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At least 19 records

Using GPUs and the Parameterization Method for Rapid Search and Refinement of Connections between Tori in Periodically Perturbed Planar Circular Restricted 3-Body Problems

When the planar circular restricted 3-body problem is periodically perturbed, most unstable periodic orbits become invariant tori. However, 2D Poincare ́ sections no longer work to find their manifolds’ intersections; new methods are needed. In this study, we first review a method of restricting the intersection search to only certain manifold subsets. We then implement this search using Julia and OpenCL, representing the manifolds as triangular meshes and gaining a 30x speedup using GPUs. We finally show how to use manifold parametrizations to refine the ap- proximate connections found in the mesh search. We demonstrate the tools on the planar elliptic RTBP.

de la Llave, Rafael↗

A new method to compute periodic orbits in general symplectic maps

The search of high-order periodic orbits has been typically restricted to problems with symmetries that help to reduce the dimension of the search space. Well-known examples include reversible maps with symmetry lines. The present work proposes a new method to compute high-order periodic orbits in twist maps without the use of symmetries. The method is a combination of the parameterization method in Fourier space and a Newton–Gauss multiple shooting scheme. The parameterization method has been successfully used in the past to compute quasi-periodic invariant circles. However, this is the first time that this method is used in the context of periodic orbits. Numerical examples are presented showing the accuracy and efficiency of the proposed method. Furthermore, the method is also applied to verify the renormalization prediction of the residues’ convergence at criticality (extensively studied in reversible maps) in the relatively unexplored case of maps without symmetries.

74 ATOMIC AND MOLECULAR PHYSICS↗

Controllers, observers, and applications thereof

Controller scaling and parameterization are described. Techniques that can be improved by employing the scaling and parameterization include, but are not limited to, controller design, tuning and optimization. The scaling and parameterization methods described here apply to transfer function based controllers, including PID controllers. The parameterization methods also apply to state feedback and state observer based controllers, as well as linear active disturbance rejection (ADRC) controllers. Parameterization simplifies the use of ADRC. A discrete extended state observer (DESO) and a generalized extended state observer (GESO) are described. They improve the performance of the ESO and therefore ADRC. A tracking control algorithm is also described that improves the performance of the ADRC controller. A general algorithm is described for applying ADRC to multi-input multi-output systems. Several specific applications of the control systems and processes are disclosed.

Gao, Zhiqiang↗

Yet another parameter-free shape optimization method

The use of node coordinates as design variables in shape optimization offers a larger design space than computer-aided design (CAD)-based shape parameterizations. It also allows for the optimization of legacy designs, i.e., a finite element mesh from an existing design can be readily optimized to meet new performance requirements without involving a CAD model. However, it is well known that the node coordinate parameterization method is fraught with numerical difficulties, which makes it impractical to use. This has led to several of “parameter-free” shape optimization methods that seek the advantages and avoid the pitfalls of the naïve node coordinate parameterization method. These methods come in two main varieties: sensitivity filtering (or gradient smoothing) and consistent filtering. The latter is analogous to the density filter method used in topology optimization (TO). In this work, we use the PDE filter from TO and energy-based filters to implement consistent shape optimization filtering schemes easily and efficiently. Numerical experiments demonstrate that consistent methods are more robust than sensitivity filtering methods.

42 ENGINEERING↗

Diesel Generator Model Parameterization for Microgrid Simulation Using Hybrid Box-Constrained Levenberg-Marquardt Algorithm

Existing generator parameterization methods, typically developed for large turbine generator units, are difficult to apply to small kW-level diesel generators in microgrid applications. Here, this article presents a model parameterization method that estimates a complete set of kW-level diesel generator parameters simultaneously using only load-step-change tests with limited measurement points. This method provides a more cost-efficient and robust approach to achieve high-fidelity modeling of diesel generators for microgrid dynamic simulation. A two-stage hybrid box-constrained Levenberg-Marquardt (H-BCLM) algorithm is developed to search the optimal parameter set given the parameter bounds. A heuristic algorithm, namely Generalized Opposition-based Learning Genetic Algorithm (GOL-GA), is applied to identify proper initial estimates at the first stage, followed by a modified Levenberg-Marquardt algorithm designed to fine tune the solution based on the first-stage result. The proposed method is validated against dynamic simulation of a diesel generator model and field measurements from a 16kW diesel generator unit.

