Temperature measurement of reflected shock wave by using chemical indicator

This report describes a new method for measuring the temperature of the gas behind the reflected shock wave in shock tube, corresponding to the reservoir temperature of a shock tunnel, based on the chemical reaction of small amount of CF4 premixed in the test gas. The final product C2F4 is used as the temperature indicator, which is sampled and detected by a gas chromatography in the experiment. The detected concentration of C2F4 is correlated to the temperature of the reflected shock wave with the initial pressure P-1 and test time tau as parameters in the temperature range 3 300 K < T < 5 600 K, pressure range 5 kPa < P1 <12 kPa and tau similar or equal to 0.4 ms.

Dynamic Characteristics of Spherically Converging Detonation Waves

The spherically converging detonation wave was numerically investigated by solving the one-dimensional multi-component Euler equations in spherical coordinates with a dispersion-controlled dissipative scheme. Finite rate and detailed chemical reaction models were used and numerical solutions were obtained for both a spherical by converging detonation in a stoichiometric hydrogen-oxygen mixture and a spherically focusing shock in air. The results showed that the post-shock pressure approximately arises to the same amplitude in vicinity of the focal point for the two cases, but the post-shock temperature level mainly depends on chemical reactions and molecular dissociations of a gas mixture. While the chemical reaction heat plays an important role in the early stage of detonation wave propagation, gas dissociations dramatically affect the post-shock flow states near the focal point. The maximum pressure and temperature, non-dimensionalized by their initial value, are approximately scaled to the propagation radius over the initial detonation diameter. The post-shock pressure is proportional to the initial pressure of the detonable mixture, and the post-shock temperature is also increased with the initial pressure, but in a much lower rate than that of the post-shock pressure.

Modeling Study on the Entrainment of Ambient Air into Subsonic Laminar and Turbulent Argon Plasma Jets

Modeling study is performed to reveal the special features of the entrainment of ambient air into subsonic laminar and turbulent argon plasma jets. Two different types of jet flows are considered, i.e., the argon plasma jet is impinging normally upon a flat substrate located in atmospheric air surroundings or is freely issuing into the ambient air. It is found that the existence of the substrate not only changes the plasma temperature, velocity and species concentration distributions in the near-substrate region, but also significantly enhances the mass flow rate of the ambient air entrained into the jet due to the additional contribution to the gas entrainment of the wall jet formed along the substrate surface. The fraction of the additional entrainment of the wall jet in the total entrained-air flow rate is especially high for the laminar impinging plasma jet and for the case with shorter substrate standoff distances. Similarly to the case of cold-gas free jets, the maximum mass flow-rate of ambient gas entrained into the turbulent impinging or free plasma jet is approximately directly proportional to the mass flow rate at the jet inlet. The maximum mass flow-rate of ambient gas entrained into the laminar impinging plasma jet slightly increases with increasing jet-inlet velocity but decreases with increasing jet-inlet temperature.

Reconsideration On The Role Of The Specific Heat Ratio In Arrhenius Law Applications

Arrhenius law implicates that only those molecules which possess the internal energy greater than the activation energy E-a can react. However, the internal energy will not be proportional to the gas temperature if the specific heat ratio gamma and the gas constant R vary during chemical reaction processes. The varying gamma may affect significantly the chemical reaction rate calculated with the Arrhenius law under the constant gamma assumption, which has been widely accepted in detonation and combustion simulations for many years. In this paper, the roles of variable gamma and R in Arrhenius law applications are reconsidered, and their effects on the chemical reaction rate are demonstrated by simulating one-dimensional C-J and two-dimensional cellular detonations. A new overall one-step detonation model with variable gamma and R is proposed to improve the Arrhenius law. Numerical experiments demonstrate that this improved Arrhenius law works well in predicting detonation phenomena with the numerical results being in good agreement with experimental data.

