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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 AgSe and
AgTe, 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
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
Sylvester Kosov’s Exegesis (1635): A Manifesto of the Kyiv-Mohyla Counter-Reformation?
Bishop Sylvester Kosov’s polemical treatise The Exegesis (1635) is regarded as evidence of new trends in Kyiv theology, reflecting the entry of Orthodox thinkers of the Polish-Lithuanian Commonwealth (Rzeczpospolita) into the spiritual sphere of European Reform, traditionally defined as the Counter-Reformation. The treatise’s author, being the closest associate of Metropolitan Petro Mohyla, denies the Byzantine theologians’ accusations of pliancy to Protestant influences. Demonstrating doctrinal differences with Calvinism, Lutheranism, and Unitarianism, Sylvester Kosov determines his own faith identity and its natural connection to the apostolic tradition and the teachings of the Church Fathers. In doing so, he uses expressive Baroque imagery
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