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At least 829 records · Page 46

Design and convergence analysis of the conforming virtual element method for polyharmonic problems

In the recent years, there has been a tremendous interest to numerical methods that approximate partial differential equations (PDEs) on computational meshes with arbitrarily-shaped polygonal/polyhedral (polytopal, for short) elements. A nonexhaustive list of such methods include the Mimetic Finite Difference method [4, 9, 21, 24, 28, 33, 35, 62, 64–67], the Polygonal Finite Element Method [68, 73, 74], the polygonal Discontinuous Galerkin Finite Element Methods [5, 7, 8, 10, 13–15, 18, 36, 38, 39, 41, 50], the Hybridizable Discontinuous Galerkin and Hybrid High-Order Methods [46–48, 51], the Gradient Discretization method [49, 53, 54], the Finite Volume Method [52], and the BEM-based FEM [71]. An alternative approach that also proved to be very successful is provided by the Virtual Element method (VEM), which was originally proposed in [19] for the numerical treatment of second-order elliptic problems [43, 44], and readily extended to linear and nonlinear elasticity [22, 25, 56], plate bending problems [37], Cahn-Hilliard equation [3], Stokes equations [2], Laplace-Beltrami equation [55], Darcy-Brinkam equation [76], discrete topology optimization problems [6], fracture networks problems [29], eigenvalue problems [59, 75]. The mixed virtual element formulation was proposed in [20, 34]; the nonconforming Virtual element formulations was proposed for second-order elliptic problems in [16], and later extended to general advection-reaction-diffusion problems, Stokes equation, the biharmonic problems, the iegenvalue problem, and the Schrodinger equation in [11, 30, 42, 45, 58, 80]. The p- and hp-version of the VEM were developed in [26, 27] and efficient multigrid methods for the resulting linear system of equations in [12]. A posteriori error estimates can be found in [40].

97 MATHEMATICS AND COMPUTING↗

Optimization of Energy Flow Through Synthetic Metabolic Modules and Regulatory Networks in a Model Photosynthetic Eukaryotic Microbe

Diatoms are important oceanic photosynthetic microorganisms, responsible for approximately 20% of all carbon fixation on Earth. Additionally, diatoms are attractive metabolic engineering candidates. This investigation leveraged Systems Biology techniques to advance our understanding of and potential to engineer diatoms for bioproducts of societal interest, such as biofuels. Systems Biology combines computational and experimental techniques to understand an organism at the whole-cell level as well as characterize the interface between the organism and its environment. Our research resulted in major contributions to the understanding of systems-level light-driven metabolism. Diatoms have a unique evolutionary history. As a result, existing understanding of photosynthetic metabolism may not be applicable to diatom physiology. We generated, validated, and published a high-quality metabolic model of diatom metabolism facilitating novel insights into these unique organisms. Additionally, we overcame a consistent challenge in the modeling of photosynthetic organisms by integrating light into metabolic models. This result allows realistic assessments of how the light environment affects cell physiology and metabolism, a necessary advancement for bioengineering. Next, we generated several methodologies for integrating large-scale datasets with models of metabolism. These “big data” approaches begin to address a constant challenge in biology, which is translating data into information and understanding. Finally, we built web-based databases for housing, distributing, and visualizing systems-level biology data. These projects created an online ecosystem for sharing, analyzing, and characterizing metabolic information and is currently being used by public and private institutions. Photosynthetic bioengineering has the promise to create high-energy products with minimal inputs. Systems Biology has a long history of facilitating bioengineering of cellular metabolism. However, photosynthetic organisms are only sparsely present in this history. This project and its outputs have accelerated the application of proven Systems Biology techniques to light-driven metabolism. The resulting methodologies will accelerate public and private endeavors leveraging photosynthetic systems in the bioengineering of bioproducts such as biofuels or carbon sequestration.

09 BIOMASS FUELS↗

Comparison of Tempered and Truncated Fractional Models

Tempered fractional operators are able to model effects that classical partial differential equations cannot quite capture. For example, this includes the super- and subdiffusion effects that are present in hydrology and geophysics models. However, tempered fractional operators are computationally intensive. We analyze a truncated variation of the fractional operators, which are less computationally intensive, in an effort to use them in place of the more complex tempered variation. In particular, we train parameters of the truncated operator using neural networks in order to optimize the difference of the actions of the two operators.

58 GEOSCIENCES↗

Optimal Power Flow Derived Sparse Linear Solver Benchmarks

Due to the changing nature of the power grid, it is increasingly important to be able to solve a high-fidelity optimal power-flow models on large power networks. This high-fidelity problem, called AC Optimal Power Flow (ACOPF), is a nonlinear, nonconvex optimization problem. One of the few reliable ways of solving such a problem is interior point methods. These methods result in sparse linear systems where the coefficient matrix is symmetric, indefinite and nearly always ill-conditioned. As such, they are particularly challenging for sparse linear solvers and represent a considerable computational bottleneck in solving the ACOPF problem. In this paper, we introduce a repository of linear systems captured from ACOPF problems when solved by the open-source optimizer IPOPT. These matrices are meant to be used as a test suite for sparse linear solver development.

