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Comprehensive survey presents current methods of fracture toughness testing that are based on linear elastic fracture mechanics. General principles of the basic two dimensional crack stress field model are discussed in relation to real three dimensional specimens. Methods of test instrumentation and procedure are described.
Methods for airplane parameter estimation, the equation error method, output error method, and two advanced methods are presented and their basic properties described. The advanced methods include the maximum likelihood and extended Kalman filter method. For a better understanding of the estimation techniques a first-order scalar differential equation is used as a model of the system under test. Application of the methods to a general multivariable linear system is briefly outlined. A note on the parameter estimation in the frequency domain is also presented. Numerical examples along with the comparison of results from various methods are given.
Formation flying is an enabling technology for many future space missions. This paper presents extensions to the equations of relative motion expressed in Keplerian orbital elements, including new initialization techniques for general formation configurations. A new linear time-varying form of the equations of relative motion is developed from Gauss Variational Equations and used in a model predictive controller. The linearizing assumptions for these equations are shown to be consistent with typical formation flying scenarios. Several linear, convex initialization techniques are presented, as well as a general, decentralized method for coordinating a tetrahedral formation using differential orbital elements. Control methods are validated using a commercial numerical propagator.
Finite-difference (FD) approaches to the numerical solution of the differential equations describing the motion of a nonlinear conservative oscillator are investigated analytically. A generalized formulation of the Duffing and modified Duffing equations is derived and analyzed using several FD techniques, and it is concluded that, although it is always possible to contstruct FD models of conservative oscillators which are themselves conservative, caution is required to avoid numerical solutions which do not accurately reflect the properties of the original equation.
A procedure for modeling a linear system by an optimal finite-dimensional approximation is developed on the basis of Sard's (1967) generalized spline. Error bounds are given, and the application of the procedure is illustrated by two presented examples. The procedure may be employed, not only in the modeling of conventional lumped-parameter and distributed-parameter continuous dynamical systems, but also in mathematical operations such as those involved in pattern recognition and picture enhancement problems.
Abstract Snow water equivalent (SWE), temperature, and precipitation biases and trends are evaluated in the atmosphere‐land simulations of the Energy Exascale Earth System Model version 1 (E3SMv1) in comparison to the Community Earth System Model version 2 (CESM2) and two other models using the ground measurement‐based University of Arizona (UA) snow product. SWE, temperature, and precipitation biases are highest in magnitude in the Western contiguous United States (CONUS). SWE errors are attributed to temperature and precipitation through multiple linear regressions of normalized errors, the coefficients of which represent the sensitivities to temperature and precipitation errors. SWE errors are more sensitive to temperature errors throughout the CONUS. Model SWE and temperature trends are generally opposite from UA product trends in the Western CONUS. SWE trend errors are also attributed to temperature and precipitation trend errors using multiple linear regressions of normalized trend errors. SWE trend errors are more sensitive to those of precipitation at higher elevations (>1,500 m) in the Western CONUS in these simulations. Thus, the sensitivity to temperature and precipitation differ for SWE errors and its trend errors. Furthermore, the SWE trend errors are more sensitive to temperature and precipitation in the atmosphere‐ocean coupled simulations in which the atmosphere‐land is coupled to an active ocean model. These results suggest that both errors in simulated temperature and precipitation contribute to SWE errors.
A study of the Antarctic ozone hole was made with a 3-D chemical transport model using linearized photochemistry for ozone based on observed distribution. The tracer model uses the winds and convection from the GISS general circulation model (8 deg x 10 deg x 23 layers). A 3-year control run of the ozone distribution is compared with the observed climatology. In two experiments, a hypothetical Antarctic ozone hole is induced on October 1 and on November 1; the tracer model is integrated for 1 year with the standard linearized chemistry. The initial depletion, 90 percent of the O sub 3 poleward of 70 S between 25 and 180 mbar, amounts to about 5 percent of the total O sub 3 in the Southerm Hemisphere. As the vortex breaks down and the hole is dispersed, significant depletions to column ozone, of order 10 D.U., occur as far north as 36 S during Austral summer. One year later, about 25 percent of the original depletion remains, mostly below 100 mbar and poleward of 30 S. Details of the calculations are shown, along with a budget analysis showing the fraction of the hole filled in by photochemistry versus that transported into the troposhere.
Contrast sensitivity is a useful measure of the ability of an observer to distinguish contrast signals from noise. Although usually applied to human observers, contrast sensitivity can also be defined operationally for individual visual neurons. In a model linear neuron consisting of a filter and noise source, this operational measure is a function of filter gain, noise power spectrum, signal duration, and a performance criterion. This definition allows one to relate the sensitivities of linear neurons at different levels in the visual pathway. Mathematical formulas describing these relationships are derived, and the general model is applied to the specific problem of relating the sensitivities of parvocellular LGN neurons and cortical simple cells in the primate.
