Freezing Transition in Decaying Burgers Turbulence and Random Matrix Dualities

We reveal a phase transition with decreasing viscosity $\nu$ at \nu=\nu_c>0 in one-dimensional decaying Burgers turbulence with a power-law correlated random profile of Gaussian-distributed initial velocities \sim|x-x'|^{-2}. The low-viscosity phase exhibits non-Gaussian one-point probability density of velocities, continuously dependent on \nu, reflecting a spontaneous one step replica symmetry breaking (RSB) in the associated statistical mechanics problem. We obtain the low orders cumulants analytically. Our results, which are checked numerically, are based on combining insights in the mechanism of the freezing transition in random logarithmic potentials with an extension of duality relations discovered recently in Random Matrix Theory. They are essentially non mean-field in nature as also demonstrated by the shock size distribution computed numerically and different from the short range correlated Kida model, itself well described by a mean field one step RSB ansatz. We also provide some insights for the finite viscosity behaviour of velocities in the latter model.Comment: Published version, essentially restructured & misprints corrected. 6 pages, 5 figure

Correlation between electric-field-induced phase transition and piezoelectricity in lead zirconate titanate films

We observed that electric field induces phase transition from tetragonal to rhombohedral in polycrystalline morphotropic lead zirconate titanate (PZT) films, as reported in 2011 for bulk PZT. Moreover, we evidenced that this field-induced phase transition is strongly correlated with PZT film piezoelectric properties, that is to say the larger the phase transition, the larger the longitudinal piezoelectric coefficient d 33,eff . Although d 33,eff is already comprised between as 150 to 170 pm/V, our observation suggests that one could obtain larger d 33,eff values, namely 250 pm/V, by optimizing the field-induced phase transition thanks to composition fine tuning

Shock statistics in higher-dimensional Burgers turbulence

We conjecture the exact shock statistics in the inviscid decaying Burgers equation in D>1 dimensions, with a special class of correlated initial velocities, which reduce to Brownian for D=1. The prediction is based on a field-theory argument, and receives support from our numerical calculations. We find that, along any given direction, shocks sizes and locations are uncorrelated.Comment: 4 pages, 8 figure

The Low Redshift Lyman Alpha Forest in Cold Dark Matter Cosmologies

We study the physical origin of the low-redshift Lyman alpha forest in hydrodynamic simulations of four CDM cosmologies. Our main conclusions are insensitive to the cosmological model but depend on our assumption that the UV background declines at low redshift. We find that the expansion of the universe drives rapid evolution of dN/dz (the number of absorbers per unit z) at z > 1.7, but that at lower redshift the fading of the UV background counters the influence of expansion, leading to slow evolution. At every redshift, weaker lines come primarily from moderate fluctuations of the diffuse, unshocked IGM, and stronger lines originate in shocked or radiatively cooled gas of higher overdensity. However, the neutral hydrogen column density associated with structures of fixed overdensity drops as the universe expands, so an absorber at z = 0 is dynamically analogous to an absorber with neutral hydrogen column density 10 to 50 times higher at z = 2-3. We find no clear distinction between lines arising in "galaxy halos" and lines arising in larger scale structures; however, galaxies tend to lie near the dense regions of the IGM that produce strong Lyman alpha lines. The simulations provide a unified physical picture that accounts for the most distinctive observed properties of the low redshift Lyman alpha forest: (1) a sharp transition in the evolution of dN/dz at z ~ 1.7, (2) stronger evolution for absorbers of higher equivalent width, (3) a correlation of increasing Lyman alpha equivalent width with decreasing galaxy impact parameter, and (4) a tendency for stronger lines to arise in close proximity to galaxies while weaker lines trace more diffuse large scale structure. (Abridged)Comment: 57 pages, 18 figures, submitted to Ap

Spatial distributions in static heavy-light mesons: a comparison of quark models with lattice QCD

Lattice measurements of spatial distributions of the light quark bilinear densities in static mesons allow to test directly and in detail the wave functions of quark models. These distributions are gauge invariant quantities directly related to the spatial distribution of wave functions. We make a detailed comparison of the recent lattice QCD results with our own quark models, formulated previously for quite different purposes. We find a striking agreement not only between our two quark models, but also with the lattice QCD data for the ground state in an important range of distances up to about 4/GeV. Moreover the agreement extends to the L=1 states [j^P=(1/2)^+]. An explanation of several particular features completely at odds with the non-relativistic approximation is provided. A rather direct, somewhat unexpected and of course approximate relation between wave functions of certain quark models and QCD has been established.Comment: 40 pages, 5 figures (version published in PRD

Field Theoretic Description of Ultrarelativistic Electron-Positron Plasmas

Ultrarelativistic electron-positron plasmas can be produced in high-intensity laser fields and play a role in various astrophysical situations. Their properties can be calculated using QED at finite temperature. Here we will use perturbative QED at finite temperature for calculating various important properties, such as the equation of state, dispersion relations of collective plasma modes of photons and electrons, Debye screening, damping rates, mean free paths, collision times, transport coefficients, and particle production rates, of ultrarelativistic electron-positron plasmas. In particular, we will focus on electron-positron plasmas produced with ultra-strong lasers.Comment: 13 pages, 7 figures, 1 table, published versio

Modeling and Optimization of Lactic Acid Synthesis by the Alkaline Degradation of Fructose in a Batch Reactor

The present work deals with the determination of the optimal operating conditions of lactic acid synthesis by the alkaline degradation of fructose. It is a complex transformation for which detailed knowledge is not available. It is carried out in a batch or semi-batch reactor. The ‘‘Tendency Modeling’’ approach, which consists of the development of an approximate stoichiometric and kinetic model, has been used. An experimental planning method has been utilized as the database for model development. The application of the experimental planning methodology allows comparison between the experimental and model response. The model is then used in an optimization procedure to compute the optimal process. The optimal control problem is converted into a nonlinear programming problem solved using the sequencial quadratic programming procedure coupled with the golden search method. The strategy developed allows simultaneously optimizing the different variables, which may be constrained. The validity of the methodology is illustrated by the determination of the optimal operating conditions of lactic acid production

Characterizing groundwater flow and heat transport in fractured rock using Fiber-Optic Distributed Temperature Sensing

International audienceWe show how fully distributed space-time measurements with Fiber-Optic Distributed Temperature Sensing (FO-DTS) can be used to investigate groundwater flow and heat transport in fractured media. Heat injection experiments are combined with temperature measurements along fiber-optic cables installed in boreholes. Thermal dilution tests are shown to enable detection of cross-flowing fractures and quantification of the cross flow rate. A cross borehole thermal tracer test is then analyzed to identify fracture zones that are in hydraulic connection between boreholes and to estimate spatially distributed temperature breakthrough in each fracture zone. This provides a significant improvement compared to classical tracer tests, for which concentration data are usually integrated over the whole abstraction borehole. However, despite providing some complementary results, we find that the main contributive fracture for heat transport is different to that for a solute tracer

Extreme value statistics from the Real Space Renormalization Group: Brownian Motion, Bessel Processes and Continuous Time Random Walks

We use the Real Space Renormalization Group (RSRG) method to study extreme value statistics for a variety of Brownian motions, free or constrained such as the Brownian bridge, excursion, meander and reflected bridge, recovering some standard results, and extending others. We apply the same method to compute the distribution of extrema of Bessel processes. We briefly show how the continuous time random walk (CTRW) corresponds to a non standard fixed point of the RSRG transformation.Comment: 24 pages, 5 figure