Velocity-height relation for antimatter meteors

A general velocity-height relation for both antimatter and ordinary matter meteor is derived. This relation can be expressed as % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq% aHfpqDdaWgaaWcbaGaamOEaaqabaaakeaacqaHfpqDdaWgaaWcbaGa% eyOhIukabeaaaaGccqGH9aqpcaqGLbGaaeiEaiaabchacaqGGaWaam% WaaeaacqGHsisldaWcaaqaaiaadkeaaeaacaWGHbaaaiaabwgacaqG% 4bGaaeiCaiaabIcacaqGTaGaamyyaiaadQhacaGGPaaacaGLBbGaay% zxaaGaeyOeI0YaaSaaaeaacaWGdbaabaGaamOqaiabew8a1naaBaaa% leaacqGHEisPaeqaaaaakmaacmaabaGaaGymaiabgkHiTiaabwgaca% qG4bGaaeiCamaadmaabaGaeyOeI0YaaSaaaeaacaWGcbaabaGaamyy% aaaacaqGLbGaaeiEaiaabchacaqGOaGaaeylaiaadggacaWG6bGaai% ykaaGaay5waiaaw2faaaGaay5Eaiaaw2haaiaacYcaaaa!64FD!\[\frac{{\upsilon _z }}{{\upsilon _\infty }} = {\text{exp }}\left[ { - \frac{B}{a}{\text{exp( - }}az)} \right] - \frac{C}{{B\upsilon _\infty }}\left\{ {1 - {\text{exp}}\left[ { - \frac{B}{a}{\text{exp( - }}az)} \right]} \right\},\]where _z is the velocity of the meteoroid at height z, its velocity before entrance into the Earth's atmosphere, is the scale-height, and C parameter proportional to the atom-antiatom annihilation cross- section, which is experimentally unknown. The parameter B (B = DA₀/m) is the well known parameter for koinomatter (ordinary matter) meteors, D is the drag factor, ₀ is the air density at sea level, A is the cross sectional area of the meteoroid and m its mass.When the annihilation cross-section is zero — in the case of ordinary meteors — the parameter C is also zero and the above derived equation becomes % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq% aHfpqDdaWgaaWcbaGaamOEaaqabaaakeaacqaHfpqDdaWgaaWcbaGa% eyOhIukabeaaaaGccqGH9aqpcaqGLbGaaeiEaiaabchacaqGGaWaam% WaaeaacqGHsisldaWcaaqaaiaadkeaaeaacaWGHbaaaiaabwgacaqG% 4bGaaeiCaiaabIcacaqGTaGaamyyaiaadQhacaGGPaaacaGLBbGaay% zxaaGaaiilaaaa!4CF5!\[\frac{{\upsilon _z }}{{\upsilon _\infty }} = {\text{exp }}\left[ { - \frac{B}{a}{\text{exp( - }}az)} \right],\]which is the well known velocity-height relation for koinomatter meteors.In the case in which the Universe contains antimatter in compact solid structure, the velocity-height relation can be found useful.Work performed mainly at the Nuclear Physics Laboratory of the National University of Athens, Greece.     

Integration error over very long time spans

The main limit to the time span of a numerical integration of the planetary orbits is no longer set by the availability of computer resources, but rather by the accumulation of the integration error. By the latter we mean the difference between the computed orbit and the dynamical behaviour of the real physical system, whatever the causes. The analysis of these causes requires an interdisciplinary effort: there are physical model and parameters errors, algorithm and discretisation errors, rounding off errors and reliability problems in the computer hardware and system software, as well as instabilities in the dynamical system. We list all the sources of integration error we are aware of and discuss their relevance in determining the present limit to the time span of a meaningful integration of the orbit of the planets. At present this limit is of the order of 10⁸ years for the outer planets. We discuss in more detail the truncation error of multistep algorithms (when applied to eccentric orbits), the coefficient error, the method of Encke and the associated coordinate change error, the procedures used to test the numerical integration software and their limitations. Many problems remain open, including the one of a realistic statistical model of the rounding off error; at present, the latter can only be described by a semiempirical model based upon the simpleN ² formula (N=number of steps, =machine accuracy), with an unknown numerical coefficient which is determined only a posteriori.     

