Analytical description of stochastic field-Line wandering in magnetic turbulence

A nonperturbative nonlinear statistical approach is presented to describe turbulent magnetic systems embedded in a uniform mean magnetic field. A general formula in the form of an ordinary differential equation for magnetic field-line wandering (random walk) is derived. By considering the solution of this equation for different limits several new results are obtained. As an example, it is demonstrated that the stochastic wandering of magnetic field-lines in a two-component turbulence model leads to superdiffusive transport, contrary to an existing diffusive picture. The validity of quasilinear theory for field-line wandering is discussed, with respect to different turbulence geometry models, and previous diffusive results are shown to be deduced in appropriate limits.

Stochastic protein folding simulation in the three-dimensional HP-model

We present results from three-dimensional protein folding simulations in the HP-model on ten benchmark problems. The simulations are executed by a simulated annealing-based algorithm with a time-dependent cooling schedule. The neighbourhood relation is determined by the pull-move set. The results provide experimental evidence that the maximum depth D of local minima of the underlying energy landscape can be upper bounded by D < n(2/3). The local search procedure employs the stopping criterion (In/delta)(D/gamma) where m is an estimation of the average number of neighbouring conformations, gamma relates to the mean of non-zero differences of the objective function for neighbouring conformations, and 1-delta is the confidence that a minimum conformation has been found. The bound complies with the results obtained for the ten benchmark problems. (c) 2008 Elsevier Ltd. All rights reserved.

Effect of quantization of vibrations on the structural properties of crystals

We study the structural effects produced by the quantization of vibrational degrees of freedom in periodic crystals at zero temperature. To this end we introduce a methodology based on mapping a suitable subspace of the vibrational manifold and solving the Schrödinger equation in it. A number of increasingly accurate approximations ranging from the quasiharmonic approximation (QHA) to the vibrational self-consistent field (VSCF) method and the exact solution are described. A thorough analysis of the approximations is presented for model monatomic and hydrogen-bonded chains, and results are presented for a linear H-F chain where the potential-energy surface is obtained via first-principles electronic structure calculations. We focus on quantum nuclear effects on the lattice constant and show that the VSCF is an excellent approximation, meaning that correlation between modes is not extremely important. The QHA is excellent for covalently bonded mildly anharmonic systems, but it fails for hydrogen-bonded ones. In the latter, the zero-point energy exhibits a nonanalytic behavior at the lattice constant where the H atoms center, which leads to a spurious secondary minimum in the quantum-corrected energy curve. An inexpensive anharmonic approximation of noninteracting modes appears to produce rather good results for hydrogen-bonded chains for small system sizes. However, it converges to the incorrect QHA results for increasing size. Isotope effects are studied for the first-principles H-F chain. We show how the lattice constant and the H-F distance increase with decreasing mass and how the QHA proves to be insufficient to reproduce this behavior.

Cost function adaptation: a stochastic gradient algorithm for data echo cancellation

A family of stochastic gradient algorithms and their behaviour in the data echo cancellation work platform are presented. The cost function adaptation algorithms use an error exponent update strategy based on an absolute error mapping, which is updated at every iteration. The quadratic and nonquadratic cost functions are special cases of the new family. Several possible realisations are introduced using these approaches. The noisy error problem is discussed and the digital recursive filter estimator is proposed. The simulation outcomes confirm the effectiveness of the proposed family of algorithms.

Control-limited perfect state transfer, quantum stochastic resonance, and many-body entangling gate in imperfect qubit registers

We propose a protocol for perfect quantum state transfer that is resilient to a broad class of realistic experimental imperfections, including noise sources that could be modeled either as independent Markovian baths or as certain forms of spatially correlated environments. We highlight interesting connections between the fidelity of state transfer and quantum stochastic resonance effects. The scheme is flexible enough to act as an effective entangling gate for the generation of genuine multipartite entanglement in a control-limited setting. Possible experimental implementations using superconducting qubits are also briefly discussed.

Stochastic analysis of free surface flow through earth dams

This research investigated the unconfined flow through dams. The hydraulic conductivity was modeled as spatially random field following lognormal distribution. Results showed that the seepage flow produced from the stochastic solution was smaller than its deterministic value. In addition, the free surface was observed to exit at a point lower than that obtained from the deterministic solution. When the hydraulic conductivity was strongly correlated in the horizontal direction than the vertical direction, the flow through the dam has markedly increased. It is suggested that it may not be necessary to construct a core in dams made from soils that exhibit high degree of variability.