Thermal fatigue on pistons induced by shaped high power laser. Part I: Experimental study of transient temperature field and temperature oscillation

Thermal fatigue behavior is one of the foremost considerations in the design and operation of diesel engines. It is found that thermal fatigue is closely related to the temperature field and temperature fluctuation in the structure. In this paper, spatially shaped high power laser was introduced to simulate thermal loadings on the piston. The incident Gaussian beam was transformed into concentric multi-circular beam of specific intensity distribution with the help of diffractive optical element (DOE), and the transient temperature fields in the piston similar to those under working conditions could be achieved by setting up appropriate loading cycles. Simulation tests for typical thermal loading conditions, i.e., thermal high cycle fatigue (HCF) and thermal shock (or thermal low cycle fatigue, LCF) were carried out. Several important parameters that affect the transient temperature fields and/or temperature oscillations, including controlling mode, intensity distribution of shaped laser, laser power, temporal profile of laser pulse, heating time and cooling time in one thermal cycle, etc., were investigated and discussed. The results show that as a novel method, the shaped high power laser can simulate thermal loadings on pistons efficiently, and it is helpful in the study of thermal fatigue behavior in pistons. (C) 2007 Elsevier Ltd. All rights reserved.

Shoreline erosion due to extreme storms and sea level rise

A summary is presented of research conducted on beach erosion associated with extreme storms and sea level rise. These results were developed by the author and graduate students under sponsorship of the University of Delaware Sea Grant Program. Various shoreline response problems of engineering interest are examined. The basis for the approach is a monotonic equilibrium profile of the form h = Ax2 /3 in which h is water depth at a distance x from the shoreline and A is a scale parameter depending primarily on sediment characteristics and secondarily on wave characteristics. This form is shown to be consistent with uniform wave energy dissipation per unit volume. The dependency of A on sediment size is quantified through laboratory and field data. Quasi-static beach response is examined to represent the effect of sea level rise. Cases considered include natural and seawalled profiles. To represent response to storms of realistic durations, a model is proposed in which the offshore transport is proportional to the "excess" energy dissipation per unit volume. The single rate constant in this model was evaluated based on large scale wave tank tests and confirmed with Hurricane Eloise pre- and post-storm surveys. It is shown that most hurricanes only cause 10% to 25% of the erosion potential associated with the peak storm tide and wave conditions. Additional applications include profile response employing a fairly realistic breaking model in which longshore bars are formed and long-term (500 years) Monte Carlo simulation including the contributions due to sea level rise and random storm occurrences. (PDF has 67 pages.)

Effects of temperature on the biology of the northern shrimp, Pandalus borealis, in the Gulf of Maine

Length-frequency data collected from inshore and offshore locations in the Gulf of Maine in 1966-1968 indicated that ovigerous female northern shrimp (Pandalus borealis) first appeared offshore in August and September and migrated inshore in the fall and winter. Once eggs hatched, surviving females returned offshore. Juveniles and males migrated offshore during their first two years of life. Sex transition occurred in both inshore and oll'shore waters, but most males changed sex offshore during their third and fourth years. Most shrimp changed sex and matured as females for the first time in their fourth year. Smaller females and females exposed to colder bottom temperatures spawned first. The incidence of egg parasitism peaked in January and was higher for shrimp exposed to warmer bottom temperatures. Accelerated growth at higher temperatures appeared to result in earlier or more rapid sex transition. Males and non-ovigerous females were observed to make diurnal vertical migrations, but were not found in near- surface waters where the temperature exceeded 6°C. Ovigerous females fed more heavily on benthic molluscs in inshore waters in the winter, presumably because the egg masses they were carrying prevented them from migrating vertically at night. Northern shrimp were more abundant in the southwestern region of the Gulf of Maine where bottom temperatures remain low throughout the year. Bottom trawl catch rates were highest in Jeffreys Basin where bottom temperatures were lower than at any other sampling location. Catch rates throughout the study area were inversely related to bottom temperature and reached a maximum at 3°C. An increase of 40% in fecundity between 1973 and 1979 was associated with a decline of 2-3°C in April-July offshore bottom temperatures. Furthermore, a decrease in mean fecundity per 25 mm female between 1965 and 1970 was linearly related to reduced landings between 1969 and 1974. It is hypothesized that temperature-induced changes in fecundity and, possibly, in the extent of egg mortality due to parasitism, may provide a mechanism which could partially account for changes in the size of the Gulf of Maine northern shrimp population during the last thirty years. (PDF file contains 28 pages.)

