A metaphor for adiabatic evolution to symmetry

In this paper we study a Hamiltonian system with a spatially asymmetric potential. We are interested in the effects on the dynamics when the potential becomes symmetric slowly in time. We focus on a highly simplified non-trivial model problem (a metaphor) to be able to pursue explicit calculations as far as possible. Using the techniques of averaging and adiabatic invariants, we are able to study all bounded solutions, which reveals significant asymmetric dynamics even when the asymmetric contributions to the potential have become negligibly small.Comment: 27 pages, LaTeX 2e, 8 figures include

Evolution towards symmetry

The dynamics of timedependent evolution towards symmetry in Hamiltonian systems poses a dicult problem as the analysis has to be global in phasespace For one and two degrees of freedom systems this leads to the presence of one respectively two global adiabatic invariants and also the persistence of asymmetric features over a long tim

Drastic fall-off of the thermal conductivity for disordered lattices in the limit of weak anharmonic interactions

We study the thermal conductivity, at fixed positive temperature, of a disordered lattice of harmonic oscillators, weakly coupled to each other through anharmonic potentials. The interaction is controlled by a small parameter $\epsilon > 0$. We rigorously show, in two slightly different setups, that the conductivity has a non-perturbative origin. This means that it decays to zero faster than any polynomial in $\epsilon$ as $\epsilon\rightarrow 0$. It is then argued that this result extends to a disordered chain studied by Dhar and Lebowitz, and to a classical spins chain recently investigated by Oganesyan, Pal and Huse.Comment: 21 page

Can translation invariant systems exhibit a Many-Body Localized phase?

This note is based on a talk by one of us, F. H., at the conference PSPDE II, Minho 2013. We review some of our recent works related to (the possibility of) Many-Body Localization in the absence of quenched disorder (in particular arXiv:1305.5127,arXiv:1308.6263,arXiv:1405.3279). In these works, we provide arguments why systems without quenched disorder can exhibit `asymptotic' localization, but not genuine localization.Comment: To appear in the Proceedings of the conference Particle systems and PDE's - II, held at the Center of Mathematics of the University of Minho in December 201

Energy transport through rare collisions

We study a one-dimensional hamiltonian chain of masses perturbed by an energy conserving noise. The dynamics is such that, according to its hamiltonian part, particles move freely in cells and interact with their neighbors through collisions, made possible by a small overlap of size $\epsilon > 0$ between near cells. The noise only randomly flips the velocity of the particles. If $\epsilon \rightarrow 0$, and if time is rescaled by a factor $1/{\epsilon}$, we show that energy evolves autonomously according to a stochastic equation, which hydrodynamic limit is known in some cases. In particular, if only two different energies are present, the limiting process coincides with the simple symmetric exclusion process.Comment: 24 pages, 2 figure

Thermal conductivity in harmonic lattices with random collisions

We review recent rigorous mathematical results about the macroscopic behaviour of harmonic chains with the dynamics perturbed by a random exchange of velocities between nearest neighbor particles. The random exchange models the effects of nonlinearities of anharmonic chains and the resulting dynamics have similar macroscopic behaviour. In particular there is a superdiffusion of energy for unpinned acoustic chains. The corresponding evolution of the temperature profile is governed by a fractional heat equation. In non-acoustic chains we have normal diffusivity, even if momentum is conserved.Comment: Review paper, to appear in the Springer Lecture Notes in Physics volume "Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer" (S. Lepri ed.

VASP, zyxin and TES are tension-dependent members of Focal Adherens Junctions independent of the α-catenin-vinculin module

Mechanical forces are integrated at cadherin-based adhesion complexes to regulate morphology and strength of cell-cell junctions and organization of associated F-actin. A central mechanosensor at the cadherin complex is α-catenin, whose stretching recruits vinculin to regulate adhesion strength. The identity of the F-actin regulating signals that are also activated by mechanical forces at cadherin-based junctions has remained elusive. Here we identify the actin-regulators VASP, zyxin and TES as members of punctate, tensile cadherin-based junctions called Focal Adherens Junctions (FAJ) and show that they display mechanosensitive recruitment similar to that of vinculin. However, this recruitment is not altered by destroying or over-activating the α-catenin/vinculin module. Structured Illumination Microscopy (SIM) indicates that these tension sensitive proteins concentrate at locations within FAJs that are distinct from the core cadherin complex proteins. Furthermore, localization studies using mutated versions of VASP and zyxin indicate that these two proteins require binding to each other in order to localize to the FAJs. We conclude that there are multiple force sensitive modules present at the FAJ that are activated at distinct locations along the cadherin-F-actin axis and regulate specific aspects of junction dynamics

Reproductive Strategy of the Giant Electric Ray in the Southern Gulf of California

The objective of the present study was to describe and characterize macroscopic and microscopic aspects of the reproductive biology of the Giant Electric Ray Narcine entemedor, a viviparous elasmobranch targeted by commercial fishers in Mexico. A total of 305 individual rays were captured (260 females, 45 males); all males were sexually mature. The median size at maturity for females was estimated to be 58.5 cm TL, the median size at pregnancy was 63.7 cm TL, and the median size at maternity was 66.2 cm TL. The range of ovarian follicles recorded per female was 1–69; the maximum ovarian fecundity of fully grown vitellogenic oocytes was 17, and uterine fecundity ranged from 1 to 24 embryos per female. The lengths of the oblong ovarian follicles varied significantly among months, and the largest ovarian follicles were found in July, August, and September. Median embryo size was largest in August, and the size at birth was between 12.4 and 14.5 cm TL. Histological evidence of secretions from the glandular tissue of the uterine villi indicate that this species probably has limited histotrophy as a reproductive mode. Vitellogenesis in the ovary occurred synchronously with gestation in the uterus. The Giant Electric Ray has a continuous annual reproductive cycle; a period of ovulation occurs between May and September and two peaks of parturition, one in January and one in August, occur, suggesting that embryonic diapause occurs in some individuals. These results provide useful information for the management of this important commercial species in Bahía de La Paz, Mexico, and will allow possible modification of the current Mexican regulations to enable better protection of this species

Keratin 8/18 Regulation of Cell Stiffness-Extracellular Matrix Interplay through Modulation of Rho-Mediated Actin Cytoskeleton Dynamics

Cell mechanical activity generated from the interplay between the extracellular matrix (ECM) and the actin cytoskeleton is essential for the regulation of cell adhesion, spreading and migration during normal and cancer development. Keratins are the intermediate filament (IF) proteins of epithelial cells, expressed as pairs in a lineage/differentiation manner. Hepatic epithelial cell IFs are made solely of keratins 8/18 (K8/K18), hallmarks of all simple epithelia. Notably, our recent work on these epithelial cells has revealed a key regulatory function for K8/K18 IFs in adhesion/migration, through modulation of integrin interactions with ECM, actin adaptors and signaling molecules at focal adhesions. Here, using K8-knockdown rat H4 hepatoma cells and their K8/K18-containing counterparts seeded on fibronectin-coated substrata of different rigidities, we show that the K8/K18 IF-lacking cells lose their ability to spread and exhibit an altered actin fiber organization, upon seeding on a low-rigidity substratum. We also demonstrate a concomitant reduction in local cell stiffness at focal adhesions generated by fibronectin-coated microbeads attached to the dorsal cell surface. In addition, we find that this K8/K18 IF modulation of cell stiffness and actin fiber organization occurs through RhoA-ROCK signaling. Together, the results uncover a K8/K18 IF contribution to the cell stiffness-ECM rigidity interplay through a modulation of Rho-dependent actin organization and dynamics in simple epithelial cells