Modular symbols and Hecke operators

We survey techniques to compute the action of the Hecke operators on the cohomology of arithmetic groups. These techniques can be seen as generalizations in different directions of the classical modular symbol algorithm, due to Manin and Ash-Rudolph. Most of the work is contained in papers of the author and the author with Mark McConnell. Some results are unpublished work of Mark McConnell and Robert MacPherson.Comment: 11 pp, 2 figures, uses psfrag.st

Particle distributions in approximately 10(14) 10(16) eV air shower cores at sea level

Experimental evidence is reported for fixed distances (0, 1.0, 2.5 and 4.0 m) from the shower centers and for core flattening. The cores become flatter, on average, as the shower size (primary energy) increases. With improved statistics on 4192 cores, the previous results are exactly confirmed

A Classical Bound on Quantum Entropy

A classical upper bound for quantum entropy is identified and illustrated, $0\leq S_q \leq \ln (e \sigma^2 / 2\hbar)$, involving the variance $\sigma^2$ in phase space of the classical limit distribution of a given system. A fortiori, this further bounds the corresponding information-theoretical generalizations of the quantum entropy proposed by Renyi.Comment: Latex2e, 7 pages, publication versio

Use of approximations of Hamilton-Jacobi-Bellman inequality for solving periodic optimization problems

We show that necessary and sufficient conditions of optimality in periodic optimization problems can be stated in terms of a solution of the corresponding HJB inequality, the latter being equivalent to a max-min type variational problem considered on the space of continuously differentiable functions. We approximate the latter with a maximin problem on a finite dimensional subspace of the space of continuously differentiable functions and show that a solution of this problem (existing under natural controllability conditions) can be used for construction of near optimal controls. We illustrate the construction with a numerical example.Comment: 29 pages, 2 figure

The Evolution of Plasma Composition during a Solar Flare

We analyze the coronal elemental abundances during a small flare using Hinode/EIS observations. Compared to the preflare elemental abundances, we observed a strong increase in coronal abundance of Ca xiv 193.84 Å, an emission line with low first ionization potential (FIP < 10 eV), as quantified by the ratio Ca/Ar during the flare. This is in contrast to the unchanged abundance ratio observed using Si x 258.38 Å/S x 264.23 Å. We propose two different mechanisms to explain the different composition results. First, the small flare-induced heating could have ionized S, but not the noble gas Ar, so that the flare-driven Alfvén waves brought up Si, S, and Ca in tandem via the ponderomotive force which acts on ions. Second, the location of the flare in strong magnetic fields between two sunspots may suggest fractionation occurred in the low chromosphere, where the background gas is neutral H. In this region, high-FIP S could behave more like a low-FIP than a high-FIP element. The physical interpretations proposed generate new insights into the evolution of plasma abundances in the solar atmosphere during flaring, and suggests that current models must be updated to reflect dynamic rather than just static scenarios

Many Roads to Synchrony: Natural Time Scales and Their Algorithms

We consider two important time scales---the Markov and cryptic orders---that monitor how an observer synchronizes to a finitary stochastic process. We show how to compute these orders exactly and that they are most efficiently calculated from the epsilon-machine, a process's minimal unifilar model. Surprisingly, though the Markov order is a basic concept from stochastic process theory, it is not a probabilistic property of a process. Rather, it is a topological property and, moreover, it is not computable from any finite-state model other than the epsilon-machine. Via an exhaustive survey, we close by demonstrating that infinite Markov and infinite cryptic orders are a dominant feature in the space of finite-memory processes. We draw out the roles played in statistical mechanical spin systems by these two complementary length scales.Comment: 17 pages, 16 figures: http://cse.ucdavis.edu/~cmg/compmech/pubs/kro.htm. Santa Fe Institute Working Paper 10-11-02

Can Subphotospheric Magnetic Reconnection Change the Elemental Composition in the Solar Corona?

Within the coronae of stars, abundances of those elements with low first ionization potential (FIP) often differ from their photospheric values. The coronae of the Sun and solar-type stars mostly show enhancements of low-FIP elements (the FIP effect) while more active stars such as M dwarfs have coronae generally characterized by the inverse-FIP effect (I-FIP). Here we observe patches of I-FIP effect solar plasma in AR 12673, a highly complex βγδ active region. We argue that the umbrae of coalescing sunspots, and more specifically strong light bridges within the umbrae, are preferential locations for observing I-FIP effect plasma. Furthermore, the magnetic complexity of the active region and major episodes of fast flux emergence also lead to repetitive and intense flares. The induced evaporation of the chromospheric plasma in flare ribbons crossing umbrae enables the observation of four localized patches of I-FIP effect plasma in the corona of AR 12673. These observations can be interpreted in the context of the ponderomotive force fractionation model which predicts that plasma with I-FIP effect composition is created by the refraction of waves coming from below the chromosphere. We propose that the waves generating the I-FIP effect plasma in solar active regions are generated by subphotospheric reconnection of coalescing flux systems. Although we only glimpse signatures of I-FIP effect fractionation produced by this interaction in patches on the Sun, on highly active M stars it may be the dominant process

Minimal size of a barchan dune

Barchans are dunes of high mobility which have a crescent shape and propagate under conditions of unidirectional wind. However, sand dunes only appear above a critical size, which scales with the saturation distance of the sand flux [P. Hersen, S. Douady, and B. Andreotti, Phys. Rev. Lett. {\bf{89,}} 264301 (2002); B. Andreotti, P. Claudin, and S. Douady, Eur. Phys. J. B {\bf{28,}} 321 (2002); G. Sauermann, K. Kroy, and H. J. Herrmann, Phys. Rev. E {\bf{64,}} 31305 (2001)]. It has been suggested by P. Hersen, S. Douady, and B. Andreotti, Phys. Rev. Lett. {\bf{89,}} 264301 (2002) that this flux fetch distance is itself constant. Indeed, this could not explain the proto size of barchan dunes, which often occur in coastal areas of high litoral drift, and the scale of dunes on Mars. In the present work, we show from three dimensional calculations of sand transport that the size and the shape of the minimal barchan dune depend on the wind friction speed and the sand flux on the area between dunes in a field. Our results explain the common appearance of barchans a few tens of centimeter high which are observed along coasts. Furthermore, we find that the rate at which grains enter saltation on Mars is one order of magnitude higher than on Earth, and is relevant to correctly obtain the minimal dune size on Mars.Comment: 11 pages, 10 figure