C1, α Partial regularity of functions minimising quasiconvex integrals

We prove C^1, almost everywhere regularity for minimisers of functionals of the form F(x,u,Du), where F is uniformly strictly quasiconvex. This extends a recent result of Evans in which F is allowed only to depend on Du.     

Conformational analysis of fluorinated copolymers of tetrafluoroethylene

Conformational analysis of fluorinated copolymers of tetrafluoroethylene (TFE) is performed by taking into account only intramolecular effects (isolated-chain model). In particular, variations of the chain conformation, which are induced by incorporating different side groups, such as –Cl, –CF₃, –OCF₃, –OCF₂CF₃, and –OCF(CF₃)₂, are investigated and discussed with respect to qualitative correlations between conformation, crystal structure, and supramolecular morphology.     

A density matrix variational calculation for atomic Be

The ground-state energy of the beryllium atom is calculated using a variational procedure in which the elements of the two-body reduced density matrix (particle–particle matrix) are the variational parameters. It is shown that, for this problem and with the limited number of spin-orbitals used, the trace condition and the simultaneous nonnegativity conditions on the particle–particle, the particle–hole, and the hole–hole matrices form a complete solution to the N-representability problem. The energy obtained is – 14.61425 a.u., practically identical to the value given by a configuration interaction calculation which uses the same states. The effects of weakening the nonnegativity conditions on each of the matrices in turn were also explored.     

Stationary motion of a self-gravitating toroidal incompressible liquid layer

We consider an incompressible fluid contained in a toroidal stratum which is only subjected to Newtonian self-attraction. Under the assumption of infinitesimal thickness of the stratum we show the existence of stationary motions during which the stratum is approximately a round torus (with radii r, R and R ? r) that rotates around its axis and at the same time rolls on itself. Therefore each particle of the stratum describes an helix-like trajectory around the circumference of radius R that connects the centers of the cross sections of the torus.     

Influence of fillers concentration on electrical properties of polystyrene matrix doped by gold nanoparticles and 8HQ

The analysis of the electrical properties of polystyrene films containing gold nanoparticles capped with 1-dodecanethiol and 8-hydroxyquinoline molecules is reported. The conductivity of the nanocomposite as a function of the doping level has been investigated both in planar and stacked configurations. While the former configuration evidenced low field tunneling between nanoparticles in the polymer matrix, stacked devices allowed us to investigate the main phenomena ruling the transport properties when switching effects are present close to critical electric fields. In particular, through the analysis of current-voltage characteristics we studied the charge transport at different fillers concentrations and sketched a physical picture of conductivity in such nanocomposite systems.     

A reduction approach for determining generalized simple waves

A reduction approach is developed in order to construct generalized simple wave solutions to quasilinear nonhomogenous hyperbolic systems of first order PDEs. The solutions sought must possess a special ansatz which permits time-evolution of the profile of a simple wave due to a source-like term. These solutions involve a free function which can be used to fit classes of initial or boundary value problems. By means of the proposed approach two governing models of interest in a variety of applications are investigated. Model constitutive laws consistent with the full reduction process are obtained and the occurence of singularities at a finite time for the resulting solutions is analysed. Furthermore a comparison is made between the results obtained within the present theoretical framework and the standard simple wave solutions of the corresponding homogeneous (source free) governing models.     

Slow Dynamics for the Cahn‐Hilliard Equation in Higher Space Dimensions: The Motion of Bubbles

It is known that the Van der Waals‐Cahn‐Hilliard (W‐C‐H) dynamics can be approximated by a Quasi‐static Stefan problem with surface tension. It turns out that the Stefan problem has a manifold of equilibria equal in dimension to that of the domain Ω: any sphere of fixed radius with interface contained in the domain is an equilibrium (indistinguishable from the point of view of the perimeter functional). We resolve this degeneracy by showing that at the W‐C‐H level this manifold is replaced by a quasi‐invariant stable manifold, on which the typical solution preserves its “bubble” like shape until it reaches the boundary. Moreover, we show that the “bubble” moves superslowly. We also obtain an equation that determines those special spheres that correspond to equilibria at the W‐C‐H level. Our work establishes the phenomenon of superslow motion in higher space dimensions in the class of single interface solutions. (Accepted February 12, 1996)     

Concerning the efficient conversion of epoxy alcohols into epoxy ketones using dioxiranes

Representative epoxy alcohols are cleanly converted into the corresponding epoxy ketones in high yield by selective oxidation using dimethyldioxirane (1a) and its trifluoro analogue (1b) under mild conditions. The oxidation is found to take place leaving the configuration at the epoxy functionality unaffected. The direct oxyfunctionalization of simple cyclic epoxides with the powerful dioxirane 1b provides another attractive method to access epoxy ketones regioselectively.     

Ostwald Ripening for Dilute Systems Under Quasistationary Dynamics

We consider a dilute mixture in 3D of a finite number of particles initially close to spherical, but of varying size, evolving according to quasistationary dynamics. Under the scaling hypotheses that (1) size/distance, (2) deviation from sphericity/size are both initially small, we show robustness of the almost spherical shape by associating centers and radii to each particle and then derive rigorously a set of O.D.E.' s for the radii which we relate to the Lifschitz-Slyozov-Wagner theory of coarsening, and also establish an estimate for the speed of the centers. Partially supported by NSF-DMS 9622791, and ENE 99/527 (funded by Greece and the European Community).