Multiple Multipole Expansions For Elastic Scattering: An Aid To Understanding The Problems In "No-Record" Areas

This paper presents a new approach to solving scattering of elastic waves in two dimensions. Wavefields are often expanded into an orthogonal set of basis functions. Unfortunately, these expansions converge rather slowly for complex geometries. The new approach enhances convergence by summing multiple expansions with different centers of expansion. This allows irregularities of the boundary to be resolved locally from a nearby center of expansion. Mathematically, the wavefields are expanded into a set of non-orthogonal basis functions. The incident wavefield and the fields induced by the scatterers are matched by evaluating the boundary conditions at discrete matching points along the domain boundaries. Due to the non-orthogonal expansions, more matching points are used than actually needed, resulting in an overdetermined system which is solved in the least squares sense. Since there are free parameters such as the location and number of expansion centers as well as the kind and orders of expansion functions used, numerical experiments are performed to measure the performance of different discretizations. An empirical set of rules governing the choice of these parameters is found from these experiments. The resulting algorithm is a general tool to solve relatively large and complex two-dimensional scattering problems.United States. Air Force Office of Scientific Research (Contract F49620-93-1-0424DEF

Scattering Of Acoustic And Elastic Waves Using A Hybrid Multiple Multipole Expansions-Finite Element Technique

In this paper, two different methods to solve scattering problems in acoustic or elastic media are coupled to enhance their usefulness. The multiple multipole (MMP) expansions are used to solve for the scattered fields in homogeneous regions which are possibly unbounded. The finite element (FE) method is used to calculate the scattered fields in heterogeneous but bounded scatterers. As the MMP method requires, the different regions and methods are coupled together in the least squares sense. For some examples, the scattered fields are calculated and compared to the analytical solutions. Finally, the seismograms are calculated for a scattering problem with several scatterers, and complex geometries. Thus, the hybrid MMP-FEM technique is a very general and useful tool to solve complex, two-dimensional scattering problems.United States. Air Force Office of Scientific Research (Contract F49620-94-1-0282)Massachusetts Institute of Technology. Earth Resources Laboratory. Reservoir Delineation Consortiu

Scale And Frequency Dependence Of Reflection And Transmission Coefficients

Well-logs show that heterogeneities occur at many different spatial scales. In this paper, we want to characterize how waves are affected by these heterogeneities, and we study how reflection and transmission coefficients depend on temporal frequency and spatial scale. We use wavelet transformations to filter certain spatial scales from the velocity logs. The scale-filtered logs serve as input for a numerical layer-stack model to calculate reflection and transmission coefficients as functions of frequency and scale. We find that transmission coefficients are largely independent of frequency or scale. They depend mostly on average slowness. Contrarily, reflection coefficients are extremely sensitive to the perturbations of the slownesses, even at low frequencies.Massachusetts Institute of Technology. Borehole Acoustics and Logging ConsortiumMassachusetts Institute of Technology. Earth Resources Laboratory. Reservoir Delineation Consortiu

An Algorithmic Framework for Labeling Road Maps

Given an unlabeled road map, we consider, from an algorithmic perspective, the cartographic problem to place non-overlapping road labels embedded in their roads. We first decompose the road network into logically coherent road sections, e.g., parts of roads between two junctions. Based on this decomposition, we present and implement a new and versatile framework for placing labels in road maps such that the number of labeled road sections is maximized. In an experimental evaluation with road maps of 11 major cities we show that our proposed labeling algorithm is both fast in practice and that it reaches near-optimal solution quality, where optimal solutions are obtained by mixed-integer linear programming. In comparison to the standard OpenStreetMap renderer Mapnik, our algorithm labels 31% more road sections in average.Comment: extended version of a paper to appear at GIScience 201

Content of health status reports of people seeking assisted suicide: a qualitative analysis

Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)Two right-to-die organisations offer assisted suicide in Switzerland. The specific legal situation allows assistance to Swiss and foreign citizens. Both organisations require a report of the person's health status before considering assistance. This qualitative study explored these reports filed to legal authorities after the deaths of individuals in the area of Zurich. Health status reports in the legal medical dossiers of the deceased were analysed using content analysis and Grounded Theory. From 421 cases of assisted suicide (2001-2004), 350 reports on health status were filed. Many cases contained diagnosis lists only. Other reports had more elaborate reports revealing that some physicians were aware about the patient's death wish and the intention to solicit assisted suicide. Physicians' attitudes ranged from neutral to rather depreciative. Few physicians openly referred the patient to the organisations and supported the patient's request by highlighting a history of suffering as well as reporting understanding and agreement with the patient's wish to hasten death. In the health status reports five categories could be identified. Some files revealed that physicians were aware of the death wish. The knowledge and recognition of the patient's death wish varied from no apparent awareness to strongly supportive. This variety might be due to difficulties to discuss the death wish with patients, but might also reflect the challenge to avoid legal prosecution in the country of origin. To require comparable health status reports as requirements for the right-to-die organisations might be difficult to pursue

