On the maslov index

In this paper we give four definitions of Maslov index and show that they all satisfy the same system of axioms and hence are equivalent to each other. Moreover, relationships of several symplectic and differential geometric, analytic, and topological invariants (including triple Maslov indices, eta invariants, spectral flow and signatures of quadratic forms) to the Maslov index are developed and formulae relating them are given. The broad presentation is designed with a view to applications both in geometry and in analysis. © 1994 John Wiley & Sons, Inc.     

Topological quantum field theory

A twisted version of four dimensional supersymmetric gauge theory is formulated. The model, which refines a nonrelativistic treatment by Atiyah, appears to underlie many recent developments in topology of low dimensional manifolds; the Donaldson polynomial invariants of four manifolds and the Floer groups of three manifolds appear naturally. The model may also be interesting from a physical viewpoint; it is in a sense a generally covariant quantum field theory, albeit one in which general covariance is unbroken, there are no gravitons, and the only excitations are topological.On leave from Department of Physics, Princeton University. Research supported in part by NSF Grants No. 80-19754, 86-16129, 86-20266     

Complex flows by nanohydrodynamics

The study of complex flows by particle simulations is speeded up over molecular dynamics (MD) by more than two orders of magnitude by employing a stochastic collision dynamics method (DSMC) extended to high density (CBA). As a consequence, a picture generated on a single processor shows the typical features of the Rayleigh–Taylor instability and is in quantitative agreement with the experimentally found long time behaviour.     

Efficient Analysis of Millimeter Wave Ferrite Circulators by the GMRES Iterative Algorithm

The finite element method (FEM) combined with the perfectly matched layers (PML) is given for simulation of waveguide ferrite circulators. The generalized minimal residual (GMRES) iterative method is applied to solve such sparse large non-symmetric system of linear equations resulting from the use of edge-based finite element method. The formulation of FEM and the algorithm of GMRES method are described in detail. The reflection and insertion losses of millimeter wave waveguide circulator are analyzed and the results are compared with those obtained from literature.     

Theodore Strong and ante-bellum American mathematics

Theodore Strong was a prolific contributor to the mathematical and scientific journals of ante-bellum America. His work was not remarkable in its originality, but it dealt with mathematics that was quite sophisticated for its time and place. Strong's published work was a significant factor in the dissemination of advanced mathematics to his countrymen, and he played an important role in the education of a few mathematicians who were active in the latter part of the 19th century, most notably George William Hill.     

Topological gauge theories and group cohomology

We show that three dimensional Chern-Simons gauge theories with a compact gauge groupG (not necessarily connected or simply connected) can be classified by the integer cohomology groupH ⁴(BG,Z). In a similar way, possible Wess-Zumino interactions of such a groupG are classified byH ³(G,Z). The relation between three dimensional Chern-Simons gauge theory and two dimensional sigma models involves a certain natural map fromH ⁴(BG,Z) toH ³(G,Z). We generalize this correspondence to topological spin theories, which are defined on three manifolds with spin structure, and are related to what might be calledZ ₂ graded chiral algebras (or chiral superalgebras) in two dimensions. Finally we discuss in some detail the formulation of these topological gauge theories for the special case of a finite group, establishing links with two dimensional (holomorphic) orbifold models.     

Threshold 3He and 3H Transverse Electron Scattering Response Functions

The threshold transverse response functions R _T (q, ω) for ³He and ³H are calculated using the AV18 nucleon–nucleon potential, the UrbanaIX three-body force, and the Coulomb potential. Final states are completely taken into account via the Lorentz integral transform technique. Consistent two-body π- and ρ-meson exchange currents as deduced using the Arenhövel-Schwamb technique are included. The convergence of the method is shown and a comparison of the corresponding MEC contribution is made to that of a consistent MEC for the meson theoretical r-space BonnA potential. The response R _T is calculated in the threshold region at q = 174, 324, and 487 MeV/c and compared with available data. The strong MEC contributions in the threshold region are nicely confirmed by the data at q = 324 and 487 MeV/c although some differences between theoretical and experimental results remain. A comparison is also made with other calculations, where the same theoretical input is used. The agreement is generally rather good, but leaves also some space for further improvement.     

Edge effects on the order and freezing of a 2D array of block copolymer spheres

The order in a single layer of spherical domains of a block copolymer melt is investigated as a function of distance from the edges of the 15 microm wide, 30 nm deep wells that confine it along a substrate. At 255 degrees C the edge induces the formation of a hexatic phase whose orientational and translational order decreases slowly away from the edge until in the center of the well the block copolymer spheres have liquidlike order.     

Matrix isolation study of S2O6F2 pyrolysis products: The infrared spectrum of SO3F radical

Infrared and visible absorption spectra of the low pressure heated products of S₂O₆F₂ trapped in inert gas matrices at 14 K are presented. The following have been identified as major infrared-absorbing species: SO₃F, SO₃, HSO₃F, and S₂O₆F₂, with matrix spectra of the latter three unequivocally confirming their presence. Reasonable reactions accounting for the production of these species are proposed, and a reassignment of the fundamental vibrations of monomeric HSO₃F is offered. The infrared absorptions of the SO₈F radical have been observed for the first time, and the six fundamental vibrations determined. These frequencies are in good accord with earlier values deduced indirectly by King and Warren from hot band transitions in the visible absorption spectrum of the vapor. This same visible system (${}^2\text{E}\text{-}\text{X}\text{?}{}^2\text{A}{}_2$) has also been observed here for the matrix isolated species.