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A new approach using phase information to view and study the properties of frequency modulation, wave group structures, and wave breaking is presented. The method is applied to ocean wave time series data and a new type of wave group (containing the large 'rogue' waves) is identified. The method also has the capability of broad applications in the analysis of time series data in general.
To assist in validating future MODIS land cover, LAI, IPAR, and NPP products, this project conducted a series of prototyping exercises that resulted in enhanced understanding of the issues regarding such validation. As a result, we have several papers to appear as a special issue of Remote Sensing of Environment in 1999. Also, we have been successful at obtaining a follow-on grant to pursue actual validation of these products over the next several years. This document consists of a delivery letter, including a listing of published papers.
While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears to be most significant in many areas of scientific computing, for example, in problems originating from acoustics, electrodynamics, solid mechanics, and fluid dynamics. In particular, in computational fluid dynamics (where external problems present a wide class of practically important formulations) the proper treatment of external boundaries may have a profound impact on the overall quality and performance of numerical algorithms. Most of the currently used techniques for setting the ABC's can basically be classified into two groups. The methods from the first group (global ABC's) usually provide high accuracy and robustness of the numerical procedure but often appear to be fairly cumbersome and (computationally) expensive. The methods from the second group (local ABC's) are, as a rule, algorithmically simple, numerically cheap, and geometrically universal; however, they usually lack accuracy of computations. In this paper we first present a survey and provide a comparative assessment of different existing methods for constructing the ABC's. Then, we describe a relatively new ABC's technique of ours and review the corresponding results. This new technique, in our opinion, is currently one of the most promising in the field. It enables one to construct such ABC's that combine the advantages relevant to the two aforementioned classes of existing methods. Our approach is based on application of the difference potentials method attributable to V. S. Ryaben'kii. This approach allows us to obtain highly accurate ABC's in the form of certain (nonlocal) boundary operator equations. The operators involved are analogous to the pseudodifferential boundary projections first introduced by A. P. Calderon and then also studied by R. T. Seeley. The apparatus of the boundary pseudodifferential equations, which has formerly been used mostly in the qualitative theory of integral equations and PDE'S, is now effectively employed for developing numerical methods in the different fields of scientific computing.
This paper presents the Fast Adaptive Composite Grid Method for Time Dependent Problems (TDFAC), a local grid refinement scheme for nonlinear, time dependent partial differential equations. The method is presented in a one dimensional setting to illustrate the basic features and components. Computational results which show the effectiveness of TDFAC as a computational tool are also included.
A design strategy for optimal design of composite grid-stiffened cylinders subjected to global and local buckling constraints and, strength constraints is developed using a discrete optimizer based on a genetic algorithm. An improved smeared stiffener theory is used for the global analysis. Local buckling of skin segments are assessed using a Rayleigh-Ritz method that accounts for material anisotropy. The local buckling of stiffener segments are also assessed. Constraints on the axial membrane strain in the skin and stiffener segments are imposed to include strength criteria in the grid-stiffened cylinder design. Design variables used in this study are the axial and transverse stiffener spacings, stiffener height and thickness, skin laminate stacking sequence, and stiffening configuration, where herein stiffening configuration is a design variable that indicates the combination of axial, transverse, and diagonal stiffener in the grid-stiffened cylinder. The design optimization process is adapted to identify the best suited stiffening configurations and stiffener spacings for grid-stiffened composite cylinder with the length and radius of the cylinder, the design in-plane loads, and material properties as inputs. The effect of having axial membrane strain constraints in the skin and stiffener segments in the optimization process is also studied for selected stiffening configuration.
A design strategy for optimal design of composite grid-stiffened cylinders subjected to global and local buckling constraints and strength constraints was developed using a discrete optimizer based on a genetic algorithm. An improved smeared stiffener theory was used for the global analysis. Local buckling of skin segments were assessed using a Rayleigh-Ritz method that accounts for material anisotropy. The local buckling of stiffener segments were also assessed. Constraints on the axial membrane strain in the skin and stiffener segments were imposed to include strength criteria in the grid-stiffened cylinder design. Design variables used in this study were the axial and transverse stiffener spacings, stiffener height and thickness, skin laminate stacking sequence and stiffening configuration, where stiffening configuration is a design variable that indicates the combination of axial, transverse and diagonal stiffener in the grid-stiffened cylinder. The design optimization process was adapted to identify the best suited stiffening configurations and stiffener spacings for grid-stiffened composite cylinder with the length and radius of the cylinder, the design in-plane loads and material properties as inputs. The effect of having axial membrane strain constraints in the skin and stiffener segments in the optimization process is also studied for selected stiffening configurations.
