361 research outputs found
The Determination of Titan Gravity Field from Doppler Tracking of the Cassini Spacecraft
In its tour of the Saturnian system, the spacecraft Cassini is carrying out measurements of the gravity field of Titan, whose knowledge is crucial for constraining the internal structure of the satellite. In the five flybys devoted to gravity science, the spacecraft is tracked in X (8.4 GHz) and Ka band (32.5 GHz) from the antennas of NASA's Deep Space Network. The use of a dual frequency downlink is used to mitigate the effects of interplanetary plasma, the largest noise source affecting Doppler measurements. Variations in the wet path delay are effectively compensated by means of advanced water vapor radiometers placed close to the ground antennas. The first three flybys occurred on February 27, 2006, December 28, 2006, and June 29, 2007. Two additional flybys are planned in July 2008 and May 2010. This paper presents the estimation of the mass and quadrupole field of Titan from the first two flybys, carried out by the Cassini Radio Science Team using a short arc orbit determination. The data from the two flybys are first independently fit using a dynamical model of the spacecraft and the bodies of the Saturnian system, and then combined in a multi-arc solution. Under the assumption that the higher degree harmonics are negligible, the estimated values of the gravity parameters from the combined, multi-arc solution are GM = 8978.1337 +/- 0.0025 km(exp 3) / s(exp 2), J (sub 2) = (2.7221 +/- 0.0185) 10 (exp -5) and C (sub 22) = (1.1159 +/- 0.0040) 10 (exp -5) The excellent agreement (within 1.7 sigma) of the results from the two flybys further increases the confidence in the solution and provides an a posteriori validation of the dynamical model
Riesz potentials and nonlinear parabolic equations
The spatial gradient of solutions to nonlinear degenerate parabolic equations
can be pointwise estimated by the caloric Riesz potential of the right hand
side datum, exactly as in the case of the heat equation. Heat kernels type
estimates persist in the nonlinear cas
On a Cahn--Hilliard--Darcy system for tumour growth with solution dependent source terms
We study the existence of weak solutions to a mixture model for tumour growth
that consists of a Cahn--Hilliard--Darcy system coupled with an elliptic
reaction-diffusion equation. The Darcy law gives rise to an elliptic equation
for the pressure that is coupled to the convective Cahn--Hilliard equation
through convective and source terms. Both Dirichlet and Robin boundary
conditions are considered for the pressure variable, which allows for the
source terms to be dependent on the solution variables.Comment: 18 pages, changed proof from fixed point argument to Galerkin
approximatio
Large time behavior for a quasilinear diffusion equation with critical gradient absorption
International audienceWe study the large time behavior of non-negative solutions to thenonlinear diffusion equation with critical gradient absorption\partial_t u-\Delta_{p}u+|\nabla u|^{q_*}=0 \quad \hbox{in} \(0,\infty)\times\mathbb{R}^N\ ,for and . We show that theasymptotic profile of compactly supported solutions is given by asource-type self-similar solution of the -Laplacian equation with suitable logarithmic time and space scales. In the process, we also get optimal decay rates for compactly supported solutions and optimal expansion rates for their supports that strongly improve previous results
Self-similar extinction for a diffusive Hamilton-Jacobi equation with critical absorption
International audienceThe behavior near the extinction time is identified for non-negative solutions to the diffusive Hamilton-Jacobi equation with critical gradient absorption â_t u â â_p u + |âu|^{pâ1} = 0 in (0, â) Ă R^N , and fast diffusion 2N/(N + 1) < p < 2. Given a non-negative and radially symmetric initial condition with a non-increasing profile which decays sufficiently fast as |x| â â, it is shown that the corresponding solution u to the above equation approaches a uniquely determined separate variable solution of the form U (t, x) = (T_e â t)^{1/(2âp)} f_* (|x|), (t, x) â (0, T_e) Ă R^N , as t â T_e , where T_e denotes the finite extinction time of u. A cornerstone of the convergence proof is an underlying variational structure of the equation. Also, the selected profile f_* is the unique non-negative solution to a second order ordinary differential equation which decays exponentially at infinity. A complete classification of solutions to this equation is provided, thereby describing all separate variable solutions of the original equation. One important difficulty in the uniqueness proof is that no monotonicity argument seems to be available and it is overcome by the construction of an appropriate Pohozaev functional
Modern optical astronomy: technology and impact of interferometry
The present `state of the art' and the path to future progress in high
spatial resolution imaging interferometry is reviewed. The review begins with a
treatment of the fundamentals of stellar optical interferometry, the origin,
properties, optical effects of turbulence in the Earth's atmosphere, the
passive methods that are applied on a single telescope to overcome atmospheric
image degradation such as speckle interferometry, and various other techniques.
These topics include differential speckle interferometry, speckle spectroscopy
and polarimetry, phase diversity, wavefront shearing interferometry,
phase-closure methods, dark speckle imaging, as well as the limitations imposed
by the detectors on the performance of speckle imaging. A brief account is
given of the technological innovation of adaptive-optics (AO) to compensate
such atmospheric effects on the image in real time. A major advancement
involves the transition from single-aperture to the dilute-aperture
interferometry using multiple telescopes. Therefore, the review deals with
recent developments involving ground-based, and space-based optical arrays.
