A variational approach to strongly damped wave equations

We discuss a Hilbert space method that allows to prove analytical well-posedness of a class of linear strongly damped wave equations. The main technical tool is a perturbation lemma for sesquilinear forms, which seems to be new. In most common linear cases we can furthermore apply a recent result due to Crouzeix--Haase, thus extending several known results and obtaining optimal analyticity angle.Comment: This is an extended version of an article appeared in \emph{Functional Analysis and Evolution Equations -- The G\"unter Lumer Volume}, edited by H. Amann et al., Birkh\"auser, Basel, 2008. In the latest submission to arXiv only some typos have been fixe

Detection of Deep Flaws in Aluminum Structure with Magneto-Resistive Sensors

It is well known that using progressively lower frequencies in eddy current detection permits deeper penetration into conductive samples since the skin depth increases as the inverse square root of the frequency. Since the signal of interest is produced by Faraday’s Law, the amplitude of the signal voltage is proportional to the excitation frequency. This fact limits the use of normal eddy current techniques as frequency decreases. This paper presents a method of detecting the field due to the induced eddy currents rather than its time derivative, so that at least the “return” portion of the signal is not proportional to frequency

Magnetic Resonance Imaging and Spectroscopy using Squid Detection

Magnetic Resonance Imaging (MRI), with its unique capability to image soft tissues, has become one of the most powerful nondestructive diagnostic tools in medicine. MRI is still a developing methodology in non-medical nondestructive evaluation (NDE); this is because solids with their broader nuclear magnetic resonance (NMR) linewidths are more difficult to image than biological tissue. However, recently MRI has been attracting increasing interest in a number of areas where the NMR linewidth is not as serious a problem. These include fluid flow determination in materials including porous media [1], detecting defects in ceramics still in the green (unfired) state [2], and the evaluation of polymers such as rubber and other elastomers [3]. Superconducting Quantum Interference Devices, or SQUIDs, with their great sensitivity and broad bandwidth have the potential to enhance MRI in both medical and non-medical applications

Perceived Sufficiency of Full-Field Digital Mammograms With and Without Irreversible Image Data Compression for Comparison with Next-Year Mammograms

Problems associated with the large file sizes of digital mammograms have impeded the integration of digital mammography with picture archiving and communications systems. Digital mammograms irreversibly compressed by the novel wavelet Access Over Network (AON) compression algorithm were compared with lossless-compressed digital mammograms in a blinded reader study to evaluate the perceived sufficiency of irreversibly compressed images for comparison with next-year mammograms. Fifteen radiologists compared the same 100 digital mammograms in three different comparison modes: lossless-compressed vs 20:1 irreversibly compressed images (mode 1), lossless-compressed vs 40:1 irreversibly compressed images (mode 2), and 20:1 irreversibly compressed images vs 40:1 irreversibly compressed images (mode 3). Compression levels were randomly assigned between monitors. For each mode, the less compressed of the two images was correctly identified no more frequently than would occur by chance if all images were identical in compression. Perceived sufficiency for comparison with next-year mammograms was achieved by 97.37% of the lossless-compressed images and 97.37% of the 20:1 irreversibly compressed images in mode 1, 97.67% of the lossless-compressed images and 97.67% of the 40:1 irreversibly compressed images in mode 2, and 99.33% of the 20:1 irreversibly compressed images and 99.19% of the 40:1 irreversibly compressed images in mode 3. In a random-effect analysis, the irreversibly compressed images were found to be noninferior to the lossless-compressed images. Digital mammograms irreversibly compressed by the wavelet AON compression algorithm were as frequently judged sufficient for comparison with next-year mammograms as lossless-compressed digital mammograms

Some examples of temperature bounds and concentration decay for a model of solid fuel combustion

Avrin, Joel D.. (1990). Some examples of temperature bounds and concentration decay for a model of solid fuel combustion. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/1410

Behaviour at ±∞ for a model of laminar flames with applications to questions of flame propagation versus extinction

