Sigma Ij Research Articles

Phase transitions in Ising square antiferromagnets with first- and second-neighbour interactions

The phase transitions occurring in the Ising square antiferromagnet with first- (J1) and second- (J2) nearest-neighbour interactions are studied using several mean-field approximations and for a wide range of R=J2/J1. The largest approximation used corresponds to a nine-point cluster approximation of the cluster variation method. In this case, the transition temperatures as a function of R are found to be in excellent agreement with those obtained by other methods. The mean-field approximations predict a first-order transition in the range 0.5<R<or approximately=1.2, where the critical exponents associated with the paramagnetic to superantiferromagnetic transition have been reported to vary continuously with R. In that range of R, the mean-field approximations also predict a crossover between two distinct instability temperatures, or spinodals, taking place immediately below the first-order transition. Mean-field results are also given for the magnetization m, the specific heat Cnu , the magnetic susceptibility X, the staggered susceptibility Xs, and the pair correlation function sigma ij between i and j sites.

Magnetism and exchange in the layered antiferromagnet NiPS3

The anisotropic susceptibility of the layered antiferromagnet NiPS3(TN=155 K) has been measured between 45 K and 650 K. The system may be described by the effective spin Hamiltonian H=DSiz2- Sigma ij JijSi.Sj, with the quadratic single-ion anisotropy terms introducing anisotropy in an otherwise isotropic situation. The exchange J and single-ion anisotropy parameter D were determined from an analysis of the anisotropic susceptibility data for two different models: (i) the Oguchi model, in which a pair of spins chosen at random is treated exactly while its interactions with the rest of the crystal are approximated by a mean field and (ii) the correlated effective field (CEF) approximation developed by Lines, which reduces the many-body problem to a single-particle, non-interacting ensemble form, by the introduction of static temperature-dependent correlation parameters, which are evaluated by forcing consistency with the fluctuation-dissipation theorem. It is found that the CEF approximation is superior to the Oguchi model in describing the susceptibility of NiPS3. The exchange and crystal held parameters for the CEF approximation are J/k=-58.0 K; D/k=16.1 K; g/sub ///=2.05 and gperpendicular to =2.13.

A non-destructive method to determine the depth-dependence of three-dimensional residual stress states by X-ray diffraction

A new non-destructive method is presented to determine the depth-dependence of the stress tensor sigma ij from measurements that apply radiations from different conventional X-ray tubes. Experimentally, the method is based on the measurement procedure for the two-dimensional stress state. A suitable parameterization of the three-dimensional state developed from elasticity theory is used to fit all diffraction peak positions simultaneously, which yields the tensor components sigma ij(z) consistently. The relationship of the new method to more conventional stress determination techniques is briefly discussed. The method has been applied to a test piece formed from a commercial titanium alloy.

Theory of dynamic similarity in neuronal systems.

1. The techniques of dynamic similarity from the engineering science of fluid mechanics are applied to neuronal systems to suggest how to scale down critical parameters (such as numbers of constituent cells and synapses, synaptic strengths, thresholds, etc.) from naturally occurring systems to computer models. 2. The interconnectivity of a prototypical neuronal junction is defined in terms of the total number of projecting fibers, receiving cells, synapses, and directly connected cell fiber pairs. Critical derivative parameters are defined in terms of these, including: a global convergence factor, alpha ij, which is the ratio of the numbers of projecting fibers to receiving cells; and an interconnectivity completeness parameter or microscopic convergence/divergence parameter, gamma ij, which measures both the percentage of cells to which a given sending fiber projects (and the percentage of fibers from which a given cell receives) and the percentage of cell fiber combinations which are directly connected. 3. Analysis of the differential equations governing neuroelectric activity in constituent neurons suggests the definition of a sensitivity parameter complex, sigma ij (with components eta ij and mu ij) for each ij junction. These numbers represent the ratio of synaptic drive to current leakage in nonactive neurons. 4. A model for quasi-steady firing suggests the definition of a parameter, rho *j, which may be used to characterize the level of activity in a given neuronal population in terms of its synaptic drive and system parameters. It may be considered as the neuronal analog of the Reynolds number in fluid mechanics. 5. The analysis implies that computer models of neuronal systems should be scaled so as to keep the parameters alpha ij, gamma ij, and sigma ij for every junction at the same values as in the corresponding junctions of naturally occurring system being modeled. Equations for a scaling factor, chi, numbers of constituent synapses, thresholds, etc., are provided. The scaling method is illustrated by a computer simulation example and by application to the junction of the perforant path fibers to the granule cells of the hippocampus. 6. The analysis shows that there is a fundamental trade-off in scaled down computer models between verisimilitude at the level of network interconnectivity and verisimilitude at the level of individual neuronal dynamics. 7. The approach of dynamic similarity is discussed with respect to compression of free parameters and predictive comparison of naturally occurring systems.

Proton relaxation mechanisms and the measurements of r phi, r psi and transannular interproton distances in gramicidin S.

Monoselective, Rio(SE), biselective, Rio(i,j), and nonselective proton spin-lattice relaxation rates have been measured for dilute solutions of gramicidin S in dimethyl sulfoxide and used to evaluate cross-relaxation rates (sigma ij = Rio(i,j)-Rio(SE)) and Fi ratios (Fi = Ri(NS)/Rio(SE)). The cross-relaxation parameters, sigma, and Fi ratios measured for backbone gramicidin S protons predict that the same correlation time, tau c = 1.2 X 10(-9)s, modulates all the dipolar proton-proton interactions and that these interactions represent the main source for the proton spin-lattice relaxation process. The larger relaxation rates for amide versus alpha-protons of the backbone are attributed to dipolar relaxation between 14N and its directly bonded protons and is an approximate measure of the extent of this. The intrabackbone proton-proton distances, evaluated from sigma values, were consistent with the antiparallel beta-plated sheet/beta II'-turn conformation previously proposed for gramicidin S in solution.

Relation of charge-changing cross sections to relative population of charge states for fast heavy ions

The relations between charge-changing cross sections sigma ij and the relative populations phi i(x) of states i=1, N are analysed. An analytic solution for the vector phi (x) is given for any number N of states in terms of eigenvalues and eigenvectors of a matrix M of the cross sections. Another solution for phi (x) is given in terms of successive multiple squarings of the matrix M, then acting on phi (0). The manifolds of ratios of various sigma ij which lead to the same equilibrium distribution phi ( infinity ) are examined along with the question of the sensitivity of phi (x) data in various cases for determining various sigma ij. The inclusion of excited states in the matrix is discussed, as well as the minor effect of complex eigenvalues.

Pressure and stress tensor expressions in the fluid mechanical formulation of the Bose condensate equations

It is shown that a momentum equation identical in form to that of the familiar Navier-Stokes fluid, can be derived for the fluid condensate of a weakly interacting Bose gas. For the condensate the pressure is given by the simple barotropic relation p= rho 2/4, while the anisotropic stress tensor sigma ij' depends only on the density and density of gradients.