Spin-dimensionality dependence of critical parameters

High-temperature series expansions for the susceptibility of isotropic classicaln-vector models are examined with special emphasis on the global dependence on the dimensionalityn of the spin field. The usual fixed-spin model and an incomplete-Gaussian model, which allows for analytic continuation to arbitrary negativen, are considered. A method of examining trends in successive estimates is employed which allows to obtain improved estimates for the extremely slowly setteling sequences as obtained for highn-values. The estimates for the two models obey the universality principle. An approximate function for the critical exponent(n) is obtained in the range –4<n. Reasonable agreement with-expansion results and 1/n-expansion values is found.     

More on limit theorems for iterates of probability measures on semigroups and groups

Summary In this paper, we continue earlier works of one of the authors on vague convergence of the sequence _k,n= _k+1 *...* _n, where _n is a sequence of probability measures on semigroups or groups. Typical results in this paper are: Theorem. Let S be a locally compact noncompact second countable group such that being the support of a probability measure on S. Suppose there exists an open set V with compact closure such that x ^–1 Vx=V for every xS. Then for all compact sets K, sup{ ⁿ (Kx): xS0 as n. Theorem. Let S be an at most countable discrete group. Let _n be a sequence of probability measures on S. Then for all nonnegative integers k, the sequence _k,n converges vaguely to some probability measure if and only if there exists a finite subgroup G such that the series and for any proper subgroup G of G and any choice of elements g_n in S, the series . A sufficient condition for the vague convergence of the sequence _k,n to a probability measure is that (i) there exists a finite subgroup G such that and (ii) _n(e)>s>0 for all n, e being the identity.The author was supported by NSF grant MCS77-03639     

Minimal paramount matrices

A real symmetric matrix of order n, n ? 2, is said to be paramount if each proper principal minor is not less than the absolute value of any other minor built from the same rows. A paramount matrix is minimal ¹ if reducing any of the diagonal entries removes the matrix from the paramount class. Minimal paramount matrices arise in the n-port realization problem of circuit theory. A condition is found that is equivalent to the minimality of a paramount matrix. Conditions are also found that guarantee that the inverse of an invertible minimal paramount matrix is itself minimal.     

The approach to normality of the distance-neighbour function when used to describe relative turbulent dispersion

Batchelor [1] suggested that the Distance-Neighbour Function when used to describe the relative turbulent dispersion of a cloud of marked fluid, whose diameter is well within the length scale range of the universal inertial sub-range of turbulence, would become of Gaussian form. This paper determines that a necessary condition for the Gaussian form to apply is that the non-dimensional time of (/v)^1/2 t 300, following the release of the marked fluid with an initial diameter <(v ³/t)^1/4, be attained.

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Zusammenfassung Batchelor [1] hat die Behauptung aufgestellt, dass die Abstands-Nachbar-Funktion (räumliche Korrelation) die Gauss'sche Form annimmt, wen man sie zur Beschreibung der relativen turbulenten Dispersion einer Wolke von markierter Flüssigkeit benützt, falls der Durchmesser der Wolke nicht über die Längenskala des universellen Inertial-Unterbereichs der Turbulenz hinausgeht. In dieser Arbeit wird gezeigt, dass eine notwendige Bedingung der Anwendbarkeit der Gauss'schen Form darin besteht, dass die dimensionsloze Zeit (/v)^1/2 t 300 nach dem Ablösen einer markierten Flüssigkeits-wolke mit dem Anfangsdurchmesser <(v ³/t)^1/4 erreicht wird.

     

On bounds for the range of ordered variates II

Letx ₁, ,x _n be real numbers with ₁ ⁿ x _j =0, |x ₁ ||x ₂ ||x _n |, and ₁ ⁿ f(|x _i |)=A>0, wheref is a continuous, strictly increasing function on [0, ) withf(0)=0. Using a generalized Chebycheff inequality (or directly) it is easy to see that an upper bound for |x _m | isf ^–1 (A/(n–m+1)). If (n–m+1) is even, this bound is best possible, but not otherwise. Best upper bounds are obtained in case (n–m+1) is odd provided either (i)f is strictly convex on [0, ), or (ii)f is strictly concave on [0, ). Explicit best bounds are given as examples of (i) and (ii), namely the casesf(x)=x ^p forp>1 and 0<p<1 respectively.     

A quasi‐dynamic procedure for coupled thermal simulations

This paper outlines the development and adaptation of a coupling strategy for transient temperature analysis in a solid via a conjugate heat transfer method. This study proposes a quasi‐dynamic coupling procedure to bridge the temporal disparities between the fluid and the solid. In this approach, dynamic thermal modeling in the solid is coupled with a sequence of steady states in the fluid. This quasi‐dynamic algorithm has been applied to the problem of convective heat transfer over, and transient conduction heat transfer within, a flat plate using the severe thermal conditions of a solid propellant rocket. Two different coupled thermal computations have been performed. In the first one—referred to as the reference computation—the coupling period is equal to the smallest solid time constant. In the second one, a very large coupling period is used. The results show that the procedure can predict accurate transient temperature fields at a reasonable computational cost. The simulation CPU time is approximately reduced by up to 90%, while maintaining a very good accuracy. All the details of the numerical test case are given in the paper. This application illustrates the capabilities and the overall efficiency of this coupled approach in a solid transient problem using long term simulations of time dependent flows. Copyright © 2013 John Wiley & Sons, Ltd.     

Book Reviews

Room temperature glass containing copper nitrate was produced using the microemulsion-gel method. Ultraviolet-visible spectroscopy and x-ray diffraction spectra were used to demonstrate the presence of copper nitrate in the gel samples. The samples were examined using optical microscopy, with and without polarized filters, and scanning electron microscopy with energy dispersive x-ray analysis, before and after the extraction of the surfactant with an organic solvent. The results indicated that copper nitrate was present throughout the silicate network formed and was associated with the microemulsion components, i.e., the interstitial liquid, remaining in the bulk material.