On the nature of the torus in the complex Lorenz equations.

The complex Lorenz equations are a nonlinear fifth-order set of physically derived differential equations which exhibit an exact analytic limit cycle which subsequently bifurcates to a torus. In this paper we build upon previously derived results to examine a connection between this torus at high and low r1 bifurcation parameter) and between zero and nonzero r2(complexity parameter); in so doing, we are able to gain insight on the effect of the rotational invariance of the system, and on how extra weak dispersion (r2 ≠ 0) affects the chaotic behavior of the real Lorenz system (which describes a weakly dissipative, dispersive instability)

A delay recruitment model of the cardiovascular control system.

Copyright will be owned by Springer. We develop a nonlinear delay-differential equation for the human cardiovascular control system, and use it to explore blood pressure and heart rate variability under short-term baroreflex control. The model incorporates an intrinsically stable heart rate in the absence of nervous control, and features baroreflex influence on both heart rate and peripheral resistance. Analytical simplifications of the model allow a general investigation of the rôles played by gain and delay, and the effects of ageing.

The Rome Convention: The Contracting Parties\u27 Choice

This Comment explores the provisions of the Rome Convention and the advantages contracting parties can benefit from through knowledge of such provisions. The main focus of this Comment is English conflict of laws rules related to contractual obligations that are governed by the Rome Convention. England and its laws on international contracts have been chosen as the appropriate subject of this Comment for the following reasons. First, because international conventions and treaties do not apply to all countries but only to those who ratify them, it is easier to see how the rules of such conventions are applied by a particular ratifying country rather than by discussing the rules in abstract terms. England, as a part of the United Kingdom, is a signatory to the Rome Convention. Thus, the English courts application of the Rome Conventions rules is a representative source from which to examine the operation of international contract rules. Second, England is a popular choice for international contracting because of London\u27s reputation as a leading world business player. And third, England acts as an excellent legal comparison to the United States because of the close connection between English common law and United States common law. This Comment consists of six parts. Part I introduces the complexities surrounding international contractual obligations and the conflict of laws rules provided by the Rome Convention to resolve such complexities. Part II describes the system of private international law for international contracts and the specific sources of English conflict of laws rules as they relate to contracts, with a focus on the Rome Convention. Part III explores English common law and conflict of laws rules related to international contracts in existence prior to the Rome Convention. Part IV examines relevant provisions of the Rome Convention in detail. The need for parties to include express choice of law clauses in their contracts is illustrated first by describing the complexity and uncertainty that result from applying the default rules in the absence of an express choice of law. These results are then contrasted with the clearer, more predictable results that follow from applying rules for contracts that contain choice of law clauses. Part V considers and compares United States conflict of laws with corresponding provisions in the Rome Convention for contracts containing choice of law clauses. This comparison illustrates why choice of law provisions are more likely to be upheld by courts under the Rome Convention than under similar United States laws. Part VI concludes that parties contracting under the Rome Convention should not rely on courts to determine their contracts\u27 applicable law. Instead, parties should control the governance of their contracts by taking advantage of the Rome Convention\u27s flexibility and predictability by including choice of law provisions in their contracts

Segmental aging underlies the development of a Parkinson phenotype in the AS/AGU rat

There is a paucity of information on the molecular biology of aging processes in the brain. We have used biomarkers of aging (SA β-Gal, p16Ink4a, Sirt5, Sirt6, and Sirt7) to demonstrate the presence of an accelerated aging phenotype across different brain regions in the AS/AGU rat, a spontaneous Parkinsonian mutant of PKCγ derived from a parental AS strain. P16INK4a expression was significantly higher in AS/AGU animals compared to age-matched AS controls (p < 0.001) and displayed segmental expression across various brain regions. The age-related expression of sirtuins similarly showed differences between strains and between brain regions. Our data clearly show segmental aging processes within the rat brain, and that these are accelerated in the AS/AGU mutant. The accelerated aging, Parkinsonian phenotype, and disruption to dopamine signalling in the basal ganglia in AS/AGU rats, suggests that this rat strain represents a useful model for studies of development and progression of Parkinson's disease in the context of biological aging and may offer unique mechanistic insights into the biology of aging

Arc Phenomena in low-voltage current limiting circuit breakers

Circuit breakers are an important safety feature in most electrical circuits, and they act to prevent excessive currents caused by short circuits, for example. Low-voltage current limiting circuit breakers are activated by a trip solenoid when a critical current is exceeded. The solenoid moves two contacts apart to break the circuit. However, as soon as the contacts are separated an electric arc forms between them, ionising the air in the gap, increasing the electrical conductivity of air to that of the hot plasma that forms, and current continues to flow. The currents involved may be as large as 80,000 amperes. Critical to the success of the circuit breaker is that it is designed to cause the arc to move away from the contacts, into a widening wedge-shaped region. This lengthens the arc, and then moves it onto a series of separator plates called an arc divider or splitter. The arc divider raises the voltage required to sustain the arcs across it, above the voltage that is provided across the breaker, so that the circuit is broken and the arcing dies away. This entire process occurs in milliseconds, and is usually associated with a sound like an explosion and a bright ash from the arc. Parts of the contacts and the arc divider may melt and/or vapourise. The question to be addressed by the Study Group was to mathematically model the arc motion and extinction, with the overall aim of an improved understanding that would help the design of a better circuit breaker. Further discussion indicated that two key mechanisms are believed to contribute to the movement of the arc away from the contacts, one being self-magnetism (where the magnetic field associated with the arc and surrounding circuitry acts to push it towards the arc divider), and the other being air flow (where expansion of air combined with the design of the chamber enclosing the arc causes gas flow towards the arc divider). Further discussion also indicated that a key aspect of circuit breaker design was that it is desirable to have as fast a quenching of the arc as possible, that is, the faster the circuit breaker can act to stop current flow, the better. The relative importance of magnetic and air pressure effects on quenching speed is of central interest to circuit design

Theory of quantum frequency translation of light in optical fiber: application to interference of two photons of different color

We study quantum frequency translation and two-color photon interference enabled by the Bragg scattering four-wave mixing process in optical fiber. Using realistic model parameters, we computationally and analytically determine the Green function and Schmidt modes for cases with various pump-pulse lengths. These cases can be categorized as either "non-discriminatory" or "discriminatory" in regards to their propensity to exhibit high-efficiency translation or high-visibility two-photon interference for many different shapes of input wave packets or for only a few input wave packets, respectively. Also, for a particular case, the Schmidt mode set was found to be nearly equal to a Hermite-Gaussian function set. The methods and results also apply with little modification to frequency conversion by sum-frequency conversion in optical crystals