To construct Venus' gravity disturbance field (or gravity anomaly) with the spacecraft-observer line of site (LOS) acceleration perturbation data, both a global and a local approach can be used. The global approach, e.g., spherical harmonic coefficients, and the local approach, e.g., the integral operator method, based on geodetic techniques are generally not the same, so that they must be used separately for mapping long wavelength features and short wavelength features. Harmonic spline, as an interpolation and extrapolation technique, is intrinsically flexible to both global and local mapping of a potential field. Theoretically, it preserves the information of the potential field up to the bound by sampling theorem regardless of whether it is global or local mapping, and is never bothered with truncation errors. The improvement of harmonic spline methodology for global mapping is reported. New basis functions, a singular value decomposition (SVD) based modification to Parker & Shure's numerical procedure, and preliminary results are presented.
Langley Stability and Transition Analysis Code (LASTRAC) is a general-purpose, physics-based transition prediction code released by NASA for laminar flow control studies and transition research. This paper describes the LASTRAC extension to general three-dimensional (3D) boundary layers such as finite swept wings, cones, or bodies at an angle of attack. The stability problem is formulated by using a body-fitted nonorthogonal curvilinear coordinate system constructed on the body surface. The nonorthogonal coordinate system offers a variety of marching paths and spanwise waveforms. In the extreme case of an infinite swept wing boundary layer, marching with a nonorthogonal coordinate produces identical solutions to those obtained with an orthogonal coordinate system using the earlier release of LASTRAC. Several methods to formulate the 3D parabolized stability equations (PSE) are discussed. A surface-marching procedure akin to that for 3D boundary layer equations may be used to solve the 3D parabolized disturbance equations. On the other hand, the local line-marching PSE method, formulated as an easy extension from its 2D counterpart and capable of handling the spanwise mean flow and disturbance variation, offers an alternative. A linear stability theory or parabolized stability equations based N-factor analysis carried out along the streamline direction with a fixed wavelength and downstream-varying spanwise direction constitutes an efficient engineering approach to study instability wave evolution in a 3D boundary layer. The surface-marching PSE method enables a consistent treatment of the disturbance evolution along both streamwise and spanwise directions but requires more stringent initial conditions. Both PSE methods and the traditional LST approach are implemented in the LASTRAC.3d code. Several test cases for tapered or finite swept wings and cones at an angle of attack are discussed.
A new method for analyzing plate and shell structures with two or more independently modeled finite element subdomains is presented, assessed, and demonstrated. This method provides a means of coupling local and global models whose grid points do not coincide along their common interface. In general, the method provides a means of coupling structural components (e.g., wing and fuselage) which may have been modeled by different analysis. In both cases, the need for transition modeling, which is often tedious and complicated, is eliminated. The coupling is accomplished through an interface for which three formulations are considered and presented. These formulations are: collocation, least-squares, and hybrid variational. Several benchmark problems were analyzed and, based on the results, the hybrid variational formulation is identified as the preferred formulation in that it provides the most accurate solutions.
Multistep predictor-corrector method for numerical solution of ordinary differential equations retains high local accuracy and convergence properties. In addition, the method was developed in a form conducive to the generation of effective criteria for the selection of subsequent step sizes in step-by-step solution of differential equations.
A variation of Sobieski's Global Sensitivity Equations (GSE) approach is implemented to obtain the sensitivity of the static aeroelastic response of a three-dimensional wing model. The formulation is quite general and accepts any aerodynamics and structural analysis capability. An interface code is written to convert one analysis's output to the other's input, and visa versa. Local sensitivity derivatives are calculated by either analytic methods or finite difference techniques. A program to combine the local sensitivities, such as the sensitivity of the stiffness matrix or the aerodynamic kernel matrix, into global sensitivity derivatives is developed. The aerodynamic analysis package FAST, using a lifting surface theory, and a structural package, ELAPS, implementing Giles' equivalent plate model are used.
We present a general protocol for detecting whether a property holds in a distributed system, where the property is a member of a subclass of stable properties we call the locally stable properties. Our protocol is based on a decentralized method for constructing a maximal subset of the local states that are mutually consistent, which in turn is based on a weakened version of vectored time stamps. The structure of our protocol lends itself to refinement, and we demonstrate its utility by deriving some specialized property-detection protocols, including two previously known protocols that are known to be effective.
