Zeta functions and Dynamical Systems

In this brief note we present a very simple strategy to investigate dynamical determinants for uniformly hyperbolic systems. The construction builds on the recent introduction of suitable functional spaces which allow to transform simple heuristic arguments in rigorous ones. Although the results so obtained are not exactly optimal the straightforwardness of the argument makes it noticeable.Comment: 7 pages, no figuer

Expanding Semiflows on Branched Surfaces and One-Parameter Semigroups of Operators

We consider expanding semiflows on branched surfaces. The family of transfer operators associated to the semiflow is a one-parameter semigroup of operators. The transfer operators may also be viewed as an operator-valued function of time and so, in the appropriate norm, we may consider the vector-valued Laplace transform of this function. We obtain a spectral result on these operators and relate this to the spectrum of the generator of this semigroup. Issues of strong continuity of the semigroup are avoided. The main result is the improvement to the machinery associated with studying semiflows as one-parameter semigroups of operators and the study of the smoothness properties of semiflows defined on branched manifolds, without encoding as a suspension semiflow

Who lives in overcrowded households in north-east London? Cross-sectional study of linked electronic health records and Energy Performance Certificate register data.

Objectives Household overcrowding is associated with adverse health outcomes, including increased risk of infectious diseases, mental health problems, and poor educational attainment. We investigated inequalities in overcrowding in an urban, ethnically diverse, and disadvantaged London population by pseudonymously linking electronic health records (EHR) to Energy Performance Certificates (EPC) data. Approach We used pseudonymised Unique Property Reference Numbers to link EHRs for 1,066,156 currently registered patients from 321,318 households in north-east London to EPC data. We measured household occupancy and derived the bedroom standard overcrowding definition (number of rooms relative to occupants’ sex and ages) to estimate overcrowding prevalence. We examined associations with: household composition (adults only, single adult+children, ≥2 working-age adults+children, ≥1 retirement-age adults+children, three-generational household); ethnic background (White, South Asian, Black, Mixed, Other, missing); and Index of Multiple Deprivation (IMD) quintile. We used multivariable logistic regression to estimate the adjusted odds (aOR) and 95% Confidence Intervals (CI) of overcrowding. Results Overall, 243,793 (22.9%) people were overcrowded. People living in households with children, or three-generational households were more likely (aOR [95% CI] 3.79 [3.74 - 3.84]; 6.53 [6.41 - 6.66] respectively), and single adults or retirement age adults with children less likely (0.36 [0.35 - 0.38]; 0.36 [0.23 - 0.57] respectively), to be overcrowded. Overcrowding was more likely among people from Asian or Black ethnic backgrounds (1.24 [1.22 - 1.25] and 1.17 [1.15 - 1.19] respectively). There was a dose-response relationship between IMD quintile and overcrowding: OR 0.20 [0.20 - 0.21] in the least deprived compared to most deprived quintile. Conclusion One in five people in north-east London live in overcrowded households with marked inequalities by ethnicity, household generational composition, and deprivation. Up-to-date estimates of household overcrowding can be derived from linked housing and health records and used to evaluate the impact of economic policies on health and housing inequalities

Eigenfunctions for smooth expanding circle maps

We construct a real-analytic circle map for which the corresponding Perron-Frobenius operator has a real-analytic eigenfunction with an eigenvalue outside the essential spectral radius when acting upon $C^1$-functions.Comment: 10 pages, 2 figure

Entropic Fluctuations in Statistical Mechanics I. Classical Dynamical Systems

Within the abstract framework of dynamical system theory we describe a general approach to the Transient (or Evans-Searles) and Steady State (or Gallavotti-Cohen) Fluctuation Theorems of non-equilibrium statistical mechanics. Our main objective is to display the minimal, model independent mathematical structure at work behind fluctuation theorems. Besides its conceptual simplicity, another advantage of our approach is its natural extension to quantum statistical mechanics which will be presented in a companion paper. We shall discuss several examples including thermostated systems, open Hamiltonian systems, chaotic homeomorphisms of compact metric spaces and Anosov diffeomorphisms.Comment: 72 pages, revised version 12/10/2010, to be published in Nonlinearit

Rare events, escape rates and quasistationarity: some exact formulae

We present a common framework to study decay and exchanges rates in a wide class of dynamical systems. Several applications, ranging form the metric theory of continuons fractions and the Shannon capacity of contrained systems to the decay rate of metastable states, are given

Ruelle-Perron-Frobenius spectrum for Anosov maps

We extend a number of results from one dimensional dynamics based on spectral properties of the Ruelle-Perron-Frobenius transfer operator to Anosov diffeomorphisms on compact manifolds. This allows to develop a direct operator approach to study ergodic properties of these maps. In particular, we show that it is possible to define Banach spaces on which the transfer operator is quasicompact. (Information on the existence of an SRB measure, its smoothness properties and statistical properties readily follow from such a result.) In dimension $d=2$ we show that the transfer operator associated to smooth random perturbations of the map is close, in a proper sense, to the unperturbed transfer operator. This allows to obtain easily very strong spectral stability results, which in turn imply spectral stability results for smooth deterministic perturbations as well. Finally, we are able to implement an Ulam type finite rank approximation scheme thus reducing the study of the spectral properties of the transfer operator to a finite dimensional problem.Comment: 58 pages, LaTe

Augmented reality applied to design for disassembly assessment for a volumetric pump with rotating cylinder

Design for Disassembly (DfD) and Augmented Reality (AR) have become promising approaches to improve sustainability, by providing efficient delivery and learning assets. This study combines DfD and AR to deliver a method that helps to streamline maintenance processes and operator training. It focuses on a common part in the process industry that requires frequent maintenance and repair. DfD was applied to the pump’s design to ease disassembly and reduce material waste, energy consumption, and maintenance time. AR was used to provide an interactive guide to improve the operator understanding of its internal parts and assembly/disassembly procedures. The resulting DfD-AR led to a reduction in maintenance time and shows potential to deliver better training. This highlights the potential of DfD and AR to enhance sustainability, learning, and productivity. The resulting disassembly sequence was taken to an AR simulation, helping process designers to better understand the procedure and further optimize the solution with other constraints

Upper bound on the density of Ruelle resonances for Anosov flows

Using a semiclassical approach we show that the spectrum of a smooth Anosov vector field V on a compact manifold is discrete (in suitable anisotropic Sobolev spaces) and then we provide an upper bound for the density of eigenvalues of the operator (-i)V, called Ruelle resonances, close to the real axis and for large real parts.Comment: 57 page

A strong pair correlation bound implies the CLT for Sinai Billiards

For Dynamical Systems, a strong bound on multiple correlations implies the Central Limit Theorem (CLT) [ChMa]. In Chernov's paper [Ch2], such a bound is derived for dynamically Holder continuous observables of dispersing Billiards. Here we weaken the regularity assumption and subsequently show that the bound on multiple correlations follows directly from the bound on pair correlations. Thus, a strong bound on pair correlations alone implies the CLT, for a wider class of observables. The result is extended to Anosov diffeomorphisms in any dimension.Comment: 13 page