Hypoxia and Sturgeons: report to the Chesapeake Bay Program Dissolved Oxygen Criteria Team

In this essay, three lines of evidence are developed that sturgeons in the Chesapeake Bay and elsewhere are unusually sensitive to hypoxic conditions: 1. In comparison to other fishes, sturgeons have a limited behavioral and physiological capacity to respond to hypoxia. Basal metabolism, growth, and consumption are quite sensitive to changes in oxygen level, which may indicate a relatively poor ability by sturgeons to oxyregulate. 2. During summertime, temperatures >20 C amplify the effect of hypoxia on sturgeons and other fishes due to a temperature*oxygen "squeeze" (Coutant 1987)- In bottom waters, this interaction results in substantial reduction of habitat; in dry years, nursery habitats in the Chesapeake Bay may be particularly reduced or even eliminated. 3. While evidence for population level effects by hypoxia are circumstantial, there are corresponding trends between the absence of Atlantic sturgeon reproduction in estuaries like the Chesapeake Bay where summertime hypoxia predominates on a system-wide scale. Also, the recent and dramatic recovery of shortnose sturgeon in the Hudson River (4-fold increase in abundance from 1980 to 1995) may have been stimulated by improvement of a large portion of the nursery habitat that was restored from hypoxia to normoxia during the period 1973-1978. (PDF contains 26 pages)

Growth, mortality, and exploitation of the Engraulidae, with special reference to the anchoveta, Cetengraulis mysticetus, and the colorado, Anchoa naso, in the Eastern Pacific Ocean

ENGLISH: Growth and mortality data for Cetengraulis mysticetus, Anchoa naso, Engraulis mordax, E. ring ens, E. anchoita, E. encraslcbolus, E. japonicus, and E. australis were assembled and compared. Estimates of the coefficients of natural mortality, M, of E. anchoita and Ancboa naso were made from the maximum age of the former and from data for the other species. The relative yields per recruit at different fishing mortality rates and lengths at entry into the fishery were calculated for each species, using what are considered to be the best estimates and other likely values of K, a constant of growth, and M. The maximum yields per recruit are theoretically obtainable at very high fishing mortality rates, except when the length at entry is low relative to the asymptotic length. K and M may be positively related to the temperature and to each other, and if such is the case at higher temperatures greater fishing effort would be needed to attain the maximum yield per recruit. The applicability of the yield-per-recruit approach to the data is discussed, and suggestions for further research are made. SPANISH: Se reunieron y compararon los datos sobre el crecimiento y mortalidad correspondientes a Cetengraulis mysticetus, Anchoa naso, Engraulis mordax, E. ringens, E. anchoíta, E. encrasicbolus, E. japonicus y E. australls. Los estimativos de los coeficientes de la mortalidad natural, M, de E. anchoita y Anchoa naso se obtuvieron según la edad máxima de E. anchoita y según los datos de las otras especies. Se calculó para cada especie el rendimiento relativo por recluta a diferentes tasas de mortalidad por la pesca y a diferentes longitudes de entrada a la pesquería, empleándose lo que se considera que son los mejores estimativos y otros valores probables de K, una constante de crecímíento, y M. El rendimiento máximo por recluta se obtiene teóricamente a tasas muy altas de la mortalidad por la pesca con excepción de cuando la longitud a la entrada es baja en relación a la longitud asintótica. K y M pueden estar relacionadas positivamente a la temperatura y mutuamente, y si este es el caso a temperaturas más altas se necesitará un esfuerzo superior de pesca para obtener el rendimiento máximo por recluta. La aplicabilidad del enfoque a los datos rendimiento-por-recluta es discutido y se hacen sugerencias para otras investigaciones. (PDF contains 66 pages.)

The influence of some environmental variables on the apparent abundance of skipjack tuna, Katsuwonus pelamis, in the Eastern Pacific Ocean

