Semiempirical determination of the atom-surface interaction

We discuss three methods of determining V(z), the lateral average (G = 0 Fourier component) of the atom-surface interaction, from the bound state spectrum found in beam scattering. One method uses the Rydberg-Klein-Rees technique, which yields the width of the potential (i.e., separation of classical turning points) as a function of energy. This method incorporates also the known asymptotic form V ～ ?C₃z^?3, whereC₃ is derived from the polarizability and dielectric function of atom and solid, respectively. The second method uses a hybrid potential, constructed from a Morse potential with shifted zero of energy connected to the asymptotic form,?C₃z^?3, requiring continuity of V and $\text{d}\text{V}\text{d}\text{z}$. The third potential is a Lennard-Jones 3–9 interaction. Results are presented for H and He scattering from LiF and NaF.     

Stream function finite element solution of Stokes flow with penalties

A finite element method for solution of the stream function formulation of Stokes flow is developed. The method involves complete cubic non-conforming (C⁰) triangular Hermite elements. This element fails the patch test. To correct the element and produce a convergent method we employ a penalty method to weakly enforce the desired continuity constraint on the normal derivative across the inter-element boundaries. Successful use of the method is demonstrated to require reduced integration of the inter-element penalty with a 1-point Gauss rule. Error estimates relate the optimal choice of penalty parameter to mesh size and are corroborated by numerical convergence studies. The need for reduced integration is interpreted using rank relations for an associated hybrid method.     

Enhanced thermal conductance at a copper-liquid helium interface in the presence of acoustic streaming

In a conventional Kapitza resistance experiment involving heat transfer across a copper surface into liquid helium, an acoustic streaming velocity field (at 10 MHz) was directed transverse to the surface normal. Ultrasound had no observable effect on the heat transfer to the superfluid phase (He-II), but in the normal fluid phase (He-I) the thermal conductance increased linearly with acoustic velocity amplitude, reaching a value 2.5 times the zero sound conductance for a sound velocity amplitude of 0.8 cm s^?1.     

Use of acousto-optic techniques to detect subharmonic and cavitation activity

Observations were made of the diffraction patterns produced by the acousto-optic effect in superfluid helium and in methanol for both cylindrical and plane wave sound fields. Thresholds for the subharmonic of order $\text{1}\text{2}$ and transient cavitation were determined by observation of abrupt changes in the diffraction patterns. The onset of the subharmonic produced additional diffracted signals in a stable diffraction pattern while onset of cavitation completely disrupted the diffraction pattern.     

Metabolites of pyrenomycetes XIII: Structure of (+) hypothemycin,an antibiotic macrolide from Hypomyces trichothecoides

(+) Hypothemycin, an antibiotic metabolite of Hypomyces trichothecoides, has been assigned the macrolide structure I, based on chemical evidence and spectroscopic data.     

A stable least-squares finite element method for non-linear hyperbolic problems

A class of stable least-square finite element methods for non-linear hyperbolic problems is developed and some exploratory studies made. The methods are based on modifying the L²-norm of the. residual and a related approximation to the H¹-norm of the residual. The effect of the additional terms in these residual functionals is to introduce a dissipative effect proportional to the solution gradient. This acts to stabilize the solution for non-linear hyperbolic problems which generate shocks. Numerical results for a one-dimensional nozzle and shock tube problem demonstrate the accuracy and stability of the method. Results are for an implicit scheme and calculations for linear, quadratic and cubic elements are given.     

The massless Thirring model: Positivity of Klaiber'sn-point functions

We present a simple solution to the problem of proving positivity of Klaiber'sn-point functions for the massless Thirring model. The corresponding fields are obtained as strong limits of explicitly given approximate fields, obviating reconstruction. By invoking recent results on the boson-fermion correspondence it is shown how the model can be formulated on the charged fermion Fock space. It is pointed out that the question of cyclicity of the vacuum is open, and that an affirmative answer is necessary to confirm the superselection sector picture of the model.     

Steinberg symbols modulo the trace class, holonomy, and limit theorems for Toeplitz determinants

Suppose that where and , and the Toeplitz operator is invertible. Let be the determinant of the Toeplitz matrix where . Let be the orthogonal projection onto where ; set , let denote the Hankel operator associated to , and set for . For the Wiener-Hopf factorization where and , put , Theorem A.    

Let be a decomposition into invariant subspaces, and , so that restricted to is invertible, is finite dimensional, and restricted to is nilpotent. Let be the basis for the null space of , and let be the top vector in a Jordan root vector chain of length lying over , i.e., where . Theorem B.     , the holonomy of a Deligne bundle with connection defined by the factorization . Note that the generalizations of the Szegö limit theorem for which have appeared in the literature with instead of have the defect that the limit of does not exist in general. An example is given with yet for infinitely many .