Chaos in thermal pulse combustion

An experimental thermal pulse combustor and a differential equation model of this device are shown to exhibit chaotic behavior under certain conditions. Chaos arises in the model by means of a progression of period-doubling bifurcations that occur when operating parameters such as combustor wall temperature or air/fuel flow are adjusted to push the system toward flameout. Bifurcation sequences have not yet been reproduced experimentally, but similarities are demonstrated between the dynamic features of pressure fluctuations in the model and experiment. Correlation dimension, Kolmogorov entropy, and projections of reconstructed attractors using chaotic time series analysis are demonstrated to be useful in classifying dynamical behavior of the experimental combustor and for comparison of test data to the model results. Ways to improve the model are suggested. (c) 1995 American Institute of Physics.     

Remarks on dispersionless KP,KdV, and 2D gravity

Summary We use the SDiff(2) framework of Takasaki and Takebe and the (L, M) program (L is the Lax operator andMω=ω_λ) to show that =semiclassical limit ofM is , where ( ) are action angle variables in the Gibbons-Kodama theory of Hamilton-Jacobi type for dispersionless KP. We also show is the semiclassical limit ofWxW ⁻¹ (W is the gauge operator), whereG=WxW ⁻¹ is a quantity studied by the author in an earlier paper in connection with symmetries. We give then a semiclassical version of the Jevicki-Yoneya action principle for 2D gravity, where again arises in calculations, and this yields directly the Landau-Ginsburg equation that corresponds to the semiclassical limit of an integrated string equation. For KdV we also show how inverse scattering data are connected to Hamiltonians for dispersionless KdV. We also discuss Hirota bilinear formulas relative to the dispersionless hierarchies and establish various limiting formulas.     

Dynamics of Abelian Higgs vortices in the near Bogomolny regime

The aim of this paper is to give an analytical discussion of the dynamics of the Abelian Higgs multi-vortices whose existence was proved by Taubes ([JT82]). For a particular value of a parameter of the theory, , called the Higgs self-coupling constant, there is no force between two vortices and there exist static configurations corresponding to vortices centred at any set of points in the plane. This is known as the Bogomolny regime. We will develop some formal asymptotic expansions to describe the dynamics of these multi-vortices for close, but not equal to, this critical value. We shall then prove the validity of these asymptotic expansions. These expansions allow us to give a finite dimensional Hamiltonian system which describes the vortex dynamics. The configuration space of this system is the moduli space—the space of solutions of the static equations modulo gauge equivalence. The kinetic energy term in the Hamiltonian is obtained from the natural metric on the moduli space given by theL ² inner product of the tangent vectors. The potential energy gives the intervortex potential which is non-zero when is not given by its critical value. Thus the reduced equations for the evolution of the vortex parameters take the form of geodesics, with force terms to express the departure from the Bogomolny regime. The geodesics are geodesics on the moduli space with respect to the metric defined by theL ² inner product of the tangent vectors, in accordance with Manton's suggestion ([Man82]). This allows an understanding of the two main phenomenological issues—first of all there is the right angle scattering phenomenon, according to which two vortices passing through one another scatter through ninety degrees. Secondly there is the conjecture from numerical calculations that vortices repel for greater than the critical value, and attract for less than this value. The results of this paper allow a rigorous understanding of the right angle scattering phenomenon ([Sam92, Hit88]) and reduce the question of attraction or repulsion in the near Bogomolny regime to an understanding of the potential energy term in the Hamiltonian ([JR79]).     

An exact numerical analysis of coupled planar electron waveguides with asymmetric rectangular potential profiles

An exact numerical analysis is given of electron waves in a pair of coupled semiconductor heterojunction electron waveguides modelled by a rectangular potential distribution. The waveguide lengths required for electron current transfer between the guides agree asymptotically with estimates from Yariv's coupled mode theory and are usefully more accurate. Moreover the electron wave coupling due to an ideal launcher can be worked out, leading to estimates of the off/on current ratio occurring in the waveguides when regarded as an ultrafast switch. For a Poisson probability distribution of the number of electrons N making up a bit-pulse, we have calculated the minimum average N, dependent upon , which would be required to keep the switching bit-error rate below prescribed limits. Pulse rise times and switching delays are derived from the explicit forms for the longitudinal electron wave group velocity. Combining the bit-error and switching-time calculations leads to estimates of the waveguide current densities which would be required in practice. Some normalized sets of curves relating to our analysis are given and used to predict the performance of particular examples of recently proposed AlGaAs/GaAs heterojunction electron waveguide switch/couplers.