Reinforcing aluminum alloys with high strength fibers

A study is made of the possibility of reinforcing aluminum and aluminum based alloys with fibers made of high strength steel wire. The method of introducing the fibers is described in detail. Additional strengthening by reinforcement of the high alloy system Al - An - Mg was investigated

Exact ground state for a class of matrix Hamiltonian models: quantum phase transition and universality in the thermodynamic limit

By using a recently proposed probabilistic approach, we determine the exact ground state of a class of matrix Hamiltonian models characterized by the fact that in the thermodynamic limit the multiplicities of the potential values assumed by the system during its evolution are distributed according to a multinomial probability density. The class includes i) the uniformly fully connected models, namely a collection of states all connected with equal hopping coefficients and in the presence of a potential operator with arbitrary levels and degeneracies, and ii) the random potential systems, in which the hopping operator is generic and arbitrary potential levels are assigned randomly to the states with arbitrary probabilities. For this class of models we find a universal thermodynamic limit characterized only by the levels of the potential, rescaled by the ground-state energy of the system for zero potential, and by the corresponding degeneracies (probabilities). If the degeneracy (probability) of the lowest potential level tends to zero, the ground state of the system undergoes a quantum phase transition between a normal phase and a frozen phase with zero hopping energy. In the frozen phase the ground state condensates into the subspace spanned by the states of the system associated with the lowest potential level.Comment: 31 pages, 13 figure

Analytical probabilistic approach to the ground state of lattice quantum systems: exact results in terms of a cumulant expansion

We present a large deviation analysis of a recently proposed probabilistic approach to the study of the ground-state properties of lattice quantum systems. The ground-state energy, as well as the correlation functions in the ground state, are exactly determined as a series expansion in the cumulants of the multiplicities of the potential and hopping energies assumed by the system during its long-time evolution. Once these cumulants are known, even at a finite order, our approach provides the ground state analytically as a function of the Hamiltonian parameters. A scenario of possible applications of this analyticity property is discussed.Comment: 26 pages, 5 figure

On the Thermodynamic Limit in Random Resistors Networks

We study a random resistors network model on a euclidean geometry \bt{Z}^d. We formulate the model in terms of a variational principle and show that, under appropriate boundary conditions, the thermodynamic limit of the dissipation per unit volume is finite almost surely and in the mean. Moreover, we show that for a particular thermodynamic limit the result is also independent of the boundary conditions.Comment: 14 pages, LaTeX IOP journal preprint style file `ioplppt.sty', revised version to appear in Journal of Physics

The low-density/high-density liquid phase transition for model globular proteins

The effect of molecule size (excluded volume) and the range of interaction on the surface tension, phase diagram and nucleation properties of a model globular protein is investigated using a combinations of Monte Carlo simulations and finite temperature classical Density Functional Theory calculations. We use a parametrized potential that can vary smoothly from the standard Lennard-Jones interaction characteristic of simple fluids, to the ten Wolde-Frenkel model for the effective interaction of globular proteins in solution. We find that the large excluded volume characteristic of large macromolecules such as proteins is the dominant effect in determining the liquid-vapor surface tension and nucleation properties. The variation of the range of the potential only appears important in the case of small excluded volumes such as for simple fluids. The DFT calculations are then used to study homogeneous nucleation of the high-density phase from the low-density phase including the nucleation barriers, nucleation pathways and the rate. It is found that the nucleation barriers are typically only a few $k_{B}T$ and that the nucleation rates substantially higher than would be predicted by Classical Nucleation Theory.Comment: To appear in Langmui

Quantum Fourier transform, Heisenberg groups and quasiprobability distributions

This paper aims to explore the inherent connection among Heisenberg groups, quantum Fourier transform and (quasiprobability) distribution functions. Distribution functions for continuous and finite quantum systems are examined first as a semiclassical approach to quantum probability distribution. This leads to studying certain functionals of a pair of "conjugate" observables, connected via the quantum Fourier transform. The Heisenberg groups emerge naturally from this study and we take a rapid look at their representations. The quantum Fourier transform appears as the intertwining operator of two equivalent representation arising out of an automorphism of the group. Distribution functions correspond to certain distinguished sets in the group algebra. The marginal properties of a particular class of distribution functions (Wigner distributions) arise from a class of automorphisms of the group algebra of the Heisenberg group. We then study the reconstruction of Wigner function from the marginal distributions via inverse Radon transform giving explicit formulas. We consider applications of our approach to quantum information processing and quantum process tomography.Comment: 39 page

Blackwell-Optimal Strategies in Priority Mean-Payoff Games

We examine perfect information stochastic mean-payoff games - a class of games containing as special sub-classes the usual mean-payoff games and parity games. We show that deterministic memoryless strategies that are optimal for discounted games with state-dependent discount factors close to 1 are optimal for priority mean-payoff games establishing a strong link between these two classes

Energy-Sensitive and "Classical-like" Distances Between Quantum States

We introduce the concept of the ``polarized'' distance, which distinguishes the orthogonal states with different energies. We also give new inequalities for the known Hilbert-Schmidt distance between neighbouring states and express this distance in terms of the quasiprobability distributions and the normally ordered moments. Besides, we discuss the distance problem in the framework of the recently proposed ``classical-like'' formulation of quantum mechanics, based on the symplectic tomography scheme. The examples of the Fock, coherent, ``Schroedinger cats,'' squeezed, phase, and thermal states are considered.Comment: 23 pages, LaTex, 2 eps figures, to appear in Physica Script