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An approximation framework is presented for computation (in finite dimensional spaces) of Riccati operators that can be guaranteed to converge to the Riccati operator in feedback controls for abstract evolution systems in a Hilbert space. It is indicated how these results may be used in the linear optimal regulator problem for a large class of parabolic systems.
Previous analyses have recognized several styles and orientations of compressional deformation, crustal convergence, and crustal thickening in Eastern Ishtar Terra. An east to west sense of crustal convergence through small scale folding, thrusting, and buckling is reflected in the high topography and ridge-and-valley morphology of Maxwell Montes and the adjacent portion of Fortuna Tessera. This east to west convergence was accompanied by up to 1000 km of lateral motion and large scale strike-slip faulting within two converging shear zones which has resulted in the present morphology of Maxwell Montes. A more northeast to southwest sense of convergence through large scale buckling and imbrication is reflected in large, northwest-trending scarps along the entire northern boundary of Ishtar Terra, with up to 2 km of relief present at many of the scarps. It was previously suggested that both styles of compression have occurred at the expense of pre-existing tessera regions which have then been overprinted by the latest convergence event. The difference in style is attributed mostly to differences in the properties of the crust converging with the tessera blocks. If one, presumably thick, tessera block converges with another tessera region, then the widespread, distributed style of deformation occurs, as observed in western Fortuna Tessera. However, if relatively thin crust (such as suggested for the North Polar Plains converges with thicker tessera regions, then localized deformation occurs, as reflected in the scarps along Northern Ishtar Terra. The purpose is to identify the types of features observed in Eastern Ishtar Terra. Their potential temporal and spatial relationships, is described, possible origins for them is suggested, and how the interpretation of some of these features has led to the multiple-style tectonic evolution model described is shown.
Observational and theoretical data converge on the conclusion that planetesimals in Jupiter's region of the solar nebula were initially composed predominantly of a mixture of roughly 39-70% H2O ice by volume, and 30-61% dark stony material resembling carbonaceous chondrites. Recent observations emphasize a division of most asteroid and satellite surfaces in this region into two distinct groups: bright icy material and dark stony material. The present model accounts for these by two main processes: an impact-induced buildup of a dark stony regolith in the absence of surface thermal disturbance, and thermal-disturbance-induced eruption of 'water magmas' that create icy surfaces. 'Thermal disturbances' include tidal and radiative effects caused by nearness of a planet. A correlation of crater density and albedo, Ganymede's dark-ray craters, and other observed phenomena (listed in the summary) appear consistent with the model discussed here.
The last two years have seen incredible development in numerical relativity: from fractions of an orbit, evolutions of an equal-mass binary have reached multiple orbits, and convergent gravitational waveforms have been produced from several research groups and numerical codes. We are now able to move our attention from pure numerics to astrophysics, and address scenarios relevant to current and future gravitational-wave detectors.Over the last 12 months at NASA Goddard, we have extended the accuracy of our Hahn-Dol code, and used it to move toward these goals. We have achieved high-accuracy simulations of black-hole binaries of low initial eccentricity, with enough orbits of inspiral before merger to allow us to produce hybrid waveforms that reflect accurately the entire lifetime of the BH binary. We are extending this work, looking at the effects of unequal masses and spins.
Aquarius satellite salinity measurements are resolving the major global and regional spatial patterns, and temporal variations, since the start of routine data collection on 25 August 2011. This description includes the principal seasonal variations over the first annual cycle as observed by the mission. In particular, we identify the evolution of low salinity anomalies associated with the Atlantic and Pacific intertropical convergence zones (ITCZ), major river outflows such as the Amazon, a seasonal low salinity anomaly in the Panama bight, and other features. We also explore the links that the salinity variations have with precipitation and surface currents. We then will describe the variations related to the presently evolving 2012 El Nino, now evident, as it progresses through the summer and fall 2012. We conclude with a brief summary of the Aquarius data products and validation
A method has been developed to solve the Euler equations on a three-dimensional unstructured grid composed of tetrahedra. The method uses an upwind flow solver with a linearized, backward-Euler time integration scheme. Each time step results in a sparse linear system of equations which is solved by an iterative, sparse matrix solver. Local-time stepping, switched evolution relaxation (SER), preconditioning and reuse of the Jacobian are employed to accelerate the convergence rate. Implicit boundary conditions were found to be extremely important for fast convergence. Numerical experiments have shown that convergence rates comparable to that of a multigrid, central-difference scheme are achievable on the same mesh. Results are presented for several grids about an ONERA M6 wing.
