On three conjectures by K. E. Shuler

Some fifteen years ago, Shuler formulated three conjectures relating to the large-time asymptotic properties of a nearest-neighbor random walk on ² that is allowed to make horizontal steps everywhere but vertical steps only on a random fraction of the columns. We give a proof of his conjectures for the situation where the column distribution is stationary and satisfies a certain mixing codition. We also prove a strong form of scaling to anisotropic Brownian motion as well as a local limit theorem. The main ingredient of the proofs is a large-deviation estimate for the number of visits to a random set made by a simple random walk on . We briefly discuss extensions to higher dimension and to other types of random walk.Dedicated to Prof. K. E. Shuler on the occasion of his 70th birthday, celebrated at a Symposium in his honor on July 13, 1992, at the University of California at San Diego, La Jolla, California.     

Heterogeneities of grain boundary arrangement in polycrystals

Data on mutual arrangements of different types of grain boundaries in polycrystals are presented. The heterogeneity in grain boundary distribution, namely, the effect of gathering low-angle or special tilt grain boundaries is found in pure aluminum thin films, in sheets of Fe-3% Si alloy and in Al₂O₃ doped with MgO or MgO and Y ₂O₃. The local texture, i.e., formation of colonies or clusters of close-oriented grains is considered as a reason of this heterogeneity. The influences of grain boundary gathering on the transport properties of polycrystals and on the crack propagation are discussed. A new concept of effective grain size is suggested to analyze the relationship between material microstructures and material properties.     

Small ball probabilities for a Wiener process under weighted sup-norms,with an application to the supremum of bessel local times

LetR be the radial part of ad-dimensional Wiener process, starting from 0. In this paper, small ball probabilities are evaluated for sup_0<11(t ^–p R(t)) and sup _t 0(e ^–1 R(t)), withp[0, 1/2]. Chung's law of the iterated logarithm is established for the supremum of the local times of a two-dimensional Bessel process.     

On the Landau-Teller approximation for energy exchanges with fast degrees of freedom

We revisit the Landau-Teller heuristic approach to adiabatic invariants and, following Rapp, use it to investigate the energy exchanges between the different degrees of freedom, in simple Hamiltonian systems describing the collision of fast rotating or vibrating molecules with a fixed wall. We critically compare the theoretical results with particularly accurate numerical computations (quite small energy exchanges, namely of one part over 10³⁰, are measured).     

Langevin dynamic simulation of hysteresis in a field-swept Landau potential

Numerical simulations are done of Langevin dynamics for a uniform-orderparameter, field-swept Landau model,= –|a/2|m ²+|b/4|m ⁴–mh(t) , to study hysteresis effects. The field is swept at a constant rateh(t)=h(0)+ht. The stochastic jump values of the field {h_J from an initially prepared metastable minimumm(0) are recorded, on passage to a global minimum m(). The results are: (a) The mean jump¯h _J(h) increases (hysteresis loop widens) with h, confirming a previous theoretical criterion based on rate competition between field-sweep and inverse mean first-passage time (FPT); (b) The broad jump distribution(h _J,h) is related to intrinsically large FPT fluctuations ( ²–²)/ ² O(1), and can be quantitatively understood. Possible experimental tests of the ideas are indicated.     

A New Method to Investigate the Clustering Phenomena in Supercritical Fluids

EstimationoflocaldensityofsolventaboutthesoluteSolvatochromicbehaviorsofspectroscopicprobesarewidelyusedtoestimatethesol-ventstrengthofsupercriticalfluids(SCF,).i-3lnthiswork,thesolvatochrondcshiftofthen-n*transitionbandforacetone(O.o37mo1.L-')insupercrihcal(SC)CO2wasde-terminedbyUVspectroscopytostUdythesolvationeffect.TheMcRae-BaylissexpressionbasedonthedielectriccontinUUInmodelgivestherelahonshipbetWeenso1vatochromicshiftandpo1arizabilityofnonPolarsolvents4-5asfollows:wherevisthewave…     

Asymptotic expansions of the distributions of some test statistics

Summary A modified Wald statistic for testing simple hypothesis against fixed as well as local alternatives is proposed. The asymptotic expansions of the distributions of the proposed statistic as well as the Wald and Rao statistics under both the null and alternative hypotheses are obtained. The powers of these statistics are compared and its is shown that for special structures of parameters some statistics have same power in the sence of order . The results obtained are applied for testing the hypothesis about the covariance matrix of the multivariate normal distribution and it is shown that none of the tests based on the above statistics is uniformly superior. Research supported by the National Science Foundation Grant MCS 830149.     

Isomerisierung bei der Komplexbildung von 3-Acetyl-tetramsäure: Struktur und magnetische Eigenschaften des CuII- und NiII-Komplexes von 2,7-Bis(1′, 5′, 5′-trimethylpyrrolidin-2′, 4′-dion-3′ -yl)-3, 6-diazaocta-2, 6-dien

Isomerization at the Complexation of 3-Acetyltetramic Acid: Structure and Magnetic Properties of the Cu^II- and Ni^II-Complex of 2,7-Bis (1′, 5′, 5′ -trimethylpyrrolidin-2′,4′ -dion-3′ -yl)-3,6-diazaocta-2,6-dien 2,7-Bis(1′, 5′, 5′ -trimethylpyrrolidin-2′, 4′ -dion-3′ -yl)-3,6-diazaoctadien formes Cu^II and Ni^II complexes with different constitutions (because of the Z/E isomerization). Results of X-ray analysis of N,N′ -ethylenbis(1′, 5′, 5′ -trimethylpyrrolidin-2′, 4′ -dion-3′ -acetiminato)nickel(II) 1 respectively -copper(II) 2 shows, that the complexing agent in 1 occurs in the E-form, whereas the ligand of the Cu^II complex forms the Z-form. Magnetic susceptibility and shift effects of the ¹³C-NMR signals point to a weak paramagnetism of the Ni^II complex. ESR-spectra are obtained from 2 only. Furthermore, the Cu^II complex reduces the relaxation times T₁ and T₂ of ¹H and ¹⁷O nuclei spins from water. From the temperature dependence of the shortening of the relaxation times an activation energy is calculated which describes the reorientation of the copper complex in the “water matrix”.     

Partitioning of <Emphasis Type="Italic">π</Emphasis> -electrons in rings of polycyclic conjugated hydrocarbons: Part 6. Comparison with other methods for estimating the local aromaticity of rings in polycyclic benzenoids

By adopting the convention that shared double bonds in polycyclic conjugated hydrocarbons contribute with one -electron and unshared ones with two -electrons, a partition of -electrons in each ring (-electron content, EC) can be obtained by averaging over all Kekulé structures, which are assumed to have equal weights. This affords a simple measure of local aromaticity that is comparable with other such local aromaticity indices in polycyclic benzenoids.