Local dynamics for fibered holomorphic transformations

Fibered holomorphic dynamics are skew-product transformations over an irrational rotation, whose fibers are holomorphic functions. In this paper we study such a dynamics on a neighborhood of an invariant curve. We obtain some results analogous to the results in the non fibered case

Perturbation theorems for Hele-Shaw flows and their applications

In this work, we give a perturbation theorem for strong polynomial solutions to the zero surface tension Hele-Shaw equation driven by injection or suction, so called the Polubarinova-Galin equation. This theorem enables us to explore properties of solutions with initial functions close to but are not polynomial. Applications of this theorem are given in the suction or injection case. In the former case, we show that if the initial domain is close to a disk, most of fluid will be sucked before the strong solution blows up. In the later case, we obtain precise large-time rescaling behaviors for large data to Hele-Shaw flows in terms of invariant Richardson complex moments. This rescaling behavior result generalizes a recent result regarding large-time rescaling behavior for small data in terms of moments. As a byproduct of a theorem in this paper, a short proof of existence and uniqueness of strong solutions to the Polubarinova-Galin equation is given.Comment: 25 page

750 MHz radio frequency quadrupole with trapezoidal vanes for carbon ion therapy

High-frequency linear accelerators are very suitable for carbon ion therapy, thanks to the reduced operational costs and the high beam quality with respect to synchrotrons, which are presently the only available technology for this application. In the framework of the development of a new linac for carbon ion therapy, this article describes the design of a compact 750 MHz Radio Frequency Quadrupole (RFQ) with trapezoidal vanes. A new semi-analytic approach to design the trapezoidal-vane RFQ is introduced together with the relevant beam dynamics properties. The RFQ is split into two decoupled rf cavities, both of which make use of a novel dipole detuning technique by means of length adjustment. The splitting is described both from the rf and the beam dynamics point of view. The paper concludes with the rf design of the full structure, including maximum surface field and thermal studies.Comment: Revised version published in Physical Review Accelerators and Beams on 31 December 202

A Novel 24 GHz One-Shot, Rapid and Portable Microwave Imaging System

Development of microwave and millimeter wave imaging systems has received significant attention in the past decade. Signals at these frequencies penetrate inside of dielectric materials and have relatively small wavelengths. Thus. imaging systems at these frequencies can produce images of the dielectric and geometrical distributions of objects. Although there are many different approaches for imaging at these frequencies. they each have their respective advantageous and limiting features (hardware. reconstruction algorithms). One method involves electronically scanning a given spatial domain while recording the coherent scattered field distribution from an object. Consequently. different reconstruction or imaging techniques may be used to produce an image (dielectric distribution and geometrical features) of the object. The ability to perform this accurate~v and fast can lead to the development of a rapid imaging system that can be used in the same manner as a video camera. This paper describes the design of such a system. operating at 2-1 GHz. using modulated scatterer technique applied to 30 resonant slots in a prescribed measurement domain

Complex maps without invariant densities

We consider complex polynomials $f(z) = z^\ell+c_1$ for $\ell \in 2\N$ and $c_1 \in \R$, and find some combinatorial types and values of $\ell$ such that there is no invariant probability measure equivalent to conformal measure on the Julia set. This holds for particular Fibonacci-like and Feigenbaum combinatorial types when $\ell$ sufficiently large and also for a class of `long-branched' maps of any critical order.Comment: Typos corrected, minor changes, principally to Section

Hydrodynamic object recognition using pressure sensing

Hydrodynamic sensing is instrumental to fish and some amphibians. It also represents, for underwater vehicles, an alternative way of sensing the fluid environment when visual and acoustic sensing are limited. To assess the effectiveness of hydrodynamic sensing and gain insight into its capabilities and limitations, we investigated the forward and inverse problem of detection and identification, using the hydrodynamic pressure in the neighbourhood, of a stationary obstacle described using a general shape representation. Based on conformal mapping and a general normalization procedure, our obstacle representation accounts for all specific features of progressive perceptual hydrodynamic imaging reported experimentally. Size, location and shape are encoded separately. The shape representation rests upon an asymptotic series which embodies the progressive character of hydrodynamic imaging through pressure sensing. A dynamic filtering method is used to invert noisy nonlinear pressure signals for the shape parameters. The results highlight the dependence of the sensitivity of hydrodynamic sensing not only on the relative distance to the disturbance but also its bearing

Analysis of Simple Two-Capacitor Low-pass Filters

The performance of typical low-pass capacitor filters is limited by the mutual inductance between the input and output sides of the filter. This paper describes how two appropriately spaced capacitors can be used to construct a low-pass filter with significantly better high-frequency performance than a one-capacitor filter. Laboratory measurements and numerical simulations are used to quantify the mutual inductance and compare the performance of one- and two-capacitor low-pass filters

Method of Edge Currents for Calculating Mutual External Inductance in a Microstrip Structure

Mutual external inductance (MEI) associated with fringing magnetic fields in planar transmission lines is a cause of socalled ground plane noise , which leads to radiation from printed circuit boards in high-speed electronic equipment. Herein, a Method of Edge Currents (MEC) is proposed for calculating the MEI associated with fringing magnetic fields that wrap the ground plane of a microstrip line. This method employs a quasi-magnetostatic approach and direct magnetic field integration, so the resultant MEI is frequency independent. It is shown that when infinitely wide ground planes are cut to form ground planes of finite width, the residual surface currents on the tails that are cut off may be redistributed on the edges of the ground planes of finite thickness, forming edge currents. These edge currents shrink to filament currents when the thickness of the ground plane becomes negligible. It is shown that the mutual external inductance is determined by the magnetic flux produced by these edge currents, while the contributions to the magnetic flux by the currents from the signal trace and the finite-size ground plane completely compensate each other. This approach has been applied to estimating the mutual inductance for symmetrical and asymmetrical microstrip lines