Shock waves in a particulate suspension

A continuum theory for the distribution of incompressible particles in an incompressible fluid is employed to study the behaviour of plane shock waves in a particulate suspension. An expression is derived for the speed of displacement in terms of the jump in the volume fraction of one of the constituents across the shock. A differential equation is derived to govern the evolutionary behaviour of the shock wave propagating into a region which is in a uniform equilibrium state before the arrival of the shock wave. The implications of this equation are examined in detail.     

On the structure of regular pairwise balanced designs

In this paper we obtain determinantal conditions necessary for the existence of (r,λ)-designs. The work is based on a paper of Connor [2]. In [3] Deza establishes an inequality which must be satisfied by the column vectors of an equidistant code; or, equivalently, the block sizes in an (r,λ)-design. We obtain a generalization of this inequality.     

High multipolarity electroexcitations in 207Pb and 206Pb

We report the identification of new high multipolarity transitions in ²⁰⁷Pb and ²⁰⁶Pb by the measurement of their form factor. A comparison to the corresponding excitations in ²⁰⁸Pb is presented.     

Global Geometric Deformations of Current Algebras as Krichever-Novikov Type Algebras

We construct algebraic-geometric families of genus one (i.e. elliptic) current and affine Lie algebras of Krichever-Novikov type. These families deform the classical current, respectively affine Kac-Moody Lie algebras. The construction is induced by the geometric process of degenerating the elliptic curve to singular cubics. If the finite-dimensional Lie algebra defining the infinite dimensional current algebra is simple then, even if restricted to local families, the constructed families are non-equivalent to the trivial family. In particular, we show that the current algebra is geometrically not rigid, despite its formal rigidity. This shows that in the infinite dimensional Lie algebra case the relations between geometric deformations, formal deformations and Lie algebra two-cohomology are not that close as in the finite-dimensional case. The constructed families are e.g. of relevance in the global operator approach to the Wess-Zumino-Witten-Novikov models appearing in the quantization of Conformal Field Theory. The algebras are explicitly given by generators and structure equations and yield new examples of infinite dimensional algebras of current and affine Lie algebra type.     

Vortex lattice formation in Bose-Einstein condensates

We show that the formation of a vortex lattice in a weakly interacting Bose condensed gas can be modeled with the nonlinear Schr?dinger equation for both T=0 and finite temperatures without the need for an explicit damping term. Applying a weak rotating anisotropic harmonic potential, we find numerically that the turbulent dynamics of the field produces an effective dissipation of the vortex motion and leads to the formation of a lattice. For T=0, this turbulent dynamics is triggered by a rotational dynamic instability of the condensate. For finite temperatures, noise is present at the start of the simulation and allows the formation of a vortex lattice at a lower rotation frequency, the Landau frequency. These two regimes have different vortex dynamics. We show that the multimode interpretation of the classical field is essential.     

Chemical surface modification of poly(p-xylylene) thin films

Electrophilic aromatic substitution reactions were studied at poly(p-xylylene) (PPX) film surface-reaction medium interfaces. The extent of the reactions (depth of penetration and degree of substitution) was determined by the interaction of the polymer with the reaction solution. Reaction with chlorosulfonic acid to produce sulfonyl chloride and sulfone functionalities occurred readily in the bulk of PPX, and yields were sensitive to time and temperature. Confinement of this reaction to the PPX surface was achieved by controlling the concentration of the acid. Functionalization of PPX with N-methylol-2-chloroacetamide in sulfuric acid to produce the chloroamidomethylated derivative occurred in high yield and was confined to the surface region of PPX. Hydrolysis of the amide to generate aminomethylated PPX was assessed by XPS and a derivatization reaction. Friedel-Crafts type chemistry (acylation and alkylation reactions) also produced functionalized surfaces, but with lower degrees of substitution than the other two reactions and was strictly surface-confined.