Many important industrial and biological processes depend on ring-opening polymerization (ROP), including large-scale production polymers, such as nylon 6, and a variety of biodegradable polymers and high-performance resins. Large-scale simulations (>200K atoms) of ROP were performed using a deep neural network-based method that captured the effect of the local chemical environment of the reactive sites using training data from quantum chemical methods. The utility of this method was demonstrated by modeling the cationic ROP of bis-benzoxazine, a promising resin for use in advanced high-temperature application composites (>200°C). Density functional theory calculations were used to map out the various ring opening and polymerization reaction paths that occur during the thermal processing of bis-benzoxazine. The probabilities of these reactions, as a function of local atomic configurations, were used to construct committor functions using a neural network approach. The learned committor functions were then used to determine when a particular reaction occurred within the REACTER framework for reactive molecular dynamics simulations. The experimentally observed exotherm that occurs during bis-benzoxazine ROP was captured in an effective manner in the simulations by imposing a local heating of the system that corresponds to the enthalpy of reaction for each reaction. The dependence of the final polymer morphology on the ROP reaction temperature was analyzed at the molecular scale. The results presented in this work indicate that machine-learned committor functions are a promising approach for incorporating high-fidelity reactivity criteria that capture the effect of local chemical environments into large-scale polymerization simulations.
Local Area Network Extensible Simulator (LANES) computer program provides method for simulating performance of high-speed local-area-network (LAN) technology. Developed as design and analysis software tool for networking computers on board proposed Space Station. Load, network, link, and physical layers of layered network architecture all modeled. Mathematically models according to different lower-layer protocols: Fiber Distributed Data Interface (FDDI) and Star*Bus. Written in FORTRAN 77.
This paper presents methods for estimating time delay margin for adaptive control of input delay systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent an adaptive law by a locally bounded linear approximation within a small time window. The time delay margin of this input delay system represents a local stability measure and is computed analytically by three methods: Pade approximation, Lyapunov-Krasovskii method, and the matrix measure method. These methods are applied to the standard model-reference adaptive control, s-modification adaptive law, and optimal control modification adaptive law. The windowing analysis results in non-unique estimates of the time delay margin since it is dependent on the length of a time window and parameters which vary from one time window to the next. The optimal control modification adaptive law overcomes this limitation in that, as the adaptive gain tends to infinity and if the matched uncertainty is linear, then the closed-loop input delay system tends to a LTI system. A lower bound of the time delay margin of this system can then be estimated uniquely without the need for the windowing analysis. Simulation results demonstrates the feasibility of the bounded linear stability method for time delay margin estimation.
Heat transfer in cavity flow is numerically analyzed by a new numerical method called the finite-analytic method. The basic idea of the finite-analytic method is the incorporation of local analytic solutions in the numerical solutions of linear or nonlinear partial differential equations. In the present investigation, the local analytic solutions for temperature, stream function, and vorticity distributions are derived. When the local analytic solution is evaluated at a given nodal point, it gives an algebraic relationship between a nodal value in a subregion and its neighboring nodal points. A system of algebraic equations is solved to provide the numerical solution of the problem. The finite-analytic method is used to solve heat transfer in the cavity flow at high Reynolds number (1000) for Prandtl numbers of 0.1, 1, and 10.
Local stress and strain fields in the unit cell of an infinite, two-dimensional, periodic fibrous lattice have been determined by an integral equation approach. The effect of the fibres is assimilated to an infinite two-dimensional array of fictitious body forces in the matrix constituent phase of the unit cell. By subtracting a volume averaged strain polarization term from the integral equation we effectively embed a finite number of unit cells in a homogenized medium in which the overall stress and strain correspond to the volume averaged stress and strain of the constrained unit cell. This paper demonstrates that the zeroth term in the governing integral equation expansion, which embeds one unit cell in the homogenized medium, corresponds to the generalized self-consistent approximation. By comparing the zeroth term approximation with higher order approximations to the integral equation summation, both the accuracy of the generalized self-consistent composite model and the rate of convergence of the integral summation can be assessed. Two example composites are studied. For a tungsten/copper elastic fibrous composite the generalized self-consistent model is shown to provide accurate, effective, elastic moduli and local field representations. The local elastic transverse stress field within the representative volume element of the generalized self-consistent method is shown to be in error by much larger amounts for a composite with periodically distributed voids, but homogenization leads to a cancelling of errors, and the effective transverse Young's modulus of the voided composite is shown to be in error by only 23% at a void volume fraction of 75%.
A method from molecular dynamics simulation is developed for determining local elastic constants of an epoxy/nanotube composite. The local values of C11, C33, K12, and K13 elastic constants are calculated for an epoxy/nanotube composite as a function of radial distance from the nanotube. While the results possess a significant amount of statistical uncertainty resulting from both the numerical analysis and the molecular fluctuations during the simulation, the following observations can be made. If the size of the region around the nanotube is increased from shells of 1 to 6 in thickness, then the scatter in the data reduces enough to observe trends. All the elastic constants determined are at a minimum 20 from the center of the nanotube. The C11, C33, and K12 follow similar trends as a function of radial distance from the nanotube. The K13 decreases greater distances from the nanotube and becomes negative which may be a symptom of the statistical averaging.