Light scattering in a fluid far from equilibrium

The integrated intensity is computed of each of the two Brillouin lines of a stationary fluid far from equilibrium in the presence of a temperature gradient. The difference in intensity found is due to mode-coupling effects and deviates appreciably from an extrapolation of earlier calculations near equilibrium.     

Staggered diffusivities in lattice gas cellular automata

The majority of LGCAs has spurious conservation laws, the so-called staggered invariants, first discovered by Kadanoff, McNamara, and Zanetti. Consequently there are additional hydrodynamic modes of diffusive type, which modify mode coupling theories and the nonlinear fluid dynamic equations. The diffusivities of these staggered modes are evaluated in the mean field approximation for LGCAs on triangular lattices, starting from the Green-Kubo formulas for the staggered diffusivities.     

Analysis of alternating direction collocation methods for parabolic and hyperbolic problems in two space variables

While alternating direction implicit (ADI) collocation methods have been used for several years to solve parabolic problems in several space variables, no convergence analysis has been derived for any of these methods. We formulate and rigorously analyze ADI collocation schemes applied to the inhomogeneous heat and wave equations on the unit square subject to homogeneous Dirichlet boundary conditions and appropriate initial conditions. We prove that each method is second-order accurate in time and of optimal accuracy in space in the L² and H₀¹ norms. Numerical experiments confirm the predicted rates of convergence. © 1993 John Wiley & Sons, Inc.     

Forest embeddings in regular graphs of large girth

This paper deals with the enumeration of distinct embeddings (both induced and partial) of arbitrary graphs in regular graphs of large girth. A simple explicit recurrence formula is presented for the number of embeddings of an arbitrary forest F in an arbitrary regular graph G of sufficiently large girth. This formula (and hence the number of embeddings) depends only on the order and degree of regularity of G, and the degree sequence and component structure (multiset of component orders) of F. A concept called c-subgraph regularity is introduced which generalizes the familiar notion of regularity in graphs. (Informally, a graph is c-subgraph regular if its vertices cannot be distinguished on the basis of embeddings of graphs of order less than or equal to c.) A central result of this paper is that if G is regular and has girth g, then G is (g ? 1)-subgraph regular.     

Kinetic theory of long time tails in velocity correlation functions in a moderately dense electron gas

The long time tails of the correlation functions that determine the self-diffusion coefficient and the kinetic parts of the shear viscosity and heat conductivity in a one-component plasma are calculated using a systematic kinetic theory. The results are in agreement with those obtained from the phenomenological mode coupling theory. The formal kinetic theory calculations of previous workers, who obtained incomplete long time tail results, are also discussed.     

Anomalous specific heat of dipolar spin glasses and ferroelectrics

We show that for a random Ising model with 1/R³ interactions, the probability distribution of molecular field p(H) goes to zero as H tends to zero. We suggest that p(H) ～ H^{$\text{1}\text{2}$} for small H. Monte Carlo calculations of p(H) for the model are performed with results consistent with this suggestion. These results are used to explain the anomalous T^{$\text{3}\text{2}$} specific heat observed in alkali halides containing off-center ions, and in ferroelectrics.     

Charge transfer and the magnetic properties of amorphous Gd0.33Co0.67

Magnetization measurements on amorphous Gd_0.33Co_0.67 films indicate that T_c is>30 per cent higher in the films than in the ordered compound, GdCo₂, of the same composition. This reverses the trend observed in isostructural Tb_0.33Fe_0.67 and many other amorphous ferromagnets, where T_c is lower in the amorphous state. A qualitative explanation of the effect of structural disorder on magnetic properties of the Co and Fe compounds is given in terms of the consequences of charge transfer to the transition metal atoms.     

Carbon-branched carbohydrate chirons: synthesis of C-3 and C-4-branched sugar lactones derived from d-erythronolactone

Two carbon chain extensions using a Wittig reaction on both a 1-deoxy ribulose derivative and a C-2-branched erythrose derivative are reported. Subsequent dihydroxylation resulted in the synthesis of C-3 and C-4 methyl-branched sugar lactones, the useful synthetic building blocks. Control of the stereoselectivity of both the Wittig reaction and the dihydroxylation is investigated, and 3-C-methyl and 4-C-methyl d-altrono-1,4-lactones and d-glucono-1,4-lactone and 4-C-hydroxymethyl-d-altrono-1,4-lactone were synthesised.     

(2S,3R,4S,5R)‐Diethyl 2‐(10,10‐dimethyl‐3,3‐dioxo‐3λ6‐thia‐4‐azatricyclo[5.2.1.01,5]decan‐4‐ylcarbonyl)‐5‐phenylpyrrolidine‐3,4‐dicarboxylate: a novel isomorphous‐by‐addition compound

The title compound, C₂₇H₃₆N₂O₇S, (I), is isomorphous by addition with the dimethyl ester analogue [Garner, Dogan, Youngs, Kennedy, Protasiewicz & Zaniewski (2001). Tetrahedron, 57 , 71–85], (II), by replacing two methyl ester H atoms with two methyl groups. With the exception of the conformation of one of the ester groups, the molecules are almost superimposable. Likewise, apart from a slightly larger c axis in (I), few differences in the cell packing of (I) and (II) are found, with both dominated by the same C—H...O hydrogen bonds. Full synthetic and spectroscopic details of (I) are given. The molecular synthesis is important as an example of chiral auxiliary‐assisted 1,3‐dipolar cycloaddition of an azomethine ylid.