Micro-interferometry for measurement of thermal displacements at fiber/matrix interfaces

A micro-interferometric technique for measuring out-of-plane thermal displacements on a scale commensurate with the dimensions of the fiber/matrix unit cell is described. A scanning micro-interferometer is used to image surface displacements of samples containing a single-pitch-based carbon fiber embedded in an epoxy matrix. The interferometer design gives the necessary resolution to detect small changes in thermal displacements in the fiber/matrix interface region. The samples were heated electrically through the fiber to create radially symmetric temperature and displacement fields. Repeatable displacement measurements were obtained on a radial line across the interface region with an accuracy of ±25 Å. A sharp expansion of the matrix surrounding the fiber was observed with each heating. Overall, the experiments demonstrate the utility of micro-interferometry for measuring submicron displacements.     

Nevanlinna–Pick interpolation on distinguished varieties in the bidisk

This article treats Nevanlinna–Pick interpolation in the setting of a special class of algebraic curves called distinguished varieties. An interpolation theorem, along with additional operator theoretic results, is given using a family of reproducing kernels naturally associated to the variety. The examples of the Neil parabola and doubly connected domains are discussed.     

Minimal genus of abelian actions on Klein surfaces with boundary

Supported in part by the National Science Foundation     

Proper analytic free maps

This paper concerns analytic free maps. These maps are free analogs of classical analytic functions in several complex variables, and are defined in terms of non-commuting variables amongst which there are no relations - they are free variables. Analytic free maps include vector-valued polynomials in free (non-commuting) variables and form a canonical class of mappings from one non-commutative domain D in say g variables to another non-commutative domain in variables. As a natural extension of the usual notion, an analytic free map is proper if it maps the boundary of D into the boundary of . Assuming that both domains contain 0, we show that if is a proper analytic free map, and f(0)=0, then f is one-to-one. Moreover, if also , then f is invertible and f−1 is also an analytic free map. These conclusions on the map f are the strongest possible without additional assumptions on the domains D and .     

Stillman's question for exterior algebras and Herzog's conjecture on Betti numbers of syzygy modules

Let K be a field of characteristic 0 and consider exterior algebras of finite dimensional K-vector spaces. In this short paper we exhibit principal quadric ideals in a family whose Castelnuovo–Mumford regularity is unbounded. This negatively answers the analogue of Stillman's Question for exterior algebras posed by I. Peeva. We show that, via the Bernstein–Gel'fand–Gel'fand correspondence, these examples also yields counterexamples to a conjecture of J. Herzog on the Betti numbers in the linear strand of syzygy modules over polynomial rings.     

Free actions on handlebodies

The equivalence (or weak equivalence) classes of orientation-preserving free actions of a finite group G on an orientable three-dimensional handlebody of genus g?1 can be enumerated in terms of sets of generators of G. They correspond to the equivalence classes of generating n-vectors of elements of G, where n=1+(g−1)/|G|, under Nielsen equivalence (or weak Nielsen equivalence). For Abelian and dihedral G, this allows a complete determination of the equivalence and weak equivalence classes of actions for all genera. Additional information is obtained for other classes of groups. For all G, there is only one equivalence class of actions on the genus g handlebody if g is at least 1+?(G)|G|, where ?(G) is the maximal length of a chain of subgroups of G. There is a stabilization process that sends an equivalence class of actions to an equivalence class of actions on a higher genus, and some results about its effects are obtained.     

Analytic model for surface-induced molecular weight segregation in thermoplastic composites

An analytic model based on a random-walk formulation for absorbing barriers is presented. The range of applicability of the model is established from results derived from Monte Carlo simulations. The model takes into account the influences of neutral, repulsive, and attractive polymer-surface interactions on the spatial variation of species concentrations in the vicinity of a surface. The model predicts that the lower molecular weight species of a polydisperse mixture will accumulate in the vicinity of a surface to create an interphase region. The extent of this surface-perturbed interphase region is on the order of three times the radius of gyration of the longest species of the mixture. The degree of molecular weight segregation is dependent upon the breadth of the molecular weight distribution. © 1994 John Wiley & Sons. Inc.