Long time behaviour of diffusing particles in constrained geometries; application to chromatin motion

Inspired by experiments that use single-particle tracking to measure the regions of confinement of selected chromosomal regions within cell nuclei, we have developed an analytical approach that takes into account various possible positions and shapes of the confinement regions. We show, in particular, that confinement of a particle into a subregion that is entirely enclosed within a spherical volume can lead to a higher limit of the mean radial square displacement value than the one associated with a particle that can explore the entire spherical volume. Finally, we apply the theory to analyse the motion of extrachromosomal chromatin rings within nuclei of living yeast.

LONG TIME CORRELATIONS OF NONLINEAR LUTTINGER LIQUIDS

An overview is given of the limitations of Luttinger liquid theory in describing the real time equilibrium dynamics of critical one-dimensional systems with nonlinear dispersion relation. After exposing the singularities of perturbation theory in band curvature effects that break the Lorentz invariance of the Tomonaga-Luttinger model, the origin of high frequency oscillations in the long time behaviour of correlation functions is discussed. The notion that correlations decay exponentially at finite temperature is challenged by the effects of diffusion in the density-density correlation due to umklapp scattering in lattice models.

Asymptotic behaviour of two-dimensional time-delayed Navier-Stokes equations

We consider the two-dimensional Navier-Stokes equations with a time-delayed convective term and a forcing term which contains some hereditary features. Some results on existence and uniqueness of solutions are established. We discuss the asymptotic behaviour of solutions and we also show the exponential stability of stationary solutions.

Long-term behaviour of railway transitions under dynamic loading application to soft soil sites

Dissertação para obtenção do Grau de Doutor em Engenharia Civil

Investigation on the intergranular corrosion resistance of the AISI 316L(N) stainless steel after long time creep testing at 600 degrees C

The effect of precipitation on the corrosion resistance of AISI 316L(N) stainless steel previously exposed to creep tests at 600 degrees C for periods of up to 10 years, has been studied. The corrosion resistance was investigated in 2 M H(2)SO(4)+0.5 M NaCl+0.01 M KSCN solution at 30 degrees C by electrochemical methods. The results showed that the susceptibility to intergranular corrosion was highly affected by aging at 600 degrees C and creep testing time. The intergranular corrosion resistance decreased by more than twenty times when the creep testing time increased from 7500 h to 85,000 h. The tendency to passivation decreased and less protective films were formed on the creep tested samples. All tested samples also showed susceptibility to pitting. Grain boundary M(23)C(6) carbides were not found after long-term exposure at 600 degrees C and the corrosion behavior of the creep tested samples was attributed to intermetallic phases (mainly sigma phase) precipitation. (C) 2007 Elsevier Inc. All rights reserved.

Semidiscretization and long-time asymptotics of nonlinear diffusion equations

We review several results concerning the long time asymptotics of nonlinear diffusion models based on entropy and mass transport methods. Semidiscretization of these nonlinear diffusion models are proposed and their numerical properties analysed. We demonstrate the long time asymptotic results by numerical simulation and we discuss several open problems based on these numerical results. We show that for general nonlinear diffusion equations the long-time asymptotics can be characterized in terms of fixed points of certain maps which are contractions for the euclidean Wasserstein distance. In fact, we propose a new scaling for which we can prove that this family of fixed points converges to the Barenblatt solution for perturbations of homogeneous nonlinearities for values close to zero.

Intermediate asymptotics beyond homogeneity and self-similarity: long time behavior for [formula]

"Vegeu el resum a l'inici del document del fitxer adjunt."

Exact long-time behavior of a network of oscillators under random fields

We present an exact solution for the order parameters that characterize the stationary behavior of a population of Kuramotos phase oscillators under random external fields [Y. Kuramoto, in International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physics, Vol. 39 (Springer, Berlin, 1975), p. 420]. From these results it is possible to generate the phase diagram of models with an arbitrary distribution of random frequencies and random fields.

Gas analysis of exhumed cadavers buried for 30 years: a case report about long time alteration.

Due to important alteration caused by long time decomposition, the gases in human bodies buried for more than a year have not been investigated. For the first time, the results of gas analysis sampled from bodies recently exhumed after 30 years are presented. Adipocere formation has prevented the bodies from too important alteration, and gaseous areas were identified. The sampling was performed with airtight syringes assisted by multi-detector computed tomography (MDCT) in those specific areas. The important amount of methane (CH4), coupled to weak amounts of hydrogen (H2) and carbon dioxide (CO2), usual gaseous alteration indicators, have permitted to confirm methanogenesis mechanism for long period of alteration. H2 and CO2 produced during the first stages of the alteration process were consumed through anaerobic oxidation by methanogenic bacteria, generating CH4.

