Divergence beneath the Brillouin sphere and the phenomenology of prediction error in spherical harmonic series approximations of the gravitational field.

The Brillouin sphere is defined as the smallest sphere, centered at the origin of the geocentric coordinate system, that incorporates all the condensed matter composing the planet. The Brillouin sphere touches the Earth at a single point, and the radial line that begins at the origin and passes through that point is called the singular radial line. For about 60 years there has been a persistent anxiety about whether or not a spherical harmonic (SH) expansion of the external gravitational potential,V, will converge beneath the Brillouin sphere. Recently, it was proven that the probability of such convergence is zero. One of these proofs provided an asymptotic relation, called Costin's formula, for the upper bound,EN, on the absolute value of the prediction error,eN, of a SH series model,VN(θ,λ,r), truncated at some maximum degree,N=nmax. When the SH series is restricted to (or projected onto) a particular radial line, it reduces to a Taylor series (TS) in1/r. Costin's formula isEN≃BN-b(R/r)N, whereRis the radius of the Brillouin sphere. This formula depends on two positive parameters:b, which controls the decay of error amplitude as a function ofNwhenris fixed, and a scale factorB. We show here that Costin's formula derives from a similar asymptotic relation for the upper bound,Anon the absolute value of the TS coefficients,an, for the same radial line. This formula,An≃Kn-k, depends on degree,n, and two positive parameters,kandK, that are analogous tobandB. We use synthetic planets, for which we can compute the potential,V, and also the radial component of gravitational acceleration,gr=∂V/∂r, to hundreds of significant digits, to validate both of these asymptotic formulas. Let superscriptVrefer to asymptotic parameters associated with the coefficients and prediction errors for gravitational potential, and superscriptgto the coefficients and predictions errors associated withgr. For polyhedral planets of uniform density we show thatbV=kV=7/2andbg=kg=5/2almost everywhere. We show that the frequency of oscillation (around zero) of the TS coefficients and the series prediction errors, for a given radial line, is controlled by the geocentric angle,α, between that radial line and the singular radial line. We also derive useful identities connectingKV,BV,Kg, andBg. These identities are expressed in terms of quotients of the various scale factors. The only other quantities involved in these identities areαandR. The phenomenology of 'series divergence' and prediction error (whenr < R) can be described as a function of the truncation degree,N, or the depth,d, beneath the Brillouin sphere. For a fixedr⩽R, asNincreases from very low values, the upper error boundENshrinks until it reaches its minimum (best) value whenNreaches some particular or optimum value,Nopt. WhenN>Nopt, prediction error grows asNcontinues to increase. Eventually, whenN≫Nopt, prediction errors increase exponentially with risingN. If we fix the value ofNand allowR/rto vary, then we find that prediction error in free space beneath the Brillouin sphere increases exponentially with depth,d, beneath the Brillouin sphere. Becausebg=bV-1everywhere, divergence driven prediction error intensifies more rapidly forgrthan forV, both in terms of its dependence onNandd. If we fix bothNandd, and focus on the 'lateral' variations in prediction error, we observe that divergence and prediction error tend to increase (as doesB) as we approach high-amplitude topography.

The 2010 Mw 8.8 Maule megathrust earthquake of Central Chile, monitored by GPS.

Large earthquakes produce crustal deformation that can be quantified by geodetic measurements, allowing for the determination of the slip distribution on the fault. We used data from Global Positioning System (GPS) networks in Central Chile to infer the static deformation and the kinematics of the 2010 moment magnitude (M(w)) 8.8 Maule megathrust earthquake. From elastic modeling, we found a total rupture length of ~500 kilometers where slip (up to 15 meters) concentrated on two main asperities situated on both sides of the epicenter. We found that rupture reached shallow depths, probably extending up to the trench. Resolvable afterslip occurred in regions of low coseismic slip. The low-frequency hypocenter is relocated 40 kilometers southwest of initial estimates. Rupture propagated bilaterally at about 3.1 kilometers per second, with possible but not fully resolved velocity variations.

Near-simultaneous great earthquakes at Tongan megathrust and outer rise in September 2009.

