Method of constructing exactly solvable chaos

We present a new systematic method of constructing rational mappings as ergordic transformations with nonuniform invariant measures on the unit interval [0,1]. As a result, we obtain a two-parameter family of rational mappings that have a special property in that their invariant measures can be explicitly written in terms of algebraic functions of parameters and a dynamical variable. Furthermore, it is shown here that this family is the most generalized class of rational mappings possessing the property of exactly solvable chaos on the unit interval, including the Ulam=Neumann map y=4x(1-x). Based on the present method, we can produce a series of rational mappings resembling the asymmetric shape of the experimentally obtained first return maps of the Beloussof-Zhabotinski chemical reaction, and we can match some rational functions with other experimentally obtained first return maps in a systematic manner.Comment: 12 pages, 2 figures, REVTEX. Title was changed. Generalized Chebyshev maps including the precise form of two-parameter generalized cubic maps were added. Accepted for publication in Phys. Rev. E(1997

Identifying the Influences on network formation in structural isomers of multifunctional epoxies using near-infrared spectroscopy

The network formation of four epoxy-rich formulations of the structural isomers of triglycidyl aminophenol and diaminodiphenyl sulfone has been monitored by using two complementary techniques, near-infrared spectroscopy and resin temperature monitoring. The differences between these networks have been described using the concentration of epoxide, primary amine, secondary amine, and tertiary amine functional groups and the actual temperature of the resin compared to the oven temperature during the cure schedule. It was found that initially, the 3,3′-diaminodiphenyl sulfone (33′DDS) formulations were more reactive and primary amines were completely consumed before the 4,4′-diaminodiphenyl sulfone (44′DDS) formulations. Secondary amines were formed more quickly in 33′DDS formulations compared to 44′DDS. The triglycidyl-meta-aminophenol (TGmAP) formulations consumed secondary amines and produced tertiary amines faster than the triglycidyl-para-aminophenol (TGpAP) formulations, indicating higher levels of cross-linking occurred earlier in the curing reaction. Etherification occurred much earlier in the TGpAP formulations than in the TGmAP formulations. Results suggest that internal cyclization occurs in the three meta isomer-containing formulations, and a corresponding lack of this effect in TGpAP/44′DDS results in a more homogeneous cross-linked network

Swinging Atwood's Machine: Experimental and Theoretical Studies

A Swinging Atwood Machine (SAM) is built and some experimental results concerning its dynamic behaviour are presented. Experiments clearly show that pulleys play a role in the motion of the pendulum, since they can rotate and have non-negligible radii and masses. Equations of motion must therefore take into account the inertial momentum of the pulleys, as well as the winding of the rope around them. Their influence is compared to previous studies. A preliminary discussion of the role of dissipation is included. The theoretical behaviour of the system with pulleys is illustrated numerically, and the relevance of different parameters is highlighted. Finally, the integrability of the dynamic system is studied, the main result being that the Machine with pulleys is non-integrable. The status of the results on integrability of the pulley-less Machine is also recalled.Comment: 37 page

Micro-evolutionary diversification among Indian Ocean parrots: temporal and spatial changes in phylogenetic diversity as a consequence of extinction and invasion

Almost 90% of global bird extinctions have occurred on islands. The loss of endemic spe- cies from island systems can dramatically alter evolutionary trajectories of insular species biodiversity, resulting in a loss of evolutionary diversity important for species adaptation to changing environments. The Western Indian Ocean islands have been the scene of evolution for a large number of endemic parrots. Since their discovery in the 16th cen- tury, many of these parrots have become extinct or have declined in numbers. Alongside the extinction of species, a number of the Indian Ocean islands have experienced coloni- zation by highly invasive parrots, such as the Ring-necked Parakeet Psittacula krameri. Such extinctions and invasions can, on an evolutionary timescale, drive changes in spe- cies composition, genetic diversity and turnover in phylogenetic diversity, all of which can have important impacts on species potential for adaptation to changing environmen- tal and climatic conditions. Using mtDNA cytochrome b data, we resolve the taxonomic placement of three extinct Indian Ocean parrots: the Rodrigues Psittacula exsul, Sey- chelles Psittacula wardi and Reunion Parakeets Psittacula eques. This case study quantifies how the extinction of these species has resulted in lost historical endemic phylogenetic diversity and reduced levels of species richness, and illustrates how it is being replaced by non-endemic invasive forms such as the Ring-necked Parakeet. Finally, we use our phylogenetic framework to identify and recommend a number of phylogenetically appro- priate ecological replacements for the extinct parrots. Such replacements may be intro- duced once invasive forms have been cleared, to rejuvenate ecosystem function and restore lost phylogenetic diversity

