Thermoelastic contact with Barber's heat exchange condition

We consider a nonlinear parabolic problem that models the evolution of a one-dimensional thermoelastic system that may come into contact with a rigid obstacle. The mathematical problem is reduced to solving a nonlocal heat equation with a nonlinear and nonlocal boundary condition. This boundary condition contains a heat-exchange coefficient that depends on the pressure when there is contact with the obstacle and on the size of the gap when there is no contact. We model the heat-exchange coefficient as both a single-valued function and as a measurable selection from a maximal monotone graph. Both of these models represent modified versions of so-called imperfect contact conditions found in the work of Barber. We show that strong solutions exist when the coefficient is taken to be a continuously differentiable function and that weak solutions exist when the coefficient is taken to be a measurable selection from a maximal monotone graph. The proofs of these results reveal an interesting interplay between the regularity of the initial condition and the behavior of the coefficient at infinity.     

TRIFLUOPERAZINE: CORNEAL ENDOTHELIAL PHOTOTOXICITY

Abstract— Trifluoperazine is a commonly used agent for the treatment of psychiatric disorders. Perfusion of corneal endothelial cells with trifluoperazine-HCI concurrent with 3 min of exposure to long wavelength ultraviolet light resulted in a corneal swelling rate which was greater than that found in corneas where endothelial cells were perfused with trifluoperazine-HCI and not exposed to ultraviolet light. Exposure of endothelial cells to 25 W incandescent light for 5 min during perfusion with trifluoperazine-HCI did not result in a corneal swelling rate in excess of that found during perfusion with trifluoperazine in the dark. The increased corneal swelling rate could be produced by pre-exposure of the trifluoperazine-HCI perfusing solution to ultraviolet light suggesting the production of toxic photo-products during exposure of trifluoperazine HCI to ultraviolet light. Perfusion of corneal endothelial cells with non-ultraviolet illuminated trifluoperazine HCI had no effect on endothelial cell membranes or ultra-structure. This is in contrast to cells perfused with trifluoperazine HCI that had been exposed to ultraviolet light in which there was an alteration of mitochondria and a loss of cytoplasmic homogeneity. The data imply that the trifluoperazine HCI photoproduct had an adverse effect on cellular transport mechanisms. The study also further demonstrates that value of the corneal endothelial cell model for identifying the physiological and anatomical changes occurring in photo-induced toxic reactions.     

Measuring transversity densities in singly polarized hadron-hadron and lepton-hadron collisions

We show how the transverse polarization of a quark initiating a jet can be probed by the azimuthal distribution of two hadrons (of large z) in the jet. This permits a twist-2 asymmetry in hard processes when only one of the initial particles is polarized transversely. Applications to hadron-hadron and lepton-hadron scattering are discussed.     

On the average number of steps of the simplex method of linear programming

The goal is to give some theoretical explanation for the efficiency of the simplex method of George Dantzig. Fixing the number of constraints and using Dantzig's self-dual parametric algorithm, we show that the number of pivots required to solve a linear programming problem grows in proportion to the number of variables on the average. Supported in part by NSF Grant #MCS-8102262.     

Stress relaxation and dynamic viscoelastic properties of end-linked poly(dimethyl siloxane) networks containing unattached poly(dimethyl siloxane)

Stress relaxation in uniaxial extension and dynamic shear moduli G′ and G″ have been studied in networks of vinyl-terminated poly(dimethyl siloxane) (PDMS) of five different molecular weights (M _n from 1800 to 29,200) crosslinked with cis-dichlorobis (diethyl sulfide) platinum (II) and containing 10 and 15 wt % of two samples of high-molecular-weight unattached linear hydroxyl-terminated PDMS (M _w 700,000 and 950,000). The M _w/M _n ratio of both the network prepolymers and the unattached linear species was approximately 2. In stress relaxation the stretch ratio was 1.25 or less and the shear relaxation modulus was calculated from the neo-Hookean stress-strain relation. In the dynamic measurements, the strain amplitude was 15% or less; after conversion to the timedependent shear relaxation modulus G(t) the two sets of measurements were combined and the contribution of the unattached species G₁(t) was calculated by difference. After multiplication by (1 − v)⁻¹G/G_e, where v₂ is the volume fraction of network, G is the plateau modulus of the uncrosslinked polymer, and G_e is the equilibrium modulus of the network containing unattached molecules, G₁(t) was compared with G₁₁(t), the relaxation modulus was essentially the same in both environments. The relaxation was slower in the networks than in the uncrosslinked polymer by 1 to 2 orders of magnitude, and it increased gradually with increasing G_e, which is a measure of total to pological obstacles represented by crosslinks plus trapped entanglements. A similar but less striking difference between relaxation in a network and in the homologous environment of a linear polymer was previously observed in end-linked polybutadiene networks and the butadiene phase of a styrene-butadiene-styrene block copolymer. It appears that, in these systems where the topology of the obstacles is fixed, the reptation is severely restricted or else alternative modes of configurational rearrangement which contribute to relaxation in the uncrosslinked polymer are suppressed.     

The Schwinger model via a local Monte Carlo algorithm

We study the massless Schwinger model with one flavor on a lattice using Monte Carlo techniques. A hamiltonian formalism is used. The locality of the algorithm employed allows us to work on quite large lattices (up to 100 × 400) and we are able to reproduce the known continuum mass gap of the model. The extension to higher dimensions is discussed.     

The basis set dependence of structures and energies of various states of cyclodisiloxane

Several common basis sets, ranging from minimal to double-zeta, are applied to study the neutral singlet and triplet as well as positive- and negative-ion doublet states of cyclodisiloxane. The effect of d-polarization function exponents on the equilibrium geometries and energies is analyzed. The d-type functions seem to be essential in the basis set of silicon, whereas their presence on oxygen is less critical. The optimum exponents (with respect to SCF energy) are determined to be 0.45 for Si and 0.60 for O, very close to those recommended for the 6–31G^** basis set. The best structural predictions are obtained with the 6–31G(2d, p) basis set, which contains two sets of d functions on the heavy atoms. The predicted Si? O bond length is 166 pm; the Si? Si and O? O distances are 237 and 232 pm, respectively, which correspond to an O—Si? O angle of 88.6°. The ground state is found to be a singlet. All higher states have longer Si? O bonds and Si—Si distances, whereas O—O distances are shorter. The energy separation between the singlet and other states is modified by electron correlation (MP treatment) by only a few kcal/mol.