A large array of state-of-the-art ground-based and airborne remote and in-situ sensors were deployed during the International H2O Project (THOP), a field experiment that took place over the Southern Great Plains (SGP) of the United States from 13 May to 30 June 2002. These instruments provided extensive measurements of water vapor mixing ratio in order to better understand the influence of its variability on convection and on the skill of quantitative precipitation prediction (Weckwerth et all, 2004). Among the instrument deployed were ground based lidars from NASA/GSFC that included the Scanning Raman Lidar (SRL), the Goddard Laboratory for Observing Winds (GLOW), and the Holographic Airborne Rotating Lidar Instrument Experiment (HARLIE). A brief description of the three lidars is given below. This study presents ground-based measurements of wind, boundary layer structure and water vapor mixing ratio measurements observed by three co-located lidars during MOP at the MOP ground profiling site in the Oklahoma Panhandle (hereafter referred as Homestead). This presentation will focus on the evolution and variability of moisture and wind in the boundary layer when frontal and/or convergence boundaries (e.g. bores, dry lines, thunderstorm outflows etc) were observed.
Deformation within the North American plate in response to various tectonic processes is modeled using an elastic finite element analysis. The tectonic processes considered in the modeling include ridge forces associated with the normal thermal evolution of oceanic lithosphere, shear and normal stresses transmitted across transforms, normal stresses transmitted across convergent boundaries, stresses due to horizontal density contrasts within the continent, and shear tractions applied along the base of the plate. Model stresses are calculated with respect to a lithostatic reference stress state. Shear stresses transmitted across transform boundaries along the San Andreas and Caribbean are small, of the order of 5-10 MPa. Also, compressive stresses of the order of 5-10 MPa transmitted across the major transforms improve the fit to the data. Compressive stresses across convergent margins along the Aleutians and the Middle America trench are important.
This study is devoted to a comparative analysis of three 'Adaptive ZOOM' (ZOom Overlapping Multi-level) methods based on similar concepts of hierarchical multigrid local refinement: LDC (Local Defect Correction), FAC (Fast Adaptive Composite), and FIC (Flux Interface Correction)--which we proposed recently. These methods are tested on two examples of a bidimensional elliptic problem. We compare, for V-cycle procedures, the asymptotic evolution of the global error evaluated by discrete norms, the corresponding local errors, and the convergence rates of these algorithms.
The way volcanic clouds evolve is very sensitive to the initial spatial 3D distributions of volcanic materials, which are often unknown. In this study, we conducted inverse modeling of the Mt. Pinatubo cloud using TOMS 2D mapping of Aerosol Index and SO 2 loading during the first three post-eruption days to estimate the time-dependent emissions profiles and initial 3D spatial distributions of volcanic ash and SO 2 . We account for aerosol radiative feedback and dynamic lofting of volcanic ash in the inversion calculations for the first time. This resulted in a lower ash injection height (by 1.5 km for ash) than without ash radiative feedback. The Pinatubo eruption ejected ≈77% of fine ash at 12 to 23 km, ≈65% of SO 2 at 18–25 km. In contrast with previous studies, which suggested that all volcanic materials were emitted above the tropopause, a significant fraction of SO 2 (5.1 of 15.5 Mt) and fine ash (37.2 of 66.5 Mt) were ejected in the troposphere, where SO 2 quickly oxidized into sulfate aerosol that is short-lived in the troposphere. This explains the early presence of sulfate aerosols in the plume and why the models can reproduce the observed volcanic aerosols' optical depth (AOD), assuming lower-than-observed SO 2 emission in the stratosphere. Despite the quicker than in observations build-up of sulfate AOD, in a month after the eruption, the evolution of the Pinatubo AOD simulated using the obtained ash and SO 2 initial distributions converges with the available stratospheric aerosol and gas experiment (SAGE) observations.
