arXiv subjects

Bruce N. Miller

Publications and source records attributed to Bruce N. Miller.

23 records · Page 2Linked to original sources

arXiv2005

Exactly Integrable Analogue of a One-dimensional Gravitating System

Exchange symmetry in acceleration partitions the configuration space of an N particle, one-dimensional, gravitational system into N! equivalent cells. We take advantage of the resulting small angular extent of each cell to construct a related integrable version of the system that takes the form of a central force problem in N-1 dimensions. The properties of the latter, including the construction of trajectories, as well as several continuum limits, are developed. Dynamical simulation is employed to compare the two models. For a class of initial conditions, excellent agreement is observed.

cond-mat.stat-mech↗

arXiv2005

Self-trapping at the liquid vapor critical point

Experiments suggest that localization via self-trapping plays a central role in the behavior of equilibrated low mass particles in both liquids and in supercritical fluids. In the latter case, the behavior is dominated by the liquid-vapor critical point which is difficult to probe, both experimentally and theoretically. Here, for the first time, we present the results of path-integral computations of the characteristics of a self-trapped particle at the critical point of a Lennard-Jones fluid for a positive particle-atom scattering length. We investigate the influence of the range of the particle-atom interaction on trapping properties, and the pick-off decay rate for the case where the particle is ortho-positronium.

cond-mat.mes-hall↗

arXiv2002

Angular momentum induced phase transition in spherical gravitational systems: N-body simulations

The role of thermodynamics in the evolution of systems evolving under purely gravitational forces is not completely established. Both the infinite range and singularity in the Newtonian force law preclude the use of standard techniques. However, astronomical observations of globular clusters suggests that they may exist in distinct thermodynamic phases. Here, using dynamical simulation, we investigate a model gravitational system which exhibits a phase transition in the mean field limit. The system consists of rotating, concentric, mass shells of fixed angular momentum magnitude and shares identical equilibrium properties with a three dimensional point mass system satisfying the same condition. The mean field results show that a global entropy maximum exists for the model, and a first order phase transition takes place between "quasi-uniform" and ''core-halo'' states, in both the microcanonical and canonical ensembles. Here we investigate the evolution and, with time averaging, the equilibrium properties of the isolated system. Simulations were carried out in the transition region, at the critical point, and in each clearly defined thermodynamic phase, and striking differences were found in each case. We find full agreement with mean field theory when finite size scaling is accounted for. In addition, we find that (1) equilibration obeys power law behavior, (2) virialization, equilibration, and the decay of correlations in both position and time, are very slow in the transition region, suggesting the system is also spending time in the metastable phase, (3) there is strong evidence of long-lived, collective, oscillations in the supercritical region.

astro-ph↗

arXiv2001

Influence of Expansion on Hierarchical Structure

We study a one dimensional model of gravitational instability in an Einstein-de Sitter universe. Scaling in both space and time results in an autonomous set of coupled Poisson-Vlasov equations for the field and phase space density, and the $N$-body problem. Using dynamical simulation, we find direct evidence of hierarchical clustering. A multi-fractal analysis reveals a bifractal geometry similar to that observed in the distribution of galaxies. To demonstrate the role of scaling, we compare the system to other one dimensional models recently employed to study structure formation. Finally we show that the model yields an estimate of the time of galaxy formation of the correct order.

astro-ph↗

arXiv2000

Mean Field Theory of Spherical Gravitating Systems

Important gaps remain in our understanding of the thermodynamics and statistical physics of self-gravitating systems. Using mean field theory, here we investigate the equilibrium properties of several spherically symmetric model systems confined in a finite domain consisting of either point masses, or rotating mass shells of different dimension. We establish a direct connection between the spherically symmetric equilibrium states of a self-gravitating point mass system and a shell model of dimension 3. We construct the equilibrium density functions by maximizing the entropy subject to the usual constraints of normalization and energy, but we also take into account the constraint on the sum of the squares of the individual angular momenta, which is also an integral of motion for these symmetric systems. Two new statistical ensembles are introduced which incorporate the additional constraint. They are used to investigate the possible occurrence of a phase transition as the defining parameters for each ensemble are altered.

cond-mat.stat-mech↗