Percolation, statistical topography, and transport in random-media

A review of classical percolation theory is presented, with an emphasis on novel applications to statistical topography, turbulent diffusion, and heterogeneous media. Statistical topography involves the geometrical properties of the isosets (contour lines or surfaces) of a random potential psi(x). For rapidly decaying correlations of psi, the isopotentials fall into the same universality class as the perimeters of percolation clusters. The topography of long-range correlated potentials involves many length scales and is associated either with the correlated percolation problem or with Mandelbrot's fractional Brownian reliefs. In all cases, the concept of fractal dimension is particularly fruitful in characterizing the geometry of random fields. The physical applications of statistical topography include diffusion in random velocity fields, heat and particle transport in turbulent plasmas, quantum Hall effect, magnetoresistance in inhomogeneous conductors with the classical Hall effect, and many others where random isopotentials are relevant. A geometrical approach to studying transport in random media, which captures essential qualitative features of the described phenomena, is advocated.Physic

Conditions for Confinement and Freeze-Out

Matter implies the existence of a large-scale connected cluster of a uniform nature. The appearance of such clusters as function of hadron density is specified by percolation theory. We can therefore formulate the freeze-out of interacting hadronic matter in terms of the percolation of hadronic clusters. The resulting freeze-out condition as function of temperature and baryo-chemical potential interpolates between resonance gas behaviour at low baryon density and repulsive nucleonic matter at low temperature, and it agrees well with data.Comment: 9 pages, 5 figure

Non-saturating magnetoresistance of inhomogeneous conductors: comparison of experiment and simulation

The silver chalcogenides provide a striking example of the benefits of imperfection. Nanothreads of excess silver cause distortions in the current flow that yield a linear and non-saturating transverse magnetoresistance (MR). Associated with the large and positive MR is a negative longitudinal MR. The longitudinal MR only occurs in the three-dimensional limit and thereby permits the determination of a characteristic length scale set by the spatial inhomogeneity. We find that this fundamental inhomogeneity length can be as large as ten microns. Systematic measurements of the diagonal and off-diagonal components of the resistivity tensor in various sample geometries show clear evidence of the distorted current paths posited in theoretical simulations. We use a random resistor network model to fit the linear MR, and expand it from two to three dimensions to depict current distortions in the third (thickness) dimension. When compared directly to experiments on Ag$_{2\pm\delta}$Se and Ag$_{2\pm\delta}$Te, in magnetic fields up to 55 T, the model identifies conductivity fluctuations due to macroscopic inhomogeneities as the underlying physical mechanism. It also accounts reasonably quantitatively for the various components of the resistivity tensor observed in the experiments.Comment: 10 pages, 7 figure

Percolation approach to phase transitions in high energy nuclear collisions

We study continuum percolation in nuclear collisions for the realistic case in which the nuclear matter distribution is not uniform over the collision volume, and show that the percolation threshold is increased compared to the standard, uniform situation. In terms of quark-gluon plasma formation this means that the phase transition threshold is pushed to higher energies.Comment: 7 pages, 4 figures (PS), LaTeX2e using fontenc, amsmath, epsfi

Cerkiew przyfrontowego Charkowa

Charków w czasach pokoju był miastem nad wyraz pełnym życia. Wstydliwie ukrywał to za szarymi ścianami budynków, wielkimi kompleksami budowli przemysłowych. Za żywiołem udawanego języka rosyjskiego miasto ukrywało swoją ukraińską istotę, co bezbłędnie zdradzało charkowian, gdziekolwiek by się nie udali – charakterystyczna wymowa i cały wachlarz ukrainizmów oraz typowo lokalnych słówek na kształt sławetnego „trempela” 1. Za tą scenografią miasta skryte było to, co określało jego rzeczywistą tożsamość – poczucie własnej godności, kreatywne podejście do pracy, subtelne, czasem sarkastyczne poczucie humoru i co chyba najważniejsze – zdolność doceniania wolności i jej obrony. Nie przypadkiem właśnie Charków wyróżniał się wśród pięciu pułkowych centrów Słobodzkiej Ukrainy – kraju będącego spełnieniem marzeń Ukraińców o „ziemi swobody” 2 – i stał się jej faktycznym centrum

Tunneling edges at strong disorder

Scattering between edge states that bound one-dimensional domains of opposite potential or flux is studied, in the presence of strong potential or flux disorder. A mobility edge is found as a function of disorder and energy, and we have characterized the extended phase. "paper_FINAL.tex" 439 lines, 20366 characters In the presence of flux and/or potential disorder, the localization length scales exponentially with the width of the barrier. We discuss implications for the random-flux problem.Comment: RevTeX, 4 page

ІСТОРИЧНА РЕТРОСПЕКТИВА В БАГАТОВИМІРНОСТІ БАРОКОВОГО ПОЛЕМІЧНОГО ДИСКУРСУ (ЗІ СПОСТЕРЕЖЕНЬ НАД ДІАЛОГОМ О. ЛЕВА КРЕВЗИ, ЧСВВ ТА О. ЗАХАРІЇ КОПИСТЕНСЬКОГО)

Polemic treatises “Obrona jednosci cerkiewnej” (1617) by Fr. Leon Kreuza and “Palinodia” (1620-1622) by Fr. Zacharias Kopystenski are treated in this article as a kind of dialogue between western and eastern Christian cultures, provoked by their authors’ search for historical foundations of their religious identity. The author of the essay singles out the main features of “Sarmatian” piety, arguing that this chronological line adds extensionality to literary texts. The place of church is defined in accordance with its concern for holiness experienced by real persons. The author states that the polemic discourse reflects the search for harmony alternating between everlasting and historically transitive elements of the local church tradition as an   ncarnation of the grace-giving action of the Holy Spirit in the human community which has its own ethnical and cultural specifics.У статті аналізуються полемічні трактати о. Лева Кревзи “Obrona jednosci cerkiewnej” (1617) і о. Захарії Копистенського “Палінодія” (1620-1622) як феномен діалогу західної та східної християнських культур, мотивованого пошуком історичних засад власної релігійної ідентичності. Виявляються риси “сарматської” релігійності. Хронологічна лінія надає об’ємності літературному просторові тексту. Місце церкви визначається в перспективі плекання досвіду святості, утіленої в конкретних персонажах. Дискурс відображає пошук гармонії між непроминущим та історично перехідним у помісній традиції як конкретному втіленні благодатної дії Святого Духа в етнічно й культурно визначеній людській спільноті