Electric-dipole optical second harmonic generation (SHG) is a second-order nonlinear process that is widely used as a sensitive probe to detect broken inversion symmetry and local polar order. Analytical modeling of the SHG polarimetry of a nonlinear optical material is essential to extract its point group symmetry and the absolute nonlinear susceptibilities. Current literature on SHG analysis involves numerous approximations and a wide range of (in)accuracies. We have developed an open-source package called the Second Harmonic Analysis of Anisotropic Rotational Polarimetry (#SHAARP.si) which derives analytical and numerical solutions of reflection SHG polarimetry from a single interface (.si) for bulk homogeneous crystals with arbitrary symmetry group, arbitrary crystal orientation, complex and anisotropic linear dielectric tensor with frequency dispersion, a general SHG tensor and arbitrary light polarization. #SHAARP.si enables accurate modeling of polarimetry measurements in reflection geometry from highly absorbing crystals or wedge-shaped transparent crystals. The package is extendable to multiple interfaces.
The applicability and evaluation of a generalized gamma(T) family of flux-based representations are examined for two different thermal analysis formulations for structures and materials which exhibit no phase change effects. The so-called H-theta and theta forms are demonstrated for numerous test models and linear and higher-order elements. The results show that the theta form with flux-based representations is generally superior to traditional approaches.
We report that current state-of-the-art gasoline direct-injection (GDI) engines use multiple injections as one of the key technologies to improve exhaust emissions and fuel efficiency. For this technology to be successful, secured adequate control of fuel quantity for each injection is mandatory. However, nonlinearity and variations in the injection quantity can deteriorate the accuracy of fuel control, especially with small fuel injections. Therefore, it is necessary to understand the complex injection behavior and to develop a predictive model to be utilized in the development process. This study presents a methodology for rate of injection (ROI) and solenoid voltage modeling using artificial neural networks (ANNs) constructed from a set of Zeuch-style hydraulic experimental measurements conducted over a wide range of conditions. A quantitative comparison between the ANN model and the experimental data shows that the model is capable of predicting not only general features of the ROI trend, but also transient and non-linear behaviors at particular conditions. In addition, the end of injection (EOI) could be detected precisely with a virtually generated solenoid voltage signal and the signal processing method, which applies to an actual engine control unit. A correlation between the detected EOI timings calculated from the modeled signal and the measurement results showed a high coefficient of determination.
The family of shear flows comprising the jet, wake, and the mixing layer are subjected to perturbations in an inviscid incompressible fluid. By modeling the basic mean flows as parallel with piecewise linear variations for the velocities, complete and general solutions to the linearized equations of motion can be obtained in closed form as functions of all space variables and time when posed as an initial value problem. The results show that there is a continuous as well as the discrete spectrum that is more familiar in stability theory and therefore there can be both algebraic and exponential growth of disturbances in time. These bases make it feasible to consider control of such flows. To this end, the possibility of enhancing the disturbances in the mixing layer and delaying the onset in the jet and wake is investigated. It is found that growth of perturbations can be delayed to a considerable degree for the jet and the wake but, by comparison, cannot be enhanced in the mixing layer. By using moving coordinates, a method for demonstrating the predominant early and long time behavior of disturbances in these flows is given for continuous velocity profiles. It is shown that the early time transients are always algebraic whereas the asymptotic limit is that of an exponential normal mode. Numerical treatment of the new governing equations confirm the conclusions reached by use of the piecewise linear basic models. Although not pursued here, feedback mechanisms designed for control of the flow could be devised using the results of this work.
Air temperature, ground temperature and relative humidity data were collected in a longitudinal transect of the Nooksack watershed at varying elevations from 500 to 1800 m above sea level. Data were collected by anchoring sensors from trees above winter snow levels and shaded from direct solar radiation. Paired sensors were also buried 3 cm under ground near each air temperature sensor to determine snow absence or presence. Select sites included relative humidity sensors to indicate whether precipitation was occurring. Data were collected every 3-4 h from December 2015 to Sept 2018 (with ongoing collection). Code for analysis of daily mean, minimum, maximum, and temperature change with elevation (lapse rates) are available on Github (https://doi.org/10.5281/zenodo.3239539). The sensor download and intermediate data products are available on HydroShare at (http://www.hydroshare.org/resource/222e832d3df24dea9bae9bbeb6f4219d) with publicly accessible visualization available from the Nooksack Observatory at data.cuahsi.org. Hydrologic models are generally structured with a single annual average lapse rate parameter which assumes a linear temperature gradient with elevation. The daily data (2016-2018) is used as part of ongoing studies on the non-linear dynamics and temporal variability of temperature with elevation to improve assessments of watershed function and salmon habitat.
