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This paper presents a frequency-domain estimator that can identify both a parametrized nominal model of a plant as well as a frequency-domain bounding function on the modeling error associated with this nominal model. This estimator, which we call a robust estimator, can be used in conjunction with a robust control-law redesign algorithm to form a robust adaptive controller.
Results are presented of the Tropical Oceans Global Atmosphere-Coupled Ocean Atmosphere Response Experiment (TOGA-COARE) conducted in the western Pacific, with particular attention given to the atmospheric component of the experiment. The climatological variables explored are the mean sea level pressure, precipitable water, sea surface-air temperature difference, zonal wind component at 200 mb and 10 m, vertical motion at 500 mb, and precipitation rates. The paper provides some of the large-scale flow patterns in which other circulation features reside. Results are presented for three of the TOGA-COARE domains bounded by the following: (1) the Upper Air Network, 30 deg N-30 deg S, 90 deg E-70 deg W; (2) the Large-Scale Array, 10 deg N-10 deg S, 140 deg E-180 deg; and (3) the Equatorial Synoptic Array, 5 deg N-5 deg S, 150 deg E-180 deg.
The mechanics of wave propagation in the presence of obstacles is of great interest in many branches of engineering and applied mathematics like electromagnetics, fluid dynamics, geophysics, seismology, etc. Such problems can be broadly classified into two categories: the bounded domain or the closed problem and the unbounded domain or the open problem. Analytical techniques have been derived for the simpler problems; however, the need to model complicated geometrical features, complex material coatings and fillings, and to adapt the model to changing design parameters have inevitably tilted the balance in favor of numerical techniques. The modeling of closed problems presents difficulties primarily in proper meshing of the interior region. However, problems in unbounded domains pose a unique challenge to computation, since the exterior region is inappropriate for direct implementation of numerical techniques. A large number of solutions have been proposed but only a few have stood the test of time and experiment. The goal of this thesis is to develop an efficient and reliable partial differential equation technique to model large three dimensional scattering problems in electromagnetics.
We generalize Harten's multiresolution representation to biorthogonal multiwavelets. Several variants are considered. For example, a given array of discrete point values is transformed to point values and derivatives or point 'values and cell averages'. Compact Hermite interpolation is used in the decomposition and reconstruction algorithm. The resulting basis functions that are symmetric or skewsymmetric, compact, and smooth with optimal order accuracy. Harten's approach has several advantages: the multiresolution scheme is inherently discrete, non-periodic boundary conditions are easy to implement, and the representation can be extended to unstructured grids in bounded domains. We demonstrate the compression features of the new mutliwavelets by application to variable scale piecewise smooth functions with jump discontinuities typical of numerical solutions of nonlinear hyperbolic conservation laws.
An outline of a strategy for automation of overset structured surface grid generation on complex geometries is described. The starting point of the process consists of an unstructured surface triangulation representation of the geometry derived from a native CAD, STEP, or IGES definition, and a set of discretized surface curves that captures all geometric features of interest. The procedure for surface grid generation is decomposed into an algebraic meshing step, a hyperbolic meshing step, and a gap-filling step. This paper will focus primarily on the high-level plan with details on the algebraic step. The algorithmic procedure for the algebraic step involves analyzing the topology of the network of surface curves, distributing grid points appropriately on these curves, identifying domains bounded by four curves that can be meshed algebraically, concatenating the resulting grids into fewer patches, and extending appropriate boundaries of the concatenated grids to provide proper overlap. Results are presented for grids created on various aerospace vehicle components.
The effects of solitons on the spectrum of fermion excitations in superfluid (He-3)-A are investigated. It is found that there is a two-dimensional manifold of bound states with energies within the gap of the bulk superfluid. The bound-state spectrum lacks inversion symmetry parallel to the wall.
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A paleogeographic reconstruction of southeastern California and southwestern Arizona at 10 Ma was made based on available geologic and geophysical data. Clockwise rotation of 39 deg was reconstructed in the eastern Transverse Ranges, consistent with paleomagnetic data from late Miocene volcanic rocks, and with slip estimates for left-lateral faults within the eastern Transverse Ranges and NW-trending right lateral faults in the Mojave Desert. This domain of rotated rocks is bounded by the Pinto Mountain fault on the north. In the absence of evidence for rotation of the San Bernardino Mountains or for significant right slip faults within the San Bernardino Mountains, the model requires that the late Miocene Pinto Mountain fault become a thrust fault gaining displacement to the west. The Squaw Peak thrust system of Meisling and Weldon may be a western continuation of this fault system. The Sheep Hole fault bounds the rotating domain on the east. East of this fault an array of NW-trending right slip faults and south-trending extensional transfer zones has produced a basin and range physiography while accumulating up to 14 km of right slip. This maximum is significantly less than the 37.5 km of right slip required in this region by a recent reconstruction of the central Mojave Desert. Geologic relations along the southern boundary of the rotating domain are poorly known, but this boundary is interpreted to involve a series of curved strike slip faults and non-coaxial extension, bounded on the southeast by the Mammoth Wash and related faults in the eastern Chocolate Mountains. Available constraints on timing suggest that Quaternary movement on the Pinto Mountain and nearby faults is unrelated to the rotation of the eastern Transverse Ranges, and was preceded by a hiatus during part of Pliocene time which followed the deformation producing the rotation. The reconstructed Clemens Well fault in the Orocopia Mountains, proposed as a major early Miocene strand of the San Andreas fault, projects eastward towards Arizona, where early Miocene rocks and structures are continuous across its trace. The model predicts a 14 deg clockwise rotation and 55 km extension along the present trace of the San Andreas fault during late Miocene and early Pliocene time. Palinspastic reconstructions of the San Andreas system based on this proposed reconstruction may be significantly modified from current models.
