Theory of continuum percolation I. General formalism

The theoretical basis of continuum percolation has changed greatly since its beginning as little more than an analogy with lattice systems. Nevertheless, there is yet no comprehensive theory of this field. A basis for such a theory is provided here with the introduction of the Potts fluid, a system of interacting $s$-state spins which are free to move in the continuum. In the $s \to 1$ limit, the Potts magnetization, susceptibility and correlation functions are directly related to the percolation probability, the mean cluster size and the pair-connectedness, respectively. Through the Hamiltonian formulation of the Potts fluid, the standard methods of statistical mechanics can therefore be used in the continuum percolation problem.Comment: 26 pages, Late

Exact solution of a one-dimensional continuum percolation model

I consider a one dimensional system of particles which interact through a hard core of diameter \si and can connect to each other if they are closer than a distance $d$. The mean cluster size increases as a function of the density $\rho$ until it diverges at some critical density, the percolation threshold. This system can be mapped onto an off-lattice generalization of the Potts model which I have called the Potts fluid, and in this way, the mean cluster size, pair connectedness and percolation probability can be calculated exactly. The mean cluster size is S = 2 \exp[ \rho (d -\si)/(1 - \rho \si)] - 1 and diverges only at the close packing density \rho_{cp} = 1 / \si . This is confirmed by the behavior of the percolation probability. These results should help in judging the effectiveness of approximations or simulation methods before they are applied to higher dimensions.Comment: 21 pages, Late

The Chandrayaan-2 Large Area Soft X-ray Spectrometer (CLASS)

The CLASS experiment on Chandrayaan-2, the second Indian lunar mission, aims tomap the abundance of the major rock forming elements on the lunar surface using the technique of X-ray fluorescence during solar flare events. CLASS is a continuation of the successful C1XS [1] XRF experiment on Chandrayaan-1. CLASS is designed to provide lunar mapping of elemental abundances with a nominal spatial resolution of 25 km (FWHM) from a 200 km polar, circular orbit of Chandrayaan-2

Structural Polymorphism of the Cytoskeleton: A Model of Linker-Assisted Filament Aggregation

The phase behavior of charged rods in the presence of inter-rod linkers is studied theoretically as a model for the equilibrium behavior underlying the organization of actin filaments by linker proteins in the cytoskeleton. The presence of linkers in the solution modifies the effective inter-rod interaction and can lead to inter-filament attraction. Depending on the system's composition and physical properties such as linker binding energies, filaments will either orient perpendicular or parallel to each other, leading to network-like or bundled structures. We show that such a system can have one of three generic phase diagrams, one dominated by bundles, another by networks, and the third containing both bundle and network-like phases. The first two diagrams can be found over a wide range of interaction energies, while the third occurs only for a narrow range. These results provide theoretical understanding of the classification of linker proteins as bundling proteins or crosslinking proteins. In addition, they suggest possible mechanisms by which the cell may control cytoskeletal morphology.Comment: 17 pages, 3 figure

Microscopic Model of Charge Carrier Transfer in Complex Media

We present a microscopic model of a charge carrier transfer under an action of a constant electric field in a complex medium. Generalizing previous theoretical approaches, we model the dynamical environment hindering the carrier motion by dynamic percolation, i.e., as a medium comprising particles which move randomly on a simple cubic lattice, constrained by hard-core exclusion, and may spontaneously annihilate and re-appear at some prescribed rates. We determine analytically the density profiles of the "environment" particles, as seen from the stationary moving charge carrier, and calculate its terminal velocity as the function of the applied field and other system parameters. We realize that for sufficiently small external fields the force exerted on the carrier by the "environment" particles shows a viscous-like behavior and define an analog of the Stokes formula for such dynamic percolative environments. The corresponding friction coefficient is also derived.Comment: appearing in Chem. Phys. Special Issue on Molecular Charge Transfer in Condensed Media - from Physics and Chemistry to Biology and Nano-Engineering, edited by A.Kornyshev (Imperial College London), M.Newton (Brookhaven Natl Lab) and J.Ulstrup (Technical University of Denmark

The Neuroscience Information Framework: A Data and Knowledge Environment for Neuroscience