97 MATHEMATICS AND COMPUTING↗

Visualizing Uranium Crystallization from Melt: Experiment-Informed Phase Field Modeling and Machine Learning

The focus of this project was to observe and simulate the solidification of uranium metal at the crystallographic level from its molten state. Melting experiments were conducted at two different scales to observe microstructural evolution using either a laboratory-scale induction furnace (hundreds of grams of metal) or a microscope heating stage (hundreds of milligrams of metal), respectively. Experimental parameters and characterization data were then used to inform a phase field model of gamma-U crystal growth as dendrites with or without secondary phase impurities in the form of uranium carbide particles. Finally, training datasets were generated by the phase field model as inputs to a neural network, developed with the aim of providing a faster, cheaper surrogate model for microstructural simulations within a given parameter space. Progress is reported herein for each of these task areas. Ultimately, 1) an optical microscope heating stage capability has been stood-up for uranium metal solidification studies, 2) a phase field model was advanced to simulate multiple uranium grains growing in the presence of carbide impurity particles and 3) a neural network was constructed and optimized to predict the microstructure features of individually growing uranium crystals.

36 MATERIALS SCIENCE↗

Towards AI Based Data Classification for Decision Making During Testing

During the development of high-consequence items, test systems should be capable of differentiating between test failures resulting from narrowly missing requirements versus those indicating potentially catastrophic faults. In many instances, classifying the data corresponds to simply identifying whether measured waveforms have approximately the anticipated shape. Cast in this light, the problem reduces to converting raw data into a form optimal for use with neural network classifiers. This manuscript investigates different means of representing raw data for image classification. Raw data plots and Short Time Fourier Transform (STFT) spectrograms are classified by both custom built, small-scale, Convolution Neural Networks (CNN) and open-source, multi-million parameter, pre-trained deep CNNs. In the case of time varying frequency content, the STFTs provide images with greater detail and can be accurately classified with simpler networks. This requires less memory and runs faster than classifying the raw data using the more sophisticated options—making STFTs optimal for applications with memory constraints. STFTs are not a panacea. In some cases the time-domain signal contains useful information that should not be discarded. Rather than using raw data or STFTs, the images can be constructed from both by using red and green channels of an RGB image to visualize the real and imaginary components of the transform, with the raw data occupying the blue channel.

97 MATHEMATICS AND COMPUTING↗

Extending the SAGA Survey (xSAGA). I. Satellite Radial Profiles as a Function of Host-galaxy Properties

We present "Extending the Satellites Around Galactic Analogs Survey" (xSAGA), a method for identifying low-z galaxies on the basis of optical imaging and results on the spatial distributions of xSAGA satellites around host galaxies. Using spectroscopic redshift catalogs from the SAGA Survey as a training data set, we have optimized a convolutional neural network (CNN) to identify z < 0.03 galaxies from more-distant objects using image cutouts from the DESI Legacy Imaging Surveys. From the sample of >100,000 CNN-selected low-z galaxies, we identify >20,000 probable satellites located between 36–300 projected kpc from NASA-Sloan Atlas central galaxies in the stellar-mass range $9.5\lt \mathrm{log}({M}_{\star }/{M}_{\odot })\lt 11$. We characterize the incompleteness and contamination for CNN-selected samples and apply corrections in order to estimate the true number of satellites as a function of projected radial distance from their hosts. Satellite richness depends strongly on host stellar mass, such that more-massive host galaxies have more satellites, and on host morphology, such that elliptical hosts have more satellites than disky hosts with comparable stellar masses. We also find a strong inverse correlation between satellite richness and the magnitude gap between a host and its brightest satellite. The normalized satellite radial distribution between 36–300 kpc does not depend on host stellar mass, morphology, or magnitude gap. The satellite abundances and radial distributions we measure are in reasonable agreement with predictions from hydrodynamic simulations. Our results deliver unprecedented statistical power for studying satellite galaxy populations and highlight the promise of using machine-learning for extending galaxy samples of wide-area surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

Analytic continuation of noisy data using Adams Bashforth residual neural network

We propose a data-driven learning framework for the analytic continuation problem in numerical quantum many-body physics. Designing an accurate and efficient framework for the analytic continuation of imaginary time using computational data is a grand challenge that has hindered meaningful links with experimental data. The standard Maximum Entropy (MaxEnt)-based method is limited by the quality of the computational data and the availability of prior information. Also, the MaxEnt is not able to solve the inversion problem under high level of noise in the data. Here we introduce a novel learning model for the analytic continuation problem using a Adams-Bashforth residual neural network (AB-ResNet). Additionally, the advantage of this deep learning network is that it is model independent and, therefore, does not require prior information concerning the quantity of interest given by the spectral function. More importantly, the ResNet-based model achieves higher accuracy than MaxEnt for data with higher level of noise. Finally, numerical examples show that the developed AB-ResNet is able to recover the spectral function with accuracy comparable to MaxEnt where the noise level is relatively small.