Emphasis is placed on the problems specific to delay-lines, beam recombination,
polarization, dispersion, fringe-tracking, bootstrapping, coherencing and
cophasing, and recovery of the visibility functions. The role of AO in
enhancing visibilities is also discussed. The applications of interferometry,
such as imaging, astrometry, and nulling are described. The mathematical
intricacies of the various `post-detection' image-processing techniques are
examined critically. The review concludes with a discussion of the
astrophysical importance and the perspectives of interferometry.Comment: 65 pages LaTeX file including 23 figures. Reviews of Modern Physics,
2002, to appear in April issu
Improved catalytic activity of rutheniumâarene complexes in the reduction of NAD+
A series of neutral Ru-II half-sandwich complexes of the type [(eta(6)-arene)Ru(N,N')Cl] where the arene is para-cymene (p-cym), hexamethylbenzene (hmb), biphenyl (bip), or benzene (bn) and N,N' is N-(2-aminoethyl) -4-(trifluoromethyl)benzenesulfonamide (TfEn), N-(2-aminoethyl)-4-toluenesulfonamide (TsEn), or N-(2-aminoethyl)-methylenesulfonamide (MsEn) were synthesized and characterized. X-ray crystal structures of [(p-cym)Ru(MsEn)Cl] (1), [(hmb)Ru(TsEn)Cl] (5), [(hmb)Ru(TfEn)Cl] (6), [(bip)Ru(MsEn)Cl] (7), and [(bip)Ru(TsEn)Cl] (8) have been determined. The complexes can regioselectively catalyze the transfer hydrogenation of NAD(+) to give 1,4-NADH in the presence of formate. The turnover frequencies (TOF) when the arene is varied decrease in the order bn > bip > p-cym > hmb for complexes with the same N,N' chelating ligand. The TOF decreased with variation in the N,N' chelating ligand in the order TfEn > TsEn > MsEn for a given arene. [(bn)Ru(TfEn)Cl] (12) was the most active, with a TOP of 10.4 h(-1). The effects of NAD(+) and formate concentration on the reaction rates were determined for [(p-cym)Ru(TsEn)Cl] (2). Isotope studies implicated the formation of [(arene)Ru(N,N')(H)] as the rate-limiting step. The coordination of formate and subsequent CO2 elimination to generate the hydride were modeled computationally by density functional theory (DFT). CO2 elimination occurs via a two-step process with the coordinated formate first twisting to present its hydrogen toward the metal center. The computed barriers for CO2 release for arene = benzene follow the order MsEn > TsEn > TfEn, and for the Ms En system the barrier followed bn < hmb, both consistent with the observed rates. The effect of methanol on transfer hydrogenation rates in aqueous solution was investigated. A study of pH dependence of the reaction in D2O gave the optimum pH* as 7.2 with a TOF of 1.58 h(-1) for 2. The series of compounds reported here show an improvement in the catalytic activity by an order of magnitude compared to the ethylenediamine analogues
Color-color Relations for Red Giants in Star Clusters
New Johnson-Cousins UBVRI photometry of giants in globular clusters is
combined with JHK photometry on the CIT system to produce color sequences for
giants from the globular clusters M3, M5, M13, and M92. UBVRI data are also
presented for giants in the metal-rich open cluster NGC 6791. These data fill a
gap in the literature, especially for the R & I bands. We provide the empirical
relations between broad band colors for various [Fe/H] values for metal-poor
giants. The color sequences for U-B and B-V show clear separations for
different [Fe/H] values. We also find weak, though unexpected, metallicity
dependences of V-R, V-I, and J-K colors. H-K is metal-insensitive. The above
colors are plotted as a function of V-K, and a literature (V-K) - T_{eff}
relation is given.Comment: 21 pages, 7 figures; AASTeX 4.0; to appear in the July 1998 edition
of PASP. Revised version; includes discussion on possible effects of
reddening error
Mechanisms and Kinetics for Sorption of CO2 on Bicontinuous Mesoporous Silica Modified with n-Propylamine
We studied equilibrium adsorption and uptake kinetics and identified molecular species that formed during sorption of carbon dioxide on amine-modified silica. Bicontinuous silicas (AMS-6 and MCM-48) were postsynthetically modified with (3-aminopropyl)triethoxysilane or (3-aminopropyl)methyldiethoxysilane, and amine-modified AMS-6 adsorbed more CO(2) than did amine-modified MCM-48. By in situ FTIR spectroscopy, we showed that the amine groups reacted with CO(2) and formed ammonium carbamate ion pairs as well as carbamic acids under both dry and moist conditions. The carbamic acid was stabilized by hydrogen bonds, and ammonium carbamate ion pairs formed preferably on sorbents with high densities of amine groups. Under dry conditions, silylpropylcarbamate formed, slowly, by condensing carbamic acid and silanol groups. The ratio of ammonium carbamate ion pairs to silylpropylcarbamate was higher for samples with high amine contents than samples with low amine contents. Bicarbonates or carbonates did not form under dry or moist conditions. The uptake of CO(2) was enhanced in the presence of water, which was rationalized by the observed release of additional amine groups under these conditions and related formation of ammonium carbamate ion pairs. Distinct evidence for a fourth and irreversibly formed moiety was observed under sorption of CO(2) under dry conditions. Significant amounts of physisorbed, linear CO(2) were detected at relatively high partial pressures of CO(2), such that they could adsorb only after the reactive amine groups were consumed.authorCount :7</p
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