Non-collapsing in fully non-linear curvature flows

We consider compact, embedded hypersurfaces of Euclidean spaces evolving by fully non-linear flows in which the normal speed of motion is a homogeneous degree one, concave or convex function of the principal curvatures, and prove a non-collapsing estimate: Precisely, the function which gives the curvature of the largest interior ball touching the hypersurface at each point is a subsolution of the linearized flow equation if the speed is concave. If the speed is convex then there is an analogous statement for exterior balls. In particular, if the hypersurface moves with positive speed and the speed is concave in the principal curvatures, the curvature of the largest touching interior ball is bounded by a multiple of the speed as long as the solution exists. The proof uses a maximum principle applied to a function of two points on the evolving hypersurface. We illustrate the techniques required for dealing with such functions in a proof of the known containment principle for flows of hypersurfaces.     

Oxidation of W(110) studied by LEED and STM

The oxidation of W(110) was studied over a temperature a range of 1000 K to 1600 K at 1 × 10^? 6 Torr oxygen. The subsequent oxide structure was then characterized using Low Energy Electron Diffraction (LEED) and Scanning Tunneling Microscopy (STM). It was found that the resulting structure was remarkably similar to that of Mo(110) oxidized under similar conditions. Using the Mo(110) oxide structure as our basis, along with atomic resolution STM images, we have constructed a model for the surface oxide of W(110).     

Spectroscopic characterization of peroxynitrous acid in cis-perp configurations

This paper presents experimental evidence, supported by two-dimensional theoretical calculations, that HOONO can be observed in cis-perp (cp) configurations in a pulsed supersonic expansion. The spectral properties (transition frequency, rotational constants, and transition type) of OH overtone transitions originating from a state with predominately cp character are predicted theoretically and compared with those associated with a weak feature at 6996.2 cm(-1) observed experimentally using infrared action spectroscopy. This spectral feature is attributed to HOONO in cp configurations based on its vibrational frequency, rotational band contour, and resultant OH product state distribution.     

Directed biosynthesis of alkaloid analogs in the medicinal plant Catharanthus roseus

Terpene indole alkaloids are plant natural products with diverse structures and biological activities. A highly branched biosynthetic pathway is responsible for the production of approximately 130 different alkaloids in Madagascar periwinkle (C. roseus) from a common biosynthetic intermediate derived from tryptamine. Although numerous biosynthetic pathways can incorporate unnatural starting materials to yield novel natural products, it was not clear how efficiently the complex, eukaryotic TIA pathway could utilize unnatural substrates to make new alkaloids. This work demonstrates that the TIA biosynthetic machinery can be used to produce novel alkaloid structures and also highlights the potential of this pathway for future metabolic engineering efforts.     

Cluster kinetics of pressure-induced glass formation

A prior correlation model for glass formation based on cluster-size distribution kinetics is here extended to account for pressure effects as well as temperature effects. The model describes how rapidly cooling or compressing a liquid or colloid leads to structural arrest and a consequent sharp rise in viscosity or dielectric relaxation time. In addition to activation energies, we include activation volumes in the rate coefficients for monomer-cluster addition and dissociation and cluster aggregation and breakage. The approach leads to scaled pressure correlations and plots for viscosity that reveal strong and fragile glass behavior, and agree with experimental data. A simple relationship among viscosity, attractive interparticle energy, and particle volume fraction displays how hard spheres with attractive forces can vitrify at small particle densities.     

Cluster kinetics and dynamics during spinodal decomposition

Spinodal decomposition (barrierless phase transition) is a spontaneous phase separation caused by conditions that force the system to become thermodynamically unstable. We consider spinodal decomposition to occur under conditions of large supersaturation S and/or small ratio of interfacial to thermal energies omega, such that the computed number of monomers in a critical nucleus xi*=(omega/ln S)3 is less than unity. The small critical nucleus size is consistent with a negligible energy barrier for initiating condensation. Thus, in contrast to conventional opinion, it is suggested that the spinodal decomposition is related to the homogeneous nucleation of metastable fluids. Population balance equations show how clusters aggregate and rapidly lead to phase separation. Different mass dependences of aggregation rate coefficients are proposed to investigate the fundamental features of spinodal decomposition. When the mass dependency is an integer, the equations are solved by the moment technique to obtain analytical solutions. When the mass dependency is a noninteger, the general cases are solved numerically. All solutions predict the two time regimes observed experimentally: the average length scale of condensed-phase domains increases as a power law with an exponent of 1/3 at early times, followed by a linear increase at longer times.     

Optical and resonant X-ray diffraction studies confirm a SmC*FI2-SmC* liquid crystal phase sequence reversal

Employing both null transmission ellipsometry and resonant x-ray diffraction, we confirmed the SmC*FI2-SmC* phase sequence reversal in one liquid crystal compound and specially prepared binary mixtures. This phase sequence reversal was predicted by two recent theoretical advances. Moreover, the temperature range for the SmC*FI2 phase increases significantly in the mixture suggesting that such a phase sequence may exist in other compounds.     

Spaces of lower semicontinuous set-valued maps I

We introduce a lower semicontinuous analog, L ^?(X), of the well-studied space of upper semicontinuous set-valued maps with nonempty compact interval images. Because the elements of L ^?(X) contain continuous selections, the space C(X) of real-valued continuous functions on X can be used to establish properties of L ^?(X), such as the two interrelated main theorems. The first of these theorems, the Extension Theorem, is proved in this Part I. The Extension Theorem says that for binormal spaces X and Y, every bimonotone homeomorphism between C(X) and C(Y) can be extended to an ordered homeomorphism between L ^?(X) and L ^?(Y). The second main theorem, the Factorization Theorem, is proved in Part II. The Factorization Theorem says that for binormal spaces X and Y, every ordered homeomorphism between L ^?(X) and L ^?(Y) can be characterized by a unique factorization.     

Function spaces and product topologies on powers of spaces

A study is made of two classes of product topologies on powers of spaces: the general box product topologies, and the general uniform product topologies. Some examples are given and some results are shown about the properties of these general product spaces. This is applied to show that certain spaces of continuous functions with the fine topology are homeomorphic to box product spaces, and certain spaces of continuous functions with the uniform topology are homeomorphic to uniform product spaces.