Space radiation is a proficient inducer of DNA damage leading to mutation, aberrant cell signaling, and cancer formation. Ku is among the first responding proteins in nucleus to recognize and bind the DNA double strand breaks (DSBs) whenever they are introduced. Once loaded Ku works as a scaffold to recruit other repair factors of non-homologous end joining and facilitates the following repair processes. The crystallographic study of the Ku70/80 heterodimer indicate the core structure of this protein shows virtually no conformational change after binding with DNA. To investigate the dynamical features as well as the energetic characteristics of Ku-DNA binding, we conduct multi-nanosecond molecular dynamics simulations of a modeled Ku70/80 structure and several complexes with two 24-bp DNA duplexes. Free energy calculations show significant energy differences between the complexes with Ku bound at DSBs and those with Ku associated at an internal site of a chromosome. The results also reveal detailed interactions between different nucleotides and the amino acids along the DNA-binding cradle of Ku, indicating subtle binding preference of Ku at specific DNA sequences. The covariance matrix analyses along the trajectories demonstrate the protein is stimulated to undergo correlated motions of different domains once bound to DNA ends. Additionally, principle component analyses identify these low frequency collective motions suitable for binding with and translocation along duplex DNA. It is proposed that the modification of dynamical properties of Ku upon binding with DSBs may provide a signal for the further recruitment of other repair factors such as DNA-PKcs, XLF, and XRCC4.
The game-theory field of Collective INtelligence (COIN) concerns the design of computer-based players engaged in a non-cooperative game so that as those players pursue their self-interests, a pre-specified global goal for the collective computational system is achieved as a side-effect. Previous implementations of COIN algorithms have outperformed conventional techniques by up to several orders of magnitude, on domains ranging from telecommunications control to optimization in congestion problems. Recent mathematical developments have revealed that these previously developed algorithms were based on only two of the three factors determining performance. Consideration of only the third factor would instead lead to conventional optimization techniques like simulated annealing that have little to do with non-cooperative games. In this paper we present an algorithm based on all three terms at once. This algorithm can be viewed as a way to modify simulated annealing by recasting it as a non-cooperative game, with each variable replaced by a player. This recasting allows us to leverage the intelligent behavior of the individual players to substantially improve the exploration step of the simulated annealing. Experiments are presented demonstrating that this recasting significantly improves simulated annealing for a model of an economic process run over an underlying small-worlds topology. Furthermore, these experiments reveal novel small-worlds phenomena, and highlight the shortcomings of conventional mechanism design in bounded rationality domains.
The relationship between sea surface temperature (SST) and albedo or cloud cover is examined for two tropical regions with high values of cloud radiative forcing and persistent marine stratocumulus (mSc)-one off the west coast of Peru, the other off the west coast of Angola. The data span five years, from December 1984 to November 1989. Albedos are from the Earth Radiation Budget Experiment (ERBE), cloud covers are from the International Satellite Cloud Climatology Project (ISCCP), and SSTS are from the Climate Analysis Center. Negative correlation coefficients between albedo and SST are found to be about -0.8 when the seasonal variation of the entire dataset is analyzed. The interannual variation and the spatial variation of individual months also yields correlation coefficients that are negative. The correlation between cloud cover and SST is found to be similar to but weaker than the correlation between albedo and SST, suggesting a decrease in cloud amount and a decrease in cloud albedo with increasing SST for these regions. The corresponding albedo sensitivity averages -0.018/K with local values reaching -0.04/K. These findings are valid from 19 C to 25 C for the Peru mSc and 22 C to 27 C for the Angola mSc. These temperatures approximately bound the domains over which mSc is the prevalent cloud type within each region. These results imply a potential positive feedback to global warming by marine stratocumulus that ranges from approximately 0.14 W/sq m/K to approximately 1 W/sq m/K, depending on whether or not our results apply to all marine stratocumulus. While these values are uncertain to at least +/- 50%, the sensitivity of albedo to sea surface temperature in the present climate may serve as a useful diagnostic tool in monitoring the performance of global climate models.
