Static spherically symmetric Einstein-Vlasov shells made up of particles with a discrete set of values of their angular momentum

In this paper we study static spherically symmetric Einstein-Vlasov shells, made up of equal mass particles, where the angular momentum L of particles takes values only on a discrete finite set. We consider first the case where there is only one value of L, and prove their existence by constructing explicit examples. Shells with either hollow or black hole interiors have finite thickness. Of particular interest is the thin shell limit of these systems and we study its properties using both numerical and analytic arguments to compare with known results. The general case of a set of values of L is also considered and the particular case where L takes only two values is analyzed, and compared with the corresponding thin shell limit already given in the literature, finding good agreement in all cases.Comment: Comments: 16 pages, 5 figures. Section on thin shell limit revised. References adde

The effect of radiative gravitational modes on the dynamics of a cylindrical shell of counter rotating particles

In this paper we consider some aspects of the relativistic dynamics of a cylindrical shell of counter rotating particles. In some sense these are the simplest systems with a physically acceptable matter content that display in a well defined sense an interaction with the radiative modes of the gravitational field. These systems have been analyzed previously, but in most cases resorting to approximations, or considering a particular form for the initial value data. Here we show that there exists a family of solutions where the space time inside the shell is flat and the equation of motion of the shell decouples completely from the gravitational modes. The motion of the shell is governed by an equation of the same form as that of a particle in a time independent one dimensional potential. We find that under appropriate initial conditions one can have collapsing, bounded periodic, and unbounded motions. We analyze and solve also the linearized equations that describe the dynamics of the system near a stable static solutions, keeping a regular interior. The surprising result here is that the motion of the shell is completely determined by the configuration of the radiative modes of the gravitational field. In particular, there are oscillating solutions for any chosen period, in contrast with the "approximately Newtonian plus small radiative corrections" motion expectation. We comment on the physical meaning of these results and provide some explicit examples. We also discuss the relation of our results to the initial value problem for the linearized dynamics of the shell

Autonomous Locomotion Mode Transition Simulation of a Track-legged Quadruped Robot Step Negotiation

Multi-modal locomotion (e.g. terrestrial, aerial, and aquatic) is gaining increasing interest in robotics research as it improves the robots environmental adaptability, locomotion versatility, and operational flexibility. Within the terrestrial multiple locomotion robots, the advantage of hybrid robots stems from their multiple (two or more) locomotion modes, among which robots can select from depending on the encountering terrain conditions. However, there are many challenges in improving the autonomy of the locomotion mode transition between their multiple locomotion modes. This work proposed a method to realize an autonomous locomotion mode transition of a track-legged quadruped robot steps negotiation. The autonomy of the decision-making process was realized by the proposed criterion to comparing energy performances of the rolling and walking locomotion modes. Two climbing gaits were proposed to achieve smooth steps negotiation behaviours for energy evaluation purposes. Simulations showed autonomous locomotion mode transitions were realized for negotiations of steps with different height. The proposed method is generic enough to be utilized to other hybrid robots after some pre-studies of their locomotion energy performances

Adsorption preference reversal phenomenon from multisite-occupancy theory fortwo-dimensional lattices

The statistical thermodynamics of polyatomic species mixtures adsorbed on two-dimensional substrates was developed on a generalization in the spirit of the lattice-gas model and the classical Guggenheim-DiMarzio approximation. In this scheme, the coverage and temperature dependence of the Helmholtz free energy and chemical potential are given. The formalism leads to the exact statistical thermodynamics of binary mixtures adsorbed in one dimension, provides a close approximation for two-dimensional systems accounting multisite occupancy and allows to discuss the dimensionality and lattice structure effects on the known phenomenon of adsorption preference reversal.Comment: 13 pages, 4 figure

Adsorption of Self-Assembled Rigid Rods on Two-Dimensional Lattices

Monte Carlo (MC) simulations have been carried out to study the adsorption on square and triangular lattices of particles with two bonding sites that, by decreasing temperature or increasing density, polymerize reversibly into chains with a discrete number of allowed directions and, at the same time, undergo a continuous isotropic-nematic (IN) transition. The process has been monitored by following the behavior of the adsorption isotherms for different values of lateral interaction energy/temperature. The numerical data were compared with mean-field analytical predictions and exact functions for noninteracting and 1D systems. The obtained results revealed the existence of three adsorption regimes in temperature. (1) At high temperatures, above the critical one characterizing the IN transition at full coverage Tc(\theta=1), the particles are distributed at random on the surface and the adlayer behaves as a noninteracting 2D system. (2) At very low temperatures, the asymmetric monomers adsorb forming chains over almost the entire range of coverage, and the adsorption process behaves as a 1D problem. (3) In the intermediate regime, the system exhibits a mixed regime and the filling of the lattice proceeds according to two different processes. In the first stage, the monomers adsorb isotropically on the lattice until the IN transition occurs in the system and, from this point, particles adsorb forming chains so that the adlayer behaves as a 1D fluid. The two adsorption processes are present in the adsorption isotherms, and a marked singularity can be observed that separates both regimes. Thus, the adsorption isotherms appear as sensitive quantities with respect to the IN phase transition, allowing us (i) to reproduce the phase diagram of the system for square lattices and (ii) to obtain an accurate determination of the phase diagram for triangular lattices.Comment: Langmuir, 201