The effect of solvent upon molecularly thin rotaxane film formation

We have investigated variations in molecularly thin rotaxane films deposited by solvent evaporation, using atomic force microscopy (AFM). Small changes in rotaxane structure result in significant differences in film morphology. The addition of exo-pyridyl moietes to the rotaxane macrocycle results in uniform domains having orientations corresponding to the underlying substrate lattice, while a larger, less symmetric molecule results in a greater lattice mismatch and smaller domain sizes. We have measured differences in film heights both as a function of the solvent of deposition and as a function of surface coverage of rotaxanes. Based on these observations we describe how the use of solvents with higher hydrogen-bond basicity results in films which are more likely to favour sub-molecular motion.     

Three-pencil lattices on triangulations

In this paper, three-pencil lattices on triangulations are studied. The explicit representation of a lattice, based upon barycentric coordinates, enables us to construct lattice points in a simple and numerically stable way. Further, this representation carries over to triangulations in a natural way. The construction is based upon group action of S ₃ on triangle vertices, and it is shown that the number of degrees of freedom is equal to the number of vertices of the triangulation.      

Multiscale Finite Element Modeling of Arc Dynamics in a DC Plasma Torch

The dynamics of the electric arc inside a direct current non-transferred arc plasma torch are simulated using a three-dimensional, transient, equilibrium model. The fluid and electromagnetic equations are solved numerically in a fully coupled approach by a multiscale finite element method. Simulations of a torch operating with argon and argon–hydrogen under different operating conditions are presented. The model is able to predict the operation of the torch in steady and takeover modes without any further assumption on the reattachment process except for the use of an artificially high electrical conductivity near the electrodes, needed because of the equilibrium assumption. The results obtained indicate that the reattachment process in these operating modes may be driven by the movement of the arc rather than by a breakdown-like process. It is also found that, for a torch operating in these modes and using straight gas injection, the arc will tend to re-attach to the opposite side of its original attachment. This phenomenon seems to be produced by a net angular momentum on the arc due to the imbalance between magnetic and fluid drag forces.     

Equivalence of regularity for the Bergman projection and the\bar \partial-neumann operator

A necessary and sufficient condition for regularity of the -Neumann operator on (0,q)-forms in a smooth bounded pseudoconvex domain in Cⁿ is that the orthogonal projections onto -closed forms of degrees (0,q−1), (0,q), and (0,q+1) all be regular. The first author partially supported by NSF Grant DMS-8701038     

Events correlated with respect to every subposet of a fixed poset

Posets are said to be (positively) correlated with respect to a third posetR onX (we writeA _R B) ifP(AR) P(AR B). HereP(CR) is the probability that a randomly chosen linear extension ofR is also a linear extension ofC. We classify posetsR onX such that(x, y) _s (u, v) holds for all posetsS onX which are subposets ofR, wherex, y, u, v are distinct elements ofX. On the way to proving this result, we show when a correlation inequality due to Shepp holds strictly.     

Sphere orders

Ann-sphere order is a finite partially ordered set representable by containment ofn-spheres in Euclidean (n+1)-space. We present a sequence {P _i } of ordered sets such that eachP _i is ann-sphere order only forni; one consequence is that we are able to determine the dimension of a Euclidean space-time manifold from the finite suborders of its causality order.Research supported by ONR grant N00014 85-K-0769.     

A Dynamic location problem for graphs

We introduce a class of optimization problems, calleddynamic location problems, involving the processing of requests that occur sequentially at the nodes of a graphG. This leads to the definition of a new parameter of graphs, called the window indexWX(G), that measures how large a window into the future is needed to solve every instance of the dynamic location problem onG optimally on-line. We completely characterize this parameter:WX(G)k if and only ifG is a weak retract of a product of complete graphs of size at mostk. As a byproduct, we obtain two (polynomially recognizable) structural characterizations of such graphs, extending a result of Bandelt.