Slow relaxation in granular compaction

Experimental studies show that the density of a vibrated granular material evolves from a low density initial state into a higher density final steady state. The relaxation towards the final density value follows an inverse logarithmic law. We propose a simple stochastic adsorption-desorption process which captures the essential mechanism underlying this remarkably slow relaxation. As the system approaches its final state, a growing number of beads have to be rearranged to enable a local density increase. In one dimension, this number grows as $N=\rho/(1-\rho)$, and the density increase rate is drastically reduced by a factor $e^{-N}$. Consequently, a logarithmically slow approach to the final state is found $\rho_{\infty}-\rho(t)\cong 1/\ln t$.Comment: revtex, 4 pages, 3 figures, also available from http://arnold.uchicago.edu/~ebn

Dynamic instabilities induced by asymmetric influence: Prisoners' dilemma game on small-world networks

A two-dimensional small-world type network, subject to spatial prisoners' dilemma dynamics and containing an influential node defined as a special node with a finite density of directed random links to the other nodes in the network, is numerically investigated. It is shown that the degree of cooperation does not remain at a steady state level but displays a punctuated equilibrium type behavior manifested by the existence of sudden breakdowns of cooperation. The breakdown of cooperation is linked to an imitation of a successful selfish strategy of the influential node. It is also found that while the breakdown of cooperation occurs suddenly, the recovery of it requires longer time. This recovery time may, depending on the degree of steady state cooperation, either increase or decrease with an increasing number of long range connections.Comment: 5 pages, 6 figure

The Physical Interpretation of X-ray Phase Lags and Coherence: RXTE Observations of Cygnus X--1 as a Case Study

There have been a number of recent spectral models that have been successful in reproducing the observed X-ray spectra of galactic black hole candidates (GBHC). However, there still exists controversy over such issues as: what are the sources of hard radiation, what is the system's geometry, is the accretion efficient or inefficient, etc. A potentially powerful tool for distinguishing among these possibilities, made possible by the Rossi X-ray Timing Explorer (RXTE), is the variability data, especially the observed phase lags and variability coherence. These data, in conjunction with spectral modeling, have the potential of determining physical sizes of the system, as well as placing strong constraints on both Compton corona and advection models. As an example, we present RXTE variability data of Cygnus X-1Comment: To Appear in the Proceedings of the Symposium "The Active X-ray Sky", held October 21-24, 1997, Rom

40 Zakażenie wirusem Epsteina-Barr w ziarnicy złośliwej. Ocena korelacji między ekspresją LMP-1 w komórkach Hodgkina i Reed-Sternberga, a ekspresją BCL-2

Wynik badań epidemiologicznych i immunologicznych wskazują na zbieżność między zachorowaniem na ziarnicę złośliwą a zakażeniem wirusem Epsteina-Barr (EBV). Wykrycie wirusa EBV w morfologicznie złośliwych komórkach ziarniczych sugeruje, że wirus wniknął do komórki przed transformacją nowotworową i klonalną proliferacją, zwłaszcza, że wyłącznie 1 na 10 limfocytów jest zainfekowany wirusem.Ekspresji LMP-1 białku błonowemu wirusa przypisuje się rolę karcynogenną Białko to poprzez indukcję protoonkogenu Bcl-2 może zapobiegać śmierci komórki w mechanizmie apoptozy. Analizowano materiał pochodzący od 43 chorych na ziarnicę złośliwą w różnym stopniu zaawansowania klinicznego oraz histopatologicznego. W oparciu o metody immunohistochemiczne oceniano ekspresję Lmp-1 i Bcl-2w komórkach Reed-Sternberga i Hodkina. Otrzymane wyniki mogą potwierdzać powyższą tezę

Analysis by x-ray microtomography of a granular packing undergoing compaction

Several acquisitions of X-ray microtomography have been performed on a beads packing while it compacts under vertical vibrations. An image analysis allows to study the evolution of the packing structure during its progressive densification. In particular, the volume distribution of the pores reveals a large tail, compatible to an exponential law, which slowly reduces as the system gets more compact. This is quite consistent, for large pores, with the free volume theory. These results are also in very good agreement with those obtained by a previous numerical model of granular compaction.Comment: 4 pages, 4 figures. Latex (revtex4). to be published in Phys. Rev.

