Time reparametrization invariance in arbitrary range p-spin models: symmetric versus non-symmetric dynamics

We explore the existence of time reparametrization symmetry in p-spin models. Using the Martin-Siggia-Rose generating functional, we analytically probe the long-time dynamics. We perform a renormalization group analysis where we systematically integrate over short timescale fluctuations. We find three families of stable fixed points and study the symmetry of those fixed points with respect to time reparametrizations. One of those families is composed entirely of symmetric fixed points, which are associated with the low temperature dynamics. The other two families are composed entirely of non-symmetric fixed points. One of these two non-symmetric families corresponds to the high temperature dynamics. Time reparametrization symmetry is a continuous symmetry that is spontaneously broken in the glass state and we argue that this gives rise to the presence of Goldstone modes. We expect the Goldstone modes to determine the properties of fluctuations in the glass state, in particular predicting the presence of dynamical heterogeneity.Comment: v2: Extensively modified to discuss both high temperature (non-symmetric) and low temperature (symmetric) renormalization group fixed points. Now 16 pages with 1 figure. v1: 13 page

Generalized hydrodynamics of a dilute finite-sized particles suspension: Dynamic viscosity

We present a mesoscopic hydrodynamic description of the dynamics of colloidal suspensions. We consider the system as a gas of Brownian particles suspended in a Newtonian heat bath subjected to stationary non-equilibrium conditions imposed by a velocity field. Using results already obtained in previous studies in the field by means of a generalized Fokker-Planck equation, we obtain a set of coupled differential equations for the local diffusion current and the evolution of the total stress tensor. We find that the dynamic shear viscosity of the system contains contributions arising from the finite size of the particles.Comment: To appear in Physical Review

Dimensionalities of Weak Solutions in Hydrogenic Systems

A close inspection on the 3D hydrogen atom Hamiltonian revealed formal eigenvectors often discarded in the literature. Although not in its domain, such eigenvectors belong to the Hilbert space, and so their time evolution is well defined. They are then related to the 1D and 2D hydrogen atoms and it is numerically found that they have continuous components, so that ionization can take place

Quasiclassical trajectory study of the dynamics of the H+N₂O reaction on a new potential energy surface

A new ab initiopotential energy surface (PES) for the H+N₂O→OH+N₂reaction has been constructed using the GROW package of Collins and co-workers. The ab initio calculations have been done using the Becke three-parameter nonlocal exchange functional with the nonlocal correlation of Lee, Yang, and Parr density functional theory. A detailed quasiclassical trajectory study of integral and differential cross sections, product rovibrational populations, and internal energy distributions on the new PES is presented. The theoretical integral cross sections as a function of collision energy are in qualitative agreement with the experimental measurements. A good correspondence is found between the calculated OH(v′=0,1) rovibrational populations and the recent measurements of Brouard and co-workers at 1.48 eV collision energy. In particular, the calculated kinetic energy release distributions for state resolved OH(v′,N′) products predict a substantial fraction of total energy going into rotational excitation of the N₂ co-product, in good agreement with the experimental findings.The Spanish part of this work has been financed by DGES of Spain (Project No. PB98-0762-C02-01) and by the European Commission within the RT Network Reaction Dynamics (Contract No. HPRN-CT-1999-00007)

A comparison between PML, infinite elements and an iterative BEM as mesh truncation methods for HP self-adaptive procedures in electromagnetics

Finite element hp-adaptivity is a technology that allows for very accurate numerical solutions. When applied to open region problems such as radar cross section prediction or antenna analysis, a mesh truncation method needs to be used. This paper compares the following mesh truncation methods in the context of hp-adaptive methods: Infinite Elements, Perfectly Matched Layers and an iterative boundary element based methodology. These methods have been selected because they are exact at the continuous level (a desirable feature required by the extreme accuracy delivered by the hp-adaptive strategy) and they are easy to integrate with the logic of hp-adaptivity. The comparison is mainly based on the number of degrees of freedom needed for each method to achieve a given level of accuracy. Computational times are also included. Two-dimensional examples are used, but the conclusions directly extrapolated to the three dimensional case

Fluctuations of two-time quantities and time-reparametrization invariance in spin-glasses

This article is a contribution to the understanding of fluctuations in the out of equilibrium dynamics of glassy systems. By extending theoretical ideas based on the assumption that time-reparametrization invariance develops asymptotically we deduce the scaling properties of diverse high-order correlation functions. We examine these predictions with numerical tests in a standard glassy model, the 3d Edwards-Anderson spin-glass, and in a system where time-reparametrization invariance is not expected to hold, the 2d ferromagnetic Ising model, both at low temperatures. Our results enlighten a qualitative difference between the fluctuation properties of the two models and show that scaling properties conform to the time-reparametrization invariance scenario in the former but not in the latter.Comment: 17 pages, 5 figure

Effect of Roughness in the Development of an Adverse Pressure Gradient Turbulent Boundary Layer

An experimental study was conducted to examine the effect of surface roughness on the development of an adverse pressure gradient turbulent boundary layer. Hot-wire anemometry measurements were carried out using single and x-wire probes in the APG region of an open return type wind tunnel test section. The same experimental conditions (i.e. T∞, Uref, and Cp) are maintained between the smooth, k+= 0, and rough, k+= 41-60, cases. Results indicate that the mean velocity deficit and Reynolds stress profiles tend to increase with surface roughness. These effects of roughness were successfully removed from the outer mean velocity profiles using the Zagarola and Smits scaling, U∞δ*/δ. Using the integrated boundary layer equation, the skin friction was computed and showed a 58% increase due to the surface roughness effect. The effects of pressure gradient were found to be significant, of which, different profile trends with similar magnitudes were found for outer Reynolds normal stresses scaled with U∞

Experimental procedures for precision measurements of the Casimir force with an Atomic Force Microscope

Experimental methods and procedures required for precision measurements of the Casimir force are presented. In particular, the best practices for obtaining stable cantilevers, calibration of the cantilever, correction of thermal and mechanical drift, measuring the contact separation, sphere radius and the roughness are discussed.Comment: 14 pages, 7 figure