One-sided versus two-sided stochastic descriptions

It is well-known that discrete-time finite-state Markov Chains, which are described by one-sided conditional probabilities which describe a dependence on the past as only dependent on the present, can also be described as one-dimensional Markov Fields, that is, nearest-neighbour Gibbs measures for finite-spin models, which are described by two-sided conditional probabilities. In such Markov Fields the time interpretation of past and future is being replaced by the space interpretation of an interior volume, surrounded by an exterior to the left and to the right. If we relax the Markov requirement to weak dependence, that is, continuous dependence, either on the past (generalising the Markov-Chain description) or on the external configuration (generalising the Markov-Field description), it turns out this equivalence breaks down, and neither class contains the other. In one direction this result has been known for a few years, in the opposite direction a counterexample was found recently. Our counterexample is based on the phenomenon of entropic repulsion in long-range Ising (or "Dyson") models.Comment: 13 pages, Contribution for "Statistical Mechanics of Classical and Disordered Systems

Secular Evolution and the Formation of Pseudobulges in Disk Galaxies

We review internal processes of secular evolution in galaxy disks, concentrating on the buildup of dense central features that look like classical, merger-built bulges but that were made slowly out of disk gas. We call these pseudobulges. As an existence proof, we review how bars rearrange disk gas into outer rings, inner rings, and gas dumped into the center. In simulations, this gas reaches high densities that plausibly feed star formation. In the observations, many SB and oval galaxies show central concentrations of gas and star formation. Star formation rates imply plausible pseudobulge growth times of a few billion years. If secular processes built dense central components that masquerade as bulges, can we distinguish them from merger-built bulges? Observations show that pseudobulges retain a memory of their disky origin. They have one or more characteristics of disks: (1) flatter shapes than those of classical bulges, (2) large ratios of ordered to random velocities indicative of disk dynamics, (3) small velocity dispersions, (4) spiral structure or nuclear bars in the bulge part of the light profile, (5) nearly exponential brightness profiles, and (6) starbursts. These structures occur preferentially in barred and oval galaxies in which secular evolution should be rapid. So the cleanest examples of pseudobulges are recognizable. Thus a large variety of observational and theoretical results contribute to a new picture of galaxy evolution that complements hierarchical clustering and merging.Comment: 92 pages, 21 figures in 30 Postscript files; to appear in Annual Review of Astronomy and Astrophysics, Vol. 42, 2004, in press; for a version with full resolution figures, see http://chandra.as.utexas.edu/~kormendy/ar3ss.htm

Secular Evolution and the Growth of Pseudobulges in Disk Galaxies

Galaxy evolution is in transition from an early universe dominated by hierarchical clustering to a future dominated by secular processes. These result from interactions involving collective phenomena such as bars, oval disks, spiral structure, and triaxial dark halos. This paper summarizes a review by Kormendy & Kennicutt (2004) using, in part, illustrations of different galaxies. In simulations, bars rearrange disk gas into outer rings, inner rings, and galactic centers, where high gas densities feed starbursts. Consistent with this picture, many barred and oval galaxies have dense central concentrations of gas and star formation rates that can build bulge-like stellar densities on timescales of a few billion years. We conclude that secular evolution builds dense central components in disk galaxies that look like classical, merger-built bulges but that were made slowly out of disk gas. We call these pseudobulges. Many pseudobulges can be recognized because they have characteristics of disks: (1) flatter shapes than those of classical bulges, (2) correspondingly large ratios of ordered to random velocities, (3) small velocity dispersions, (4) spiral structure or nuclear bars, (5) nearly exponential brightness profiles, and (6) starbursts. These structures occur preferentially in barred and oval galaxies in which secular evolution should be most rapid. Thus a variety of observational and theoretical results contribute to a new paradigm of secular evolution that complements hierarchical clustering.Comment: 19 pages, 9 Postscript figures; requires kapproc.cls and procps.sty; to appear in "Penetrating Bars Through Masks of Cosmic Dust: The Hubble Tuning Fork Strikes a New Note", ed. Block, Freeman, Puerari, Groess, and Block, Dordrecht: Kluwer, in press; for a version with full resolution figures, see http://chandra.as.utexas.edu/~kormendy/ar3ss.htm

Dynamics of Disks and Warps

This chapter reviews theoretical work on the stellar dynamics of galaxy disks. All the known collective global instabilities are identified, and their mechanisms described in terms of local wave mechanics. A detailed discussion of warps and other bending waves is also given. The structure of bars in galaxies, and their effect on galaxy evolution, is now reasonably well understood, but there is still no convincing explanation for their origin and frequency. Spiral patterns have long presented a special challenge, and ideas and recent developments are reviewed. Other topics include scattering of disk stars and the survival of thin disks.Comment: Chapter accepted to appear in Planets, Stars and Stellar Systems, vol 5, ed G. Gilmore. 32 pages, 17 figures. Includes minor corrections made in proofs. Uses emulateapj.st

Mod-ϕ Convergence, II: Estimates on the Speed of Convergence

In this paper, we give estimates for the speed of convergence towards a limiting stable law in the recently introduced setting of mod-ϕ convergence. Namely, we define a notion of zone of control, closely related to mod-ϕ convergence, and we prove estimates of Berry–Esseen type under this hypothesis. Applications include: - the winding number of a planar Brownian motion; - classical approximations of stable laws by compound Poisson laws; - examples stemming from determinantal point processes (characteristic polynomials of random matrices and zeroes of random analytic functions); - sums of variables with an underlying dependency graph (for which we recover a result of Rinott, obtained by Stein’s method); - the magnetization in the d-dimensional Ising model; - and functionals of Markov chains

Wheat Flour Enriched with Calcium and Inulin: A Study of Hydration and Rheological Properties of Dough

The aim of this work was to study the effect of calcium (Ca) carbonate-inulin (In) systems on hydration and rheological properties of wheat flour dough. Wheat flour, Ca carbonate from 108 to 252 (mg Ca/100 g flour) content, and enriched In oligofructose at levels of 1% to 13% (flour basis), were used. Hydration dough properties were researched analyzing water absorption (Wabs), moisture content (Mcont), water activity (aw), and relaxation time (λ). Wabs and aw decreased with increasing In levels independently of Ca content. Dough development time increased with the amount of Ca. In the presence of In, samples with the lowest content of Ca were those showing the highest development time values. Inulin was the main component that controled Wabs in dough. In the presence of CaCO3, although water seemed to be in a free state according to the high aw value measured (>0.975), the low value of relaxation time obtained suggests less molecular mobility. Rheological properties of dough were studied by texture, relaxation, and viscoelasticity assays. Dough hardness and consistency significantly increased with Ca and mainly with In content. At high In content, dough texture was enhanced by CaCO3 due to the fact that this salt could behave as dough strengthener. Adhesiveness of dough was not modified by CaCO3 at low In levels. However, Ca affected adhesiveness at intermediate In levels. Adhesiveness was significantly increased by In presence. Calcium and In both diminished dough cohesiveness. The In presence increased dough elasticity, independently of Ca content. A second-order polynomial model and response surface methodology were used for studying hydration dependence and rheological parameters (R2 > 0.771) on Ca and In. Dough Mcont varied with In2 and mainly inversely proportional to In. An inverse dependence of λ on In was detected. Dynamic and relaxation elastic moduli (G′ and E3) showed a linear dependence on In.Facultad de Ciencias Exacta