The Earth's largest earthquakes and tsunamis are usually caused by thrust-faulting earthquakes on the shallow part of the subduction interface between two tectonic plates, where stored elastic energy due to convergence between the plates is rapidly released. The tsunami that devastated the Samoan and northern Tongan islands on 29 September 2009 was preceded by a globally recorded magnitude-8 normal-faulting earthquake in the outer-rise region, where the Pacific plate bends before entering the subduction zone. Preliminary interpretation suggested that this earthquake was the source of the tsunami. Here we show that the outer-rise earthquake was accompanied by a nearly simultaneous rupture of the shallow subduction interface, equivalent to a magnitude-8 earthquake, that also contributed significantly to the tsunami. The subduction interface event was probably a slow earthquake with a rise time of several minutes that triggered the outer-rise event several minutes later. However, we cannot rule out the possibility that the normal fault ruptured first and dynamically triggered the subduction interface event. Our evidence comes from displacements of Global Positioning System stations and modelling of tsunami waves recorded by ocean-bottom pressure sensors, with support from seismic data and tsunami field observations. Evidence of the subduction earthquake in global seismic data is largely hidden because of the earthquake's slow rise time or because its ground motion is disguised by that of the normal-faulting event. Earthquake doublets where subduction interface events trigger large outer-rise earthquakes have been recorded previously, but this is the first well-documented example where the two events occur so closely in time and the triggering event might be a slow earthquake. As well as providing information on strain release mechanisms at subduction zones, earthquakes such as this provide a possible mechanism for the occasional large tsunamis generated at the Tonga subduction zone, where slip between the plates is predominantly aseismic.

Non-conventional injection molding of poly(lactide) and poly(epsilon-caprolactone) intended for orthopedic applications.

Biodegradable polymers such as poly(lactide) (PLA) and poly(epsilon-caprolactone) (PCL) are increasingly used in biomedical applications as temporary implants. However, melt processing of these materials in particular of PLA is difficult due to the temperature sensitivity. Within this study, PLA and PCL were injection molded conventionally and by using the process shear controled orientation in injection molding (SCORIM) in order to investigate the effect of processing parameters on the physical properties of the moldings. Therefore, flexural testing, differential scanning calorimetry (DSC), wide-angle X-ray diffraction (WAXD), molecular weight (MW) and orientation measurements were performed. PLA showed high sensitivity to melt temperature. In the case of amorphous poly(DL-lactide), the molecular weight and subsequently the ductility is substantially reduced by processing at higher melt temperatures. In the case of crystallizable poly(L-lactide), higher melt temperatures and shear induced by the SCORIM process resulted in enhanced crystallinity, which compromised the mechanical properties. Generally, SCORIM processing improved the mechanical properties, in particular the ductility, by orientating the molecular structure. PCL was shown to be less sensitive to shear and temperature than PLA. Stress at yield and stiffness are more improved by SCORIM processing. However, the processing temperature in combination with the grade used proved to be influential for the mechanical properties of resulting moldings.

Coupling of HDPE/hydroxyapatite composites by silane-based methodologies.

Several coupling treatments based on silane chemicals were investigated for the development of high density (HDPE)/hydroxyapatite (HA) composites. Two HA powders, sintered HA (HAs) and non sintered HA (HAns), were studied in combination with five silanes, namely y-methacryloxy propyltrimethoxy silane (MEMO), 3-(2-aminoethyl)aminopropyltrimethoxy silane (DAMO), vinyltrimethoxy silane (VTMO), 3-aminopropyltriethoxy silane (AMEO) and trimethoxypropyl silane (PTMO). The HA particles were treated by a dipping in method or by spraying with silane solutions. After drying, the treated powders were compounded with HDPE or HDPE with acrylic acid and/or organic peroxide and subsequently compression molded. The tensile test specimens obtained from the molded plates were tensile tested and their fracture surfaces were observed by scanning electron microscopy (SEM). For the sintered HA (HAs) composites, the most effective coupling treatments concerning stiffness are those based on MEMO and AMEO. The low influence of these coupling procedures on strength is believed to be associated to the low volume fraction and the relatively smooth surface of the used HA particles. For the non-sintered HA (HAns) composites, it was possible to improve significantly both the stiffness and the strength. Amino silanes demonstrated to be highly efficient concerning strength enhancement. The higher effectiveness of the coupling treatments for HAns filled composites is attributed to their higher particle surface area, smaller particle size distribution and expected higher chemical reactivity. For both cases, the improvement in mechanical performance after the coupling treatment is consistent with the enhancement in interfacial adhesion observed by SEM.

Bi-composite sandwich moldings: processing, mechanical performance and bioactive behavior.

Two composite systems composed of high-density polyethylene (HDPE) filled with hydroxyapatite (HA) and carbon fiber (C fiber) were compounded in a co-rotating twin screw extruder and subsequently molded in a two component injection molding machine in order to produce test bars with a sandwich-like morphology. These moldings are based on a HDPE/HA composite outer layer and a HDPE/C fiber composite core. The mechanical performance of the obtained specimens was assessed by tensile and impact testing. The fracture surfaces were observed by scanning electron microscopy (SEM) and optical reflectance microscopy was used to characterize the morphology within the moldings. In order to study the bioactivity of the molded specimens, the samples were immersed for different periods of time up to 30 days in a simulated-body fluid (SBF) with an ion composition similar to human blood plasma. After each immersion period, the surfaces of the specimens were characterized by SEM. The chemical composition and the structure of the deposited films were studied by electron dispersive spectroscopy (EDS) and thin-film X-ray diffraction (TF-XRD). The evolution of the elemental concentrations in the SBF solution was determined by induced coupled plasma emission (ICP) spectroscopy. Bi-composite moldings featuring a sandwich-like morphology were successfully produced. These moldings present a high stiffness as a result of the C fiber reinforcement present in the molding core. Furthermore, as a result of the HA loading, the sandwich moldings exhibit a clear in vitro bioactive behavior under simulated physiological conditions, which indicates that an in vivo bone-bonding behavior can be expected for these materials.