Cloud and precipitation systems are simulated with a multi‐scale modeling framework (MMF) and compared over the Tropics and Subtropics against the Tropical Rainfall Measuring Mission (TRMM) Radar‐defined Precipitation Features (RPFs) product. A methodology, in close analogy to the TRMM RPFs, is developed to produce simulated precipitation features (PFs) from the output of the embedded two‐dimensional (2D) cloud‐resolving models (CRMs) within an MMF. Despite the limitations of 2D CRMs, the simulated population distribution, horizontal and vertical structure of PFs, and the geographical location and local rainfall contribution of mesoscale convective systems (MCSs) are in good agreement with the TRMM observations. However, some model discrepancies are found and can be identified and quantified within the PF distributions. Using model biases in relative population and rainfall contributions, PFs can be characterized into four size categories: small, medium to large, very large, and extremely large. Four different major mechanisms might account for the model biases in each different category: (1) the two‐dimensionality of the CRMs, (2) a positive convection‐wind‐evaporation feedback loop, (3) an artificial dynamic constraint in a bounded CRM domain with cyclic boundaries, and (4) the limited CRM domain size. The second and fourth mechanisms tend to contribute to the excessive tropical precipitation biases commonly found in most MMFs, whereas the other mechanisms reduce rainfall contributions from small and very large PFs. MMF sensitivity experiments with various CRM domain sizes and grid spacings showed that larger domains (higher resolutions) tend to shift PF populations toward larger (smaller) sizes.
This note addresses the issue of 'conservatism' in the time domain stability robustness bounds obtained by the Liapunov approach. A state transformation is employed to improve the upper bounds on the linear time-varying perturbation of an asymptotically stable linear time-invariant system for robust stability. This improvement is due to the variance of the conservatism of the Liapunov approach with respect to the basis of the vector space in which the Liapunov function is constructed. Improved bounds are obtained, using a transformation, on elemental and vector norms of perturbations (i.e., structured perturbations) as well as on a matrix norm of perturbations (i.e., unstructured perturbations). For the case of a diagonal transformation, an algorithm is proposed to find the 'optimal' transformation. Several examples are presented to illustrate the proposed analysis.
This paper proposes a reliability analysis framework for systems subject to multiple design requirements that depend polynomially on the uncertainty. Uncertainty is prescribed by probability boxes, also known as p-boxes, whose distribution functions have free or fixed functional forms. An approach based on the Bernstein expansion of polynomials and optimization is proposed. In particular, we search for the elements of a multi-dimensional p-box that minimize (i.e., the best-case) and maximize (i.e., the worst-case) the probability of inner and outer bounding sets of the failure domain. This technique yields intervals that bound the range of failure probabilities. The offset between this bounding interval and the actual failure probability range can be made arbitrarily tight with additional computational effort.
The General Interpolants Method (GIM) code which solves the multidimensional Navier-Stokes equations for arbitrary geometric domains is described. The geometry module in the GIM code generates two and three dimensional grids over specified flow regimes, establishes boundary condition information and computes finite difference analogs for use in the GIM code numerical solution module. The technique can be classified as an algebraic equation approach. The geometry package uses multivariate blending function interpolation of vector-values functions which define the shapes of the edges and surfaces bounding the flow domain. By employing blending functions which conform to the cardinality conditions the flow domain may be mapped onto a unit square (2-D) or unit cube (3-D), thus producing an intrinsic coordinate system for the region of interest. The intrinsic coordinate system facilitates grid spacing control to allow for optimum distribution of nodes in the flow domain.
The modal element method for acoustic scattering from 2-D body is presented. The body may be acoustically soft (absorbing) or hard (reflecting). The infinite computational region is divided into two subdomains - the bounded finite element domain, which is characterized by complicated geometry and/or variable material properties, and the surrounding unbounded homogeneous domain. The acoustic pressure field is represented approximately in the finite element domain by a finite element solution, and is represented analytically by an eigenfunction expansion in the homogeneous domain. The two solutions are coupled by the continuity of pressure and velocity across the interface between the two subdomains. Also, for hard bodies, a compact modal ring grid system is introduced for which computing requirements are drastically reduced. Analysis for 2-D scattering from solid and coated (acoustically treated) bodies is presented, and several simple numerical examples are discussed. In addition, criteria are presented for determining the number of modes to accurately resolve the scattered pressure field from a solid cylinder as a function of the frequency of the incoming wave and the radius of the cylinder.
Three-dimensional supersonic vortex-breakdown problems in bound and unbound domains are solved. The solutions are obtained using the time-accurate integration of the unsteady, compressible, full Navier-Stokes (NS) equations. The computational scheme is an implicit, upwind, flux-difference splitting, finite-volume scheme. Two vortex-breakdown applications are considered in the present paper. The first is for a supersonic swirling jet which is issued from a nozzle into a supersonic uniform flow at a lower Mach number than that of the swirling jet. The second is for a supersonic swirling flow in a configured circular duct. In the first application, an extensive study of the effects of grid fineness, shape and grid-point distribution on the vortex breakdown is presented. Four grids are used in this study and they show a substantial dependence of the breakdown bubble and shock wave on the grid used. In the second application, the bubble-type and helix-type vortex breakdown have been captured.
Existing numerical simulations and physical aspects of subsonic and supersonic vortex-breakdown modes are reviewed. The solution to the problem of supersonic vortex breakdown is emphasized in this paper and carried out with the full Navier-Stokes equations for compressible flows. Numerical simulations of vortex-breakdown modes are presented in bounded and unbounded domains. The effects of different types of downstream-exit boundary conditions are studied and discussed.