The evolution of accelerated particle distributions in a magnetized plasma and the resulting radiation are calculated, and the results are applied to solar flares. To study the radiation on timescales of order the particle lifetimes, the evolution of the particle distribution is determined by the use of the Fokker-Planck equation including Coulomb collisions and magnetic mirroring. Analytic solution to the equations are obtained for limiting cases such as homogeneous injection in a homogeneous plasma, and for small pitch angle. These analytic solutions are then used to place constraints on flare parameters such as density, loop length, and the injection timescale for very short implusive solar flares. For general particle distributions in arbitrary magnetic field and background density, the equation is solved numerically. The relative timing of microwaves and X-rays during individual flares is investigated. A number of possible sources for excessive microwave flux are discussed including a flattening in the electron spectrum above hard X-ray energies, thermal synchrotron emission, and trapping of electron by converging magnetic fields. Over shorter timescales, the Fokker-Planck equation is solved numerically to calculate the temporal evolution of microwaves and X-rays from nonthermal thick target models. It is shown that magnetic trapping will not account for the observed correlation of microwaves of approximately 0.15 seconds behind X-rays in flares with rapid time variation, and thus higher energy electrons must be accelerated later than lower energy electrons.
A numerical approximation scheme for the estimation of functional parameters in Euler-Bernoulli models for the transverse vibration of flexible beams with tip bodies is developed. The method permits the identification of spatially varying flexural stiffness and Voigt-Kelvin viscoelastic damping coefficients which appear in the hybrid system of ordinary and partial differential equations and boundary conditions describing the dynamics of such structures. An inverse problem is formulated as a least squares fit to data subject to constraints in the form of a vector system of abstract first order evolution equations. Spline-based finite element approximations are used to finite dimensionalize the problem. Theoretical convergence results are given and numerical studies carried out on both conventional (serial) and vector computers are discussed.
In vitro selection is a powerful tool that can be used to understand basic principles of molecular evolution. We used in vitro selection to understand how changes in length and the accumulation of point mutations enable the evolution of functional RNAs. Using RNA populations of various lengths, we performed a series of in vitro experiments to select for ribozymes with RNA ligase activity. We identified a core ribozyme structure that was robust to changes in RNA length, high levels of mutagenesis, and increased selection pressure. Elaboration on this core structure resulted in improved activity which we show is consistent with a larger trend among functional RNAs in which increasing motif size can lead to an exponential improvement in fitness. We conclude that elaboration on conserved core structures is a preferred mechanism in RNA evolution. This conclusion, drawn from selections of RNAs from random sequences, is consistent with proposed evolutionary histories of specific biological RNAs. More generally, our results indicate that modern RNA structures can be used to infer ancestral structures. Our observations also suggest a mechanism by which structural outcomes of early RNA evolution would be largely reproducible even though RNA fitness landscapes consist of disconnected clusters of functional sequences.
The evolution of hydrodynamic instability modes self-excited by harmonically related natural screech tones was experimentally investigated. A convergent rectangular nozzle with an aspect ratio of 9.63 was used to produce a supersonic shock containing jet. Measurements in the flow-field were made using standard hot-film probes positioned only in the subsonic (outer) portions of the flow. The hydrodynamic instability mode observed in the shear layer at the screech frequency was observed to be antisymmetric (sinuous) about the smaller dimension of the jet, whereas its harmonic was observed to be symmetric (varicose). In addition, the near-field noise measurements indicated that the radiated screech tone noise was out of phase on either side of the small jet dimension whereas its harmonic was in phase over the same region. To our knowledge such an observation on the nature of the harmonic has thus far gone unreported and therefore is the focus of the present work. The hydrodynamic instability modes occurring at the screech frequency and its harmonic satisfied the conditions for resonance. Detailed measurements of the coherent wave evolution in the streamwise and spanwise directions indicated that strong spanwise variations were present beyond x/h = 8. Details of the screech noise radiated by the coherent instability modes are also presented in this paper.
