A Stochastic Description for Extremal Dynamics

We show that extremal dynamics is very well modelled by the "Linear Fractional Stable Motion" (LFSM), a stochastic process entirely defined by two exponents that take into account spatio-temporal correlations in the distribution of active sites. We demonstrate this numerically and analytically using well-known properties of the LFSM. Further, we use this correspondence to write an exact expressions for an n-point correlation function as well as an equation of fractional order for interface growth in extremal dynamics.Comment: 4 pages LaTex, 3 figures .ep

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.

Early presentation of primary glioblastoma

Background Clinical and neuroimaging findings of glioblastomas (GBM) at an early stage have rarely been described and those tumors are most probably under-diagnosed. Furthermore, their genetic alterations, to our knowledge, have never been previously reported. Methods We report the clinical as well as neuroimaging findings of four early cases of patients with GBM. Results In our series, early stage GBM occurred at a mean age of 57 years. All patients had seizures as their first symptom. In all early stages, MRI showed a hyperintense signal on T2-weighted sequences and an enhancement on GdE-T1WI sequences. A hyperintense signal on diffusion sequences with a low ADC value was also found. These early observed occurrences of GBM developed rapidly and presented the MRI characteristics of classic GBM within a few weeks. The GBM size was multiplied by 32 in one month. Immunohistochemical analysis indicated the de novo nature of these tumors, i.e. absence of mutant IDH1 R132H protein expression, which is a diagnostic marker of low-grade diffuse glioma and secondary GBM. Conclusions A better knowledge of early GBM presentation would allow a more suitable management of the patients and may improve their prognosis

Inhomogeneous elastic response of silica glass

Using large scale molecular dynamics simulations we investigate the properties of the {\em non-affine} displacement field induced by macroscopic uniaxial deformation of amorphous silica,a strong glass according to Angell's classification. We demonstrate the existence of a length scale $\xi$ characterizing the correlations of this field (corresponding to a volume of about 1000 atoms), and compare its structure to the one observed in a standard fragile model glass. The "Boson-peak'' anomaly of the density of states can be traced back in both cases to elastic inhomogeneities on wavelengths smaller than $\xi$, where classical continuum elasticity becomes simply unapplicable

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.

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

From Individual to Collective Pinning: Effect of Long-range Elastic Interactions

We study the effect of long-range elastic interactions in the dynamical behavior of an elastic chain driven quasi-statically in a quenched random pinning potential and in the strong pinning limit. This is a generic situation occuring in solid friction, crack propagation, wetting front motion, ... Tuning the exponent of the algebraic decay of the elastic interaction with the distance is shown to give rise to three regimes: a Mean-Field (MF) regime, a Laplacian (L) regime and an intermediate regime where the critical exponents interpolate continuously between the MF and L limit cases. The effect of the driving mode on the avalanche statistics is also analyzed.Comment: 28 pages in RevTex, 17 figure

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

Unique and universal dew-repellency of nanocones

Surface structuring provides a broad range of water-repellent materials known for their ability to reflect millimetre-sized raindrops. Dispelling water at the considerably reduced scale of fog or dew, however, constitutes a significant challenge, owing to the comparable size of droplets and structures. Nonetheless, a surface comprising nanocones was recently reported to exhibit strong anti-fogging behaviour, unlike pillars of the same size. To elucidate the origin of these differences, we systematically compare families of nanotexture that transition from pillars to sharp cones. Through environmental electron microscopy and modelling, we show that microdroplets condensing on sharp cones adopt a highly non-adhesive state, even at radii as low as 1.5 µm, contrasting with the behaviour on pillars where pinning results in impedance of droplet ejection. We establish the antifogging abilities to be universal over the range of our cone geometries, which speaks to the unique character of the nanocone geometry to repel dew. Truncated cones are finally shown to provide both pinning and a high degree of hydrophobicity, opposing characteristics that lead to a different, yet efficient, mechanism of dew ejection that relies on multiple coalescences