42 ENGINEERING↗

Sensitivity of Spacebased Microwave Radiometer Observations to Ocean Surface Evaporation

Ocean surface evaporation and the latent heat it carries are the major components of the hydrologic and thermal forcing on the global oceans. However, there is practically no direct in situ measurements. Evaporation estimated from bulk parameterization methods depends on the quality and distribution of volunteer-ship reports which are far less than satisfactory. The only way to monitor evaporation with sufficient temporal and spatial resolutions to study global environment changes is by spaceborne sensors. The estimation of seasonal-to-interannual variation of ocean evaporation, using spacebased measurements of wind speed, sea surface temperature (SST), and integrated water vapor, through bulk parameterization method,s was achieved with reasonable success over most of the global ocean, in the past decade. Because all the three geophysical parameters can be retrieved from the radiance at the frequencies measured by the Scanning Multichannel Microwave Radiometer (SMMR) on Nimbus-7, the feasibility of retrieving evaporation directly from the measured radiance was suggested and demonstrated using coincident brightness temperatures observed by SMMR and latent heat flux computed from ship data, in the monthly time scale. However, the operational microwave radiometers that followed SMMR, the Special Sensor Microwave/Imager (SSM/I), lack the low frequency channels which are sensitive to SST. This low frequency channels are again included in the microwave imager (TMI) of the recently launched Tropical Rain Measuring Mission (TRMM). The radiance at the frequencies observed by both TMI and SSM/I were simulated through an atmospheric radiative transfer model using ocean surface parameters and atmospheric temperature and humidity profiles produced by the reanalysis of the European Center for Medium Range Weather Forecast (ECMWF). From the same ECMWF data set, coincident evaporation is computed using a surface layer turbulent transfer model. The sensitivity of the radiance to evaporation over various seasons and geographic locations are examined. The microwave frequencies with radiance that are significant correlated with evaporation are identify and capability of estimating evaporation directly from TMI will be discussed.

Liu, Timothy W.↗

A numerical method for parameterization of atmospheric chemistry - Computation of tropospheric OH

An efficient and stable computational scheme for parameterization of atmospheric chemistry is described. The 24-hour-average concentration of OH is represented as a set of high-order polynomials in variables such as temperature, densities of H2O, CO, O3, and NO(t) (defined as NO + NO2 + NO3 + 2N2O5 + HNO2 + HNO4) as well as variables determining solar irradiance: cloud cover, density of the overhead ozone column, surface albedo, latitude, and solar declination. This parameterization of OH chemistry was used in the three-dimensional study of global distribution of CH3CCl3. The proposed computational scheme can be used for parameterization of rates of chemical production and loss or of any other output of a full chemical model.

