing and localizing electronic energy degeneracies is important for describing and controlling electronic energy flow in molecules. We show, using topological phase considerations, that the Renner effect in polyatomic molecules with more than three nuclei is necessarily accompanied by 'satellite' conical intersections. In these intersections the non-adiabatic coupling term is on average half an integer. We present ab initio results on the tetra-atomic radical cation C2H+2 to demonstrate the theory. (fast track communication)
[en] We present a novel way to apply the singularity confinement property as a discrete integrability criterion. We shall use what we call a full deautonomization approach, which consists in treating the free parameters in the mapping as functions of the independent variable, applied to a mapping complemented with terms that are absent in the original mapping but which do not change the singularity structure. We shall show, on a host of examples including the well-known mapping of Hietarinta–Viallet, that our approach offers a way to compute the algebraic entropy for these mappings exactly, thereby allowing one to distinguish between the integrable and non-integrable cases even when both have confined singularities. (fast track communication)
[en] Hawking radiation, originally derived in the ray optics limit, exhibits the unfortunate trans-Planckian problem—a Hawking photon near spatial infinity, if back-tracked to the immediate vicinity of the horizon is hugely blue-shifted and found to have had trans-Planckian energy. (And if back-tracked all the way to the horizon, the photon is formally infinitely blue-shifted, and formally acquires infinite energy.) Unruh has forcefully argued that this implies that the Hawking flux represents a vacuum instability in the presence of a horizon, and that the Hawking photons are actually emitted from some region exterior to the horizon. We seek to make this idea more precise and somewhat explicit by building a purely kinematical model for Hawking evaporation based on two Vaidya spacetimes (outer and inner) joined across a thin time-like boundary layer. The kinematics of this model is already quite rich, and we shall defer consideration of the dynamics for subsequent work. In particular we shall present an explicit calculation of the 4-acceleration of the shell (including the effects of gravity, motion, and the outgoing null flux) and relate this 4-acceleration to the Unruh temperature.
[en] Repeated elastic collisions of point particles on a finite frictionless linear track with perfectly reflecting endpoints are considered. The problem is analysed by means of an elementary linear algebra approach. It is found that, starting with a state consisting of a projectile particle in motion at constant velocity and a target particle at rest in a fixed known position, the points at which collisions occur on track, when plotted versus progressive numerals, corresponding to the collisions themselves, show periodic patterns for a rather large choice of values of the initial position x(0) and on the mass ratio r. For certain values of these parameters, however, only regular behaviour over a large number of collisions is detected
[en] Hadron inelastic interactions in nuclear emulsion with a small target-nucleus excitation in the energy range 7.5-200 GeV have been studied. Possible reasons for the differences in production cross-section for events with even and odd number of S-particles are analysed
[en] The experimental results of Kocsis et al., Mahler et al. and the proposed experiments of Morley et al. show that it is possible to construct “trajectories” in interference regions in a two-slit interferometer. These results call for a theoretical re-appraisal of the notion of a “quantum trajectory” first introduced by Dirac and in the present paper we re-examine this notion from the Bohm perspective based on Hamiltonian flows. In particular, we examine the short-time propagator and the role that the quantum potential plays in determining the form of these trajectories. These trajectories differ from those produced in a typical particle tracker and the key to this difference lies in the active suppression of the quantum potential necessary to produce Mott-type trajectories. We show, using a rigorous mathematical argument, how the active suppression of this potential arises. Finally we discuss in detail how this suppression also accounts for the quantum Zeno effect.