Performance analysis of software run-time behaviour using 3D-visualisation

Monimutkaisen tietokonejärjestelmän suorituskykyoptimointi edellyttää järjestelmän ajonaikaisen käyttäytymisen ymmärtämistä. Ohjelmiston koon ja monimutkaisuuden kasvun myötä suorituskykyoptimointi tulee yhä tärkeämmäksi osaksi tuotekehitysprosessia. Tehokkaampien prosessorien käytön myötä myös energiankulutus ja lämmöntuotto ovat nousseet yhä suuremmiksi ongelmiksi, erityisesti pienissä, kannettavissa laitteissa. Lämpö- ja energiaongelmien rajoittamiseksi on kehitetty suorituskyvyn skaalausmenetelmiä, jotka edelleen lisäävät järjestelmän kompleksisuutta ja suorituskykyoptimoinnin tarvetta. Tässä työssä kehitettiin visualisointi- ja analysointityökalu ajonaikaisen käyttäytymisen ymmärtämisen helpottamiseksi. Lisäksi kehitettiin suorituskyvyn mitta, joka mahdollistaa erilaisten skaalausmenetelmien vertailun ja arvioimisen suoritusympäristöstä riippumatta, perustuen joko suoritustallenteen tai teoreettiseen analyysiin. Työkalu esittää ajonaikaisesti kerätyn tallenteen helposti ymmärrettävällä tavalla. Se näyttää mm. prosessit, prosessorikuorman, skaalausmenetelmien toiminnan sekä energiankulutuksen kolmiulotteista grafiikkaa käyttäen. Työkalu tuottaa myös käyttäjän valitsemasta osasta suorituskuvaa numeerista tietoa, joka sisältää useita oleellisia suorituskykyarvoja ja tilastotietoa. Työkalun sovellettavuutta tarkasteltiin todellisesta laitteesta saatua suoritustallennetta sekä suorituskyvyn skaalauksen simulointia analysoimalla. Skaalausmekanismin parametrien vaikutus simuloidun laitteen suorituskykyyn analysoitiin.

Small- and waiting-time behaviour of the thin-film-equation

We consider the small-time behavior of interfaces of zero contact angle solutions to the thin-film equation. For a certain class of initial data, through asymptotic analyses, we deduce a wide variety of behavior for the free boundary point. These are supported by extensive numerical simulations. © 2007 Society for Industrial and Applied Mathematics

On the long time behavior of free stochastic Schrödinger evolutions

We discuss the time evolution of the wave function which is the solution of a stochastic Schrödinger equation describing the dynamics of a free quantum particle subject to spontaneous localizations in space. We prove global existence and uniqueness of solutions. We observe that there exist three time regimes: the collapse regime, the classical regime and the diffusive regime. Concerning the latter, we assert that the general solution converges almost surely to a diffusing Gaussian wave function having a finite spread both in position as well as in momentum. This paper corrects and completes earlier works on this issue.

The population dynamics of disease on short and long time-scales

Observational evidence is scarce concerning the distribution of plant pathogen population sizes or densities as a function of time-scale or spatial scale. For wild pathosystems we can only get indirect evidence from evolutionary patterns and the consequences of biological invasions.We have little or no evidence bearing on extermination of hosts by pathogens, or successful escape of a host from a pathogen. Evidence over the last couple of centuries from crops suggest that the abundance of particular pathogens in the spectrum affecting a given host can vary hugely on decadal timescales. However, this may be an artefact of domestication and intensive cultivation. Host-pathogen dynamics can be formulated mathematically fairly easily–for example as SIR-type differential equation or difference equation models, and this has been the (successful) focus of recent work in crops. “Long-term” is then discussed in terms of the time taken to relax from a perturbation to the asymptotic state. However, both host and pathogen dynamics are driven by environmental factors as well as their mutual interactions, and both host and pathogen co-evolve, and evolve in response to external factors. We have virtually no information about the importance and natural role of higher trophic levels (hyperpathogens) and competitors, but they could also induce long-scale fluctuations in the abundance of pathogens on particular hosts. In wild pathosystems the host distribution cannot be modelled as either a uniform density or even a uniform distribution of fields (which could then be treated as individuals). Patterns of short term density-dependence and the detail of host distribution are therefore critical to long-term dynamics. Host density distributions are not usually scale-free, but are rarely uniform or clearly structured on a single scale. In a (multiply structured) metapopulation with coevolution and external disturbances it could well be the case that the time required to attain equilibrium (if it exists) based on conditions stable over a specified time-scale is longer than that time-scale. Alternatively, local equilibria may be reached fairly rapidly following perturbations but the meta-population equilibrium be attained very slowly. In either case, meta-stability on various time-scales is a more relevant than equilibrium concepts in explaining observed patterns.