Associations between adult and child bicycle helmet use.

PURPOSE: To observe the incidence of proper and improper use or non-use of bicycle helmets by children and adults when riding bicycles in groups. STUDY DESIGN: An observational survey of bicycle riders on a recreational bicycle path. METHODS: In eight half-day sessions, two observers independently rated all riders in groups that consisted of adults and children either wearing or not wearing helmets. Those who wore helmets were then rated as wearing them properly or improperly. RESULTS: Two-thirds of children wore helmets, but less than one-half wore them properly. One third of the adults wore helmets, and one-half of those wore them properly. Adult helmet use affected child helmet negatively. The strongest correlations were between adult helmet use or non-use and improper or no helmet use in accompanying children. CLINICAL IMPLICATIONS: Primary care nurses who work with healthy populations should collaborate with other groups involved with families to not only exhort them to wear helmets when riding bicycles but also to instruct those riders how to wear their helmets properly.

What do school teachers know about asthma?

The results of a survey of 98 primary school teachers in inner London showed that they had only limited understanding of asthma and its management. Few teachers had received any teaching or training about the condition; the arrangements for giving antiasthmatic drugs were generally unsatisfactory and caused unnecessary disruption to the child's school life as well as preventing effective treatment. Training in the nature and treatment of common diseases like asthma should be made available for groups such as school-teachers who are responsible for children so that optimal health care is ensured.

Seismic slip and down-dip strain rates in wadati-benioff zones.

The rate of accumulation of seismic moment in Wadati-Benioff zones is used to estimate strain rates in subducting slabs that are sinking through the asthenosphere. Between depths of 75 and 175 kilometers a typical down-dip strain rate is about 10(-15) per second, which implies that slabs in this depth range typically accumulate strain of order 10(-1). This result is in accord with geometrical arguments that subducted slabs must experience large membrane strains to deform to their observed shapes. Mantle seismicity (repeated catastrophic shear failure) is apparently a primary mechanism by which large membrane strains accumulate in the cold cores of subducting slabs. Slabs are penetratively deformed, and they have low flexural rigidity compared to oceanic plates at the earth's surface.

Clinical nurse researchers: strategies for success.

One response to nursing's growing commitment to grounding practice in a research base has been the development of clinical nurse researcher positions in hospitals throughout the country. Drawing on data from a nationwide survey, the authors describe goals and strategies that clinical nurse researchers and their chief nurse executives identify as contributing to successfully carrying out the clinical nurse researcher role.

Research activities of clinical nurse researchers.

A nationwide telephone survey was carried out on 34 nurses employed as researchers in clinical settings (CNRs). CNRs reported current involvement in over 200 projects with a range from 1 to 29 projects. Projects were categorized into the following types: clinical practice, nursing administration, evaluation, education, or methodology. Almost half (47%) of the projects were in clinical practice. Type of involvement in research was used as a basis for conceptualizing the CNR's role as traditional scientist, associate, or facilitator. Results are discussed regarding the variations found in how the CNR role is enacted across settings and the focus of the research in which CNRs are engaged.

Hormonal effects of tamoxifen in oligospermic men.

The hormonal effects of tamoxifen (10 mg daily for 6 months) have been studied in nine men with oligospermia. Basal concentrations of serum LH (1-7 +/- 0-1 (S.E.M.) i.u./l) increased to a maximum of 4-1 +/- 1-3 i.u./l (P less than 0-001) after 6 months, and FSH rose from 4-9 +/- 1-0 to a maximum of 7-7 +/- 1-3 i.u./l after 4 months of treatment (P less than 0-01). The response to luteinizing hormone releasing hormone (LH-RH) was studied at monthly intervals. Sums of increments of serum LH increased from 35 +/- 4 to 92 +/- 17 i.u./l at 4 months (P less than 0-001) and of FSH from 14 +/- 3-4 to 23 +/- 3-5 i.u./l at 4 months (P less than 0-01). Basal serum androgens rose from 25 +/- 2-7 to 38 +/- 2-4 nmol/l after 4 months of treatment (P less than 0-05), and serum oestradiol-17beta increased from 185 +/- 25 to 631 +/- 90 pmol/l by 6 months (P less than 0-001). No significant changes occurred in sperm counts. Five normal men acted as controls: they were given tamoxifen for 1 week. No significant changes were observed in serum LH, FSH or release of these hormones following administration of LH-RH. Serum androgens and oestrogens however, increased significantly by day 4 of treatment (P less than 0-05).