Multiple windbreaks: An aeolean ensemble

Near-neutral measurements of the turbulent wind field within and above a sequence of 15 parallel windbreaks on a flat pastoral site are presented. The windbreak fences each had a porosity of 60% and were equally-spaced at 6 times their height (h = 2 m). The following conclusions seem justified for wind directions within 10 ° of the normal to the array:

1. Above the windbreaks (2h), mean windspeeds first decreased and then increased asymptotically to a value in equilibrium with the new surface roughness. At 0.5h, windspeeds exhibited a slow increase down the entire array.
2. Reflecting differences in approach flows, the drag on the initial fence was almost twice that on barriers farther downstream. This reduction in momentum extraction per windbreak was associated with an elevation in the zero-plane displacement to a level equal to 0.8h.
3. At positions well-removed from the initial fences, mean windspeeds were reduced throughout the entire region below shelter height. In this region, the flow became increasingly dominated by downward moving air with velocities much greater than the local average. The zone of reduced turbulence was small, extending only 2h downstream of a barrier at a height of 0.25h. This corresponded with the region excluded from smoke trails released at the top of windbreaks.
4. An approximate TKE budget mid-way between windbreaks 7 and 8 suggests that shear and wake production peak near z = h and that production is balanced by dissipation and vertical transport components. Advective and inertial interaction terms are negligible at this midway position but are likely to be major sources of TKE closer to the windbreak. Local equilibrium is attained above z = 1.5h implying the existence of a constant-stress layer.

The measurements show the practical difficulty of simultaneously reducing both mean windspeeds and turbulence levels with repeated windbreaks at conventional spacings for horticultural applications.     

Surface drag and turbulence over an inhomogeneous land surface

Data collected over an inhomogeneous semi-rural area are presented. The data are compared with previous surface-layer data to determine how representative the fixed-point flux measurements are of area averages. Departures from the standard surface-layer results are found to be relatively small (~10–20%), which supports the concept of a blending height above which the flow ceases to respond to variations in the underlying surface and becomes horizontally homogeneous.Effective roughness lengths are derived for different wind directions and the relationship between the effective roughness length and upwind surface is examined in the light of recent ideas on averaging surface roughness lengths. It is found that by averaging drag coefficients, realistic values of the effective roughness length can be calculated which are not very sensitive to the precise choice of the component roughness lengths.     

Model of geomagnetic paleosecular variations for the Northern Hemisphere

Summary A model of radial drifting and oscillating dipoles to represent geomagnetic palaeosecular variations, which showed to be appropriate for the Southern Hemisphere, is evaluated for the Northern Hemisphere. After a new fitting of some involved parameters, its theoretical results are compared with the palaeomagnetic data of Lake de Bouchet (France) and the Black Sea. A time lag between the declination and inclination profiles is observed in both cases. A good cross-correlation coefficient is obtained for the declination and inclination data.Presented at 2nd conference on New Trends in Geomagnetism, Castle of Bechyn, Czechoslovakia, September 24–29, 1990.     

Tidal contribution of the satellites to removing the angular momentum of Jupiter

Summary It has been shown that dynamically, on the basis of the distribution of angular momenta, the Jovian system cannot be considered an analogue within the Solar system. The total tidal decrease in the angular momentum of Jupiter and in its angular velocity of rotation have been estimated, as well as the loss of mechanical energy due to tidal dissipation. It has been concluded that there are no dynamical contradictions with the hypothesis of the common cosmogonic origin of Jupiter and of its eight close satellites.

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Ion microprobe analysis of oxygen isotope ratios in granulite facies magnetites: diffusive exchange as a guide to cooling history

Ion microprobe analysis of magnetites from the Adirondack Mountains, NY, yields oxygen isotope ratios with spatial resolution of 2–8 m and precision in the range of 1 (1 sigma). These analyses represent 11 orders of magnitude reduction in sample size compared to conventional analyses on this material and they are the first report of routinely reproducible precision in the 1 per mil range for analysis of ¹⁸O at this scale. High precision micro-analyses of this sort will permit wide-ranging new applications in stable isotope geochemistry. The analyzed magnetites form nearly spherical grains in a calcite matrix with diopside and monticellite. Textures are characteristic of granulite facies marbles and show no evidence for retrograde recrystallization of magnetite. Magnetites are near to Fe₃O₄ in composition, and optically and chemically homogeneous. A combination of ion probe plus conventional BrF₅ analysis shows that individual grains are homogeneous with ¹⁸O=8.9±1 SMOW from the core to near the rim of 0.1–1.2 mm diameter grains. Depth profiling into crystal growth faces of magnetites shows that rims are 9 depleted in ¹⁸O. These low ¹⁸O values increase in smooth gradients across the outer 10 m of magnetite rims in contact with calcite. These are the sharpest intracrystalline gradients measured to date in geological materials. This discovery is confirmed by bulk analysis of 150–350 m diameter magnetites which average 1.2 lower in ¹⁸O than coarse magnetites due to low ¹⁸O rims. Conventional analysis of coexisting calcite yields °¹⁸O=18.19, suggesting that bulk ¹⁸O (Cc-Mt)=9.3 and yielding an apparent equilibration temperature of 525° C, over 200° C below the temperature of regional metamorphism. Consideration of experimental diffusion data and grain size distribution for magnetite and calcite suggests two contrasting cooling histories. The data for oxygen in calcite under hydrothermal conditions at high P(H₂O) indicates that diffusion is faster in magnetite and modelling of the low ¹⁸O rims on magnetite would suggest that the Adirondacks experienced slow cooling after Grenville metamorphism, followed by a brief period of rapid cooling, possibly related to uplift. Conversely, the data for calcite at low P(H₂O) show slower oxygen diffusion than in magnetite. Modelling based on these data is consistent with geochronology that shows slow cooling through the blocking temperature of both minerals, suggesting that the low ¹⁸O rims form by exchange with late, low temperature fluids similar to those that infiltrated the rock to serpentinize monticellite and which infiltrated adjacent anorthosite to form late calcite veinlets. In either case, the ion microprobe results indicate that two distinct events are recorded in the post-metamorphic exchange history of these magnetites. Recognition of these events is only possible through microanalysis and has important implications for geothermometry.     

