Newton's method and Baker domains

We show that there exists an entire function f without zeros for which the associated Newton function N(z)=z-f(z)/f'(z) is a transcendental meromorphic functions without Baker domains. We also show that there exists an entire function f with exactly one zero for which the complement of the immediate attracting basin has at least two components and contains no invariant Baker domains of N. The second result answers a question of J. Rueckert and D. Schleicher while the first one gives a partial answer to a question of X. Buff.Comment: 6 page

Fabrication of high temperature surface acoustic wave devices for sensor applications

Surface acoustic devices have been shown to be suitable not only for signal processing but also for sensor applications. In this paper high temperature surface acoustic wave devices based on gallium orthophosphate have been fabricated, using a lift-off technique and tested for high frequency applications at temperatures up to 600 ºC. The measured S-parameter (S11) has been used to study the mass loading effect of the platinum electrodes and turnover temperature of GaPO4 with a 5? cut. The analysis of these results shows that the mass loading effect can be used to predict the desired resonant frequency of the SAW devices. Also two different adhesion layers for Pt metallisation were studied. Our results show that Zirconium is a more suitable under layer than Titanium

Thurston's pullback map on the augmented Teichm\"uller space and applications

Let $f$ be a postcritically finite branched self-cover of a 2-dimensional topological sphere. Such a map induces an analytic self-map $\sigma_f$ of a finite-dimensional Teichm\"uller space. We prove that this map extends continuously to the augmented Teichm\"uller space and give an explicit construction for this extension. This allows us to characterize the dynamics of Thurston's pullback map near invariant strata of the boundary of the augmented Teichm\"uller space. The resulting classification of invariant boundary strata is used to prove a conjecture by Pilgrim and to infer further properties of Thurston's pullback map. Our approach also yields new proofs of Thurston's theorem and Pilgrim's Canonical Obstruction theorem.Comment: revised version, 28 page

Pre-dewetting transition on a hydrophobic wall: Statics and dynamics

For one-component fluids, we predict a pre-dewetting phase transition between a thin and thick low-density layer in liquid on a wall repelling the fluid. This is the case of a hydrophobic wall for water. A pre-dewetting line starts from the coexistence curve and ends at a surface critical point in the phase diagram. We calculate this line numerically using the van der Waals model and analytically using the free energy expansion up to the quartic order. We also examine the pre-dewetting dynamics of a layer created on a hydrophobic spot on a heterogeneous wall. It is from a thin to thick layer during decompression and from a thick to thin layer during compression. Upon the transition, a liquid region above the film is cooled for decompression and heated for compression due to latent heat convection and a small pressure pulse is emitted from the film into the liquid.Comment: 14 pages, 17 figure

Some examples of Baker domains

We construct entire functions with hyperbolic and simply parabolic Baker domains on which the functions are not univalent. The Riemann maps from the unit disk to these Baker domains extend continuously to certain arcs on the unit circle. The results answer questions posed by Fagella and Henriksen, Baker and Dominguez, and others.Comment: 13 page

Intrinsic profiles and capillary waves at homopolymer interfaces: a Monte Carlo study

A popular concept which describes the structure of polymer interfaces by ``intrinsic profiles'' centered around a two dimensional surface, the ``local interface position'', is tested by extensive Monte Carlo simulations of interfaces between demixed homopolymer phases in symmetric binary (AB) homopolymer blends, using the bond fluctuation model. The simulations are done in an LxLxD geometry. The interface is forced to run parallel to the LxL planes by imposing periodic boundary conditions in these directions and fixed boundary conditions in the D direction, with one side favoring A and the other side favoring B. Intrinsic profiles are calculated as a function of the ``coarse graining length'' B by splitting the system into columns of size BxBxD and averaging in each column over profiles relative to the local interface position. The results are compared to predictions of the self-consistent field theory. It is shown that the coarse graining length can be chosen such that the interfacial width matches that of the self-consistent field profiles, and that for this choice of B the ``intrinsic'' profiles compare well with the theoretical predictions.Comment: to appear in Phys. Rev.

