A Gallavotti-Cohen-Evans-Morriss Like Symmetry for a Class of Markov Jump Processes

We investigate a new symmetry of the large deviation function of certain time-integrated currents in non-equilibrium systems. The symmetry is similar to the well-known Gallavotti-Cohen-Evans-Morriss-symmetry for the entropy production, but it concerns a different functional of the stochastic trajectory. The symmetry can be found in a restricted class of Markov jump processes, where the network of microscopic transitions has a particular structure and the transition rates satisfy certain constraints. We provide three physical examples, where time-integrated observables display such a symmetry. Moreover, we argue that the origin of the symmetry can be traced back to time-reversal if stochastic trajectories are grouped appropriately.     

A Lagrangian Approach for the Incompressible Navier‐Stokes Equations with Variable Density

We investigate the Cauchy problem for the inhomogeneous Navier‐Stokes equations in the whole n‐dimensional space. Under some smallness assumption on the data, we show the existence of global‐in‐time unique solutions in a critical functional framework. The initial density is required to belong to the multiplier space of \input amssym $\dot {B}^{n/p‐1}_{p,1}({\Bbb R}^n)$ . In particular, piecewise‐constant initial densities are admissible data provided the jump at the interface is small enough and generate global unique solutions with piecewise constant densities. Using Lagrangian coordinates is the key to our results, as it enables us to solve the system by means of the basic contraction mapping theorem. As a consequence, conditions for uniqueness are the same as for existence. © 2012 Wiley Periodicals, Inc.     

Dewetting as an investigative tool for studying properties of thin polymer films

Employing mass conservation, time-resolved dewetting experiments of thin polymer films allow to determine in real time the dynamic contact angle and the slippage length. Moreover, based on a systematic variation of interfacial properties of a polymer brush, dewetting makes it possible to calculate the force it needs to extract a single polymer chain from its own melt. In the visco-elastic regime close to the glass transition, the temperature and molecular weight dependence of the relaxation time of residual stresses resulting from film preparation by spin-coating can be obtained from the evolution of the shape of the dewetting rim. The presented examples demonstrate that dewetting represents a powerful approach for a sensitive characterization of rheological, frictional and interfacial properties of thin polymer films.     

A collocated finite volume scheme to solve free convection for general non-conforming grids

We present a new collocated numerical scheme for the approximation of the Navier–Stokes and energy equations under the Boussinesq assumption for general grids, using the velocity–pressure unknowns. This scheme is based on a recent scheme for the diffusion terms. Stability properties are drawn from particular choices for the pressure gradient and the non-linear terms. Convergence of the approximate solutions may be proven mathematically. Numerical results show the accuracy of the scheme on irregular grids.     

Eulerian and Lagrangian Pictures of Non-equilibrium Diffusions

We show that a non-equilibrium diffusive dynamics in a finite-dimensional space takes in the Lagrangian frame of its mean local velocity an equilibrium form with the detailed balance property. This explains the equilibrium nature of the fluctuation-dissipation relations in that frame observed previously. The general considerations are illustrated on few examples of stochastic particle dynamics.     

Rough blowup solutions to the <Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript> critical NLS

We study the singularity formation for the cubic focusing L ²-critical nonlinear Schrödinger equation on \({\mathbb{R}^{2}}\) . In a series of recent works, Merle and Raphaël have completely described the so called log–log blowup regime and proven its stability in the energy space H ¹. Our aim in this paper is to investigate the stability of this blowup regime under rough perturbations in the direction of developing a theory at the level of the critical space L ². By blending the Merle, Raphaël techniques with the quantitative I-method developed by Colliander, Keel, Staffilani, Takaoka and Tao for the study of the Cauchy problem for rough data, we obtain the stability of the log–log regime in H ^s for all s > 0.     

Experimental evidence and theoretical analysis for the chiral symmetry breaking in the growth front of conglomerate crystal phase of 1,1'-binaphthyl

Chirally asymmetric states, chemical oscillations, propagating chemical waves, and spatial patterns, are examples of far-from-equilibrium self-organization. We have found that the crystal growth front of 1,1(')-binaphthyl shows many of the characteristics of an open system in which chiral symmetry breaking has occurred. From its supercooled molten phase, 1,1(')-binaphthyl crystallizes as a conglomerate of R and S crystals when the temperature is above 145 degrees C. In addition, 1,1(')-binaphthyl in its molten phase is always racemic due to its high racemization rate. Under appropriate conditions, bimodal probability distribution of enantiomeric excess (ee) with maxima around 60% was observed. The ee was mass independent, indicating that the growth front maintains a constant ee. A kinetic model that theoretically analyzes the chiral symmetry breaking transition in the growth front of a conglomerate crystal phase was formulated. Computer simulation of the model reproduced not only the average but also the large variation of the ee observed in crystallization experiments.     

Glycosylated Quantum Dots for the Selective Labelling of <Emphasis Type="Italic">Kluyveromyces bulgaricus</Emphasis> and <Emphasis Type="Italic">Saccharomyces cerevisiae</Emphasis> Yeast Strains

Highly fluorescent CdTe quantum dots (QDs) stabilized by thioglycolic acid (TGA) were prepared by an aqueous solution approach and used as fluorescent labels in detecting yeast cells. Sugars (mannose, galactose or glucose) were adsorbed on CdTe@TGA QDs and the interaction of these nanoparticles with yeast cells was studied by fluorescence microscopy. Results obtained demonstrate that galactose and mannose functionalized QDs associate respectively with Kluyveromyces bulgaricus and Saccharomyces cerevisiae yeast strains due to saccharide/lectin specific recognition. Glucose-functionalized CdTe QDs, which are not recognized by cell lectins, preferentially localize in the bud scars of S. cerevisiae.