SynopsisWe consider the behaviour at x = ±∞ of solutions to reaction-diffusion equations modelling laminar flames in a premixed reactive gas. We show that if the initial data have limits at ±∞, then the solutions satisfy ODEs at ±∞ for all positive time. We then analyse the qualitative behaviour of solutions to the ODEs. Our applications include extensions of previous results on questions of flame propagation versus extinction, and a new decay result: if the initial temperature is above ignition temperature at one end of the domani and if the initial concentration vanishes at the other, then we show that the concentration decays^to zero uniformly as the time variable goes to infinity.</jats:p

Large-Eigenvalue Global Existence and Regularity Results for the Navier–Stokes Equation

AbstractRecently Raugel and Sell obtained global existence results for the Navier–Stokes equation requiring that certain products involving the size of the data and the thinness of the domain be small. Thus the initial and forcing data could actually be quite large if the domain was thin enough. These results were obtained for periodic, and a case of homogeneous mixed periodic-Dirichlet, boundary conditions. We develop integral-equation techniques that allow us to obtain similar results in the case of purely homogeneous-Dirichlet boundary conditions. Our results are fairly simple to state and hold in a general setting, whereby we replace the role of the thinness of the domain by the reciprocal of the first eigenvalue of the Laplacian. We show further utulity of the integral-equation techniques by bootstrapping globalH1-bounds, whenever available in 2-dor 3-d, into higher-order global bounds with slightly smoother forcing functions than those assumed by Guillope, but otherwise more general in thatLp-integrable singularities in time are allowed

Qualitative theory for a model of laminar flames with arbitrary nonnegative initial data

AbstractWe consider a system of nonlinear parabolic partial differential equations arising as a model of laminar flames in a premixed reactive gas. The existence of traveling wave solutions has been established for positive ignition temperature by Berestycki, Nicolaenko, and Scheurer and by Terman for zero ignition temperature. Stability and instability of these solutions have been established in various situations by Sivashinsky, Clavin, and recently Terman. Our goal is to study the equations with initial data that are bounded, uniformly continuous, and nonnegative but otherwise arbitrary. We establish the existence of unique global strong solutions satisfying appropriate a priori estimates. With a positivity condition imposed on the initial data for the temperature, we show that the concentration decays exponentially. This result, while easy to obtain, plays an important role in results that follow. Of greatest physical interest are the cases where ignition occurs precisely at one end. Our main result is that if the average of the initial temperature values at the ends of the chamber is above ignition temperature, then on any ray coming from the ignition end the temperature is uniformly above ignition temperature, and the concentration decays uniformly to zero. We can continually advance the endpoint of this zone of ignition, thus roughly mimicking the motion of traveling wave solutions. We also point out the appropriateness of the averaging condition on the initial temperature and discuss two examples where this averaging condition is not satisfied: in one, we eventually have flame propagation and in the other example we have eventual flame extinguishment on any ray coming from the cold end of the chamber

Asymptotic behaviour of some reaction-diffusion systems modelling complex combustion on bounded domains

SynopsisWe consider three models of multiple-step combustion processes on bounded spatial domains. Previously, steady-state convergence results have been established for these models with zero Neumann boundary conditions imposed on the temperature as well as the mass fractions. We retain here throughout the same boundary conditions on the mass fractions, but in our first set of results we establish steady-state convergence results with fixed Dirichlet boundary conditions on the temperature. Next, under certain physically reasonable assumptions, we develop, for two of the models, estimates on the decay rates of both mass fractions to zero, while for the remaining model we develop estimates on the decay rate of one concentration to zero and establish a positive lower bound on the other mass fraction. These results hold under either set of boundary conditions, but when the Dirichlet conditions are imposed on the temperature, we are able to obtain estimates on the rate of convergence of the temperature to its (generally nonconstant) steady-state. Finally, we improve the results of a previous paper by adding a temperature convergence result.</jats:p