ENGLISH: The abundance of skipjack larvae in the central and western Pacific approximately doubled for every 1°C increase in sea-surface temperature (SST) from 23°C to a maximum of about 29°C, and then usually decreased with further increases in SST. Skipjack larvae are scarce in the eastern Pacific Ocean (EPO), so most skipjack recruits and adults in this area are believed to have originated in the central and, possibly, the western Pacific. The catch per unit of effort (CPUE), in short tons per day's fishing, and the catch rate, in number of fish per day's fishing, are estimates of apparent abundance in a fishery. The logarithm of the annual CPUE for skipjack for international baitboats in the EPO for the 1934-1960 period was positively correlated with SST in the spawning area in the central Pacific 18 months earlier (r2 0.31), during the July-June period when most of the recruits in each cohort were presumed to have been spawned. Adequate data for other environmental variables were not available for testing with the baitboat data. The other environmental variables available and selected for testing for correlation with estimates of skipjack abundance for purse seiners for the 1961-1984 period and the reasons for their selection are as follows. 1)Wind-mixing index (WMI). The degree of mixing in the upper layers of the ocean is proportional to the cube of the wind speed, called WMI. The degree of mixing in the spawning areas of the central and the western Pacific may affect the concentration of organisms that skipjack larvae feed upon, thereby influencing their survival, and ultimately determining cohort strength and the number of recruits to the eastern Pacific fishery. 2) SST in the fishing areas at the time of fishing (SST). The CPUE for yellowfin tuna has been shown to be inversely related to SST in the fishing areas, and there are indications that skipjack CPUE is lower during EI Nino events when SST is higher than normal. 3) North-south SST gradient across the thermal front off the Gulf of Guayaquil. This is a measure of the degree of upwelling and nutrient enrichment of the upper waters south of the front and ultimately of the production of food for tunas. 4) Speed of the North Equatorial Countercurrent (NECC). Young skipjack may migrate from the central Pacific to the EPO in the eastward flowing NECC; if so, the number of recruits might be affected by variations in the speed of the current. The logarithm of the annual catch rate of skipjack recruits by international purse seiners in the EPO for the 1961-1984 period was positively correlated with SST in the spawning area of the central Pacific 18 months earlier (r2 = 0.21),and inversely correlated with WMI in the spawning area 18 months earlier (r2 0.46). The logarithm of CPUE for purse seiners in the area off the Gulf of Guayaquil was not correlated with SST in the spawning area 18 months earlier, but was inversely correlated with WMI in the spawning area 18 months earlier (r2 = 0.19), and inversely correlated with the north-south SST gradient in the fishing area at the time of fishing (r2 0.32). Neither of these estimates of apparent abundance from purse seiners were correlated with SST in the fishing areas, or with the speed of the NECC at earlier times. SPANISH: La abundancia de larvas de barrilete en el Pacífico central y occidental se multiplicó por dos, aproximadamente, por cada aumento de 1°Cen la temperatura de la superficie del mar (TSM) entre 23°C y un máximo de unos 29°C, y luego generalmente disminuyó con más aumentos en la TSM. Las larvas de barrilete son escasas en el Océano Pacífico oriental (OPO), y por lo tanto se cree que la mayoría de los reclutas y adultos en esta zona surgieron del Pacífico central, y posiblemente también del Pacífico occidental. La captura por unidad de esfuerzo (CPUE), en toneladas cortas por día de pesca, y la tasa de captura, en número de peces por día de pesca, son estimaciones de la abundancia aparente en una pesquería. El logaritmo de la CPUE anual de barrilete lograda por barcos de carnada en el OPO en el período 1934-1960 se correlacionó positivamente con la TSM en la zona de desove en el Pacífico central de 18 meses antes (r2 = 0.31), durante el período de junio-julio en el cual se cree que nació la mayoría de los reclutas en cada cohorte. No se dispuso de datos suficientes sobre otras variables ambientales para comprobarlos con los datos de los barcos de carnada. Las demás variables ambientales disponibles y seleccionadas para someterlas a pruebas de correlación con las estimaciones de la abundancia del barrilete de barcos cerqueros en el período 1961-1984, y las razones por su selección, son las siguientes: 1) Indice de mezcla por el viento (IMV). El grado de mezcla en las capas superiores del océano es proporcional al cubo de la velocidad del viento, llamado IMV. Es posible que el grado de mezcla en las zonas de desove del Pacífico central y occidental afecte la concentración de los organismos que alimentan a las larvas del barrilete, afectando así la supervivencia de éstas, y finalmente determinando el tamaño de las cohortes y el número de reclutas a la pesquería del OPO. 2) TSM en la zona de pesca al realizarse la pesca (TSM). Se ha mostrado que la relación de la CPUE del atún aleta amarilla a la TSM en la zona de pesca es inversa, y existen indicaciones que la CPUE de barrilete es inferior durante eventos del Niño, cuando las TSM son superiores a lo normal. 3) Gradiente norte-sur de las TSM a través del frente térmico frente al Golfo de Guayaquil. Esto es una medida del grado de afloramiento y enriquecimiento nutritivo del nivel superior de las aguas al sur de dicho frente, y finalmente de la producción de alimento para los atunes. 4) La velocidad de la Contracorriente Ecuatorial del Norte (CCEN). Es posible que los bariletes juveniles migren del Pacífico central al Pacífico oriental en la CCEN, que fluye hacia el este; de ser así, es posible que la cantidad de reclutas se vea afectada por variaciones en la velocidad de la corriente. El logaritmo de la tasa anual de captura de reclutas de barrilete por cerqueros de varias banderas en el OPO en el período 1961-1964 estuvo correlacionado de forma positiva con las TSM en la zona de desove del Pacífico central de 18meses antes (r2 0.21),y de forma inversa con el IMV de la zona de desove de 18 meses antes (r2 0.46). El logaritmo de la CPUE de los cerqueros en la zona frente al Golfo de Guayaquil no estuvo correlacionado con las TSM en la zona de desove de 18 meses antes, pero sí estuvo correlacionado de forma inversa con el IMV en la zona de desove de 18 meses antes (r2 0.19),y con el gradiente norte-sur de las TSM en la zona de pesca al realizarse la pesca (r2 0.32). Ninguna de estas estimaciones de abundancia aparente provenientes de barcos cerqueros estuvo correlacionada con las TSM en las zonas de pesca o con la velocidad de la CCEN en épocas anteriores. (PDF contains 140 pages.)

