On the parametric dependences of a class of non-linear singular maps

We discuss a two-parameter family of maps that generalize piecewise linear, expanding maps of the circle. One parameter measures the effect of a non-linearity which bends the branches of the linear map. The second parameter rotates points by a fixed angle. For small values of the nonlinearity parameter, we compute the invariant measure and show that it has a singular density to first order in the nonlinearity parameter. Its Fourier modes have forms similar to the Weierstrass function. We discuss the consequences of this singularity on the Lyapunov exponents and on the transport properties of the corresponding multibaker map. For larger non-linearities, the map becomes non-hyperbolic and exhibits a series of period-adding bifurcations.Comment: 17 pages, 13 figures, to appear in Discrete and Continuous Dynamical Systems, series B Higher resolution versions of Figures 5 downloadable at http://www.glue.umd.edu/~jrd

Fractal Dimensions of the Hydrodynamic Modes of Diffusion

We consider the time-dependent statistical distributions of diffusive processes in relaxation to a stationary state for simple, two dimensional chaotic models based upon random walks on a line. We show that the cumulative functions of the hydrodynamic modes of diffusion form fractal curves in the complex plane, with a Hausdorff dimension larger than one. In the limit of vanishing wavenumber, we derive a simple expression of the diffusion coefficient in terms of this Hausdorff dimension and the positive Lyapunov exponent of the chaotic model.Comment: 20 pages, 6 figures, submitted to Nonlinearit

Twilight Intensity Variation of the Infrared Hydroxyl Airglow

The vibration rotation bands of the hydroxyl radical are the strongest features in the night airglow and are exceeded in intensity in the dayglow only by the infrared atmospheric bands of oxygen. The variation of intensity during evening twilight is discussed. Using a ground-based Fourier Transform Spectrometer (FTS), hydroxyl intensity measurements as early as 3 deg solar depression were made. Models of the twilight behavior show that this should be sufficient to provide measurement of the main portion of the twilight intensity change. The instrument was equipped with a liquid nitrogen-cooled germanium detector whose high sensitivity combined with the efficiency of the FTS technique permits spectra of the region 1.1 to 1.6 microns at high signal-to-noise to be obtained in two minutes. The use of a polarizer at the entrance aperture of the instrument reduces the intensity of scattered sunlight by a factor of at least ten for zenith observations

Field Driven Thermostated System : A Non-Linear Multi-Baker Map

In this paper, we discuss a simple model for a field driven, thermostated random walk that is constructed by a suitable generalization of a multi-baker map. The map is a usual multi-baker, but perturbed by a thermostated external field that has many of the properties of the fields used in systems with Gaussian thermostats. For small values of the driving field, the map is hyperbolic and has a unique SRB measure that we solve analytically to first order in the field parameter. We then compute the positive and negative Lyapunov exponents to second order and discuss their relation to the transport properties. For higher values of the parameter, this system becomes non-hyperbolic and posseses an attractive fixed point.Comment: 6 pages + 5 figures, to appear in Phys. Rev.

Clearing and settlement of U.S. dollar payments: back to the future?

Federal Reserve banks - Service charges ; Payment systems

Effects of high energy radiation on the mechanical properties of epoxy/graphite fiber reinforced composites

Publications and theses generated on composite research are listed. Surface energy changes of an epoxy based on tetraglycidyl diaminodiphenyl methane (TGDDM)/diaminodiphenyl sulfone (DDS), T-300 graphite fiber and T-300/5208 (graphite fiber/epoxy) composites were investigated after irradiation with 0.5 MeV electrons. Electron spin resonance (ESR) investigations of line shapes and the radical decay behavior were made of an epoxy based on tetraglycidyl diaminodiphenyl methane (TGDDM)/diaminodiphenyl sulfone (DDS), T-300 graphite fiber, and T-300/5208 (graphite fiber/epoxy) composites after irradiation with Co(60) gamma-radiation or 0.5 MeV electrons. The results of the experiments are discussed

Algorithmic linear dimension reduction in the l_1 norm for sparse vectors

This paper develops a new method for recovering m-sparse signals that is simultaneously uniform and quick. We present a reconstruction algorithm whose run time, O(m log^2(m) log^2(d)), is sublinear in the length d of the signal. The reconstruction error is within a logarithmic factor (in m) of the optimal m-term approximation error in l_1. In particular, the algorithm recovers m-sparse signals perfectly and noisy signals are recovered with polylogarithmic distortion. Our algorithm makes O(m log^2 (d)) measurements, which is within a logarithmic factor of optimal. We also present a small-space implementation of the algorithm. These sketching techniques and the corresponding reconstruction algorithms provide an algorithmic dimension reduction in the l_1 norm. In particular, vectors of support m in dimension d can be linearly embedded into O(m log^2 d) dimensions with polylogarithmic distortion. We can reconstruct a vector from its low-dimensional sketch in time O(m log^2(m) log^2(d)). Furthermore, this reconstruction is stable and robust under small perturbations