Understanding how individual animals respond to stressors behaviourally and physiologically is a critical step towards quantifying long-term population consequences and informing management efforts. Glucocorticoid (GC) metabolite accumulation in various matrices provides an integrated measure of adrenal activation in baleen whales and could thus be used to investigate physiological changes following exposure to stressors. In this study, we measured GC concentrations in faecal samples of Pacific Coast Feeding Group (PCFG) gray whales (Eschrichtius robustus) collected over seven consecutive years to assess the association between GC content and metrics of exposure to sound levels and vessel traffic at different temporal scales, while controlling for contextual variables such as sex, reproductive status, age, body condition, year, time of year and location. We develop a Bayesian Generalized Additive Modelling approach that accommodates the many complexities of these data, including non-linear variation in hormone concentrations, missing covariate values, repeated samples, sampling variability and some hormone concentrations below the limit of detection. Estimated relationships showed large variability, but emerging patterns indicate a strong context-dependency of physiological variation, depending on sex, body condition and proximity to a port. Our results highlight the need to control for baseline hormone variation related to context, which otherwise can obscure the functional relationship between faecal GCs and stressor exposure. Therefore, extensive data collection to determine sources of baseline variation in well-studied populations, such as PCFG gray whales, could shed light on cetacean stress physiology and be used to extend applicability to less-well-studied taxa. GC analyses may offer greatest utility when employed as part of a suite of markers that, in aggregate, provide a multivariate measure of physiological status, better informing estimates of individuals’ health and ultimately the consequences of anthropogenic stressors on populations.
Three-dimensional viscous flow in a conceptual hot gas manifold (HGM) for the Space Shuttle Main Engine High Pressure Fuel Turbopump (SSME HPFTP) was numerically analyzed. A finite difference scheme was used to solve the Navier-Stokes equations. The exact geometry of the SSME HGM was modeled using boundary fitted curvilinear coordinates and the General Interpolants Method (GIM) code. Slight compressibility of the subsonic flow was modeled using a linearized equation of state with artificial compressibility. A time relaxation method was used to obtain a steady state solution. The feasibility and potential usefulness of computational methods in assisting the design of SSME components which involves the flow of fluids within complex geometrical shapes is demonstrated.
A probabilistic finite element analysis procedure for laminated composite shells has been developed. A total Lagrangian finite element formulation, employing a degenerated 3-D laminated composite shell with the full Green-Lagrange strains and first-order shear deformable kinematics, forms the modeling foundation. The first-order second-moment technique for probabilistic finite element analysis of random fields is employed and results are presented in the form of mean and variance of the structural response. The effects of material nonlinearity are included through the use of a rate-independent anisotropic plasticity formulation with the macroscopic point of view. Both ply-level and micromechanics-level random variables can be selected, the latter by means of the Aboudi micromechanics model. A number of sample problems are solved to verify the accuracy of the procedures developed and to quantify the variability of certain material type/structure combinations. Experimental data is compared in many cases, and the Monte Carlo simulation method is used to check the probabilistic results. In general, the procedure is quite effective in modeling the mean and variance response of the linear and nonlinear behavior of laminated composite shells.
The Global Modeling and Assimilation Office (GMAO) has been working to promote its prototype four-dimensional variational (4DVAR) system to a version that can be exercised at operationally desirable configurations. Beyond a general circulation model (GeM) and an analysis system, traditional 4DV AR requires availability of tangent linear (TL) and adjoint (AD) models of the corresponding GeM. The GMAO prototype 4DVAR uses the finite-volume-based GEOS GeM and the Grid-point Statistical Interpolation (GSI) system for the first two, and TL and AD models derived ITom an early version of the finite-volume hydrodynamics that is scientifically equivalent to the present GEOS nonlinear GeM but computationally rather outdated. Specifically, the TL and AD models hydrodynamics uses a simple (I-dimensional) latitudinal MPI domain decomposition, which has consequent low scalability and prevents the prototype 4DV AR ITom being used in realistic applications. In the near future, GMAO will be upgrading its operational GEOS GCM (and assimilation system) to use a cubed-sphere-based hydrodynamics. This versions of the dynamics scales to thousands of processes and has led to a decision to re-derive the TL and AD models for this more modern dynamics, thus taking advantage of a two-dimensional MPI decomposition and improved scalability properties. With the aid of the Transformation of Algorithms in FORTRAN (l'AF) automatic adjoint generation tool and some hand-coding, a version of the cubed-sphere-based TL and AD models, with a simplified vertical diffusion scheme, is now available, enabling multiple configurations of standard implementations of 4DV AR in GEOS. Concurrent to this development, collaboration with the National Centers for Environmental Prediction (NCEP) and the Earth System Research Laboratory (ESRL) has allowed GMAO to implement a hybrid-ensemble capability within the GEOS data assimilation system. Both 3Dand 4D-ensemble capabilities are presently available thus allowing GMAO to now evaluate the performance and benefit of various ensemble and variational assimilation strategies. This presentation will cover the most recent developments taking place at GMAO and show results from various comparisons from traditional techniques to more recent ensemble-based ones.
The Mars Global Surveyor spacecraft, in a highly elliptical polar orbit about Mars, obtained vector magnetic field measurements just above the surface of Mars (altitudes > 100 kilometers). Crustal magnetization, largely confined to the most ancient, heavily cratered Mars highlands, is frequently organized in east-west trending linear features, the largest of which extends over 2000 km. A representative set of survey passes are modeled using uniformly magnetized thin plates and a generalized inverse methodology. Crustal remanent magnetization exceeds that deduced for the largest terrestrial magnetic anomalies by more than an order of magnitude. Groups of quasi-parallel linear features of alternating magnetic polarity are found. They are reminiscent of similar magnetic features associated with sea floor spreading and crustal genesis on Earth but with a much larger spatial scale.