I. Application of multi-Regge theory to production processes. II. High energy model for proton-proton scattering

This dissertation consists of two parts. The first part presents an explicit procedure for applying multi-Regge theory to production processes. As an illustrative example, the case of three body final states is developed in detail, both with respect to kinematics and multi-Regge dynamics. Next, the experimental consistency of the multi-Regge hypothesis is tested in a specific high energy reaction; the hypothesis is shown to provide a good qualitative fit to the data. In addition, the results demonstrate a severe suppression of double Pomeranchon exchange, and show the coupling of two "Reggeons" to an external particle to be strongly damped as the particle's mass increases. Finally, with the use of two body Regge parameters, order of magnitude estimates of the multi-Regge cross section for various reactions are given.

The second part presents a diffraction model for high energy proton-proton scattering. This model developed by Chou and Yang assumes high energy elastic scattering results from absorption of the incident wave into the many available inelastic channels, with the absorption proportional to the amount of interpenetrating hadronic matter. The assumption that the hadronic matter distribution is proportional to the charge distribution relates the scattering amplitude for pp scattering to the proton form factor. The Chou-Yang model with the empirical proton form factor as input is then applied to calculate a high energy, fixed momentum transfer limit for the scattering cross section, This limiting cross section exhibits the same "dip" or "break" structure indicated in present experiments, but falls significantly below them in magnitude. Finally, possible spin dependence is introduced through a weak spin-orbit type term which gives rather good agreement with pp polarization data.

A fundamental approach to phase noise reduction in hybrid Si/III-V lasers

Spontaneous emission into the lasing mode fundamentally limits laser linewidths. Reducing cavity losses provides two benefits to linewidth: (1) fewer excited carriers are needed to reach threshold, resulting in less phase-corrupting spontaneous emission into the laser mode, and (2) more photons are stored in the laser cavity, such that each individual spontaneous emission event disturbs the phase of the field less. Strong optical absorption in III-V materials causes high losses, preventing currently-available semiconductor lasers from achieving ultra-narrow linewidths. This absorption is a natural consequence of the compromise between efficient electrical and efficient optical performance in a semiconductor laser. Some of the III-V layers must be heavily doped in order to funnel excited carriers into the active region, which has the side effect of making the material strongly absorbing.

This thesis presents a new technique, called modal engineering, to remove modal energy from the lossy region and store it in an adjacent low-loss material, thereby reducing overall optical absorption. A quantum mechanical analysis of modal engineering shows that modal gain and spontaneous emission rate into the laser mode are both proportional to the normalized intensity of that mode at the active region. If optical absorption near the active region dominates the total losses of the laser cavity, shifting modal energy from the lossy region to the low-loss region will reduce modal gain, total loss, and the spontaneous emission rate into the mode by the same factor, so that linewidth decreases while the threshold inversion remains constant. The total spontaneous emission rate into all other modes is unchanged.

Modal engineering is demonstrated using the Si/III-V platform, in which light is generated in the III-V material and stored in the low-loss silicon material. The silicon is patterned as a high-Q resonator to minimize all sources of loss. Fabricated lasers employing modal engineering to concentrate light in silicon demonstrate linewidths at least 5 times smaller than lasers without modal engineering at the same pump level above threshold, while maintaining the same thresholds.