Several deep PSPC observations of the Coma Cluster reveal a very large scale halo of soft X-ray emission, substantially in excess of the well-known radiation from the hot intracluster medium. The excess emission, previously reported in the central region of the cluster using lower sensitivity Extreme Ultraviolet Explorer (EUVE) and ROSAT data, is now evident out to a radius of 2.6 Mpc, demonstrating that the soft excess radiation from clusters is a phenomenon of cosmological significance. The X-ray spectrum at these large radii cannot be modeled nonthermally but is consistent with the original scenario of thermal emission from warm gas at approx. 10(exp 6) K. The mass of the warm gas is on par with that of the hot X-ray-emitting plasma and significantly more massive if the warm gas resides in low-density filamentary structures. Thus, the data lend vital support to current theories of cosmic evolution, which predict that at low redshift approx. 30%-40% of the baryons reside in warm filaments converging at clusters of galaxies.
Cyclotron maser and plasma wave growth which results from electrons accelerated in magnetic loops are studied. The evolution of the accelerated electron distribution is determined by solving the kinetic equation including Coulomb collisions and magnetic convergence. It is found that for modest values of the column depth of the loop the growth rates of instabilities are significantly reduced and that the reduction is much larger for the cyclotron modes than for the plasma wave modes. The large decrease in the growth rate with column depth suggests that solar coronal densities must be much lower than commonly accepted in order for the cyclotron maser to operate. The density depletion has to be similar to that which occurs during auroral kilometric radiation events in the magnetosphere. The resulting distributions are much more complicated than the idealized distributions used in many theoretical studies, but the fastest growing mode can still simply be determined by the ratio of electron plasma to gyrofrequency, U=omega(sub p)/Omega(sub e). However, the dominant modes are different than for the idealized situations with growth of the z-mode largest for U approximately less than 0.5, and second harmonic x-mode (s=2) or fundamental o-mode (s=1) the dominant modes for 0.5 approximately less than U approximately less than 1. The electron distributions typically contain more than one inverted feature which could give rise to wave growth. It is shown that this can result in simultaneous amplification of more than one mode with each mode driven by a different feature and can be observed, for example, by differences in the rise times of the right and left circularly polarized components of the associated spike bursts.
The evolution of nonthermal electrons accelerated in magnetic loops is determined by solving the kinetic equation, including magnetic field convergence and Coulomb collisions in order to determine the effects of these interactions on the induced cyclotron maser and plasma wave growth. It is found that the growth rates are larger and the possibility of cyclotron maser action is stronger for smaller loop column density, for larger magnetic field convergence, for a more isotropic injected electron pitch angle distribution, and for more impulsive acceleration. For modest values of the column density in the coronal portion of a flaring loop, the growth rates of instabilities are significantly reduced, and the reduction is much larger for the cyclotron modes than for the plasma wave modes. The rapid decrease in the growth rates with increasing loop column density suggests that, in flare loops when such phenomena occur, the densities are lower than commonly accepted.
Steady state solutions to the two-fluid equations of cosmic-ray-modified shock structure were investigated first by Drury and Volk (1981). Their analysis revealed, among other properties, that there exist regions of upstream parameter space where the equations possess three different downstream solutions for a given upstream state. In this paper we investigate whether or not all these solutions can occur as time-asymptotic states in a physically realistic evolution. To do this, we investigate the time-dependent evolution of the two-fluid cosmic-ray equations in going from a specified initial condition to a steady state. Our results indicate that the time-asymptotic solution is strictly single-valued, and it undergoes a transition from weakly to strongly cosmic-ray-modified at a critical value of the upstream cosmic ray energy density. The expansion of supernova remnant shocks is considered as an example, and it is shown that the strong to weak transition is in fact more likely. The third intermediate solution is shown to influence the time-dependent evolution of the shock, but it is not found to be a stable time-asymptotic state. Timescales for convergence to these states and their implications for the efficiency of shock acceleration are considered. We also investigate the effects of a recently introduced model for the injection of seed particles into the shock accelerated cosmic-ray population. The injection is found to result in a more strongly cosmic-ray-dominated shock, which supports our conclusion that for most classes of intermediate and strong cosmic-ray-modified shocks, the downstream cosmic-ray pressure component is at least as large as the thermal gas pressure, independent of the upstream state. As a result, cosmic rays almost always play a significant role in determining the shock structure and dissipation and they cannot be regarded as test particles.