Entropy Production in Random Billiards

We introduce a class of random mechanical systems called random billiards to study the problem of quantifying the irreversibility of nonequilibrium macroscopic systems. In a random billiard model, a point particle evolves by free motion through the interior of a spatial domain, and reflects according to a reflection operator, specified in the model by a Markov transition kernel, upon collision with the boundary of the domain. We derive a formula for entropy production rate that applies to a general class of random billiard systems. This formula establishes a relation between the purely mathematical concept of entropy production rate and textbook thermodynamic entropy, recovering in particular Clausius' formulation of the second law of thermodynamics. We also study an explicit class of examples whose reflection operator, referred to as the Maxwell-Smolukowski thermostat, models systems with boundary thermostats kept at possibly different temperatures. We prove that, under certain mild regularity conditions, the class of models are uniformly ergodic Markov chains and derive formulas for the stationary distribution and entropy production rate in terms of geometric and thermodynamic parameters.Comment: 30 pages, 9 figure

Limit Theorems for Random Billiard Models

The central objects of study in this dissertation are random billiard systems. These are Markov chain systems with general state spaces derived from deterministic billiard systems by selecting one or more dynamical variables and replacing them with random variables with fixed probability distributions. In particular, we study two specific model systems; one which models gas diffusion through cylindrical channels whose walls have a microscopic structure, and another which models a minimalistic heat engine. The main results for the gas diffusion model, a series of probabilistic limit theorems, allow us to express transport characteristics such as mean exit times of the gas from the channel in terms of characteristics of the channel walls. Preliminary results for the heat engine model present some beginning steps in the study of stochastic thermodynamics of billiard-like mechanical systems

Revisiting Maxwell-Smoluchowski theory: low surface roughness in straight channels

The Maxwell-Smoluchowski (MS) theory of gas diffusion is revisited here in the context of gas transport in straight channels in the Knudsen regime of large mean free path. This classical theory is based on a phenomenological model of gas-surface interaction that posits that a fraction $\vartheta$ of molecular collisions with the channel surface consists of diffuse collisions, i.e., the direction of post-collision velocities is distributed according to the Knudsen Cosine Law, and a fraction $1-\vartheta$ undergoes specular reflection. From this assumption one obtains the value $\mathcal{D}=\frac{2-\vartheta}{\vartheta}\mathcal{D}_K$ for the self-diffusivity constant, where $\mathcal{D}_K$ is a reference value corresponding to $\vartheta=1$. In this paper we show that $\vartheta$ can be expressed in terms of micro- and macro-geometric parameters for a model consisting of hard spheres colliding elastically against a rigid surface with prescribed microgeometry. Our refinement of the MS theory is based on the observation that the classical surface scattering operator associated to the microgeometry has a canonical velocity space diffusion approximation by a generalized Legendre differential operator whose spectral theory is known explicitly. More specifically, starting from an explicit description of the effective channel surface microgeometry -- a concept which incorporates both the actual surface microgeometry and the molecular radius -- and using this operator approximation, we show that $\vartheta$ can be resolved into easily obtained geometric parameters.Comment: 19 pages, 5 figure

Comparative chloroplast genomics: analyses including new sequences from the angiosperms Nuphar advena and Ranunculus macranthus

<p>Abstract</p> <p>Background</p> <p>The number of completely sequenced plastid genomes available is growing rapidly. This array of sequences presents new opportunities to perform comparative analyses. In comparative studies, it is often useful to compare across wide phylogenetic spans and, within angiosperms, to include representatives from basally diverging lineages such as the genomes reported here: <it>Nuphar advena </it>(from a basal-most lineage) and <it>Ranunculus macranthus </it>(a basal eudicot). We report these two new plastid genome sequences and make comparisons (within angiosperms, seed plants, or all photosynthetic lineages) to evaluate features such as the status of <it>ycf15 </it>and <it>ycf68 </it>as protein coding genes, the distribution of simple sequence repeats (SSRs) and longer dispersed repeats (SDR), and patterns of nucleotide composition.</p> <p>Results</p> <p>The <it>Nuphar </it>[GenBank:<ext-link ext-link-type="gen" ext-link-id="NC_008788">NC_008788</ext-link>] and <it>Ranunculus </it>[GenBank:<ext-link ext-link-type="gen" ext-link-id="NC_008796">NC_008796</ext-link>] plastid genomes share characteristics of gene content and organization with many other chloroplast genomes. Like other plastid genomes, these genomes are A+T-rich, except for rRNA and tRNA genes. Detailed comparisons of <it>Nuphar </it>with <it>Nymphaea</it>, another Nymphaeaceae, show that more than two-thirds of these genomes exhibit at least 95% sequence identity and that most SSRs are shared. In broader comparisons, SSRs vary among genomes in terms of abundance and length and most contain repeat motifs based on A and T nucleotides.</p> <p>Conclusion</p> <p>SSR and SDR abundance varies by genome and, for SSRs, is proportional to genome size. Long SDRs are rare in the genomes assessed. SSRs occur less frequently than predicted and, although the majority of the repeat motifs do include A and T nucleotides, the A+T bias in SSRs is less than that predicted from the underlying genomic nucleotide composition. In codon usage third positions show an A+T bias, however variation in codon usage does not correlate with differences in A+T-richness. Thus, although plastome nucleotide composition shows "A+T richness", an A+T bias is not apparent upon more in-depth analysis, at least in these aspects. The pattern of evolution in the sequences identified as <it>ycf15 </it>and <it>ycf68 </it>is not consistent with them being protein-coding genes. In fact, these regions show no evidence of sequence conservation beyond what is normal for non-coding regions of the IR.</p

