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 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

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

Global well-posedness of the Kirchhoff equation and Kirchhoff systems

This article is devoted to review the known results on global well-posedness for the Cauchy problem to the Kirchhoff equation and Kirchhoff systems with small data. Similar results will be obtained for the initial-boundary value problems in exterior domains with compact boundary. Also, the known results on large data problems will be reviewed together with open problems.Comment: arXiv admin note: text overlap with arXiv:1211.300

Near-Infrared H and K band studies of the 2006 outburst of the recurrent nova RS Ophiuchi

We present near-IR photo-spectroscopy in the H and K bands of the 2006 outburst of the recurrent nova RS Ophiuchi (RS Oph). The observations cover the period between 1 to 94 days after the eruption. The near IR light curve and an extensive set of spectra are presented, lines identified and the general characteristics of the spectra discussed. Analysis of the HI line profiles show the presence of broad wings on both flanks of a strong central component indicating the presence of a bipolar velocity flow in the ejecta. Such a flow is kinematically consistent with the bipolar structure that the object displays in high-resolution spatial images. We discuss the behaviour and origin of the Fe II lines at 1.6872 and 1.7414 micron and show that Lyman alpha and Lyman continuum fluorescence are viable mechanisms to excite these lines. We draw upon the result, that collisional excitation can also contribute in exciting and significantly enhancing the strength of these Fe II lines, to propose that these lines originate from a site of high particle density. Such a likely site could be the high-density, low temperature contact surface that should exist in the shockfront in between the shocked ejecta and red giant wind. Recombination analysis of the HI lines indicate deviations from Case B conditions during most of the span of our observations indicating optical depth effects. It appears likely that the breakout of the shockfront had not yet occured till the end of our observations. An analysis is made of the temporal evolution of the [Si VI] 1.9641 micron coronal line and another coronal line at 2.0894 micron which is attributed to [Mn XIV]. Assuming collisional effects to dominate in the hot coronal gas, estimates are made of the ion temperature in the gas.Comment: Accepted in MNRAS. Accepted version with inclusion of additional analysi