Some aspects of diffusion: fluctuations in reaction diffusion,and geometric influences in nonuniform media

Summary We deal with two diffusion problems: Space-integrated conserved entities characterizing very fast - diffusion - controlled reactions, such as time lags, etc. are universal. They are given by relationships which do not reflect the failure of the mean field hydrodynamic equations. We present another application which does not reflect this failure, for determining the surface flux via a diffusion controlled reaction producing a colored product. Another anomalous diffusion process we considered is transport through cellular materials whose cell sizes are highly nonuniform. We have analyzed the effects of extreme nonuniformity by considering fractal-like models of cellular solids. The diffusion current through these models can exhibit anomalous time-dependencies which are not predicted by the diffusion equation. In particular, it is shown that the initial diffusion current can be characterized by a power-law dependence on the time. Furthermore, the exponent of the power law is given in terms of the distribution of cell sizes in the fractal-like cellular solid.     

Interpenetrating polymer networks of poly(carbonate-urethane) and polyvinyl pyridine

Simultaneous interpenetrating polymer networks (IPN's), pseudo IPN's, and liner blends of aliphatic poly(carbonate-urethane) (PCU) and polyvinyl pyridine (PVP) have been prepared and characterized by DSC, DMA, and TEM. The full IPN's of PCU and PVP had a single phase morphology only above 50 wt % PCU, as determined by both DSC and DMA and confirmed by transmission electron microscopy (TEM). However, in both pseudo IPN's of PCU and PVP and in their linear blends there exist multiple glass transitions and melting points seen by DSC and DMA indicating phase incompatibility. The full IPN's exhibited superior ultimate mechanical properties and solvent resistance as compared to the pseudo IPN's, liner blends, and the pure crosslinked PCU and PVP networks.     

Graft copolymer of polymethyl methacrylate-g-polycarbonate urethane and the fully gelled grafted networks

We have synthesized and characterized the graft copolymer of polymethyl methacrylate (PMMA)-graft-polycarbonate urethane (PCU) (designated PMMA-g-PCU) and the fully gelled mutually crosslinked network composed of both PMMA and PCU (designated as PMMA-PCU-N). Unlike the previously synthesized one phase PCU/PMMA simultaneous interpenetrating polymer networks (IPN's), both of these new materials exhibited two distinct T_g's (from DSC and DMA studies) at all compositions which we have studied. The two-phase nature of the graft and network polymer was confirmed by TEM with domain sizes smaller than those found in the blends of the linear PCU and PMMA chains. In comparison with the corresponding IPN's, the PMMA-g-PCU and the PMMA-PCU-N were thermally less stable and had a lower ultimate strength. © 1992 John Wiley & Sons, Inc.     

The ground-state singlet potential surface for C2H4

Calculations with an extended polarized basis set and Møller-Plesset perturbation theory including triple substitution correlation corrections in the fourth-order treatment indicate that singlet ethylidene (CH₃CH:) is not a local minimum on the C₂H₄ potential energy surface. Rearrangement to ethylene occurs without actuation. Barriers for hydrogen scrambling and for 1,1-hydrogen elimination are estimated.     

A Polytope Approach to the Optimal Assembly Problem

The problem of assembling components into series modules to maximize the system reliability has been intensively studied in the literature. Invariably, the methods employed exploit special properties of the reliability function through standard analytical optimization techniques. We propose a geometric approach by exploiting the assembly polytope – a polytope generated by the potential assembly configurations. The new approach yields simpler proofs of known results, as well as new results about systems where the number of components in a module is not fixed, but subject to lower and upper bounds.     

A conforming decomposition theorem,a piecewise linear theorem of the alternative,and scalings of matrices satisfying lower and upper bounds

A scaling of a nonnegative matrixA is a matrixXAY ^?1, whereX andY are nonsingular, nonnegative diagonal matrices. Some condition may be imposed on the scaling, for example, whenA is square,X=Y or detX=detY. We characterize matrices for which there exists a scaling that satisfies predetermined upper and lower bound. Our principal tools are a piecewise linear theorem of the alternative and a theorem decomposing a solution of a system of equations as a sum of minimal support solutions which conform with the given solutions.     

Optimal stopping,exponential utility,and linear programming

This paper uses linear programming to compute an optimal policy for a stopping problem whose utility function is exponential. This is done by transforming the problem into an equivalent one having additive utility and nonnegative (not necessarily substochastic) transition matrices.Research was supported by NSF Grant ENG 76-15599.     

Characterizations of optimal scalings of matrices

A scaling of a non-negative, square matrixA ≠ 0 is a matrix of the formDAD ^?1, whereD is a non-negative, non-singular, diagonal, square matrix. For a non-negative, rectangular matrixB ≠ 0 we define a scaling to be a matrixCBE ^?1 whereC andE are non-negative, non-singular, diagonal, square matrices of the corresponding dimension. (For square matrices the latter definition allows more scalings.) A measure of the goodness of a scalingX is the maximal ratio of non-zero elements ofX. We characterize the minimal value of this measure over the set of all scalings of a given matrix. This is obtained in terms of cyclic products associated with a graph corresponding to the matrix. Our analysis is based on converting the scaling problem into a linear program. We then characterize the extreme points of the polytope which occurs in the linear program.