Investigations of noise and of quantum interference in proximity effect bridges

This work reports investigations upon weakly superconducting proximity effect bridges. These bridges, which exhibit the Josephson effects, are produced by bisecting a superconductor with a short (<1µ) region of material whose superconducting transition temperature is below that of the adjacent superconductors. These bridges are fabricated from layered refractory metal thin films whose transition temperature will depend upon the thickness ratio of the materials involved. The thickness ratio is changed in the area of the bridge to lower its transition temperature. This is done through novel photolithographic techniques described in the text, Chapter 2.

If two such proximity effect bridges are connected in parallel, they form a quantum interferometer. The maximum zero voltage current through this circuit is periodically modulated by the magnetic flux through the circuit. At a constant bias current, the modulation of the critical current produces a modulation in the dc voltage across the bridge. This change in dc voltage has been found to be the result of a change in the internal dissipation in the device. A simple model using lumped circuit theory and treating the bridges as quantum oscillators of frequency ω = 2eV/h, where V is the time average voltage across the device, has been found to adequately describe the observed voltage modulation.

The quantum interferometers have been converted to a galvanometer through the inclusion of an integral thin film current path which couples magnetic flux through the interferometer. Thus a change in signal current produces a change in the voltage across the interferometer at a constant bias current. This work is described in Chapter 3 of the text.

The sensitivity of any device incorporating proximity effect bridges will ultimately be determined by the fluctuations in their electrical parameters. He have measured the spectral power density of the voltage fluctuations in proximity effect bridges using a room temperature electronics and a liquid helium temperature transformer to match the very low (~ 0.1 Ω) impedances characteristic of these devices.

We find the voltage noise to agree quite well with that predicted by phonon noise in the normal conduction through the bridge plus a contribution from the superconducting pair current through the bridge which is proportional to the ratios of this current to the time average voltage across the bridge. The total voltage fluctuations are given by <V^2(f ) > = 4kTR^2_d I/V where R_d is the dynamic resistance, I the total current, and V the voltage across the bridge . An additional noise source appears with a strong 1/f^(n) dependence , 1.5 < n < 2, if the bridges are fabricated upon a glass substrate. This excess noise, attributed to thermodynamic temperature fluctuations in the volume of the bridge, increases dramatically on a glass substrate due to the greatly diminished thermal diffusivity of the glass as compared to sapphire.

Conduction-electron localized-moment interaction in palladium-silicon base amorphous alloys containing transition metals

The electrical and magnetic properties of amorphous alloys obtained by rapid quenching from the liquid state have been studied. The composition of these alloys corresponds to the general formula M_xPd_80-xSi₂₀, in which M stands for a metal of the first transition series between chromium and nickel and x is its atomic concentration. The concentration ranges within which an amorphous structure could be obtained were: from 0 to 7 for Cr, Mn and Fe, from 0 to 11 for Co and from 0 to 15 for Ni. A well-defined minimum in the resistivity vs temperature curve was observed for all alloys except those containing nickel. The alloys for which a resistivity minimum was observed had a negative magnetoresistivity approximately proportional to the square of the magnetization and their susceptibility obeyed the Curie-Weiss law in a wide temperature range. For concentrated Fe and Co alloys the resistivity minimum was found to coexist with ferromagnetism. These observations lead to the conclusion that the present results are due to a s-d exchange interaction. The unusually high resistivity minimum temperature observed in the Cr alloys is interpreted as a result of a high Kondo temperature and a large s-d exchange integral. A low Fermi energy of the amorphous alloys (3.5 eV) is also responsible for the anomalies due to the s-d exchange interaction.

The Equation of State and Petrogenesis of Komatiite

(1) Equation of State of Komatiite

The equation of state (EOS) of a molten komatiite (27 wt% MgO) was detennined in the 5 to 36 GPa pressure range via shock wave compression from 1550°C and 0 bar. Shock wave velocity, U_S, and particle velocity, U_P, in km/s follow the linear relationship U_S = 3.13(±0.03) + 1.47(±0.03) U_P. Based on a calculated density at 1550°C, 0 bar of 2.745±0.005 glee, this U_S-U_P relationship gives the isentropic bulk modulus K_S = 27.0 ± 0.6 GPa, and its first and second isentropic pressure derivatives, K'_S = 4.9 ± 0.1 and K"_S = -0.109 ± 0.003 GPa^-1.

