Coherent Solid-State Phase Transitions with Atomic Diffusion: A Thermomechanical Treatment

Using the framework of modern continuum thermomechanics, we develop sharp- and diffuse-interface theories for coherent solid-state phase transitions. These theories account for atomic diffusion and for deformation. Of essential importance in our formulation of the sharp-interface theory are a system of configurational forces and an associated configurational force balance. These forces, which are distinct from standard Newtonian forces, describe the intrinsic material structure of a body. The configurational balance, when restricted to the interface, leads to a generalization of the classical Gibbs–Thomson relation, a generalization that accounts for the orientation dependence of the interfacial energy density and also for a broad spectrum of dissipative transition kinetics. Our diffuse-interface theory involves nonstandard microforces and an associated microforce balance. These forces arise naturally from an interpretation of the atomic densities as macroscopic parameters that describe atomistic kinematics distinct from the motion of material particles. When supplemented by thermodynamically consistent constitutive relations, the microforce balance yields a generalization of the Cahn–Hilliard relation giving the chemical potentials as variational derivatives of the total free energy with respect to the atomic densities. A formal asymptotic analysis (thickness of the transition layer approaching zero) demonstrates the correspondence between versions of our theories specialized to the case of a single mobile species for situations in which the time scale for interface propagation is small compared to that for bulk diffusion. While the configurational force balance is redundant in the diffuse-interface theory, when integrated over the transition layer, the limit of this balance is the interfacial configurational force balance (i.e., generalized Gibbs–Thomson relation) of the sharp-interface theory.     

Spectrophotometric determination of traces of palladium after coprecipitation with tellurium

A spectrophotometric method for the determination of microgram amounts of palladium in the présence of much iron, copper, nickel, cobalt and other common elements (~ 0.5 g) is described. Palladium is separated by stannous chloride precipitation with tellurium as collector. p-Nitroso-diphenylamine is used as the colorimetric reagent, and diethyl oxalate as extradant for the palladium complex (sensitivity = 0.0015 μg $\text{Pd}\text{cm}{}^2$ ≡ log {I₀/I} = 0.001). Silver, selenium and tungsten lead to low results and should not exceed ~ 0.1 mg. The weight ratio Au/Pd should not exceed 10, else results for palladium are high. For Pd > 1 μg, recoveries average 90% or. better.     

Chemistry of condensed thiophenes. III. Acetylation of triphenyleno [1,12-bcd]thiophene

Friedel-Crafts reaction of triphenyleno[1,12-bcd]thiophene (2) by means of aluminum chloride, nitrobenzene, and a limited excess of acetyl chloride yielded 3-acetyl-2 (78%) and 3,5-diacetyl-2 (7%). Use of a large excess of acetyl chloride gave yields of 42% and 22%, respectively. Wolff-Kishner reduction of the acetyl compounds produced 3-ethyl-2 (15%) and 3,5-diethyl-2 (8%). Structures were assigned largely on the basis of ¹H nmr and ultraviolet absorption spectra of the products.     

Stability of the local gamma factor in the unitary case

In [Stephen Rallis, David Soudry, Stability of the local gamma factor arising from the doubling method, Math. Ann. 333 (2) (2005) 291-313, MR2195117 (2006m:22026)], Rallis and Soudry prove the stability under twists by highly ramified characters of the local gamma factor arising from the doubling method, in the case of a symplectic group or orthogonal group G over a local non-archimedean field F of characteristic zero, and a representation π of G, which is not necessarily generic. This paper extends their arguments to show the stability in the case when G is a unitary group over a quadratic extension E of F, thereby completing the proof of the stability for classical groups. This stability property is important in Cogdell, Kim, Piatetski-Shapiro, and Shahidi's use of the converse theorem to prove the existence of a weak lift from automorphic, cuspidal, generic representations of G(A) to automorphic representations of GLn(A) for appropriate n, to which references are given in [Stephen Rallis, David Soudry, Stability of the local gamma factor arising from the doubling method, Math. Ann. 333 (2) (2005) 291-313, MR2195117 (2006m:22026)].     

Instability Paths in the Kirchhoff–Plateau Problem

The Kirchhoff–Plateau problem concerns the equilibrium shapes of a system in which a flexible filament in the form of a closed loop is spanned by a soap film, with the filament being modeled as a Kirchhoff rod and the action of the spanning surface being solely due to surface tension. Adopting a variational approach, we define an energy associated with shape deformations of the system and then derive general equilibrium and (linear) stability conditions by considering the first and second variations of the energy functional. We analyze in detail the transition to instability of flat circular configurations, which are ground states for the system in the absence of surface tension, when the latter is progressively increased. Such a theoretical study is particularly useful here, since the many different perturbations that can lead to instability make it challenging to perform an exhaustive experimental investigation. We generalize previous results, since we allow the filament to possess a curved intrinsic shape and also to display anisotropic flexural properties (as happens when the cross section of the filament is noncircular). This is accomplished by using a rod energy which is familiar from the modeling of DNA filaments. We find that the presence of intrinsic curvature is necessary to obtain a first buckling mode which is not purely tangent to the spanning surface. We also elucidate the role of twisting buckling modes, which become relevant in the presence of flexural anisotropy.     

Engineered biosynthesis of hybrid macrolide polyketides containing D-angolosamine and D-mycaminose moieties

The glycosylation of natural product scaffolds with highly modified deoxysugars is often essential for their biological activity, being responsible for specific contacts to molecular targets and significantly affecting their pharmacokinetic properties. In order to provide tools for the targeted alteration of natural product glycosylation patterns, significant strides have been made to understand the biosynthesis of activated deoxysugars and their transfer. We report here efforts towards the production of plasmid-borne biosynthetic gene cassettes capable of producing TDP-activated forms of D-mycaminose, D-angolosamine and D-desosamine. We additionally describe the transfer of these deoxysugars to macrolide aglycones using the glycosyl transferases EryCIII, TylMII and AngMII, which display usefully broad substrate tolerance.