Free energies in the presence of electric and magnetic fields

We discuss different free energies for materials in static electric and magnetic fields. We explain what the corresponding Hamiltonians are, and describe which choice gives rise to which result for the free energy change, dF, in the thermodynamic identity. We also discuss which Hamiltonian is the most appropriate for calculations using statistical mechanics, as well as the relationship between the various free energies and the "Landau function", which has to be minimized to determine the equilibrium polarization or magnetization, and is central to Landau's theory of second order phase transitions

Combining Hebbian and reinforcement learning in a minibrain model

A toy model of a neural network in which both Hebbian learning and reinforcement learning occur is studied. The problem of `path interference', which makes that the neural net quickly forgets previously learned input-output relations is tackled by adding a Hebbian term (proportional to the learning rate $\eta$) to the reinforcement term (proportional to $\rho$) in the learning rule. It is shown that the number of learning steps is reduced considerably if $1/4 < \eta/\rho < 1/2$, i.e., if the Hebbian term is neither too small nor too large compared to the reinforcement term

Conserving Approximations in Time-Dependent Density Functional Theory

In the present work we propose a theory for obtaining successively better approximations to the linear response functions of time-dependent density or current-density functional theory. The new technique is based on the variational approach to many-body perturbation theory (MBPT) as developed during the sixties and later expanded by us in the mid nineties. Due to this feature the resulting response functions obey a large number of conservation laws such as particle and momentum conservation and sum rules. The quality of the obtained results is governed by the physical processes built in through MBPT but also by the choice of variational expressions. We here present several conserving response functions of different sophistication to be used in the calculation of the optical response of solids and nano-scale systems.Comment: 11 pages, 4 figures, revised versio

Measuring the impact of observations on the predictability of the Kuroshio Extension in a shallow-water model

In this paper sequential importance sampling is used to assess the impact of observations on a ensemble prediction for the decadal path transitions of the Kuroshio Extension (KE). This particle filtering approach gives access to the probability density of the state vector, which allows us to determine the predictive power — an entropy based measure — of the ensemble prediction. The proposed set-up makes use of an ensemble that, at each time, samples the climatological probability distribution. Then, in a post-processing step, the impact of different sets of observations is measured by the increase in predictive power of the ensemble over the climatological signal during one-year. The method is applied in an identical-twin experiment for the Kuroshio Extension using a reduced-gravity shallow water model. We investigate the impact of assimilating velocity observations from different locations during the elongated and the contracted meandering state of the KE. Optimal observations location correspond to regions with strong potential vorticity gradients. For the elongated state the optimal location is in the first meander of the KE. During the contracted state of the KE it is located south of Japan, where the Kuroshio separates from the coast

On plasma rotation and drifting subpulses in pulsars; using aligned pulsar B0826-34 as a voltmeter

We derive the exact drift velocity of plasma in the pulsar polar cap, in contrast to the order-of-magnitude expressions presented by Ruderman & Sutherland (1975) and generally used throughout the literature. We emphasize that the drift velocity depends not on the absolute value, as is generally used, but on the variation of the accelerating potential across the polar cap. If we assume that drifting subpulses in pulsars are indeed due to this plasma drift, several observed subpulse-drift phenomena that are incompatible with the Ruderman & Sutherland family of models can now be explained: we show that variations of drift rate, outright drift reversals, and the connection between drift rates and mode changes have natural explanations within the frame of the "standard" pulsar model, when derived exactly. We apply this model for drifting subpulses to the case of PSR B0826-34, an aligned pulsar with two separate subpulse-drift regions emitted at two different colatitudes. Careful measurement of the changing and reversing drift rate in each band independently sets limits on the variation of the accelerating potential drop. The derived variation is small, ~10^{-3} times the vacuum potential drop voltage. We discuss the implications of this result for pulsar modeling.Comment: version published in Ap

Crossover from Reptation to Rouse dynamics in the Cage Model

The two-dimensional cage model for polymer motion is discussed with an emphasis on the effect of sideways motions, which cross the barriers imposed by the lattice. Using the Density Matrix Method as a solver of the Master Equation, the renewal time and the diffusion coefficient are calculated as a function of the strength of the barrier crossings. A strong crossover influence of the barrier crossings is found and it is analyzed in terms of effective exponents for a given chain length. The crossover scaling functions and the crossover scaling exponents are calculated.Comment: RevTeX, 11 PostScript figures include

NGC 2362: a Template for Early Stellar Evolution

We present UBVRI photometry for the young open cluster NGC 2362. From analysis of the appropriate color-color and color-magnitude diagrams we derive the fundamental parameters of the NGC 2362 cluster to be: age = 5 (+1-2) Myr, distance = 1480 pc, E(B-V)=0.10 mag. The cluster age was independently determined for both high mass (2.1 - 36Msun) and low mass (0.7 - 1.2Msun) stars with excellent agreement between the ages derived using post-main sequence and pre-main sequence evolutionary tracks for the high and low mass stars respectively. Analysis of this cluster's color-magnitude diagram reveals a well defined pre-main sequence (covering DeltaV ~ 9 magnitudes in V and extending from early A stars to near the hydrogen burning limit) which makes this cluster an ideal laboratory for pre-main sequence evolution studies.Comment: 9 pages, 3 figures, to be published in ApJ