Na-rich carbonate inclusions in perovskite and calzirtite from the Guli intrusive Ca-carbonatite,polar Siberia

Carbonate phases, some rich in Na₂O and comparatively rich in SrO and BaO, occur as inclusions in perovskite and calzirtite (Ca₂Zr₅Ti₂O₁₆) in the carbonatite of the Guli complex, Siberia. This is the first record of alkali carbonates, akin to nyerereite [Na₂Ca(CO₃)₂], in plutonic igneous rocks. The inclusion populations suggest that the parental magma of the complex was Ca-rich but developed Na-rich differentiates during the latest stages. This points to the dominant calcic carbonatites of the complex not being derivatives of alkali-rich parental carbonatites. These alkali-rich carbonate inclusions (and rare inclusions of djerfisherite) have been preserved due to the resistance of perovskite and calzirtite to processes of leaching, hydrothermal alteration and weathering.     

An Example of Island-Arc Petrogenesis: Geochemistry and Petrology of the Southern Luzon Arc, Philippines

Volcanism throughout the Luzon arc is associated with eastwardsubduction of the South China Sea floor along the Manila Trench.The southern section of the arc, the focus of this study, extendsfrom the Lingayen-Dingalan fault to the small islands just southof Luzon. Two segments appear to exist along this section ofthe arc the northern Bataan and southern Mindoro segments whichare separated by the Macolod Corridor. The volcanic rocks have typical arc phenocryst mineralogies:olivine, clinopyroxene, plagioclase, and titanomagnetite inthe most mafic rocks and clinopyroxene, plagioclase, orthopyroxene,titanomagnetite, ? amphibole in the more felsic samples. Complexzoning, sieve textures, and decoupling of incompatible traceelements suggest that processes such as assimilation have takenplace. The rocks from the study area range from basalts to rhyolitesand show typical calc-alkaline features. The rocks of the MacolodCorridor and Mindoro segment are particularly enriched in largeion lithophile elements (LILE), light rare earth elements (LREE),and radiogenic Sr compared with the Bataan segment. The datafall within the mantle array on Sr-Nd isotopic diagrams andgrade toward higher Sr and lower Nd isotopic values from northto south. A likely source for the volcanics of this study is either amid-ocean ridge basalt (MORB)-type mantle that undergoes higherdegrees of partial melting than regions involved in MORB generationor a previously depleted source. We suggest that the high fieldstrength element (HFSE) anomalies have been derived throughdifferential element partitioning during fluid transport fromthe subducted lithosphere to the mantle wedge. Continental crustal material seems to play a significant roleparticularly in the Macolod Corridor and the Mindoro segment,based on the high LILE, La/Sm ratios, radiogenic Sr isotopes,and ¹⁸O values. The Macolod Corridor and the Mindoro segmenthave undergone source contamination by crustal material fromthe North Palawan-Mindoro crustal block either during the collisionof this block with the Manila Trench or by subduction of sedimentsrich in this crustal material. A similar component has alsobeen detected in the Bataan segment but in minor amounts. Thetrace element and isotopic differences between the northernand southern sections of the arc are interpreted in terms ofvariable composition (i. e., variable amounts of a crustal componentintroduced from the Palawan-Mindoro crustal terrain) of themetasomatic fluids released into the source.