The calculated liquidus compression curve agrees within error with the static compression results of Agee and Walker [1988a] to 6 GPa. We detennine that olivine (FO₉₄) will be neutrally buoyant in komatiitic melt of the composition we studied near 8.2 GPa. Clinopyroxene would also be neutrally buoyant near this pressure. Liquidus garnet-majorite may be less dense than this komatiitic liquid in the 20-24 GPa interval, however pyropic-garnet and perovskite phases are denser than this komatiitic liquid in their respective liquidus pressure intervals to 36 GPa. Liquidus perovskite may be neutrally buoyant near 70 GPa.

At 40 GPa, the density of shock-compressed molten komatiite would be approximately equal to the calculated density of an equivalent mixture of dense solid oxide components. This observation supports the model of Rigden et al. [1989] for compressibilities of liquid oxide components. Using their theoretical EOS for liquid forsterite and fayalite, we calculate the densities of a spectrum of melts from basaltic through peridotitic that are related to the experimentally studied komatiitic liquid by addition or subtraction of olivine. At low pressure, olivine fractionation lowers the density of basic magmas, but above 14 GPa this trend is reversed. All of these basic to ultrabasic liquids are predicted to have similar densities at 14 GPa, and this density is approximately equal to the bulk (PREM) mantle. This suggests that melts derived from a peridotitic mantle may be inhibited from ascending from depths greater than 400 km.

The EOS of ultrabasic magmas was used to model adiabatic melting in a peridotitic mantle. If komatiites are formed by >15% partial melting of a peridotitic mantle, then komatiites generated by adiabatic melting come from source regions in the lower transition zone (≈500-670 km) or the lower mantle (>670 km). The great depth of incipient melting implied by this model, and the melt density constraint mentioned above, suggest that komatiitic volcanism may be gravitationally hindered. Although komatiitic magmas are thought to separate from their coexisting crystals at a temperature =200°C greater than that for modern MORBs, their ultimate sources are predicted to be diapirs that, if adiabatically decompressed from initially solid mantle, were more than 700°C hotter than the sources of MORBs and derived from great depth.

We considered the evolution of an initially molten mantle, i.e., a magma ocean. Our model considers the thermal structure of the magma ocean, density constraints on crystal segregation, and approximate phase relationships for a nominally chondritic mantle. Crystallization will begin at the core-mantle boundary. Perovskite buoyancy at > 70 GPa may lead to a compositionally stratified lower mantle with iron-enriched mangesiowiistite content increasing with depth. The upper mantle may be depleted in perovskite components. Olivine neutral buoyancy may lead to the formation of a dunite septum in the upper mantle, partitioning the ocean into upper and lower reservoirs, but this septum must be permeable.

(2) Viscosity Measurement with Shock Waves

We have examined in detail the analytical method for measuring shear viscosity from the decay of perturbations on a corrugated shock front The relevance of initial conditions, finite shock amplitude, bulk viscosity, and the sensitivity of the measurements to the shock boundary conditions are discussed. The validity of the viscous perturbation approach is examined by numerically solving the second-order Navier-Stokes equations. These numerical experiments indicate that shock instabilities may occur even when the Kontorovich-D'yakov stability criteria are satisfied. The experimental results for water at 15 GPa are discussed, and it is suggested that the large effective viscosity determined by this method may reflect the existence of ice VII on the Rayleigh path of the Hugoniot This interpretation reconciles the experimental results with estimates and measurements obtained by other means, and is consistent with the relationship of the Hugoniot with the phase diagram for water. Sound waves are generated at 4.8 MHz at in the water experiments at 15 GPa. The existence of anelastic absorption modes near this frequency would also lead to large effective viscosity estimates.

(3) Equation of State of Molybdenum at 1400°C

Shock compression data to 96 GPa for pure molybdenum, initially heated to 1400°C, are presented. Finite strain analysis of the data gives a bulk modulus at 1400°C, K'_S. of 244±2 GPa and its pressure derivative, K'_OS of 4. A fit of shock velocity to particle velocity gives the coefficients of U_S = C_O+S U_P to be C_O = 4.77±0.06 km/s and S = 1.43±0.05. From the zero pressure sound speed, C_O, a bulk modulus of 232±6 GPa is calculated that is consistent with extrapolation of ultrasonic elasticity measurements. The temperature derivative of the bulk modulus at zero pressure, θK_OSθT|_P, is approximately -0.012 GPa/K. A thermodynamic model is used to show that the thermodynamic Grüneisen parameter is proportional to the density and independent of temperature. The Mie-Grüneisen equation of state adequately describes the high temperature behavior of molybdenum under the present range of shock loading conditions.