Extended Scaling for the high dimension and square lattice Ising Ferromagnets

In the high dimension (mean field) limit the susceptibility and the second moment correlation length of the Ising ferromagnet depend on temperature as chi(T)=tau^{-1} and xi(T)=T^{-1/2}tau^{-1/2} exactly over the entire temperature range above the critical temperature T_c, with the scaling variable tau=(T-T_c)/T. For finite dimension ferromagnets temperature dependent effective exponents can be defined over all T using the same expressions. For the canonical two dimensional square lattice Ising ferromagnet it is shown that compact "extended scaling" expressions analogous to the high dimensional limit forms give accurate approximations to the true temperature dependencies, again over the entire temperature range from T_c to infinity. Within this approach there is no cross-over temperature in finite dimensions above which mean-field-like behavior sets in.Comment: 6 pages, 6 figure

Determination of Gd concentration profile in UO2-Gd2O3 fuel pellets

A transversal mapping of the Gd concentration was measured in UO2-Gd2O3 nuclear fuel pellets by electron paramagnetic resonance spectroscopy (EPR). The quantification was made from the comparison with a Gd2O3 reference sample. The nominal concentration in the pellets is UO2: 7.5 % Gd2O3. A concentration gradient was found, which indicates that the Gd2O3 amount diminishes towards the edges of the pellets. The concentration varies from (9.3 +/- 0.5)% in the center to (5.8 +/- 0.3)% in one of the edges. The method was found to be particularly suitable for the precise mapping of the distribution of Gd3+ ions in the UO2 matrix.Comment: 10 pages, 5 figures, 2 tables. Submitted to Journal of Nuclear Material

Neuronal bursting: interactions of the persistent sodium and CAN currents

The pre-Botzinger complex (pBC) is a heterogeneous neuronal network within the mammalian brainstem and has been experimentally found to generate robust, synchronous bursts [1]. Significant modeling research has been conducted on characterizing the dynamics of individual neurons within the pBC. [2, 3] It is well known that the persistent sodium current (INaP) contributes to square-wave bursting seen in the pBC [4]. Recent experimental work within the pBC identified a signaling cascade that starts with presynaptic glutamate and ends with the release of intracellular calcium that activates a nonspecific cationic current (ICAN) [5]. A subsequent model demonstrated that ICAN may contribute to bursts within the pBC that exhibit depolarization block [6]. With these two mechanisms for generating bursts present within the pBC, an open question is how do they combine to generate the robust bursts seen in the network? The present work seeks to analyze the result of including both INaP and ICAN within the same model. We consider the effects of heterogeneity in the conductance gNaP of INaP and the conductance gCAN of ICAN; with this heterogeneity in mind, the model cell may be quiescent, tonically active, have only square-wave bursts, have only depolarization-block exhibiting bursts, or may show both types of bursting. Using the mathematical tools of bifurcation analysis and slow-fast decomposition, we illuminate the mechanisms underlying the transitions of a model cell between the types of dynamics listed above. Our results show that, in cases where gCAN is relatively high, increasing gNaP increases the range of gCAN where the resultant cell has depolarization-block exhibiting bursts. On the other hand, when gCAN is relatively low, increasing gNaP may cause the cell to transition from quiescence, to square wave bursting, to tonic activity, to square wave bursts with high duty cycles, and finally further increase of gNaP causes the cell to again be tonically active. The latter two transitions do not occur if ICAN is absent. The interactions of ICAN and INaP are relevant to many systems beyond the pBC. Individually, ICAN and INaP have been focused on as important to rhythmic burst generation in other systems such as the entorhinal cortex [7]; however, it is likely that both currents are present in these systems. Thus, a detailed account for the interaction of ICAN and INaP may help explain the rhythm generation encountered in other systems beyond the pBC

New extended high temperature series for the N-vector spin models on three-dimensional bipartite lattices

High temperature expansions for the susceptibility and the second correlation moment of the classical N-vector model (O(N) symmetric Heisenberg model) on the sc and the bcc lattices are extended to order $\beta^{19}$ for arbitrary N. For N= 2,3,4.. we present revised estimates of the critical parameters from the newly computed coefficients.Comment: 11 pages, latex, no figures, to appear in Phys. Rev.

High-Temperature series for the RPn−1RP^{n-1} lattice spin model (generalized Maier-Saupe model of nematic liquid crystals) in two space dimensions and with general spin dimensionality n

High temperature series expansions of the spin-spin correlation functions of the RP^{n-1} spin model on the square lattice are computed through order beta^{8} for general spin dimensionality n. Tables are reported for the expansion coefficients of the energy per site, the susceptibility and the second correlation moment.Comment: 6 pages, revtex, IFUM 419/FT, 2 figures not include

Correlation between magnetic interactions and domain structure in A1 FePt ferromagnetic thin films

We have investigated the relationship between the domain structure and the magnetic interactions in a series of FePt ferromagnetic thin films of varying thickness. As-made films grow in the magnetically soft and chemically disordered A1 phase that may have two distinct domain structures. Above a critical thickness $d_{cr}\sim 30$ nm the presence of an out of plane anisotropy induces the formation of stripes, while for $d<d_{cr}$ planar domains occur. Magnetic interactions have been characterized using the well known DCD-IRM remanence protocols, $\delta M$ plots, and magnetic viscosity measurements. We have observed a strong correlation between the domain configuration and the sign of the magnetic interactions. Planar domains are associated with positive exchange-like interactions, while stripe domains have a strong negative dipolar-like contribution. In this last case we have found a close correlation between the interaction parameter and the surface dipolar energy of the stripe domain structure. Using time dependent magnetic viscosity measurements, we have also estimated an average activation volume for magnetic reversal, $\langle V_{ac}\rangle \sim 1.37\times 10^{4}$ nm$^{3},$ which is approximately independent of the film thickness or the stripe period.Comment: 25 pages, 11 figure

The RANLUX generator: resonances in a random walk test

Using a recently proposed directed random walk test, we systematically investigate the popular random number generator RANLUX developed by Luescher and implemented by James. We confirm the good quality of this generator with the recommended luxury level. At a smaller luxury level (for instance equal to 1) resonances are observed in the random walk test. We also find that the lagged Fibonacci and Subtract-with-Carry recipes exhibit similar failures in the random walk test. A revised analysis of the corresponding dynamical systems leads to the observation of resonances in the eigenvalues of Jacobi matrix.Comment: 18 pages with 14 figures, Essential addings in the Abstract onl

High-temperature expansions through order 24 for the two-dimensional classical XY model on the square lattice

The high-temperature expansion of the spin-spin correlation function of the two-dimensional classical XY (planar rotator) model on the square lattice is extended by three terms, from order 21 through order 24, and analyzed to improve the estimates of the critical parameters.Comment: 7 pages, 2 figure

Universality Class of O(N)O(N) Models

We point out that existing numerical data on the correlation length and magnetic susceptibility suggest that the two dimensional $O(3)$ model with standard action has critical exponent $\eta=1/4$, which is inconsistent with asymptotic freedom. This value of $\eta$ is also different from the one of the Wess-Zumino-Novikov-Witten model that is supposed to correspond to the $O(3)$ model at $\theta=\pi$.Comment: 8 pages, with 3 figures included, postscript. An error concerning the errors has been correcte