Dimension-Splitting for Simplifying Diffusion in Lattice-Gas Models

We introduce a simplified technique for incorporating diffusive phenomena into lattice-gas molecular dynamics models. In this method, spatial interactions take place one dimension at a time, with a separate fractional timestep devoted to each dimension, and with all dimensions treated identically. We show that the model resulting from this technique is equivalent to the macroscopic diffusion equation in the appropriate limit. This technique saves computational resources and reduces the complexity of model design, programming, debugging, simulation and analysis. For example, a reaction-diffusion simulation can be designed and tested as a one-dimensional system, and then directly extended to two or more dimensions. We illustrate the use of this approach in constructing a microscopically reversible model of diffusion-limited aggregation as well as in a model of growth of biological films.     

Study of spontaneous fission with EUROGAM

Prompt γ radiation following spontaneous fission has been measured using the EUROGAM 2 array. Using these data and newly developed analysis techniques a number of subjects were studied, which are briefly discussed. One of these subjects, shape transition in A≈100 Sr and Zr nuclei is discussed in more detail. Quadrupole moments were determined for rotational bands in the N=58,59,60,62 and 64 Sr and Zr isotopes. Deformation parameters, which increase from β₂ ≈ 0.1 at N=56 to β₂ ≈ 0.4 at N=64, suggest that in strontium and zirconium isotopes shape change happens gradually between N=56 and N=62 and is probably due to an occupancy of three or more deformation-driving orbitals of h_11/2 parentage.     

Air traverse time in grain bins

To maintain the quality of cereal grains during storage, it is necessary to keep the grain cool and free from insects, and typical methods for dealing with these problems are considered in this paper. In particular the insect population is controlled by fumigating the grain bed with carbon dioxide gas and the grain is cooled by forcing ambient air through the bed. In both problems, the equations which describe the physical processes contain a mixture of advection and diffusion or conduction terms. This paper explores the relationship between traverse time and heat and mass transfer and gains an insight into the grain storage processes that are controlled by forced convection. When heat and mass transport is dominated by the advection terms, the equations are simplified by changing variables from the (x,y) space coordinates to (ψ,τ), where ψ is the stream function for the problem and the traverse time τ at a point in the storage bin is the time taken for the air to travel to the point from the inlet duct. The conditions are described for the equations to be independent of ψ, with the main condition being that the derivatives of the metrics g₁₁, g₁₂ and g₂₂ with respect to ψ are small enough. If the equations are independent of ψ then the dependent variable (concentration or temperature) will be constant on lines of constant traverse time τ. This relationship between traverse time and the cooling or fumigation pattern can be used in the design of storage bins since it implies that the best outlet surface is a line of constant τ.     

Encapsulation of organotin compounds in metal acetate glasses

Triorganotin halides, oxides and sulphides can be dissolved in molten, mixed-metal acetates at ca 140–160°C without decomposition; quenching provides glasses into which are encapsulated the organotin species. Halide/acetate and oxide/acetate, but not sulphide/acetate, exchanges occur in the melt. Only partial exchange was found for hindered trineophyl tin chloride [(PhCMe₂CH₂)₃SnCl], in contrast to the complete exchanges observed for the butyl (Bu), phenyl (Ph) and cyclohexyl (Cy) analogues. Complete oxide/acetate exchange was found for (Bu₃Sn)₂O, partial exchange occurred for (Cy₃Sn)₂O, whilst no exchange resulted with bis(trineophyltin) oxide or (Ph₃Sn)₂O. Tin–tin bonds (e.g. as in Ph₃SnSnPh₃) and carbon–tin bonds (even the allyl–Sn bond in Bu₃SnCH₂CH?CH₂) are not affected. The acetate glasses dissolve in aqueous media with release of the organotin species and they have potential as slow-release systems which is currently being investigated.     

Diffusion competition between solvent and nonsolvent during the coagulation process of cellulose / ammonia / ammonium thiocynate fiber spinning system

An investigation of the diffusion competition between solvent and nonsolvent in a coagulation bath is presented for the formation of a new cellulosic fiber by wet-spinning. The system consisted of the spinnable cellulose solution with a mixture of liquid ammonia/ammonia thiocynate as the solvent and low-molecular-weight alcohols as the nonsolvents. The diffusion competition between solvent and nonsolvent was quantitatively characterized in terms of their mass transfer rate differences. The measurements of this rate difference were performed on the model filament shaped from gelled cellulose solutions. Results revealed that an increase in molecular size of coagulant, bath temperature, and coagulant concentration in the bath enhanced preferential diffusion of solvent from cellulose solution. Fiber spinning experiments showed that a higher value of the initial modulus of the fiber was attained with a coagulation condition providing a lower value of mass transfer rate difference. The importance of mass transfer rate difference was also shown in the influence of the fiber cross-sectional shapes.     

A measurement of the neutral current electroweak parameters using the fermilab narrow band neutrino beam

We report a measurement of the electroweak parameters sin₂θ ^w and ? based on the ratios of neutral current to charged current events measured in the Fermilab narrow-band neutrino beam at energies of 30–240 GeV. The data are fully corrected for radiative effects, heavy-quark production, and other effects. The best value for sin₂θ ^w obtained, sin₂θ ^w =0.239±0.011, is consistent with the most recent values fromW andZ production, as well as from other neutrino experiments.     

Factorization in dedekind domains with finite class group

LetD be a Dedekind domain. It is well known thatD is then an atomic integral domain (that is to say, a domain in which each nonzero nonunit has a factorization as a product of irreducible elements). We study factorization properties of elements in Dedekind domains with finite class group. IfD has the property that any factorization of an elementα into irreducibles has the same length, thenD is called a half factorial domain (HFD, see [41]). IfD has the property that any factorization of an elementα into irreducibles has the same length modulor (for somer>1), thenD is called a congruence half factorial domain of orderr. In Section I we consider some general factorization properties of atomic integral domains as well as the interrelationship of the HFD and CHFD property in the Dedekind setting. In Section II we extend many of the results of [41], [42] and [36] concerning HFDs when the class group ofD is cyclic. Finally, in Section III we consider the CHFD property in detail and determine some basic properties of Dedekind CHFDs. IfG is any Abelian group andS any subset ofG−[0], then {G, S} is called a realizable pair if there exists a Dedekind domainD with class groupG such thatS is the set of nonprincipal classes ofG which contain prime ideals. We prove that for a finite abelian groupG there exists a realizable pair {G, S} such that any Dedekind domain associated to {G, S} is CHFD for somer>1 but not HFD if and only ifG is not isomorphic toZ ₂,Z ₂,Z ₂ ⊕Z ₂, orZ ₃ ⊕Z ₃. The first author received support under the John M. Bennett Fellowship at Trinity University and also gratefully acknowledges the support of The University of North Carolina at Chapel Hill.