Successive approximations for charged particle motion

Single particle dynamics in electron microscopes, ion or electron lithographic instruments, particle accelerators, and particle spectrographs is described by weakly nonlinear ordinary differential equations. Therefore, the linear part of the equation of motion is usually solved and the nonlinear effects are then found in successive order by iteration methods. A Hamiltonian nature of these equations can lead to simplified computations of particle transport through an optical device when a suitable computational method is used. Many ingenious microscopic and lithographic devices were found by H. Rose and his group due to the simple structure of the eikonal method. In the area of accelerator physics the eikonal method has never become popular. Here I will therefore generalize the eikonal method and derive it from a Hamiltonian quite familiar to the accelerator physics community. With the event of high energy polarized electron beams and plans for high energy proton beams, nonlinear effects in spin motion have become important in high energy accelerators. I will introduce a successive approximation for the nonlinear effects in the coupled spin and orbit motion of charged particles which resembles some of the simplifications resulting from the eikonal method for the pure orbit motion

On the correlation structure of microstructure noise in theory and practice

We argue for incorporating the financial economics of market microstructure into the financial econometrics of asset return volatility estimation. In particular, we use market microstructure theory to derive the cross-correlation function between latent returns and market microstructure noise, which feature prominently in the recent volatility literature. The cross-correlation at zero displacement is typically negative, and cross-correlations at nonzero displacements are positive and decay geometrically. If market makers are sufficiently risk averse, however, the cross-correlation pattern is inverted. Our results are useful for assessing the validity of the frequently-assumed independence of latent price and microstructure noise, for explaining observed cross-correlation patterns, for predicting as-yet undiscovered patterns, and for making informed conjectures as to improved volatility estimation methods

Orbit and Optics Improvement by Evaluating the Nonlinear BPM Response in CESR

We present an improved system for orbit and betatron phase measurement utilizing nonlinear models of BPM pickup response. We first describe the calculation of the BPM pickup signals as nonlinear functions of beam position using Green's reciprocity theorem with a two-dimensional formalism. We then describe the incorporation of these calculations in our beam position measurements by inverting the nonlinear functions, giving us beam position as a function of the pickup signals, and how this is also used to improve our measurement of the betatron phase advance. Measurements are presented comparing this system with the linearized pickup response used historically at CESR.Comment: 7 pages, 11 figure

A review of the municipal bond market

An abstract for this article is not available.Bond market

On the structure of the Nx phase of symmetric dimers: inferences from NMR

NMR measurements on a selectively deuterated liquid crystal dimer CB-C9-CB, exhibiting two nematic phases, show that the molecules in the lower temperature nematic phase, NX, experience a chiral environment and are ordered about a uniformly oriented director throughout the macroscopic sample. The results are contrasted with previous interpretations that suggested a twist-bend spatial variation of the director. A structural picture is proposed wherein the molecules are packed into highly correlated chiral assemblies

A parabolic free boundary problem with Bernoulli type condition on the free boundary

Consider the parabolic free boundary problem $$\Delta u - \partial_t u = 0 \textrm{in} \{u>0\}, |\nabla u|=1 \textrm{on} \partial\{u>0\} .$$ For a realistic class of solutions, containing for example {\em all} limits of the singular perturbation problem $$\Delta u_\epsilon - \partial_t u_\epsilon = \beta_\epsilon(u_\epsilon) \textrm{as} \epsilon\to 0,$$ we prove that one-sided flatness of the free boundary implies regularity. In particular, we show that the topological free boundary $\partial\{u>0\}$ can be decomposed into an {\em open} regular set (relative to $\partial\{u>0\}$) which is locally a surface with H\"older-continuous space normal, and a closed singular set. Our result extends the main theorem in the paper by H.W. Alt-L.A. Caffarelli (1981) to more general solutions as well as the time-dependent case. Our proof uses methods developed in H.W. Alt-L.A. Caffarelli (1981), however we replace the core of that paper, which relies on non-positive mean curvature at singular points, by an argument based on scaling discrepancies, which promises to be applicable to more general free boundary or free discontinuity problems