Metric trees of generalized roundness one

Every finite metric tree has generalized roundness strictly greater than one. On the other hand, some countable metric trees have generalized roundness precisely one. The purpose of this paper is to identify some large classes of countable metric trees that have generalized roundness precisely one. At the outset we consider spherically symmetric trees endowed with the usual combinatorial metric (SSTs). Using a simple geometric argument we show how to determine decent upper bounds on the generalized roundness of finite SSTs that depend only on the downward degree sequence of the tree in question. By considering limits it follows that if the downward degree sequence $(d_{0}, d_{1}, d_{2}...)$ of a SST $(T,\rho)$ satisfies $|\{j \, | \, d_{j} > 1 \}| = \aleph_{0}$, then $(T,\rho)$ has generalized roundness one. Included among the trees that satisfy this condition are all complete $n$-ary trees of depth $\infty$ ($n \geq 2$), all $k$-regular trees ($k \geq 3$) and inductive limits of Cantor trees. The remainder of the paper deals with two classes of countable metric trees of generalized roundness one whose members are not, in general, spherically symmetric. The first such class of trees are merely required to spread out at a sufficient rate (with a restriction on the number of leaves) and the second such class of trees resemble infinite combs.Comment: 14 pages, 2 figures, 2 table

The Role of Friction in Compaction and Segregation of Granular Materials

We investigate the role of friction in compaction and segregation of granular materials by combining Edwards' thermodynamic hypothesis with a simple mechanical model and mean-field based geometrical calculations. Systems of single species with large friction coefficients are found to compact less. Binary mixtures of grains differing in frictional properties are found to segregate at high compactivities, in contrary to granular mixtures differing in size, which segregate at low compactivities. A phase diagram for segregation vs. friction coefficients of the two species is generated. Finally, the characteristics of segregation are related directly to the volume fraction without the explicit use of the yet unclear notion of compactivity.Comment: 9 pages, 6 figures, submitted to Phys. Rev.

Linear response of vibrated granular systems to sudden changes in the vibration intensity

The short-term memory effects recently observed in vibration-induced compaction of granular materials are studied. It is shown that they can be explained by means of quite plausible hypothesis about the mesoscopic description of the evolution of the system. The existence of a critical time separating regimes of ``anomalous'' and ``normal'' responses is predicted. A simple model fitting into the general framework is analyzed in the detail. The relationship between this work and previous studies is discussed.Comment: 10 pages, 6 figures; fixed errata, updtated reference

Granular packings with moving side walls

The effects of movement of the side walls of a confined granular packing are studied by discrete element, molecular dynamics simulations. The dynamical evolution of the stress is studied as a function of wall movement both in the direction of gravity as well as opposite to it. For all wall velocities explored, the stress in the final state of the system after wall movement is fundamentally different from the original state obtained by pouring particles into the container and letting them settle under the influence of gravity. The original packing possesses a hydrostatic-like region at the top of the container which crosses over to a depth-independent stress. As the walls are moved in the direction opposite to gravity, the saturation stress first reaches a minimum value independent of the wall velocity, then increases to a steady-state value dependent on the wall-velocity. After wall movement ceases and the packing reaches equilibrium, the stress profile fits the classic Janssen form for high wall velocities, while it has some deviations for low wall velocities. The wall movement greatly increases the number of particle-wall and particle-particle forces at the Coulomb criterion. Varying the wall velocity has only small effects on the particle structure of the final packing so long as the walls travel a similar distance.Comment: 11 pages, 10 figures, some figures in colo