The semiclassical limit of a quantum Fermi accelerator

A classical Fermi accelerator model (FAM) is known to show chaotic behavior. The FAM is defined by a free particle bouncing elastically from two rigid walls, one fixed and the other oscillating periodically in time. The central aim of this paper is to connect the quantum and the classical solutions to the FAM in the semiclassical limit. This goal is accomplished using a finite inverted parametric oscillator (FIPO), confined to a box withfixed walls, as an alternative representation of the FAM. In the FIPO representation, an explicit correspondence between classical and quantum limits is accomplished using a Husimi representation of the quasienergy eigenfunctions.     

Point-to-Periodic and Periodic-to-Periodic Connections

In this work we consider computing and continuing connecting orbits in parameter dependent dynamical systems. We give details of algorithms for computing connections between equilibria and periodic orbits, and between periodic orbits. The theoretical foundation for these techniques is given by the seminal work of Beyn in 1994, “On well-posed problems for connecting orbits in dynamical systems”, where a numerical technique is also proposed. Our algorithms consist of splitting the computation of the connection from that of the periodic orbit(s). To set up appropriate boundary conditions, we follow the algorithmic approach used by Demmel, Dieci, and Friedman, for the case of connecting orbits between equilibria, and we construct and exploit the smooth block Schur decomposition of the monodromy matrices associated to the periodic orbits. Numerical examples illustrate the performance of the algorithms. This revised version was published online in July 2006 with corrections to the Cover Date.     

An approximation property of harmonic functions in Lipschitz domains and some of its consequences

An extension of an inequality of J. B. Garnett (1979), with improvements by B. E. J. Dahlberg (1980), on an approximation property of harmonic functions is proved. The weighted inequality proved here was suggested by the work of J. Pipher (1993) and it implies an extension of a result of S. Y. A. Chang, J. Wilson and T. Wolff (1985) and C. Sweezy (1991) on exponential square integrability of the boundary values of solutions to second-order linear differential equations in divergence form. This implies a solution of a problem left open by R. Bañuelos and C. N. Moore (1989) on sharp estimates for the area integral of harmonic functions in Lipschitz domains.

     

Magnetic structures and crystal field in the heavy electron materials YbAgGe and YbPtIn

We have examined the magnetic properties of the heavy electron compounds YbAgGe and YbPtIn by ¹⁷⁰Yb M?ssbauer spectroscopy down to 0.1 K, and the crystal field properties of YbAgGe by Perturbed Angular Correlations (PAC) measurements up to 900 K. In YbAgGe, we show that each of the two magnetically ordered phases below 0.8 K involves a specific incommensurate modulation of the Yb moment. An analysis of existing low temperature specific heat data suggests the persistence of fluctuations of the correlated Yb spins down to 0.1 K. The PAC data allow to discriminate among proposed Yb³⁺ crystal field level schemes. In YbPtIn, we show that the low temperature magnetic order phase has an antiferro-para structure, where zero moment Yb ions coexist with large moment ones, and that a 90° moment reorientation occurs at 1.4 K.     

Synthesis of poly(vinyl chloride)‐b‐poly(n‐butyl acrylate)‐b‐poly(vinyl chloride) by the competitive single‐electron‐transfer/degenerative‐chain‐transfer‐mediated living radical polymerization in water

The synthesis of a block copolymer poly(vinyl chloride)‐b‐poly(n‐butyl acrylate)‐b‐poly(vinyl chloride) is reported. This new material was synthesized by single‐electron‐transfer/degenerative‐chain‐transfer‐mediated living radical polymerization (SET‐DTLRP) in two steps. First, a bifunctional macroinitiator of α,ω‐di(iodo)poly (butyl acrylate) [α,ω‐di(iodo)PBA] was synthesized by SET‐DTLRP in water at 25 °C. The macroinitiator was further reinitiated by SET‐DTLRP, leading to the formation of the desired product. This ABA block copolymer was synthesized with high initiator efficiency. The kinetics of the copolymerization reaction was studied for two PBA macroinitiators with number–average molecular weight of 10 k and 20 k. The relationship between the conversion and the number–average molecular weight was found to be linear. The dynamic mechanical thermal analysis suggests just one phase, indicating that copolymer behaves as a single material with no phase separation. This methodology provides the access to several block copolymers and other complex architectures that result from combinations of thermoplastics (PVC) and elastomers (PBA). From industrial standpoint, this process is attractive, because of easy experimental setup and the environmental friendly reaction medium. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3001–3008, 2006     

