Finite Prandtl number 2-D convection at high Rayleigh numbers

Finite Prandtl number thermal convection is important to the dynamics of planetary bodies in the solar system. For example, the complex geology on the surface of the Jovian moon Europa is caused by a convecting, brine-rich global ocean that deforms the overlying icy “lithosphere”. We have conducted a systematic study on the variations of the convection style, as Prandtl numbers are varied from 7 to 100 at Rayleigh numbers 106 and 108. Numerical simulations show that changes in the Prandtl number could exert significant effects on the shear flow, the number of convection cells, the degree of layering in the convection, and the number and size of the plumes in the convecting fluid. We found that for a given Rayleigh number, the convection style can change from single cell to layered convection, for increasing Prandtl number from 7 to 100. These results are important for determining the surface deformation on the Jovian moon Europa. They also have important implications for surface heat flow on Europa, and for the interior heat transfer of the early Earth during its magma ocean phase. Electronic Supplementary Material is available if you access this article at . On that page (frame on the left side), a link takes you directly to the supplementary material. Electronic Supplementary Material is available if you access this article at . On that page (frame on the left side), a link takes you directly to the supplementary material.     

Algebraic Solution of GPS Pseudo-Ranging Equations

Several procedures for solving, in a closed form the GPS pseudo-ranging four-point problem P4P in matrix form already exist. We present here alternative algebraic procedures using Multipolynomial resultant and Groebner basis to solve the same problem. The advantage is that these algebraic algorithms have already been implemented in algebraic software such as “Mathematica” and “Maple”. The procedures are straightforward and simple to apply. We illustrate here how the algebraic techniques of Multipolynomial resultant and Groebner basis explicitly solve the nonlinear GPS pseudo-ranging four-point equations once they have been converted into algebraic (polynomial) form and reduced to linear equations. In particular, the algebraic tools of Multipolynomial resultant and Groebner basis provide symbolic solutions to the GPS four-point pseudo-ranging problem. The various forward and backward substitution steps inherent in the clasical closed form solutions of the problem are avoided. Similar to the Gauss elimination techniques in linear systems of equations, the Multipolynomial resultant and Groebner basis approaches eliminate several variables in a multivariate system of nonlinear equations in such a manner that the end product normally consists of univariate polynomial equations (in this case quadratic equations for the range bias expressed algebraically using the given quantities) whose roots can be determined by existing programs (e. g., the roots command in MATLAB). © 2002 Wiley Periodicals, Inc.     

GPS Solutions: Closed Forms, Critical and Special Configurations of P4P

P4P is the pseudo-ranging 4-point problem as it appears as the basic configuration of satellite positioning with pseudo-ranges as observables. In order to determine the ground receiver/satellite receiver (LEO networks) position from four positions of satellite transmitters given, a system of four nonlinear (algebraic) equations has to be solved. The solution point is the intersection of four spherical cones if the ground receiver/satellite receiver clock bias is implemented as an unknown. Here we determine the critical configuration manifold (Determinantal Loci, Inverse Function Theorem, Jacobi map) where no solution of P4P exists. Four examples demonstrate the critical linear manifold. The algorithm GS solves in a closed form P4P in a manner similar to Groebner bases: The algebraic nonlinear observational equations are reduced in the forward step to one quadratic equation in the clock bias unknown. In the backward step two solutions of the position unknowns are generated in closed form. Prior information in P4P has to be implemented in order to decide which solution is acceptable. Finally, the main target of our contribution is formulated: Can we identify a special configuration of satellite transmitters and ground receiver/satellite receiver where the two solutions are reduced to one. A special geometric analysis of the discriminant solves this problem. ? 2002 Wiley Periodicals, Inc.     

Elektronenmikroskopische Untersuchungen an mikritischen Kalken

Zusammenfassung Es werden die Entstehungsmöglichkeiten von mikritischen Kalken diskutiert und an Hand von elektronenmikroskopischen Aufnahmen Hinweise auf genetische Interpretationen vorgeführt.

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The origin of micritic limestones is discussed and genetic interpretation of micrites from different environments, studied by electron microscope, is given.

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Résumé L'origine des calcaires micritic est discutée et une interprétation génétique des micrites de milieux différents est donnée à l'aide de la microscopie électronique.

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Vorgetragen auf der 56. Jahresversammlung der Geologischen Vereinigung in Wien im Februar 1966.     