Analysis of high resolution satellite data for cosmic gamma ray bursts

Cosmic gamma ray bursts detected a germanium spectrometer on the low altitude satellite 1972-076B were surveyed. Several bursts with durations ranging from approximately 0.032 to 15 seconds were found and are tabulated. The frequency of occurrence/intensity distribution of these events was compared with the S to the -3/2 power curve of confirmed events. The longer duration events fall above the S to the -3/2 power curve of confirmed events, suggesting they are perhaps not all true cosmic gamma-ray bursts. The narrow duration events fall closely on the S to the -3/2 power curve. The survey also revealed several counting rate spikes, with durations comparable to confirmed gamma-ray bursts, which were shown to be of magnetospheric origin. Confirmation that energetic electrons were responsible for these bursts was achieved from analysis of all data from the complete payload of gamma-ray and energetic particle detectors on board the satellite. The analyses also revealed that the narrowness of the spikes was primarily spatial rather than temporal in character

Kinetic pathways of the Nematic-Isotropic phase transition as studied by confocal microscopy on rod-like viruses

We investigate the kinetics of phase separation for a mixture of rodlike viruses (fd) and polymer (dextran), which effectively constitutes a system of attractive rods. This dispersion is quenched from a flow-induced fully nematic state into the region where the nematic and the isotropic phase coexist. We show experimental evidence that the kinetic pathway depends on the overall concentration. When the quench is made at high concentrations, the system is meta-stable and we observe typical nucleation-and-growth. For quenches at low concentration the system is unstable and the system undergoes a spinodal decomposition. At intermediate concentrations we see the transition between both demixing processes, where we locate the spinodal point.Comment: 11 pages, 6 figures, accepted in J. Phys.: Condens. Matter as symposium paper for the 6th Liquid Matter Conference in Utrech

Reasons why people in Switzerland seek assisted suicide : the view of patients and physicians

Background: Assisted suicide is permitted in Switzerland provided that assistance is not motivated by selfish reasons. Suicides are commonly performed with the assistance of right-to-die organisations and the use of a lethal dose of barbiturates prescribed by a participating physician. We examined the reasons physicians provided for writing the prescription and the reasons patients gave for requesting assistance in dying. Methods: We analysed all reported cases of assisted suicide that were facilitated by right-to-die organisations between 2001 and 2004 in the city of Zurich, and for which both the medical report and the optional letter written by the decedent providing information on their reasons for seeking assistance in suicide (N = 165). Results: The reasons most often reported by physicians (ph), as well as persons who sought help (p), were: pain (ph: 56% of all assisted suicides, p: 58%), need for long-term care (ph: 37%, p: 39%), neurological symptoms (ph: 35%, p: 32%), immobility (ph: 23%, p: 30%) and dyspnoea (ph: 23%, p: 23%). Control of circumstances over death (ph: 12%, p: 39%); loss of dignity (ph: 6%, p: 38%); weakness (ph: 13%, p: 26%); less able to engage in activities that make life enjoyable (ph: 6%, p: 18%); and insomnia and loss of concentration (ph: 4%, p: 13%) were significantly more often mentioned by decedents than by physicians. Conclusions: Both prescribing physicians and;patients provided with assistance to die quite often mentioned pain and other concerns, many of which were objectively assessable and related to unbearable suffering or unreasonable disability. Concerns referable to autonomy and individual judgement were more often noted by people seeking help than by the prescribing physicians

Nematic-Isotropic Spinodal Decomposition Kinetics of Rod-like Viruses

We investigate spinodal decomposition kinetics of an initially nematic dispersion of rod-like viruses (fd virus). Quench experiments are performed from a flow-stabilized homogeneous nematic state at high shear rate into the two-phase isotropic-nematic coexistence region at zero shear rate. We present experimental evidence that spinodal decomposition is driven by orientational diffusion, in accordance with a very recent theory.Comment: 17 pages, 6 figures, accepted in Phys. Rev.