The influence of oscillations on energy estimates for damped wave models with time-dependent propagation speed and dissipation

The aim of this paper is to derive higher order energy estimates for solutions to the Cauchy problem for damped wave models with time-dependent propagation speed and dissipation. The model of interest is \begin{equation*} u_{tt}-\lambda^2(t)\omega^2(t)\Delta u +\rho(t)\omega(t)u_t=0, \quad u(0,x)=u_0(x), \,\, u_t(0,x)=u_1(x). \end{equation*} The coefficients $\lambda=\lambda(t)$ and $\rho=\rho(t)$ are shape functions and $\omega=\omega(t)$ is an oscillating function. If $\omega(t)\equiv1$ and $\rho(t)u_t$ is an "effective" dissipation term, then $L^2-L^2$ energy estimates are proved in [2]. In contrast, the main goal of the present paper is to generalize the previous results to coefficients including an oscillating function in the time-dependent coefficients. We will explain how the interplay between the shape functions and oscillating behavior of the coefficient will influence energy estimates.Comment: 37 pages, 2 figure

Magnetic aftereffect in rare earth-iron-boron magnets

The temperature dependences of the aftereffect coefficient Sv and the coercive force iHc have been measured from 4.2K to 300K on two specimens prepared from sintered magnets of Pr8Y7Fe77B8(sintered at 1060°C and 1100°C). The latter has higher maximum energy products. The Sv values of both have a maximum at 60K and 150K respectively. This is a new behavior which can not be explained by any theory proposed until now. </p

Magnetic domain observation of hydrogenation disproportionation desorption recombination processed Nd－Fe－B powder with a high-resolution Kerr microscope using ultraviolet light

A Kerr microscope that uses ultraviolet (UV) light for high-resolution domain observation was built, and the domain structure and magnetization process of hydrogenation disproportionation desorption recombination (HDDR) powder were examined. The UV Kerr microscope could observe nanometer-sized domain patterns. Applying a dc field of 1.0 kOe to HDDR powder at a desorption recombination (DR) time of 12 min produced abrupt wall motion. The pinning force exerted by the grain boundaries is inadequate for producing high coercivity because the Nd-rich phase layers along these boundaries are absent at a DR time of 12 min. For HDDR powder at a DR time greater than 14 min, changing the magnetic field by up to 1.0 kOe produced no observable wall motion. It follows that the high coercivity of HDDR powder is due to domain wall pinning at the grain boundaries

V723 Cas (Nova Cassiopeiae 1995): MERLIN observations from 1996 to 2001

MERLIN observations of the unusually slow nova V723 Cas are presented. Nine epochs of 6-cm data between 1996 and 2001 are mapped, showing the initial expansion and brightening of the radio remnant, the development of structure and the final decline. A radio light curve is presented and fitted by the standard Hubble flow model for radio emission from novae in order to determine the values of various physical parameters for the shell. The model is consistent with the overall development of the radio emission. Assuming a distance of 2.39 (+/-0.38) kpc and a shell temperature of 17000 K, the model yields values for expansion velocity of 414 +/- 0.1 km s^-1 and shell mass of 1.13 +/- 0.04 * 10^-4 Msolar. These values are consistent with those derived from other observations although the ejected masses are rather higher than theoretical predictions. The structure of the shell is resolved by MERLIN and shows that the assumption of spherical symmetry in the standard model is unlikely to be correct.Comment: 6 pages, 6 figure

The historical vanishing of the Blazhko effect of RR Lyr from GEOS and Kepler surveys

RR Lyr is one of the most studied variable stars. Its light curve has been regularly monitored since the discovery of the periodic variability in 1899. Analysis of all observed maxima allows us to identify two primary pulsation states defined as pulsation over a long (P0 longer than 0.56684 d) and a short (P0 shorter than 0.56682 d) primary pulsation period. These states alternate with intervals of 13-16 yr, and are well defined after 1943. The 40.8 d periodical modulations of the amplitude and the period (i.e. Blazhko effect) were noticed in 1916. We provide homogeneous determinations of the Blazhko period in the different primary pulsation states. The Blazhko period does not follow the variations of P0 and suddenly diminished from 40.8 d to around 39.0 d in 1975. The monitoring of these periodicities deserved and deserves a continuous and intensive observational effort. For this purpose we have built dedicated, transportable and autonomous small instruments, Very Tiny Telescopes (VTTs), to observe the times of maximum brightness of RR Lyr. As immediate results the VTTs recorded the last change of P0 state in mid-2009 and extended the time coverage of the Kepler observations, thus recording a maximum O-C amplitude of the Blazhko effect at the end of 2008, followed by the historically smallest O-C amplitude in late 2013. This decrease is still ongoing and VTT instruments are ready to monitor the expected increase in the next few years.Comment: 10 pages, 6 figures. Accepted for publication in MNRAS. Contents of appendix B may be requested to first autho

Cholesterol- and actin-centered view of the plasma membrane: updating the Singer–Nicolson fluid mosaic model to commemorate its 50th anniversary

Two very polarized views exist for understanding the cellular plasma membrane (PM). For some, it is the simple fluid described by the original Singer–Nicolson fluid mosaic model. For others, due to the presence of thousands of molecular species that extensively interact with each other, the PM forms various clusters and domains that are constantly changing and therefore, no simple rules exist that can explain the structure and molecular dynamics of the PM. In this article, we propose that viewing the PM from its two predominant components, cholesterol and actin filaments, provides an excellent and transparent perspective of PM organization, dynamics, and mechanisms for its functions. We focus on the actin-induced membrane compartmentalization and lipid raft domains coexisting in the PM and how they interact with each other to perform PM functions. This view provides an important update of the fluid mosaic model

Intrasellar Chondroid Chordoma: A Case Report

Chordomas are tumors derived from cells that are remnants of the notochord, particularly from its proximal and distal extremes, they are mainly midline and represent approximately 1% of all malignant bone tumors and 0.1 to 0.2% of intracranial neoplasms. Chordomas involving the sellar region are rare. Herein, we describe a 57-year-old male patient presenting with a history of retro-orbital headache, progressive loss of vision, and clinical features of hypopituitarism, for over 2 months. During evaluation, the CT scan revealed a large contrast-enhancing intrasellar tumor with a 3.6-cm largest diameter. The patient underwent transsphenoidal partial resection of the tumor, and histological examination was consistent with the diagnosis of chondroid chordoma. Although chordomas are rare, they may be considered to constitute a differential diagnostic of pituitary adenomas, especially if a calcified intrasellar tumor with bone erosion is diagnosed