Spivakovsky, C. M.↗

Methods of testing parameterizations: Vertical ocean mixing

The ocean's velocity field is characterized by an exceptional variety of scales. While the small-scale oceanic turbulence responsible for the vertical mixing in the ocean is of scales a few centimeters and smaller, the oceanic general circulation is characterized by horizontal scales of thousands of kilometers. In oceanic general circulation models that are typically run today, the vertical structure of the ocean is represented by a few tens of discrete grid points. Such models cannot explicitly model the small-scale mixing processes, and must, therefore, find ways to parameterize them in terms of the larger-scale fields. Finding a parameterization that is both reliable and plausible to use in ocean models is not a simple task. Vertical mixing in the ocean is the combined result of many complex processes, and, in fact, mixing is one of the less known and less understood aspects of the oceanic circulation. In present models of the oceanic circulation, the many complex processes responsible for vertical mixing are often parameterized in an oversimplified manner. Yet, finding an adequate parameterization of vertical ocean mixing is crucial to the successful application of ocean models to climate studies. The results of general circulation models for quantities that are of particular interest to climate studies, such as the meridional heat flux carried by the ocean, are quite sensitive to the strength of the vertical mixing. We try to examine the difficulties in choosing an appropriate vertical mixing parameterization, and the methods that are available for validating different parameterizations by comparing model results to oceanographic data. First, some of the physical processes responsible for vertically mixing the ocean are briefly mentioned, and some possible approaches to the parameterization of these processes in oceanographic general circulation models are described in the following section. We then discuss the role of the vertical mixing in the physics of the large-scale ocean circulation, and examine methods of validating mixing parameterizations using large-scale ocean models.

Tziperman, Eli↗

Optimization of a Remote Sensing Energy Balance Method over Different Canopy Applied at Global Scale

Parameterization methods which calculate turbulent heat and water fluxes with thermal remote sensing data were evaluated in the revised remote sensing surface energy balance system (SEBS) model (Chen et al., 2013). The model calculates sensible heat (H) based on the Monin-Obukhov similarity theory (MOST) and determines latent heat (LE) as the residual of energy balance. We examined the uncertainties of H and LE in the SEBS model due to five key parameters at the local station point scale. Observations at 27 flux towers located in seven land cover types (needle-leaf forest, broad leaf forest, shrub, savanna, grassland, cropland, and sparsely vegetated land) and an artificial intelligence particle swarm optimization (PSO) algorithm was combined to calibrate the five parameters (leaf drag coefficient, leaf heat transfer coefficients, roughness length for soil, and two parameters for ground heat calculation) in the SEBS model. The root-mean-square error at the site scale was reduced by 9 W/sq.m for H, and 92 W/sq.m for LE, and their correlation coefficients were increased by 0.07 (H) and 0.11 (LE) after using the calibrated parameters. The updated model validation was further conducted globally for the remotely sensed evapotranspiration (ET) calculations. Overestimation of SEBS global ET was significantly improved by using the optimized values of the parameters. The results suggested PSO was able to consistently locate the global optimum of the SEBS model, and appears to be capable of solving the ET model optimization problem.

Chen, Xuelong↗

The Parameterization of Solid Metal-Liquid Metal Partitioning of Siderophile Elements

The composition of a metallic liquid can significantly affect the partitioning behavior of elements. For example, some experimental solid metal-liquid metal partition coefficients have been shown to increase by three orders of magnitude with increasing S-content of the metallic liquid. Along with S, the presence of other light elements, such as P and C, has also been demonstrated to affect trace element partitioning behavior. Understanding the effects of metallic composition on partitioning behavior is important for modeling the crystallization of magmatic iron meteorites and the chemical effects of planetary differentiation. It is thus useful to have a mathematical expression that parameterizes the partition coefficient as a function of the composition of the metal. Here we present a revised parameterization method, which builds on the theory of the current parameterization of Jones and Malvin and which better handles partitioning in multi-light-element systems.

Chabot, N. L.↗

Developments in variational methods for high performance plate and shell elements

High performance elements are simple finite elements constructed to deliver engineering accuracy with coarse arbitrary grids. This is part of a series on the variational foundations of high-performance elements, with emphasis on plate and shell elements constructed with the free formulation (FF) and assumed natural strain (ANS) methods. Parameterized variational principles are studied that provide a common foundation for the FF and ANS methods, as well as for a combination of both. From this unified formulation a variant of the ANS formulation, called the assumed natural deviatoric strain (ANDES) formulation, emerges as an important special case. The first ANDES element, a high-performance 9 degrees of freedom triangular Kirchhoff plate bending element, is briefly described to illustrate the use of the new formulation.