Methods for Obtaining and Analyzing Whole Chloroplast Genome Sequences

During the past decade there has been a rapid increase in our understanding of plastid genome organization and evolution due to the availability of many new completely sequenced genomes. Currently there are 43 complete genomes published and ongoing projects are likely to increase this sampling to nearly 200 genomes during the next five years. Several groups of researchers including ours have been developing new techniques for gathering and analyzing entire plastid genome sequences and details of these developments are summarized in this chapter. The most important recent developments that enhance our ability to generate whole chloroplast genome sequences involve the generation of pure fractions of chloroplast genomes by whole genome amplification using rolling circular amplification, cloning genomes into Fosmid or BAC vectors, and the development of an organellar annotation program (DOGMA). In addition to providing details of these methods, we provide an overview of methods for analyzing complete plastid genome sequences for repeats and gene content, as well as approaches for using gene order and sequence data for phylogeny reconstruction. This explosive increase in the number of sequenced plastid genomes and improved computational tools will provide many insights into the evolution of these genomes and much new data for assessing relationships at deep nodes in plants and other photosynthetic organisms

Dissociation of EphB2 Signaling Pathways Mediating Progenitor Cell Proliferation and Tumor Suppression

SummarySignaling proteins driving the proliferation of stem and progenitor cells are often encoded by proto-oncogenes. EphB receptors represent a rare exception; they promote cell proliferation in the intestinal epithelium and function as tumor suppressors by controlling cell migration and inhibiting invasive growth. We show that cell migration and proliferation are controlled independently by the receptor EphB2. EphB2 regulated cell positioning is kinase-independent and mediated via phosphatidylinositol 3-kinase, whereas EphB2 tyrosine kinase activity regulates cell proliferation through an Abl-cyclin D1 pathway. Cyclin D1 regulation becomes uncoupled from EphB signaling during the progression from adenoma to colon carcinoma in humans, allowing continued proliferation with invasive growth. The dissociation of EphB2 signaling pathways enables the selective inhibition of the mitogenic effect without affecting the tumor suppressor function and identifies a pharmacological strategy to suppress adenoma growth

Analysis of 81 Genes From 64 Plastid Genomes Resolves Relationships in Angiosperms and Identifies Genome-Scale Evolutionary Patterns

Angiosperms are the largest and most successful clade of land plants with \u3e250,000 species distributed in nearly every terrestrial habitat. Many phylogenetic studies have been based on DNA sequences of one to several genes, but, despite decades of intensive efforts, relationships among early diverging lineages and several of the major clades remain either incompletely resolved or weakly supported. We performed phylogenetic analyses of 81 plastid genes in 64 sequenced genomes, including 13 new genomes, to estimate relationships among the major angiosperm clades, and the resulting trees are used to examine the evolution of gene and intron content. Phylogenetic trees from multiple methods, including model-based approaches, provide strong support for the position of Amborella as the earliest diverging lineage of flowering plants, followed by Nymphaeales and Austrobaileyales. The plastid genome trees also provide strong support for a sister relationship between eudicots and monocots, and this group is sister to a clade that includes Chloranthales and magnoliids. Resolution of relationships among the major clades of angiosperms provides the necessary framework for addressing numerous evolutionary questions regarding the rapid diversification of angiosperms. Gene and intron content are highly conserved among the early diverging angiosperms and basal eudicots, but 62 independent gene and intron losses are limited to the more derived monocot and eudicot clades. Moreover, a lineage-specific correlation was detected between rates of nucleotide substitutions, indels, and genomic rearrangements