32,301 research outputs found
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
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
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 and is independent of the initial notch size
and disorder in breaking thresholds. The global roughness exponent scales as
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
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 . Choosing equal chemical
potentials for the two species, the SGMC switches identities () to generate well-equilibrated configurations of the system on
the coexistence curve for and at the critical concentration, ,
for . A finite-size scaling analysis of the concentration susceptibility
above and of the order parameter below 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
- …