Connecting the vulcanization transition to percolation

The vulcanization transition is addressed via a minimal replica-field-theoretic model. The appropriate long-wave-length behavior of the two- and three-point vertex functions is considered diagrammatically, to all orders in perturbation theory, and identified with the corresponding quantities in the Houghton-Reeve-Wallace field-theoretic approach to the percolation critical phenomenon. Hence, it is shown that percolation theory correctly captures the critical phenomenology of the vulcanization transition associated with the liquid and critical states.Comment: 9 pages, 5 figure

Freezing of dynamical exponents in low dimensional random media

A particle in a random potential with logarithmic correlations in dimensions $d=1,2$ is shown to undergo a dynamical transition at $T_{dyn}>0$. In $d=1$ exact results demonstrate that $T_{dyn}=T_c$, the static glass transition temperature, and that the dynamical exponent changes from $z(T)=2 + 2 (T_c/T)^2$ at high temperature to $z(T)= 4 T_c/T$ in the glass phase. The same formulae are argued to hold in $d=2$. Dynamical freezing is also predicted in the 2D random gauge XY model and related systems. In $d=1$ a mapping between dynamics and statics is unveiled and freezing involves barriers as well as valleys. Anomalous scaling occurs in the creep dynamics.Comment: 5 pages, 2 figures, RevTe

Thermal fluctuations in pinned elastic systems: field theory of rare events and droplets

Using the functional renormalization group (FRG) we study the thermal fluctuations of elastic objects, described by a displacement field u and internal dimension d, pinned by a random potential at low temperature T, as prototypes for glasses. A challenge is how the field theory can describe both typical (minimum energy T=0) configurations, as well as thermal averages which, at any non-zero T as in the phenomenological droplet picture, are dominated by rare degeneracies between low lying minima. We show that this occurs through an essentially non-perturbative *thermal boundary layer* (TBL) in the (running) effective action Gamma[u] at T>0 for which we find a consistent scaling ansatz to all orders. The TBL resolves the singularities of the T=0 theory and contains rare droplet physics. The formal structure of this TBL is explored around d=4 using a one loop Wilson RG. A more systematic Exact RG (ERG) method is employed and tested on d=0 models. There we obtain precise relations between TBL quantities and droplet probabilities which are checked against exact results. We illustrate how the TBL scaling remains consistent to all orders in higher d using the ERG and how droplet picture results can be retrieved. Finally, we solve for d=0,N=1 the formidable "matching problem" of how this T>0 TBL recovers a critical T=0 field theory. We thereby obtain the beta-function at T=0, *all ambiguities removed*, displayed here up to four loops. A discussion of d>4 case and an exact solution at large d are also provided

Electro-mechanical de-icer modeling with aeronautics application

International audienceThe development of a multi physics model, for a new electro-mechanical de-icing solution, is presented in thisarticle. The technology proposed by aeronautics industry resides in the principles of Laplace forces and plate elastic deformation.Electro-magneto-mechanical modeling is intended for expressing the interdependence between the mechanical response and the electrical stimulus. The resulting expressions incorporate the dynamics of the call and the particular topology of the structural elements of the system. Measurements issue from previous prototypes served to validate the final model. As the goal was to obtain a model adapted for optimization process, some results and perspectives are also discussed.</p

Freezing transitions and the density of states of 2D random Dirac Hamiltonians

Using an exact mapping to disordered Coulomb gases, we introduce a novel method to study two dimensional Dirac fermions with quenched disorder in two dimensions which allows to treat non perturbative freezing phenomena. For purely random gauge disorder it is known that the exact zero energy eigenstate exhibits a freezing-like transition at a threshold value of disorder $\sigma=\sigma_{th}=2$. Here we compute the dynamical exponent $z$ which characterizes the critical behaviour of the density of states around zero energy, and find that it also exhibits a phase transition. Specifically, we find that $\rho(E=0 + i \epsilon) \sim \epsilon^{2/z-1}$ (and $\rho(E) \sim E^{2/z-1}$) with $z=1 + \sigma$ for $\sigma < 2$ and $z=\sqrt{8 \sigma} - 1$ for $\sigma > 2$. For a finite system size $L<\epsilon^{-1/z}$ we find large sample to sample fluctuations with a typical $\rho_{\epsilon}(0) \sim L^{z-2}$. Adding a scalar random potential of small variance $\delta$, as in the corresponding quantum Hall system, yields a finite noncritical $\rho(0) \sim \delta^{\alpha}$ whose scaling exponent $\alpha$ exhibits two transitions, one at $\sigma_{th}/4$ and the other at $\sigma_{th}$. These transitions are shown to be related to the one of a directed polymer on a Cayley tree with random signs (or complex) Boltzmann weights. Some observations are made for the strong disorder regime relevant to describe transport in the quantum Hall system

Localization properties of the anomalous diffusion phase x tμx ~ t^{\mu} in the directed trap model and in the Sinai diffusion with bias