Effects of inhomogeneous broadening on reflection spectra of Bragg multiple quantum well structures with a defect

The reflection spectrum of a multiple quantum well structure with an inserted defect well is considered. The defect is characterized by the exciton frequency different from that of the host's wells. It is shown that for relatively short structures, the defect produces significant modifications of the reflection spectrum, which can be useful for optoelectronic applications. Inhomogeneous broadening is shown to affect the spectrum in a non-trivial way, which cannot be described by the standard linear dispersion theory. A method of measuring parameters of both homogeneous and inhomogeneous broadenings of the defect well from a single CW reflection spectrum is suggested.Comment: 27 pages, 6 eps figures; RevTe

The Japanese model in retrospective : industrial strategies, corporate Japan and the 'hollowing out' of Japanese industry

This article provides a retrospective look at the Japanese model of industrial development. This model combined an institutional approach to production based around the Japanese Firm (Aoki's, J-mode) and strategic state intervention in industry by the Japanese Ministry of International Trade and Industry (MITI). For a long period, the alignment of state and corporate interests appeared to match the wider public interest as the Japanese economy prospered. However, since the early 1990s, the global ambitions of the corporate sector have contributed to a significant 'hollowing out' of Japan's industrial base. As the world today looks for a new direction in economic management, we suggest the Japanese model provides policy-makers with a salutary lesson in tying the wider public interest with those of the corporate sector

Open string wavefunctions in flux compactifications

We consider compactifications of type I supergravity on manifolds with SU(3) structure, in the presence of RR fluxes and magnetized D9-branes, and analyze the generalized Dirac and Laplace-Beltrami operators associated to the D9-brane worldvolume fields. These compactifications are T-dual to standard type IIB toroidal orientifolds with NSNS and RR 3-form fluxes and D3/D7 branes. By using techniques of representation theory and harmonic analysis, the spectrum of open string wavefunctions can be computed for Lie groups and their quotients, as we illustrate with explicit twisted tori examples. We find a correspondence between irreducible unitary representations of the Kaloper-Myers algebra and families of Kaluza-Klein excitations. We perform the computation of 2- and 3-point couplings for matter fields in the above flux compactifications, and compare our results with those of 4d effective supergravity.Comment: 89 pages, 4 figures. v3: more typos corrected, version published in JHE

Stochastic processes with finite correlation time: modeling and application to the generalized Langevin equation

The kangaroo process (KP) is characterized by various forms of the covariance and can serve as a useful model of random noises. We discuss properties of that process for the exponential, stretched exponential and algebraic (power-law) covariances. Then we apply the KP as a model of noise in the generalized Langevin equation and simulate solutions by a Monte Carlo method. Some results appear to be incompatible with requirements of the fluctuation-dissipation theorem because probability distributions change when the process is inserted into the equation. We demonstrate how one can construct a model of noise free of that difficulty. This form of the KP is especially suitable for physical applications.Comment: 22 pages (RevTeX) and 4 figure

Keldysh Green's function approach to coherence in a non-equilibrium steady state: connecting Bose-Einstein condensation and lasing

Solid state quantum condensates often differ from previous examples of condensates (such as Helium, ultra-cold atomic gases, and superconductors) in that the quasiparticles condensing have relatively short lifetimes, and so as for lasers, external pumping is required to maintain a steady state. On the other hand, compared to lasers, the quasiparticles are generally more strongly interacting, and therefore better able to thermalise. This leads to questions of how to describe such non-equilibrium condensates, and their relation to equilibrium condensates and lasers. This chapter discusses in detail how the non-equilibrium Green's function approach can be applied to the description of such a non-equilibrium condensate, in particular, a system of microcavity polaritons, driven out of equilibrium by coupling to multiple baths. By considering the steady states, and fluctuations about them, it is possible to provide a description that relates both to equilibrium condensation and to lasing, while at the same time, making clear the differences from simple lasers