Reconstructing the historical changes in Daphnia mean size and planktivorous fish abundance in lakes from the size of Daphnia ephippia in the sediment

The zooplankton community structure in lakes is highly influenced by size-selective predation by fish, with small zooplankton species dominating at high predation pressure. Remains of cladocerans are preserved in the sediment and may be used to trace historical changes in fish predation. We determined how contemporary data on planktivorous fish were related to the size of Daphnia ephippia (dorsal length) in the surface sediment (0-1 cm) of 52 mainly shallow lakes with contrasting densities of fish and nutrients (TP: 0.002-0.60 mg P l^-1). Density of fish expressed as catch per unit effort, in terms of numbers in multiple mesh-sized gill nets (CPUE_n), decreased significantly with increasing mean size of ephippia. The relationship was improved by adding TP as an independent variable, now explaining 90% of the variation in CPUE_n on the full data set covering lakes in Denmark, Greenland and New Zealand, and 78% if only data on Danish lakes were used. CPUE by weight of planktivorous fish and mean weight of Daphnia in the pelagial during summer were also related to ephippial size. By including contemporary data on established relationships between the sizes of egg-bearing female Daphnia and ephippia, we inferred changes in the CPUE_n, mean size of ephippia-bearing Daphnia and summer mean body weight of Daphnia from ephippial size in four lakes during the past 1-2 centuries. In a hypertrophic lake subject to periodic fish kills, Daphnia mean body weight was high and CPUE_n was low compared with those in two eutrophic lakes, while CPUE_n was low and Daphnia body weight was high in the least eutrophic, clearwater lake. Estimated CPUE_n and Daphnia mean weight in the surface sediment of these four lakes corresponded well with contemporary data. Only small changes in ephippial size with time were observed in the clearwater lake and in one of the lakes that had suffered early eutrophication, while major changes occurred in the two other lakes that had been subjected to a major increase in nutrient input or fish kills. We conclude that Daphnia ephippia preserved in the surface sediments of lakes may be a useful and efficient method to quantify the present-day abundance of planktivorous fish and Daphnia mean size. The method is particularly valid in surveys aimed to give a general picture of the fish stock and the ecological state in a set of lakes in a region rather than a precise estimate for a single lake. Though some evidence is provided, more work is needed to evaluate whether the equations are valid for hind-casting in down-core palaeoecological studies.     

Catalogue of large alluvial fans in martian impact craters

We conducted a systematic, global survey using Thermal Emission Imaging System Infrared (THEMIS IR) coverage (∼100 m/pixel) to search for large alluvial fans in impact craters on Mars. Our survey has focused on large fans (apron areas greater than ∼40 km², usually located in craters greater than 20 km in diameter) due to the resolution of the THEMIS images and Mars Orbiter Laser Altimeter (MOLA) coverage. We find that the host craters are found to have a distinctive diameter range from 30-150 km. The fans generally cluster in three geographic areas—southern Margaritifer Terra, southwestern Terra Sabaea, and southwestern Tyrrhena Terra, however several outliers do exist. The alluvial fans do not form in a particular orientation along the crater rim nor are they associated with the location of current high rim topography. Fan area magnitude and variability increase with crater diameter while fan concavity magnitude and variability increase with decreasing crater diameter. Smaller fan aprons in general have higher, more variable concavity. The source of the water forming these fans is uncertain given the challenges of accommodating the global distribution pattern and formation patterns within the craters.     

The Transition from Three-Dimensional Embedding to Two-Dimensional Euler-Lagrange Deformation Tensor of the Second Kind: Variation of Curvature Measures

Based on the Stein formulation of changes of curvature parameters, we describe the changes of Riemann two-dimensional manifolds of surface geometries. The three-dimensional left and right Euclidean manifolds with the curvature parameters “geodetic curvature, normal curvature, geodetic torsion” characterize the embedding “Riemann to Euclid” or 2d into 3d. The variation in time of the Euler-Lagrange deformation tensor of the second kind, in short “curvature variation” is studied.     

Multivariate statistical analysis of deformation tensors: independent vs. correlated tensor observations

In the presence of errors in measuring a random displacement field (under the normal distribution assumption of displacement field), stochastic behaviors of principal components of deformation tensors (strain tensor and tensor of change of curvature (TCC)), based on the intrinsic assumption of geometrical modeling of surface deformation analysis, are discussed. We divided the contents into two parts: In the first, we considered independent random vectors of repeated tensor measurements. In the second step, we considered correlations among repeated measurements. Then, covariance components between tensor elements by Helmert estimator, based on prior information of variance components, are estimated. As a case study, both assumptions are applied to the estimation of principal components of deformation rate tensor observations in Zagros region (Western Iran). The results of numerical analysis showed that greatest shortening is accommodated in oblique orientation (NS) with respect to the Main Recent Fault (MRF), northwest part of North Zagros, Central Iran block and MRF, respectively. Most of the extensions occurred in the east part of the belt. The pattern of eigenspace components of TCC shows highest positive values across the NW region, nearly in orthogonal direction to the MRF and Main Zagros Fault (MZF). The pattern has insignificant values in the Central Zagros. It takes the significant negative values across the SW part, especially along the SPF and Persian Gulf shore. The effect of non-independent observations on the estimation of eigenspace components of deformation tensors (strain tensor and TCC) shows that the estimation of covariance components has influence on the confidence intervals of eigenspace components, especially in seismically active regions of the belt (along the Persian Gulf shore, NW of the belt and region between the Central Iran block and MRF). The results demonstrate the importance of considering the correlation structure among the observations on statistical behavior of principal components of deformation tensors in seismically active regions.