With support from the Institutes and Centers forming the NIH Blueprint for Neuroscience Research, we have designed and implemented a new initiative for integrating access to and use of Web-based neuroscience resources: the Neuroscience Information Framework. The Framework arises from the expressed need of the neuroscience community for neuroinformatic tools and resources to aid scientific inquiry, builds upon prior development of neuroinformatics by the Human Brain Project and others, and directly derives from the Society for Neuroscience’s Neuroscience Database Gateway. Partnered with the Society, its Neuroinformatics Committee, and volunteer consultant-collaborators, our multi-site consortium has developed: (1) a comprehensive, dynamic, inventory of Web-accessible neuroscience resources, (2) an extended and integrated terminology describing resources and contents, and (3) a framework accepting and aiding concept-based queries. Evolving instantiations of the Framework may be viewed at http://nif.nih.gov, http://neurogateway.org, and other sites as they come on line

Dependence of binaural gain for infrasound on interaural phase difference

Increasing complaints about infrasound have generated interest in understanding its perception, including binaural effects. This study investigated the level difference between monaural and binaural presentation required for detection and equal loudness (binaural gain) for pure tones with frequencies of 8, 32, and 400 Hz and an 8 Hz sinusoidally amplitude-modulated tone with diotic 400 Hz carrier. Monaural stimuli were compared to binaural stimuli with interaural phase differences (IPDs) of 0°, 90°, and 180° in two experiments: absolute threshold measurements and loudness matching at 40 phons. The latter was repeated with transposed tones (400 Hz carrier multiplied by a half-wave-rectified 8 Hz sinusoid). When expressed as differences in sound pressure level, similar binaural gain was found across all stimulus types under the diotic condition. Confirming previous studies, the gain was larger at supra-threshold levels (40 phons) than at threshold. However, when the loudness-matching results were expressed as binaural gain with respect to the loudness level, they became 17.5, 11.2, and 5.8 phons for the 8, 32, and 400 Hz stimuli, respectively. Results for the 8 Hz pure tone and the transposed stimulus were IPD dependent

Generalized model for dynamic percolation

We study the dynamics of a carrier, which performs a biased motion under the influence of an external field E, in an environment which is modeled by dynamic percolation and created by hard-core particles. The particles move randomly on a simple cubic lattice, constrained by hard-core exclusion, and they spontaneously annihilate and re-appear at some prescribed rates. Using decoupling of the third-order correlation functions into the product of the pairwise carrier-particle correlations we determine the density profiles of the "environment" particles, as seen from the stationary moving carrier, and calculate its terminal velocity, V_c, as the function of the applied field and other system parameters. We find that for sufficiently small driving forces the force exerted on the carrier by the "environment" particles shows a viscous-like behavior. An analog Stokes formula for such dynamic percolative environments and the corresponding friction coefficient are derived. We show that the density profile of the environment particles is strongly inhomogeneous: In front of the stationary moving carrier the density is higher than the average density, $\rho_s$, and approaches the average value as an exponential function of the distance from the carrier. Past the carrier the local density is lower than $\rho_s$ and the relaxation towards $\rho_s$ may proceed differently depending on whether the particles number is or is not explicitly conserved.Comment: Latex, 32 pages, 4 ps-figures, submitted to PR

Transitions in the Horizontal Transport of Vertically Vibrated Granular Layers

Motivated by recent advances in the investigation of fluctuation-driven ratchets and flows in excited granular media, we have carried out experimental and simulational studies to explore the horizontal transport of granular particles in a vertically vibrated system whose base has a sawtooth-shaped profile. The resulting material flow exhibits novel collective behavior, both as a function of the number of layers of particles and the driving frequency; in particular, under certain conditions, increasing the layer thickness leads to a reversal of the current, while the onset of transport as a function of frequency occurs gradually in a manner reminiscent of a phase transition. Our experimental findings are interpreted here with the help of extensive, event driven Molecular Dynamics simulations. In addition to reproducing the experimental results, the simulations revealed that the current may be reversed as a function of the driving frequency as well. We also give details about the simulations so that similar numerical studies can be carried out in a more straightforward manner in the future.Comment: 12 pages, 18 figure