The Vlasov limit and its fluctuations for a system of particles which interact by means of a wave field

In two recent publications [Commun. PDE, vol.22, p.307--335 (1997), Commun. Math. Phys., vol.203, p.1--19 (1999)], A. Komech, M. Kunze and H. Spohn studied the joint dynamics of a classical point particle and a wave type generalization of the Newtonian gravity potential, coupled in a regularized way. In the present paper the many-body dynamics of this model is studied. The Vlasov continuum limit is obtained in form equivalent to a weak law of large numbers. We also establish a central limit theorem for the fluctuations around this limit.Comment: 68 pages. Smaller corrections: two inequalities in sections 3 and two inequalities in section 4, and definition of a Banach space in appendix A1. Presentation of LLN and CLT in section 4.3 improved. Notation improve

The Einstein-Vlasov sytem/Kinetic theory

The main purpose of this article is to guide the reader to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades where the main focus has been on nonrelativistic- and special relativistic physics, e.g. to model the dynamics of neutral gases, plasmas and Newtonian self-gravitating systems. In 1990 Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. The Vlasov equation describes matter phenomenologically and it should be stressed that most of the theorems presented in this article are not presently known for other such matter models (e.g. fluid models). The first part of this paper gives an introduction to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental in order to get a good comprehension of kinetic theory in general relativity.Comment: 31 pages. This article has been submitted to Living Rev. Relativity (http://www.livingreviews.org

Material Symmetry to Partition Endgame Tables

Many games display some kind of material symmetry . That is, some sets of game elements can be exchanged for another set of game elements, so that the resulting position will be equivalent to the original one, no matter how the elements were arranged on the board. Material symmetry is routinely used in card game engines when they normalize their internal representation of the cards. Other games such as chinese dark chess also feature some form of material symmetry, but it is much less clear what the normal form of a position should be. We propose a principled approach to detect material symmetry. Our approach is generic and is based on solving multiple rel- atively small sub-graph isomorphism problems. We show how it can be applied to chinese dark chess , dominoes , and skat . In the latter case, the mappings we obtain are equivalent to the ones resulting from the standard normalization process. In the two former cases, we show that the material symmetry allows for impressive savings in memory requirements when building endgame tables. We also show that those savings are relatively independent of the representation of the tables

Characterization of an alpha-L-fucosidase from the periodontal pathogen Tannerella forsythia

The periodontal pathogen Tannerella forsythia expresses several glycosidases which are linked to specific growth requirements and are involved in the invasion of host tissues. α-l-Fucosyl residues are exposed on various host glycoconjugates and, thus, the α-l-fucosidases predicted in the T. forsythia ATCC 43037 genome could potentially serve roles in host-pathogen interactions. We describe the molecular cloning and characterization of the putative fucosidase TfFuc1 (encoded by the bfo_2737 = Tffuc1 gene), previously reported to be present in an outer membrane preparation. In terms of sequence, this 51-kDa protein is a member of the glycosyl hydrolase family GH29. Using an artificial substrate, p-nitrophenyl-α-fucose (KM 670 μM), the enzyme was determined to have a pH optimum of 9.0 and to be competitively inhibited by fucose and deoxyfuconojirimycin. TfFuc1 was shown here to be a unique α(1,2)-fucosidase that also possesses α(1,6) specificity on small unbranched substrates. It is active on mucin after sialidase-catalyzed removal of terminal sialic acid residues and also removes fucose from blood group H. Following knock-out of the Tffuc1 gene and analyzing biofilm formation and cell invasion/adhesion of the mutant in comparison to the wild-type, it is most likely that the enzyme does not act extracellularly. Biochemically interesting as the first fucosidase in T. forsythia to be characterized, the biological role of TfFuc1 may well be in the metabolism of short oligosaccharides in the periplasm, thereby indirectly contributing to the virulence of this organism. TfFuc1 is the first glycosyl hydrolase in the GH29 family reported to be a specific α(1,2)-fucosidase

Trapped and excited w modes of stars with a phase transition and R>=5M

The trapped $w$-modes of stars with a first order phase transition (a density discontinuity) are computed and the excitation of some of the modes of these stars by a perturbing shell is investigated. Attention is restricted to odd parity (``axial'') $w$-modes. With $R$ the radius of the star, $M$ its mass, $R_{i}$ the radius of the inner core and $M_{i}$ the mass of such core, it is shown that stars with $R/M\geq 5$ can have several trapped $w$-modes, as long as $R_{i}/M_{i}<2.6$. Excitation of the least damped $w$-mode is confirmed for a few models. All of these stars can only exist however, for values of the ratio between the densities of the two phases, greater than $\sim 46$. We also show that stars with a phase transition and a given value of $R/M$ can have far more trapped modes than a homogeneous single density star with the same value of $R/M$, provided both $R/M$ and $R_{i}/M_{i}$ are smaller than 3. If the phase transition is very fast, most of the stars with trapped modes are unstable to radial oscillations. We compute the time of instability, and find it to be comparable to the damping of the $w$-mode excited in most cases where $w$-mode excitation is likely. If on the other hand the phase transition is slow, all the stars are stable to radial oscillations.Comment: To appear in Physical Review

Relics of the Cosmological QCD Phase Transition

The abundance and size distribution of quark nuggets (QN), formed a few microseconds after the big bang due to first order QCD phase transition in the early universe, has been estimated. It appears that stable QNs could be a viable candidate for cosmological dark matter. The evolution of baryon inhomogeneity due to evaporated (unstable) QNs are also examined.Comment: To appear in Physical Review

A non-variational approach to nonlinear stability in stellar dynamics applied to the King model

In previous work by Y. Guo and G. Rein, nonlinear stability of equilibria in stellar dynamics, i.e., of steady states of the Vlasov-Poisson system, was accessed by variational techniques. Here we propose a different, non-variational technique and use it to prove nonlinear stability of the King model against a class of spherically symmetric, dynamically accessible perturbations. This model is very important in astrophysics and was out of reach of the previous techniques

M87, Globular Clusters, and Galactic Winds: Issues in Giant Galaxy Formation

New VRI photometry is presented for the globular clusters in the innermost 140'' of the M87 halo. The results are used to discuss several issues concerning the formation and evolution of globular cluster systems in supergiant ellipticals like M87. (1) we find no significant change in the globular cluster luminosity function (GCLF) with galactocentric radius, for cluster masses M < 10^5 solar masses, indicating that the main effects of dynamical evolution may be only on lower-mass clusters. (2) Within the core radius (1') of the globular cluster system, the metallicity distribution is uniform, but at larger radii the mean metallicity declines steadily as Z ~ r^-0.9. (3) The various options for explaining the existence of high specific frequency galaxies like M87 are evaluated, and scaling laws for the GCSs in these galaxies are given. Interpretations involving secondary evolution (formation of many globular clusters during mergers, intergalactic globular clusters, etc.) are unlikely to be the primary explanation for high-S_N galaxies. (4) We suggest that central-supergiant E galaxies may have formed in an exceptionally turbulent or high-density environment in which an early, powerful galactic wind drove out a high fraction of the protogalactic gas, thus artificially boosting the specificComment: 67 pages, 17 figures. To appear in Astronomical Journal, in press for May 1998. Preprints also available from W.Harris; send e-mail request to [email protected]