The Ranger 4 Flight Path and Its Determination from Tracking Data

The ranger iv flight path and its determination from tracking dat

Anisotropic Magnification Distortion of the 3D Galaxy Correlation: II. Fourier and Redshift Space

In paper I of this series we discuss how magnification bias distorts the 3D correlation function by enhancing the observed correlation in the line-of-sight (LOS) orientation, especially on large scales. This lensing anisotropy is distinctive, making it possible to separately measure the galaxy-galaxy, galaxy-magnification {\it and} magnification-magnification correlations. Here we extend the discussion to the power spectrum and also to redshift space. In real space, pairs oriented close to the LOS direction are not protected against nonlinearity even if the pair separation is large; this is because nonlinear fluctuations can enter through gravitational lensing at a small transverse separation (or i.e. impact parameter). The situation in Fourier space is different: by focusing on a small wavenumber $k$, as is usually done, linearity is guaranteed because both the LOS and transverse wavenumbers must be small. This is why magnification distortion of the galaxy correlation appears less severe in Fourier space. Nonetheless, the effect is non-negligible, especially for the transverse Fourier modes, and should be taken into account in interpreting precision measurements of the galaxy power spectrum, for instance those that focus on the baryon oscillations. The lensing induced anisotropy of the power spectrum has a shape that is distinct from the more well known redshift space anisotropies due to peculiar motions and the Alcock-Paczynski effect. The lensing anisotropy is highly localized in Fourier space while redshift space distortions are more spread out. This means that one could separate the magnification bias component in real observations, implying that potentially it is possible to perform a gravitational lensing measurement without measuring galaxy shapes.Comment: 14 pages, minor revisions, as accepted for publication in Physical Review

Optimal Estimation of Several Linear Parameters in the Presence of Lorentzian Thermal Noise

In a previous article we developed an approach to the optimal (minimum variance, unbiased) statistical estimation technique for the equilibrium displacement of a damped, harmonic oscillator in the presence of thermal noise. Here, we expand that work to include the optimal estimation of several linear parameters from a continuous time series. We show that working in the basis of the thermal driving force both simplifies the calculations and provides additional insight to why various approximate (not optimal) estimation techniques perform as they do. To illustrate this point, we compare the variance in the optimal estimator that we derive for thermal noise with those of two approximate methods which, like the optimal estimator, suppress the contribution to the variance that would come from the irrelevant, resonant motion of the oscillator. We discuss how these methods fare when the dominant noise process is either white displacement noise or noise with power spectral density that is inversely proportional to the frequency ($1/f$ noise). We also construct, in the basis of the driving force, an estimator that performs well for a mixture of white noise and thermal noise. To find the optimal multi-parameter estimators for thermal noise, we derive and illustrate a generalization of traditional matrix methods for parameter estimation that can accommodate continuous data. We discuss how this approach may help refine the design of experiments as they allow an exact, quantitative comparison of the precision of estimated parameters under various data acquisition and data analysis strategies.Comment: 16 pages, 10 figures. Accepted for publication in Classical and Quantum Gravit

The Generalized Ricci Flow for 3D Manifolds with One Killing Vector

We consider 3D flow equations inspired by the renormalization group (RG) equations of string theory with a three dimensional target space. By modifying the flow equations to include a U(1) gauge field, and adding carefully chosen De Turck terms, we are able to extend recent 2D results of Bakas to the case of a 3D Riemannian metric with one Killing vector. In particular, we show that the RG flow with De Turck terms can be reduced to two equations: the continual Toda flow solved by Bakas, plus its linearizaton. We find exact solutions which flow to homogeneous but not always isotropic geometries

Ricci flows with unbounded curvature

We show that any noncompact Riemann surface admits a complete Ricci flow g(t), t\in[0,\infty), which has unbounded curvature for all t\in[0,\infty).Comment: 12 pages, 1 figure; updated reference

Influence of Potamogeton crispus growth on nutrients in the sediment and water of Lake Tangxunhu

An incubation experiment was performed on Potamogeton crispus (P. crispus) using sediment collected from Lake Tangxunhu in the center of China, in order to determine the effects of plant growth on Fe, Si, Cu, Zn, Mn, Mg, P, and Ca concentrations in the sediments and overlying waters. After 3 months of incubation, Ca, Mg, and Si concentrations in the water column were significantly lower, and P and Cu concentrations were significantly higher than in unplanted controls. The effect of P. crispus growth on sediment pore waters and water-extractable elements varied. Concentrations of Ca, Mg, Si, Fe, Cu, and Zn were significantly higher, and P was significantly lower, than in pore waters of the control. Water-extracted concentrations of Fe, Mg, and Si in the sediments were lower, and P was higher, than in the control. Presence of P. crispus generally enhanced concentration gradients of elements between pore waters and overlying waters but not for P. The growth of P. crispus was associated with an increase in water pH and formation of root plaques, resulting in complex effects on the sediment nutritional status

Computer model calibration with large non-stationary spatial outputs: application to the calibration of a climate model

Bayesian calibration of computer models tunes unknown input parameters by comparing outputs with observations. For model outputs that are distributed over space, this becomes computationally expensive because of the output size. To overcome this challenge, we employ a basis representation of the model outputs and observations: we match these decompositions to carry out the calibration efficiently. In the second step, we incorporate the non-stationary behaviour, in terms of spatial variations of both variance and correlations, in the calibration. We insert two integrated nested Laplace approximation-stochastic partial differential equation parameters into the calibration. A synthetic example and a climate model illustration highlight the benefits of our approach

Evidence of volcanic ash at a K-T boundary section: Ocean drilling program hole 690 C, Maud Rise, Weddell Sea off East Antarctica

Rare vitric volcanogenic ash but more abundant clay minerals considered volcanogenic in origin are associated with an expanded and essentially complete K-T boundary sequence from Ocean Drilling Project (ODP) Hole 690 C on Maud Rise in the Weddell Sea off East Antarctica. Results at this writing are preliminary and are still based to some extent on shipboard descriptions. Further shore-based studies are in progress. It would appear, however, that the presence of volcanic ash and altered ash in the Danian section beginning at the biostratigraphically and paleomagnetically determined K-T boundary on Maud Rise can be cited as evidence of significant volcanic activity within the South Atlantic-Indian Ocean sector of the Southern Ocean coincident with the time of biotic crises at the end of the Maestrichtian. This is a postulated time of tectonic and volcanic activity within this Southern Hemisphere region, including possible initiation of the Reunion hot spot and a peak in explosive volcanism on Walvis Ridge (1) among other events. A causal relationship with the biotic crisis is possible and volcanism should be given serious consideration as a testable working hypothesis to explain these extinctions