Continuum limit of amorphous elastic bodies (III): Three dimensional systems

Extending recent numerical studies on two dimensional amorphous bodies, we characterize the approach of elastic continuum limit in three dimensional (weakly polydisperse) Lennard-Jones systems. While performing a systematic finite-size analysis (for two different quench protocols) we investigate the non-affine displacement field under external strain, the linear response to an external delta force and the low-frequency harmonic eigenmodes and their density distribution. Qualitatively similar behavior is found as in two dimensions. We demonstrate that the classical elasticity description breaks down below an intermediate length scale $\xi$, which in our system is approximately 23 molecular sizes. This length characterizes the correlations of the non-affine displacement field, the self-averaging of external noise with distance from the source and gives the lower wave length bound for the applicability of the classical eigenfrequency calculations. We trace back the "Boson-peak" of the density of eigenfrequencies (obtained from the velocity auto-correlation function) to the inhomogeneities on wave lengths smaller than $\xi$.Comment: 27 pages, 11 figures, submitted to Phys. Rev.

Particle displacements in the elastic deformation of amorphous materials: local fluctuations vs. non-affine field

We study the local disorder in the deformation of amorphous materials by decomposing the particle displacements into a continuous, inhomogeneous field and the corresponding fluctuations. We compare these fields to the commonly used non-affine displacements in an elastically deformed 2D Lennard-Jones glass. Unlike the non-affine field, the fluctuations are very localized, and exhibit a much smaller (and system size independent) correlation length, on the order of a particle diameter, supporting the applicability of the notion of local "defects" to such materials. We propose a scalar "noise" field to characterize the fluctuations, as an additional field for extended continuum models, e.g., to describe the localized irreversible events observed during plastic deformation.Comment: Minor corrections to match the published versio

Vibrations of amorphous, nanometric structures: When does continuum theory apply?

Structures involving solid particles of nanometric dimensions play an increasingly important role in material sciences. These structures are often characterized through the vibrational properties of their constituent particles, which can be probed by spectroscopic methods. Interpretation of such experimental data requires an extension of continuum elasticity theory down to increasingly small scales. Using numerical simulation and exact diagonalization for simple models, we show that continuum elasticity, applied to disordered system, actually breaks down below a length scale of typically 30 to 50 molecular sizes. This length scale is likely related to the one which is generally invoked to explain the peculiar vibrational properties of glassy systems.Comment: 4 pages, 5 figures, LATEX, Europhysics Letters accepte

Storage Device Sizing for a Hybrid Railway Traction System by Means of Bicausal Bond Graphs

In this paper, the application of bicausal bond graphs for system design in electrical engineering is emphasized. In particular, it is shown how this approach is very useful for model inversion and parameter dimensioning. To illustrate these issues, a hybrid railway traction device is considered as a case study. The synthesis of a storage device (a supercapacitor) included in this system is then discussed

What is the probability of connecting two points ?

The two-terminal reliability, known as the pair connectedness or connectivity function in percolation theory, may actually be expressed as a product of transfer matrices in which the probability of operation of each link and site is exactly taken into account. When link and site probabilities are $p$ and $\rho$, it obeys an asymptotic power-law behavior, for which the scaling factor is the transfer matrix's eigenvalue of largest modulus. The location of the complex zeros of the two-terminal reliability polynomial exhibits structural transitions as $0 \leq \rho \leq 1$.Comment: a few critical polynomials are at the end of the .tex source fil

Collective Behavior of Asperities in Dry Friction at Small Velocities

We investigate a simple model of dry friction based on extremal dynamics of asperities. At small velocities, correlations develop between the asperities, whose range becomes infinite in the limit of infinitely slow driving, where the system is self-organized critical. This collective phenomenon leads to effective aging of the asperities and results in velocity dependence of the friction force in the form $F\sim 1- \exp(-1/v)$.Comment: 7 pages, 8 figures, revtex, submitted to Phys. Rev.

Growth of Infants Fed Formula with Evolving Nutrition Composition: A Single-Arm Non-Inferiority Study.

The nutritional composition of human milk evolves over the course of lactation, to match the changing needs of infants. This single-arm, non-inferiority study evaluated growth against the WHO standards in the first year of life, in infants consecutively fed four age-based formulas with compositions tailored to infants' nutritional needs during the 1st, 2nd, 3rd-6th, and 7th-12th months of age. Healthy full-term formula-fed infants (n = 32) were enrolled at ≤14 days of age and exclusively fed study formulas from enrollment, to the age of four months. Powdered study formulas were provided in single-serving capsules that were reconstituted using a dedicated automated preparation system, to ensure precise, hygienic preparation. The primary outcome was the weight-for-age z-score (WAZ) at the age of four months (vs. non-inferiority margin of -0.5 SD). Mean (95% CI) z-scores for the WAZ (0.12 (-0.15, 0.39)), as well as for the length-for-age (0.05 (-0.19, 0.30)), weight-for-length (0.16 (-0.16, 0.48)), BMI-for-age (0.11 (-0.20, 0.43)), and head circumferencefor-age (0.41 (0.16, 0.65)) at the age of four months, were non-inferior. Throughout the study, anthropometric z-scores tracked closely against the WHO standards (within ±1 SD). In sum, a fourstage, age-based infant formula system with nutritional compositions tailored to infants' evolving needs, supports healthy growth consistent with WHO standards, for the first year of life