Functional Methods and Effective Potentials for Nonlinear Composites

A formulation of variational principles in terms of functional integrals is proposed for any type of local plastic potentials. The minimization problem is reduced to the computation of a path integral. This integral can be used as a starting point for different approximations. As a first application, it is shown how to compute to second-order the weak-disorder perturbative expansion of the effective potentials in random composite. The three-dimensional results of Suquet and Ponte-Casta\~neda (1993) for the plastic dissipation potential with uniform applied tractions are retrieved and extended to any space dimension, taking correlations into account. In addition, the viscoplastic potential is also computed for uniform strain rates.Comment: 20 pages, accepted for publication in JMP

Exact results and scaling properties of small-world networks

We study the distribution function for minimal paths in small-world networks. Using properties of this distribution function, we derive analytic results which greatly simplify the numerical calculation of the average minimal distance, $\bar{\ell}$, and its variance, $\sigma^2$. We also discuss the scaling properties of the distribution function. Finally, we study the limit of large system sizes and obtain some analytic results.Comment: RevTeX, 4 pages, 5 figures included. Minor corrections and addition

Phase diagram of the Bose-Hubbard Model on Complex Networks

Critical phenomena can show unusual phase diagrams when defined in complex network topologies. The case of classical phase transitions such as the classical Ising model and the percolation transition has been studied extensively in the last decade. Here we show that the phase diagram of the Bose-Hubbard model, an exclusively quantum mechanical phase transition, also changes significantly when defined on random scale-free networks. We present a mean-field calculation of the model in annealed networks and we show that when the second moment of the average degree diverges the Mott-insulator phase disappears in the thermodynamic limit. Moreover we study the model on quenched networks and we show that the Mott-insulator phase disappears in the thermodynamic limit as long as the maximal eigenvalue of the adjacency matrix diverges. Finally we study the phase diagram of the model on Apollonian scale-free networks that can be embedded in 2 dimensions showing the extension of the results also to this case.Comment: (6 pages, 4 figures

Nearly total spin polarization in La2/3Sr1/3MnO3 from tunneling experiments

We have performed magnetotransport measurements on La2/3Sr1/3MnO3 / SrTiO3 / La2/3Sr1/3MnO3 magnetic tunnel junctions. A magnetoresistance ratio of more than 1800 % is obtained at 4K, from which we infer an electrode spin polarization of at least 95 %. This result strongly underscores the half-metallic nature of mixed-valence manganites and demonstrates its capability as a spin analyzer. The magnetoresistance extends up to temperatures of more than 270K. We argue that these improvements over most previous works may result from optimizing the patterning process for oxide heterostructures.Comment: to appear in Applied Physics Letter

Surface effects on nanowire transport: numerical investigation using the Boltzmann equation

A direct numerical solution of the steady-state Boltzmann equation in a cylindrical geometry is reported. Finite-size effects are investigated in large semiconducting nanowires using the relaxation-time approximation. A nanowire is modelled as a combination of an interior with local transport parameters identical to those in the bulk, and a finite surface region across whose width the carrier density decays radially to zero. The roughness of the surface is incorporated by using lower relaxation-times there than in the interior. An argument supported by our numerical results challenges a commonly used zero-width parametrization of the surface layer. In the non-degenerate limit, appropriate for moderately doped semiconductors, a finite surface width model does produce a positive longitudinal magneto-conductance, in agreement with existing theory. However, the effect is seen to be quite small (a few per cent) for realistic values of the wire parameters even at the highest practical magnetic fields. Physical insights emerging from the results are discussed.Comment: 15 pages, 7 figure

XY model in small-world networks

The phase transition in the XY model on one-dimensional small-world networks is investigated by means of Monte-Carlo simulations. It is found that long-range order is present at finite temperatures, even for very small values of the rewiring probability, suggesting a finite-temperature transition for any nonzero rewiring probability. Nature of the phase transition is discussed in comparison with the globally-coupled XY model.Comment: 5 pages, accepted in PR

Time evolution of damage under variable ranges of load transfer

We study the time evolution of damage in a fiber bundle model in which the range of interaction of fibers varies through an adjustable stress transfer function recently introduced. We find that the lifetime of the material exhibits a crossover from mean field to short range behavior as in the static case. Numerical calculations showed that the value at which the transition takes place depends on the system's disorder. Finally, we have performed a microscopic analysis of the failure process. Our results confirm that the growth dynamics of the largest crack is radically different in the two limiting regimes of load transfer during the first stages of breaking.Comment: 8 pages, 7 figures, revtex4 styl

Density of states in random lattices with translational invariance

We propose a random matrix approach to describe vibrational excitations in disordered systems. The dynamical matrix M is taken in the form M=AA^T where A is some real (not generally symmetric) random matrix. It guaranties that M is a positive definite matrix which is necessary for mechanical stability of the system. We built matrix A on a simple cubic lattice with translational invariance and interaction between nearest neighbors. We found that for certain type of disorder phonons cannot propagate through the lattice and the density of states g(w) is a constant at small w. The reason is a breakdown of affine assumptions and inapplicability of the elasticity theory. Young modulus goes to zero in the thermodynamic limit. It strongly reminds of the properties of a granular matter at the jamming transition point. Most of the vibrations are delocalized and similar to diffusons introduced by Allen, Feldman et al., Phil. Mag. B v.79, 1715 (1999).Comment: 4 pages, 5 figure