An algebraic criterion for the onset of chaos in nonlinear dynamic systems

The correspondence between iterated integrals and a noncommutative algebra is used to recast the given dynamical system from the time domain to the Laplace-Borel transform domain. It is then shown that the following algebraic criterion has to be satisfied for the outset of chaos: the limit (as tau approaches infinity and x sub 0 approaches infinity) of ((sigma(k=0) (tau sup k) / (k* x sub 0 sup k)) G II G = 0, where G is the generating power series of the trajectories, the symbol II is the shuffle product (le melange) of the noncommutative algebra, x sub 0 is a noncommutative variable, and tau is the correlation parameter. In the given equation, symbolic forms for both G and II can be obtained by use of one of the currently available symbolic languages such as PLI, REDUCE, and MACSYMA. Hence, the criterion is a computer-algebraic one

Bifurcations in unsteady aerodynamics

Nonlinear algebraic functional expansions are used to create a form for the unsteady aerodynamic response that is consistent with solutions of the time dependent Navier-Stokes equations. An enumeration of means of invalidating Frechet differentiability of the aerodynamic response, one of which is aerodynamic bifurcation, is proposed as a way of classifying steady and unsteady aerodynamic phenomena that are important in flight dynamics applications. Accomodating bifurcation phenomena involving time dependent equilibrium states within a mathematical model of the aerodynamic response raises an issue of memory effects that becomes more important with each successive bifurcation

Hedging and Coordinated Risk Management: Evidence from Thrift Conversions

The authors propose an approach to analyzing risk management activities when multiple risks are bundled within a firm's assets or liabilities. They classify potentially bundled risks into two types: compensated risk and hedgeable risk. Firms earn rents for bearing compensated risk such as credit risk, and earn zero economic rents for bearing hedgeable risk such as interest rate risk. Because the costs associated with reducing hedgeable risk are lower than those associated with compensated risk, firms rationally eliminate hedgeable risks using either on- or off-balance sheet strategies. Thus, hedging becomes desirable even for risk-neutral or risk-seeking firms as a means of allocating risk. They denote this approach of optimal risk allocation among multiple risks with a firm as Coordinated Risk Management. The authors test the coordinated risk management approach by examining the interaction between interest rate risk (hedgeable risk) and credit risk (compensated risk) management at thrift institutions following conversion form a mutual-to-stock form of ownership. Although the concept of coordinated risk management applies to any firm, they use this sample because of data availability for the sample of converting thrifts and the control groups of non-converting institutions. The time-series findings are consistent with the coordinated management of interest rate risk and credit risk. In particular, immediately at conversion they observe decreased interest rate risk across institutions combined with a more gradual trend toward increasing credit risk. The negative relation between interest rate risk and credit risk is also significant in pooled tests. In addition, institutions use both on-balance sheet strategies and derivative instruments to reduce interest rate risk. This finding of decreasing interest rate risk occurs despite incentives to increase total risk following conversion. In light of the current discussions on the use of derivatives, this finding also indicates that thrifts use derivatives instruments for hedging rather than for speculative purposes. The cross-sectional results support models of optimal hedging. The authors provide evidence that interest rate risk hedging within an institution is positively associated with ex ante growth opportunities. They also provide evidence that managerial security holdings are a significant determinant of hedging activity. Finally, they report a negative association between managerial option holdings and interest rate risk hedging. Managers holding relatively high numbers of options maintain a risky position on-balance sheet with respect to unexpected changes in interest rates.

On the Outbursts of Soft X-ray Transients

We suggest a new scenario to explain the outburst light curves of black hole soft X-ray transients together with the secondary maximum and the bump seen on their decay phases. Our explanations are based on the disk instability models considering the effect of X-ray irradiation. The scenario is consistent with the observed X-ray delays by a few days with respect to the optical rise for both the main outburst and the later maxima. We test our scenario by numerically solving the disk diffusion equation. The obtained model curve fits well to the observed X-ray outburst photon flux curve of the black hole soft X-ray transient GS/GRS 1124-68, a typical representative of the four BH SXTs with very similar light curves.Comment: 11 pages, 8 figures, accepted for publication in A&

Application of the Laplace-Borel transformation to the representation of analytical solutions of Duffing's equation

Various features of the solutions of Duffing's equation are described using a representation of the solutions in the Laplace-Borel transform domain. An application of this technique is illustrated for the symmetry-breaking bifurcation of a hard spring

Fallback disks, magnetars and other neutron stars

The presence of matter with angular momentum, in the form of a fallback disk around a young isolated neutron star will determine its evolution. This leads to an understanding of many properties of different classes of young neutron stars, in particular a natural explanation for the period clustering of AXPs, SGRs and XDINs. The spindown or spinup properties of a neutron star are determined by the dipole component of the magnetic field. The natural possibility that magnetars and other neutron stars may have different strengths of the dipole and higher multipole components of the magnetic field is now actually required by observations on the spindown rates of some magnetars. This talk gives a broad overview and some applications of the fallback disk model to particular neutron stars. Salient points are: (i) A fallback disk has already been observed around the AXP 4U 0142+61 some years ago. (ii) The low observed spindown rate of the SGR 0418+5729 provides direct evidence that the dipole component of the field is in the 1012G range. All properties of the SGR 0418+5729 at its present age can be explained by spindown under torques from a fallback disk. (iii) The anomalous braking index of PSR J1734-3333 can also be explained by the fallback disk model which gives the luminosity, period, period derivative and the period second derivative at the present age. (iv) These and all applications to a variety of other sources employ the same disk physics and evolution, differing only in the initial conditions of the disk

One-degree-of-freedom motion induced by modeled vortex shedding

The motion of an elastically supported cylinder forced by a nonlinear, quasi-static, aerodynamic model with the unusual feature of a motion-dependent forcing frequency was studied. Numerical solutions for the motion and the Lyapunov exponents are presented for three forcing amplitudes and two frequencies (1.0 and 1.1 times the Strouhal frequency). Initially, positive Lyapunov exponents occur and the motion can appear chaotic. After thousands of characteristic times, the motion changes to a motion (verified analytically) that is periodic and damped. This periodic, damped motion was not observed experimentally, thus raising questions concerning the modeling

The anomalous x-ray pulsar 4U 0142+61: a neutron star with a gaseous fallback disk

The recent detection of the anomalous X-ray pulsar (AXP) 4U 0142+61 in the mid infrared with the Spitzer Observatory (Wang, Chakrabarty & Kaplan 2006) constitutes the first instance for a disk around an AXP. We show, by analyzing earlier optical and near IR data together with the recent data, that the overall broad band data can be reproduced by a single irradiated and viscously heated disk model