Felippa, Carlos A.↗

Preliminary Design of Low-Thrust Interplanetary Missions

For interplanetary missions, highly efficient electric propulsion systems can be used to increase the mass delivered to the destination and/or reduce the trip time over typical chemical propulsion systems. This technology is being demonstrated on the Deep Space 1 mission - part of NASA's New Millennium Program validating technologies which can lower the cost and risk and enhance the performance of future missions. With the successful demonstration on Deep Space 1, future missions can consider electric propulsion as a viable propulsion option. Electric propulsion systems, while highly efficient, produce only a small amount of thrust. As a result, the engines operate during a significant fraction of the trajectory. This characteristic makes it much more difficult to find optimal trajectories. The methods for optimizing low-thrust trajectories are typically categorized as either indirect, or direct. Indirect methods are based on calculus of variations, resulting in a two-point boundary value problem that is solved by satisfying terminal constraints and targeting conditions. These methods are subject to extreme sensitivity to the initial guess of the variables - some of which are not physically intuitive. Adding a gravity assist to the trajectory compounds the sensitivity. Direct methods parameterize the problem and use nonlinear programming techniques to optimize an objective function by adjusting a set of variables. A variety of methods of this type have been examined with varying results. These methods are subject to the limitations of the nonlinear programming techniques. In this paper we present a direct method intended to be used primarily for preliminary design of low-thrust interplanetary trajectories, including those with multiple gravity assists. Preliminary design implies a willingness to accept limited accuracy to achieve an efficient algorithm that executes quickly.

Sims, Jon A.↗

Effects of dynamic heat fluxes on model climate sensitivity Meridional sensible and latent heat fluxes

The high- and low-latitude radiative-dynamic (HLRD) climatic model of Wang et al. (1984) was used to study the effect of meridional heat (MH) fluxes on climate changes caused by increases of CO2 abundance and solar constant variations. However, the empirical MH parameterization of the HLRD model was replaced by physically based parameterization, which gives separate meridional sensible and latent heat fluxes and provides a complete representation of the dependence of the flux on the mean temperature field. Both parameterization methods yielded about the same changes in global mean surface temperature and ice line, and both produced only small changes in meridional temperature gradient, although the latter were even smaller with the physically based parameterizations. At any latitude, the hemispheric mean surface temperature, rather than MH fluxes, dominates the surface temperature changes.

Gutowski, W. J., Jr.↗

A bespoke model of Arctic river basins based on hillslope delineation: Model Archive