We study the anomalous diffusion phase $x ~ t^{\mu}$ with $0<\mu<1$ which exists both in the Sinai diffusion at small bias, and in the related directed trap model presenting a large distribution of trapping time $p(\tau) \sim 1/\tau^{1+\mu}$. Our starting point is the Real Space Renormalization method in which the whole thermal packet is considered to be in the same renormalized valley at large time : this assumption is exact only in the limit $\mu \to 0$ and corresponds to the Golosov localization. For finite $\mu$, we thus generalize the usual RSRG method to allow for the spreading of the thermal packet over many renormalized valleys. Our construction allows to compute exact series expansions in $\mu$ of all observables : at order $\mu^n$, it is sufficient to consider a spreading of the thermal packet onto at most $(1+n)$ traps in each sample, and to average with the appropriate measure over the samples. For the directed trap model, we show explicitly up to order $\mu^2$ how to recover the diffusion front, the thermal width, and the localization parameter $Y_2$. We moreover compute the localization parameters $Y_k$ for arbitrary $k$, the correlation function of two particles, and the generating function of thermal cumulants. We then explain how these results apply to the Sinai diffusion with bias, by deriving the quantitative mapping between the large-scale renormalized descriptions of the two models.Comment: 33 pages, 3 eps figure

Hiperuricemia y componentes del síndrome metabólico en niños y adolescentes obesos

ResumenIntroducciónLa hiperuricemia se ha observado como una alteración metabólica adicional en pacientes adultos obesos, pero es poco conocida su magnitud en pacientes pediátricos.ObjetivosAnalizar la asociación entre ácido úrico sérico (AUS) con magnitud de la obesidad general y visceral y con otras mediciones bioquímicas en niños y adolescentes obesos de Santiago, Chile.Sujetos y métodoEn un estudio transversal se evaluaron 770 niños (edades: 6-15 años) de un colegio público de Santiago, Chile, encontrando 227 obesos (29%) (IMC>2 DE, estándares OMS). Se seleccionaron aleatoriamente 90 niños y aceptaron participar 77, sin otras enfermedades crónicas. Se evaluó: peso, talla, perímetro abdominal, adiposidad visceral con ultrasonografía abdominal y mediciones metabólicas: insulinemia, glucemia (HOMA), lípidos séricos, aspartato aminotransferasa, alanina aminotransferasa (ALT) y AUS.ResultadosLas concentraciones de AUS fueron 0,200±0,065mmol/l. El AUS fue mayor en niños con valores de hiperinsulinismo (ajustado según edad): 0,221±0,075 vs 0,183±0,054mmol/l (p<0,01), sin diferencias según HOMA; las diferencias también se observaron según ALT (>vs<26 U/ml): 0,238±0,070 vs 0,178±0,054mmol/l, p<0,001; la regresión logística controlando por sexo, edad e intensidad de la obesidad mostró solo las ALT asociadas a aumento de AUS. No hubo asociación de mayor AUS con magnitud de IMC, adiposidad visceral o hígado graso.ConclusionesLos niños y adolescentes obesos de Santiago, Chile, tienen una uricemia mayor en asociación a un aumento de la actividad de la enzima ALT e hiperinsulinismo. Se justifica analizar uricemia en el estudio de niños obesos y en su seguimiento.AbstractIntroductionHyperuricaemia has been suggested as an additional metabolic factor in adult obese patients, but it has not been sufficiently studied in paediatric.ObjectivesTo assess the relationship between serum uric acid levels (SUAL) with the level of general and visceral obesity, and other biochemical parameters in children and adolescents of Santiago, Chile.Subjects and methodA cross sectional study was conducted on 770 children and adolescents (ages: 6-15 y.) from a public school in Santiago, Chile, of whom 227 (29%) were obese (BMI>2 SD, WHO growth standards). Ninety subjects were randomly selected and 77 with no other chronic disease (41 males) accepted to participate. Data was collected on weight, stature, abdominal circumference (AC), visceral adiposity using ultrasound, and other biochemical measurements including fasting glucose, insulin, serum lipids, aspartate aminotransferase (AST), alanine aminotransferase (ALT), and SUAL.ResultsThe mean SUAL was 0.200±0.065mmol/L, and was increased in children with hyperinsulinism (adjusted by age: 0.221±0.075 vs 0.183±0.054mmol/L; P<.01), with no significant differences according to HOMA. Differences were also found between children with ALT>or<26 U/mL: 0.238±0.070 vs 0.178±0.054mmol/L, P<.001. The logistic regression showed the increased SUAL was only associated with increased ALT. No significant differences were found in general or visceral adiposity measurements or fatty liver.ConclusionsChildren and adolescents from Santiago, Chile have higher uric acid serum uric acid levels as well as an association with increased ALT and insulin. It is demonstrated in this study that uric acid should be measured in obese children and adolescents, and in their follow up

Experimental observation of nonlinear Thomson scattering

A century ago, J. J. Thomson showed that the scattering of low-intensity light by electrons was a linear process (i.e., the scattered light frequency was identical to that of the incident light) and that light's magnetic field played no role. Today, with the recent invention of ultra-high-peak-power lasers it is now possible to create a sufficient photon density to study Thomson scattering in the relativistic regime. With increasing light intensity, electrons quiver during the scattering process with increasing velocity, approaching the speed of light when the laser intensity approaches 10^18 W/cm^2. In this limit, the effect of light's magnetic field on electron motion should become comparable to that of its electric field, and the electron mass should increase because of the relativistic correction. Consequently, electrons in such high fields are predicted to quiver nonlinearly, moving in figure-eight patterns, rather than in straight lines, and thus to radiate photons at harmonics of the frequency of the incident laser light, with each harmonic having its own unique angular distribution. In this letter, we report the first ever direct experimental confirmation of these predictions, a topic that has previously been referred to as nonlinear Thomson scattering. Extension of these results to coherent relativistic harmonic generation may eventually lead to novel table-top x-ray sources.Comment: including 4 figure