Operation of repetitively pulsed virtual cathode oscillators on theTEMPO pulser

The design and performance characteristics of two virtual cathode oscillators operated at a 1-Hz repetition rate for a 10-shot burst using the TEMPO pulser are presented. The 2.4-GHz hardware generated a 300 MW per pulse (radiated) in the TM₀₂ mode with a 1.3% total energy conversion efficiency and with a 10.5% frequency bandwidth. A 2:1 scale-tip of this hardware was used to achieve an 840-MHz operation, but it only radiated 70 MW per pulse in the TM₀₁ mode with a 7.3% bandwidth, since hardware constraints prevented the TM₀₂ component from being radiated. The relatively low beam current density of the TEMPO VCOs yielded a low diode gap closure rate that should make them suitable for long-pulse operation. In addition, the low beam current density minimized damage to the thin anode screen     

Evolution in complex systems

What features characterize complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena. Here we argue that slow, directed dynamics, during which the system's properties change significantly, is fundamental. The underlying dynamics is related to a slow, decelerating but spasmodic release of an intrinsic strain or tension. Time series of a number of appropriate observables can be analyzed to confirm this effect. The strain arises from local frustration. As the strain is released through “quakes,” some system variable undergoes record statistics with accompanying log‐Poisson statistics for the quake event times. We demonstrate these phenomena via two very different systems: a model of magnetic relaxation in type II superconductors and the Tangled Nature model of evolutionary ecology and show how quantitative indications of aging can be found. © 2004 Wiley Periodicals, Inc. Complexity 10: 49–56, 2004     

Diffeomorphism finiteness for manifolds with ricci curvature andL n/2-norm of curvature bounded

Partially supported by NSF Grants.     

Periodic solutions for a nonautonomous ordinary differential equation

We consider the nonautonomous differential equation of second order x^″+a(t)x−b(t)x²+c(t)x³=0, where a(t),b(t),c(t) are T-periodic functions. This is a biomathematical model of an aneurysm in the circle of Willis. We prove the existence of at least two positive T-periodic solutions for this equation, using coincidence degree theories.     

On a new class of dynamic Hardy-type inequalities and some related generalizations

Aequationes mathematicae - In this paper, we establish a new class of dynamic inequalities of Hardy’s type which generalize and improve some recent results given in the literature. More...     

Geometric modules and Quinn homology theory

LetR be a ring with unit and invariant basis property. In [1], the authors define a functorK(_;R):TOP/LIP _c-LPEP by combining the open cone construction of [7] with a geometric module construction and show this functor is a homology theory. This paper shows that if attention is restricted to objects TOP/LIP _c with a homotopy colimit structure, then the functorK(_;R) is a Quinn homology theory, In particular, for each having a homotopy colimit structure,K(;R) is a homotopy colimit in the category of -spectra. Furthermore, the constituent spectra of this homotopy colimit are obtained naturally from the fibres of .Partially supported by the National Science Foundation under grant number DMS88-03148.Partially supported by the SNF (Denmark) under grant number 11-7792.     

The visual core of a hyperbolic 3-manifold

In this note we introduce the notion of the visual core of a hyperbolic 3-manifold , and explore some of its basic properties. We investigate circumstances under which the visual core of a cover of N embeds in N, via the usual covering map . We go on to show that if the algebraic limit of a sequence of isomorphic Kleinian groups is a generalized web group, then the visual core of the algebraic limit manifold embeds in the geometric limit manifold. Finally, we discuss the relationship between the visual core and Klein-Maskit combination along component subgroups. Received: 16 March 1999 / Revised version: 14 May 2001 / Published online: 19 October 2001     

Multiple domain dynamics simulated with coupled level sets

We adapt the level-set method to simulate epitaxial growth of thin films on a surface that consists of different reconstruction domains. Both the island boundaries and the boundaries of the reconstruction domains are described by different level-set functions. A formalism of coupled level-set functions that describe entirely different physical properties is introduced, where the velocity of each level-set function is determined by the value of the other level-set functions.     

Mod 2 cohomology of combinatorial Grassmannians

Matroid bundles, introduced by MacPherson, are combinatorial analogues of real vector bundles. This paper sets up the foundations of matroid bundles. It defines a natural transformation from isomorphism classes of real vector bundles to isomorphism classes of matroid bundles. It then gives a transformation from matroid bundles to spherical quasifibrations, by showing that the geometric realization of a matroid bundle is a spherical quasifibration. The poset of oriented matroids of a fixed rank classifies matroid bundles, and the above transformations give a splitting from topology to combinatorics back to topology. A consequence is that the mod 2 cohomology of the poset of rank k oriented matroids (this poset classifies matroid bundles) contains the free polynomial ring on the first k Stiefel-Whitney classes.     

Coxeter–Petrie Complexes of Regular Maps

Coxeter–Petrie complexes naturally arise as thin diagram geometries whose rank 3 residues contain all of the dual forms of a regular algebraic map M. Corresponding to an algebraic map is its classical dual, which is obtained simply by interchanging the vertices and faces, as well as its Petrie dual, which comes about by replacing the faces by the so-called Petrie polygons. Jones and Thornton have shown that these involutory duality operations generate the symmetric groupS₃ , giving in all six dual forms, and whose source is the outer automorphism group of the infinite triangle group generated by involutions s₁, s₂, s₃, subject to the additional relation s₁s₃ =  s₃s₁. In fact, this outer automorphism group is parametrized by the permutations of the three commuting involutions s₁,s₃ , s₁s₃. These involutions together with the involutions₂ can be taken to define the nodes of a Coxeter diagram of shape D₄(with the involution s₂at the central node), and when the original map M is regular, there is a natural extension from M to a thin Coxeter complex of rank 4 all of whose rank 3 residues are isomorphic to the various dual forms of M. These are fully explicated in case the original algebraic map is a Platonic map.