2-D Magnetohydrodynamic Simulations of Induced Plasma Dynamics in the Near-Core Region of a Galaxy Cluster

We present results from numerical simulations of the cooling-core cluster A2199 produced by the two-dimensional (2-D) resistive magnetohydrodynamics (MHD) code MACH2. In our simulations we explore the effect of anisotropic thermal conduction on the energy balance of the system. The results from idealized cases in 2-D axisymmetric geometry underscore the importance of the initial plasma density in ICM simulations, especially the near-core values since the radiation cooling rate is proportional to ${n_e}^2$. Heat conduction is found to be non-effective in preventing catastrophic cooling in this cluster. In addition we performed 2-D planar MHD simulations starting from initial conditions deliberately violating both thermal balance and hydrostatic equilibrium in the ICM, to assess contributions of the convective terms in the energy balance of the system against anisotropic thermal conduction. We find that in this case work done by the pressure on the plasma can dominate the early evolution of the internal energy over anisotropic thermal conduction in the presence of subsonic flows, thereby reducing the impact of the magnetic field. Deviations from hydrostatic equilibrium near the cluster core may be associated with transient activity of a central active galactic nucleus and/or remnant dynamical activity in the ICM and warrant further study in three dimensions.Comment: 16 pages, 13 figures, accepted for publication in MNRA

A critical assessment of methods for the intrinsic analysis of liquid interfaces: 2. density profiles

Substantial improvements in the molecular level understanding of fluid interfaces have recently been achieved by recognizing the importance of detecting the intrinsic surface of the coexisting condensed phases in computer simulations (i.e., after the removal of corrugations caused by capillary waves) and by developing several methods for identifying the molecules that are indeed located at the boundary of the two phases. In our previous paper [J. Phys. Chem. C 2010, 114, 11169], we critically compared those methods in terms of reliability, robustness, and computation speed. Once the intrinsic surface of a given phase is detected, various profiles, such as the density profiles of the components, can be calculated relative to this intrinsic surface rather than to the macroscopically planar Gibbs dividing surface. As a continuation of our previous study, here we present a detailed and critical comparison of various methods that can be used to calculate intrinsic density profiles once the full set of truly interfacial molecules has been identified. Two of the methods, the Fourier function and the Voronoi tessellation, are already described in the literature; two other methods, the covering surface and the triangular interpolation, are newly proposed algorithms; one method, the modified grid-based intrinsic profile (GIP) method, is an improvement over an existing procedure. The different methods are again compared in terms of accuracy and computational cost. On the basis of this comparison, we propose a fast and accurate protocol to be routinely used for intrinsic surface analyses in computer simulations

Dynamic in vitro measurement of patellar movement after total knee arthroplasty: an in vitro study

BACKGROUND: Changing the kinematic behaviour of patellar movement could be one of the reasons for anterior knee pain after implantation of a total knee arthroplasty (TKA). The aim of the current study was to measure the potential influence on patellar kinematics of patellar resurfacing during TKA. METHODS: Patellar movement before and after TKA with and without patellar resurfacing was measured under dynamic conditions in an in vitro cadaver simulation. Physiologic Musculus quadriceps forces were applied to five physiologic human knee specimens undergoing simulated isokinetic extension motions, patellar movement was measured using an ultrasonic measurement system. Thereafter, the Interax(® )I.S.A.-prosthesis system was implanted without and with resurfacing the patella, and patellar movement was again measured. RESULTS: The physiologic patella center moved on a semilunar path up to 6.4 mm (SD 6.4 mm) medially during extension. After TKA, the unresurfaced patella showed significantly less medial translation (p = 0.04) than the resurfaced patella. Subsequent resurfacing of the patella then resulted in a return to mediolateral positioning of the patella similar to the physiological case, whereas the resurfaced patella tilted up to twice as much as physiologic. CONCLUSION: The results of this study suggest that resurfacing of the patella during TKA can result in a restoration of the physiologic mediolateral shift of the patellofemoral joint while angulation of the patella remains unphysiologic