Statistical properties of fracture in a random spring model

Using large scale numerical simulations we analyze the statistical properties of fracture in the two dimensional random spring model and compare it with its scalar counterpart: the random fuse model. We first consider the process of crack localization measuring the evolution of damage as the external load is raised. We find that, as in the fuse model, damage is initially uniform and localizes at peak load. Scaling laws for the damage density, fracture strength and avalanche distributions follow with slight variations the behavior observed in the random fuse model. We thus conclude that scalar models provide a faithful representation of the fracture properties of disordered systems.Comment: 12 pages, 17 figures, 1 gif figur

Experimental Comparisons of Derivative Free Optimization Algorithms

In this paper, the performances of the quasi-Newton BFGS algorithm, the NEWUOA derivative free optimizer, the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), the Differential Evolution (DE) algorithm and Particle Swarm Optimizers (PSO) are compared experimentally on benchmark functions reflecting important challenges encountered in real-world optimization problems. Dependence of the performances in the conditioning of the problem and rotational invariance of the algorithms are in particular investigated.Comment: 8th International Symposium on Experimental Algorithms, Dortmund : Germany (2009

Static and Dynamic Critical Behavior of a Symmetrical Binary Fluid: A Computer Simulation

A symmetrical binary, A+B Lennard-Jones mixture is studied by a combination of semi-grandcanonical Monte Carlo (SGMC) and Molecular Dynamics (MD) methods near a liquid-liquid critical temperature $T_c$. Choosing equal chemical potentials for the two species, the SGMC switches identities (${\rm A} \to {\rm B} \to {\rm A}$) to generate well-equilibrated configurations of the system on the coexistence curve for $T<T_c$ and at the critical concentration, $x_c=1/2$, for $T>T_c$. A finite-size scaling analysis of the concentration susceptibility above $T_c$ and of the order parameter below $T_c$ is performed, varying the number of particles from N=400 to 12800. The data are fully compatible with the expected critical exponents of the three-dimensional Ising universality class. The equilibrium configurations from the SGMC runs are used as initial states for microcanonical MD runs, from which transport coefficients are extracted. Self-diffusion coefficients are obtained from the Einstein relation, while the interdiffusion coefficient and the shear viscosity are estimated from Green-Kubo expressions. As expected, the self-diffusion constant does not display a detectable critical anomaly. With appropriate finite-size scaling analysis, we show that the simulation data for the shear viscosity and the mutual diffusion constant are quite consistent both with the theoretically predicted behavior, including the critical exponents and amplitudes, and with the most accurate experimental evidence.Comment: 35 pages, 13 figure

Pearson's random walk in the space of the CMB phases: evidence for parity asymmetry

The temperature fluctuations of the Cosmic Microwave Background (CMB) are supposed to be distributed randomly in both magnitude and phase, following to the simplest model of inflation. In this paper, we look at the odd and even multipoles of the spherical harmonic decomposition of the CMB, and the different characteristics of these, giving rise to a parity asymmetry. We compare the even and odd multipoles in the CMB power spectrum, and also the even and odd mean angles. We find for the multipoles of the power spectrum, that there is power excess in odd multipoles, compared to even ones, meaning that we have a parity asymmetry. Further, for the phases, we present a random walk for the mean angles, and find a significant separation for even/odd mean angles, especially so for galactic coordinates. This is further tested and confirmed with a directional parity test, comparing the parity asymmetry in galactic and ecliptic coordinates.Comment: Accepted for publication in Phys. Rev. D, 10 pages, 10 figures, 1 table. Some typographical errors corrected, and further references adde

Solvated dissipative electro-elastic network model of hydrated proteins

Elastic netwok models coarse grain proteins into a network of residue beads connected by springs. We add dissipative dynamics to this mechanical system by applying overdamped Langevin equations of motion to normal-mode vibrations of the network. In addition, the network is made heterogeneous and softened at the protein surface by accounting for hydration of the ionized residues. Solvation changes the network Hessian in two ways. Diagonal solvation terms soften the spring constants and off-diagonal dipole-dipole terms correlate displacements of the ionized residues. The model is used to formulate the response functions of the electrostatic potential and electric field appearing in theories of redox reactions and spectroscopy. We also formulate the dielectric response of the protein and find that solvation of the surface ionized residues leads to a slow relaxation peak in the dielectric loss spectrum, about two orders of magnitude slower than the main peak of protein relaxation. Finally, the solvated network is used to formulate the allosteric response of the protein to ion binding. The global thermodynamics of ion binding is not strongly affected by the network solvation, but it dramatically enhances conformational changes in response to placing a charge at the active site of the protein

Complex light: Dynamic phase transitions of a light beam in a nonlinear non-local disordered medium

The dynamics of several light filaments (spatial optical solitons) propagating in an optically nonlinear and non-local random medium is investigated using the paradigms of the physics of complexity. Cluster formation is interpreted as a dynamic phase transition. A connection with the random matrices approach for explaining the vibrational spectra of an ensemble of solitons is pointed out. General arguments based on a Brownian dynamics model are validated by the numerical simulation of a stochastic partial differential equation system. The results are also relevant for Bose condensed gases and plasma physics.Comment: 11 pages, 20 figures. Small revisions, added a referenc

Effect of Disorder and Notches on Crack Roughness

We analyze the effect of disorder and notches on crack roughness in two dimensions. Our simulation results based on large system sizes and extensive statistical sampling indicate that the crack surface exhibits a universal local roughness of $\zeta_{loc} = 0.71$ and is independent of the initial notch size and disorder in breaking thresholds. The global roughness exponent scales as $\zeta = 0.87$ and is also independent of material disorder. Furthermore, we note that the statistical distribution of crack profile height fluctuations is also independent of material disorder and is described by a Gaussian distribution, albeit deviations are observed in the tails.Comment: 6 pages, 6 figure

Suppression of hole-hole scattering in GaAs/AlGaAs heterostructures under uniaxial compression

Resistance, magnetoresistance and their temperature dependencies have been investigated in the 2D hole gas at a [001] p-GaAs/Al$_{0.5}$Ga$_{0.5}$As heterointerface under [110] uniaxial compression. Analysis performed in the frame of hole-hole scattering between carriers in the two spin splitted subbands of the ground heavy hole state indicates, that h-h scattering is strongly suppressed by uniaxial compression. The decay time $\tau_{01}$ of the relative momentum reveals 4.5 times increase at a uniaxial compression of 1.3 kbar.Comment: 5 pages, 3 figures. submitted to Phys.Rev.

Critical Dynamics in a Binary Fluid: Simulations and Finite-size Scaling

We report comprehensive simulations of the critical dynamics of a symmetric binary Lennard-Jones mixture near its consolute point. The self-diffusion coefficient exhibits no detectable anomaly. The data for the shear viscosity and the mutual-diffusion coefficient are fully consistent with the asymptotic power laws and amplitudes predicted by renormalization-group and mode-coupling theories {\it provided} finite-size effects and the background contribution to the relevant Onsager coefficient are suitably accounted for. This resolves a controversy raised by recent molecular simulations.Comment: 4 pages, 4 figure