Apparatus for handling micron size range particulate material

An apparatus for handling, transporting, or size classifying comminuted material was described in detail. Electrostatic acceleration techniques for classifying particles as to size in the particle range from 0.1 to about 100 microns diameter were employed

Geographic range size and evolutionary age in birds

Together with patterns of speciation and extinction, post-speciation transformations in the range sizes of individual species determine the form of contemporary species-range-size distributions. However, the methodological problems associated with tracking the dynamics of a species' range size over evolutionary time have precluded direct study of such range-size transformations, although indirect evidence has led to several models being proposed describing the form that they might take. Here, we use independently derived molecular data to estimate ages of species in six monophyletic groups of birds, and examine the relationship between species age and global geographic range size. We present strong evidence that avian range sizes are not static over evolutionary time. In addition, it seems that, with the regular exception of certain taxa (for example island endemics and some threatened species), range-size transformations are non-random in birds. In general, range sizes appear to expand relatively rapidly post speciation; subsequently, and perhaps more gradually, they then decline as species age. We discuss these results with reference to the various models of range-size dynamics that have been proposed

Finite-size effects in dynamics of zero-range processes

The finite-size effects prominent in zero-range processes exhibiting a condensation transition are studied by using continuous-time Monte Carlo simulations. We observe that, well above the thermodynamic critical point, both static and dynamic properties display fluid-like behavior up to a density {\rho}c (L), which is the finite-size counterpart of the critical density {\rho}c = {\rho}c (L \rightarrow \infty). We determine this density from the cross-over behavior of the average size of the largest cluster. We then show that several dynamical characteristics undergo a qualitative change at this density. In particular, the size distribution of the largest cluster at the moment of relocation, the persistence properties of the largest cluster and correlations in its motion are studied.Comment: http://pre.aps.org/abstract/PRE/v82/i3/e03111

Finite-size scaling in systems with long-range interaction

The finite-size critical properties of the ${\cal O}(n)$ vector $\phi^4$ model, with long-range interaction decaying algebraically with the interparticle distance $r$ like $r^{-d-\sigma}$, are investigated. The system is confined to a finite geometry subject to periodic boundary condition. Special attention is paid to the finite-size correction to the bulk susceptibility above the critical temperature $T_c$. We show that this correction has a power-law nature in the case of pure long-range interaction i.e. $0<\sigma<2$ and it turns out to be exponential in case of short-range interaction i.e. $\sigma=2$. The results are valid for arbitrary dimension $d$, between the lower ($d_=2\sigma$) critical dimensions

Finite-size effects on the dynamics of the zero-range process

We study finite-size effects on the dynamics of a one-dimensional zero-range process which shows a phase transition from a low-density disordered phase to a high-density condensed phase. The current fluctuations in the steady state show striking differences in the two phases. In the disordered phase, the variance of the integrated current shows damped oscillations in time due to the motion of fluctuations around the ring as a dissipating kinematic wave. In the condensed phase, this wave cannot propagate through the condensate, and the dynamics is dominated by the long-time relocation of the condensate from site to site.Comment: 5 pages, 5 figures, version published in Phys. Rev. E Rapid Communication

Quasi-long-range ordering in a finite-size 2D Heisenberg model

We analyse the low-temperature behaviour of the Heisenberg model on a two-dimensional lattice of finite size. Presence of a residual magnetisation in a finite-size system enables us to use the spin wave approximation, which is known to give reliable results for the XY model at low temperatures T. For the system considered, we find that the spin-spin correlation function decays as 1/r^eta(T) for large separations r bringing about presence of a quasi-long-range ordering. We give analytic estimates for the exponent eta(T) in different regimes and support our findings by Monte Carlo simulations of the model on lattices of different sizes at different temperatures.Comment: 9 pages, 3 postscript figs, style files include

Coarsening dynamics in condensing zero-range processes and size-biased birth death chains

Zero-range processes with decreasing jump rates are well known to exhibit a condensation transition under certain conditions on the jump rates, and the dynamics of this transition continues to be a subject of current research interest. Starting from homogeneous initial conditions, the time evolution of the condensed phase exhibits an interesting coarsening phenomenon of mass transport between cluster sites characterized by a power law. We revisit the approach in [C. Godreche, J. Phys. A: Math. Gen., 36(23) 6313 (2003)] to derive effective single site dynamics which form a non-linear birth death chain describing the coarsening behaviour. We extend these results to a larger class of parameter values, and introduce a size-biased version of the single site process, which provides an effective tool to analyze the dynamics of the condensed phase without finite size effects and is the main novelty of this paper. Our results are based on a few heuristic assumptions and exact computations, and are corroborated by detailed simulation data.Comment: In addition to some minor changes, Figure 7(a) and the text below have been adapted to correct a mistake in the published version, pointed out to us by C. Godrech