Single electron transfer–degenerative chain transfer living radical polymerization of N‐butyl acrylate catalyzed by Na2S2O4 in water media

Living radical polymerization of n‐butyl acrylate was achieved by single electron transfer/degenerative‐chain transfer mediated living radical polymerization in water catalyzed by sodium dithionate. The plots of number–average molecular weight versus conversion and ln[M]₀/[M] versus time are linear, indicating a controlled polymerization. This methodology leads to the preparation of α,ω‐di(iodo) poly (butyl acrylate) (α,ω‐di(iodo)PBA) macroinitiators. The influence of polymerization degree ([monomer]/[initiator]), amount of catalyst, concentration of suspending agents and temperature were studied. The molecular weight distributions were determined using a combination of three detectors (TriSEC): right‐angle light scattering (RALLS), a differential viscometer (DV), and refractive index (RI). The methodology studied in this work represents a possible route to prepare well‐tailored macromolecules made of butyl acrylate in an environmental friendly reaction medium. Moreover, such materials can be subsequently functionalized leading to the formation of different block copolymers of composition ABA. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2809–2825, 2006     

The extended loop group: An infinite dimensional manifold associated with the loop space

A set of coordinates in the non-parametric loop-space is introduced. We show that these coordinates transform under infinite dimensional linear representations of the diffeomorphism group. An extension of the group of loops in terms of these objects is proposed. The enlarged group behaves locally as an infinite dimensional Lie group. Ordinary loops form a subgroup of this group. The algebraic properties of this new mathematical structure are analyzed in detail. Applications of the formalism to field theory, quantum gravity and knot theory are considered.     

An analysis of reduced Hessian methods for constrained optimization

We study the convergence properties of reduced Hessian successive quadratic programming for equality constrained optimization. The method uses a backtracking line search, and updates an approximation to the reduced Hessian of the Lagrangian by means of the BFGS formula. Two merit functions are considered for the line search: the ₁ function and the Fletcher exact penalty function. We give conditions under which local and superlinear convergence is obtained, and also prove a global convergence result. The analysis allows the initial reduced Hessian approximation to be any positive definite matrix, and does not assume that the iterates converge, or that the matrices are bounded. The effects of a second order correction step, a watchdog procedure and of the choice of null space basis are considered. This work can be seen as an extension to reduced Hessian methods of the well known results of Powell (1976) for unconstrained optimization.This author was supported, in part, by National Science Foundation grant CCR-8702403, Air Force Office of Scientific Research grant AFOSR-85-0251, and Army Research Office contract DAAL03-88-K-0086.This author was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under contracts W-31-109-Eng-38 and DE FG02-87ER25047, and by National Science Foundation Grant No. DCR-86-02071.     

The algebra of implicit operations

For an ordinal and a class of topological algebras of a given type (which may be infinite and may contain inflnitary operations), an-aryimplicit operation on is any new-ary operation whose introduction does not eliminate any continuous homomorphisms between members of . The set of all-ary implicit operations on is denoted by and forms an algebra of the given type which is endowed with the least topology making continuous all homomorphisms into members of . With this topology, is a topological algebra in which the subalgebra of all-ary operations on which are induced by terms is dense, provided that is closed under the formation of closed subalgebras and finitary direct products. This is obtained by realizing as an inverse limit of-generated members of . These results are applied to pseudovarieties of topological and finite algebras.This work was supported, in part, by INIC grant 85/CEX/4. This paper was written while the author was a faculty member at the Universidade do Minho.Presented by Ralph McKenzie.