This dataset is a model archive of the paper A bespoke model of Arctic river basins based on hillslope delineation (in prep), which introduces a watershed decomposition and parameterization method for large scale permafrost hydrology simulation. With this dataset, this study aims to address the research question: whether a computationally efficient hillslope-based modeling framework can reliably simulate discharge at Arctic river-basin scales. This dataset contains model input and output data for five modeling scenarios at a study site located in the Sagavanirktok River basin. The five modeling scenarios include three modeling cases under temperate conditions using full 3D, decomposed 3D, and decomposed 2D modeling strategies; and two modeling cases under actual Arctic conditions with permafrost using full 3D and decomposed 2D modeling strategies. Simulations were performed using the Advanced Terrestrial Simulator (ATS, v1.6 for three temperate scenarios and v1.5 for two Arctic scenarios), a physics-rich integrated surface–subsurface hydrologic model with cryo-hydrology features. For the three temperate models, simulations were conducted for the period of 10/01/1993 - 09/30/2002; and for the two Arctic models, simulations were conducted for the period of 01/01/1994 - 12/31/2002. To facilitate reproducibility of simulations, all datasets are organized hierarchically. The dataset contains: (1) Mesh files (.exo) for full 3D model, decomposed 3D models, and decomposed 2D models, located in huc/190604020802_gauge15906000/mesh/. Mesh files can be visualized through Paraview or read by Python. (2) Climate forcings (.h5) for full 3D model and decomposed 3D/2D models are located in huc/190604020802_gauge15906000/daymet_onePiece/, and huc/190604020802_gauge15906000/vp_pr_revised_daymet_1980_2006_with_wind/ separately. Accessible by Python. (3) Raw measured gage discharge (.csv) from USGS, located in huc/190604020802_gauge15906000/gaged_basin15906000_discharge_usgs/. Accessible by Python. (4) Delineated subdomain raster (.tif) and shape files (.shp), and the final parameterized results (.npy) for decomposed models, located in huc/190604020802_gauge15906000/data_preprocessed-meshing. Accessible by Python. (5) Temperate models are located in nonpermaf_huc190604020802_gauge15906000/, which includes three cases: decomposed 2D models (inside model_0*-hillslope_*), decomposed 3D models (inside model_1*-subcatchment_*), and full 3D model (inside model_2*-onepiece_*). Two step spin-up results (checkpoint_final.h5) are located in model_*1-*_spinup_steadystate and model_*2-*_spinup_cycle, separately, which are used to initialize real transient models. The input files (.xml) and output results (.dat) of the real transient models are located in model_*3-*_transient/. Especially, for two example hillslope models (ID=-11 and 11), additional h5py files are included in model_03-hillslope_transient/hillslope-11/, model_03-hillslope_transient/hillslope11, model_13-subcatchment_transient/subcatchment-11/, model_13-subcatchment_transient/subcatchment/11, respectively, which are used to plot the saturation figure (Figure 5) in the manuscript. Accessible by Python. (6) Arctic models are located in huc190604020802_gauge15906000/, which includes two cases: decomposed 2D models (inside model_04-hillslope_transient), and full 3D model (inside model_05-onepiece_transient_mannp1_ra). Three step spin-up results (checkpoint_final.h5) are located in model_01-column_freezeup/, model_02-column_spinup/, model_03-hillslope_spinup/, respectively, which are used to initialize real 2D transient hillslope models. The input files (.xml) and output results (.dat) of transient 2D hillslope models are located in model_04-hillslope_transient/. The input files (.xml) and output results (.dat) of the full 3D transient model is located in model_05-onepiece_transient_mannp1_ra/. The full 3D transient model is initialized by model_02-column_spinup/. Accessible by Python. (7) The MOSART routed discharge results (.csv) under Arctic conditions is located in huc190604020802_gauge15906000/MOSART/. Accessible by Python. (8) All Python codes (.py) used to parameterize full 3D model to decomposed 2D models are located in script/. These codes fit with watershed workflow (a watershed delineation tool) v1.4 under the branch gaob/v1.4 from https://github.com/gaobhub/watershed-workflow.git.

EARTH SCIENCE > CRYOSPHERE↗

A dynamic kinetic model captures cell-free metabolism for improved butanol production

Cell-free systems are useful tools for prototyping metabolic pathways and optimizing the production of various bioproducts. Mechanistically-based kinetic models are uniquely suited to analyze dynamic experimental data collected from cell-free systems and provide vital qualitative insight. However, to date, dynamic kinetic models have not been applied with rigorous biological constraints or trained on adequate experimental data to the degree that they would give high confidence in predictions and broadly demonstrate the potential for widespread use of such kinetic models. In this work, we construct a large-scale dynamic model of cell-free metabolism with the goal of understanding and optimizing butanol production in a cell-free system. Using a combination of parameterization methods, the resultant model captures experimental metabolite measurements across two experimental conditions for nine metabolites at timepoints between 0 and 24 hours. Here, we present analysis of the model predictions, provide recommendations for butanol optimization, and identify the aldehyde/alcohol dehydrogenase as the primary bottleneck in butanol production. Sensitivity analysis further reveals the extent to which various parameters are constrained, and our approach for probing valid parameter ranges can be applied to other modeling efforts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