97 MATHEMATICS AND COMPUTING↗

Quantum Software Engineering (Dagstuhl Seminar 24512)

The Dagstuhl Seminar 24512 on "Quantum Software Engineering" was held from December 15 to 20, 2024. It brought together 26 participants from industry and academia from 13 different countries, including senior and junior researchers as well as practitioners in the field of Quantum Software Engineering. The aim of the seminar was to advance software engineering methods and tools for the engineering of hybrid quantum systems by promoting personal interaction and open discussion among researchers who are already working in this emerging area of knowledge. The first day of the seminar was devoted to the topic "When software engineering meets quantum mechanics", while the second day focused on "Quantum software engineering and its challenges." During both days, 16 invited presentations were given. The rest of the seminar was organized into three working groups to address the topics "Quantum Software Design, Modelling and Architecturing", "Adaptive Hybrid Quantum Systems", and "Quantum Software Quality Assurance". The seminar was a very fruitful experience for all participants both in terms of scientific outcomes and in terms of the personal relationships that were generated to jointly address future experiences.

97 MATHEMATICS AND COMPUTING↗

A remote sensing algorithm for vertically resolved cloud condensation nuclei number concentrations from airborne and spaceborne lidar observations

Cloud condensation nuclei (CCN) are mediators of aerosol–cloud interactions (ACIs), contributing to the largest uncertainties in the understandings of global climate change. We present a novel remote-sensing-based algorithm that quantifies the vertically resolved CCN number concentrations (N CCN ) using aerosol optical properties measured by a multiwavelength lidar. The algorithm considers five distinct aerosol subtypes with bimodal size distributions. The inversion used the lookup tables developed in this study, based on the observations from the Aerosol Robotic Network, to efficiently retrieve optimal particle size distributions from lidar measurements. The method derives dry aerosol optical properties by implementing hygroscopic enhancement factors in lidar measurements. The retrieved optically equivalent particle size distributions and aerosol-type-dependent particle composition are utilized to calculate critical diameters using κ-Köhler theory and N CCN at six supersaturations ranging from 0.07 % to 1.0 %. Sensitivity analyses indicate that uncertainties in extinction coefficients and relative humidity greatly influence the retrieval error in N CCN . The potential of this algorithm is further evaluated by retrieving N CCN using airborne lidar from the NASA ObseRvations of Aerosols above CLouds and their intEractionS (ORACLES) campaign and is validated against simultaneous measurements from the CCN counter. The independent validation with robust correlation demonstrates promising results. Furthermore, the N CCN has been retrieved for the first time using a proposed algorithm from spaceborne lidar – Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) – measurements. The application of this new capability demonstrates the potential for constructing a 3D CCN climatology at a global scale, which helps to better quantify ACI effects and thus reduce the uncertainty in aerosol climate forcing.

54 ENVIRONMENTAL SCIENCES↗

An algorithmic approach to crustal deformation analysis

In recent years the analysis of crustal deformation measurements has become important as a result of current improvements in geodetic methods and an increasing amount of theoretical and observational data provided by several earth sciences. A first-generation data analysis algorithm which combines a priori information with current geodetic measurements was proposed. Relevant methods which can be used in the algorithm were discussed. Prior information is the unifying feature of this algorithm. Some of the problems which may arise through the use of a priori information in the analysis were indicated and preventive measures were demonstrated. The first step in the algorithm is the optimal design of deformation networks. The second step in the algorithm identifies the descriptive model of the deformation field. The final step in the algorithm is the improved estimation of deformation parameters. Although deformation parameters are estimated in the process of model discrimination, they can further be improved by the use of a priori information about them. According to the proposed algorithm this information must first be tested against the estimates calculated using the sample data only. Null-hypothesis testing procedures were developed for this purpose. Six different estimators which employ a priori information were examined. Emphasis was put on the case when the prior information is wrong and analytical expressions for possible improvements under incompatible prior information were derived.

Iz, Huseyin Baki↗

Krylov methods preconditioned with incompletely factored matrices on the CM-2

The performance is measured of the components of the key interative kernel of a preconditioned Krylov space interative linear system solver. In some sense, these numbers can be regarded as best case timings for these kernels. Sweeps were timed over meshes, sparse triangular solves, and inner products on a large 3-D model problem over a cube shaped domain discretized with a seven point template. The performance of the CM-2 is highly dependent on the use of very specialized programs. These programs mapped a regular problem domain onto the processor topology in a careful manner and used the optimized local NEWS communications network. The rather dramatic deterioration in performance was documented when these ideal conditions no longer apply. A synthetic workload generator was developed to produce and solve a parameterized family of increasingly irregular problems.

Berryman, Harry↗

Digital optical computers at the optoelectronic computing systems center

The Digital Optical Computing Program within the National Science Foundation Engineering Research Center for Opto-electronic Computing Systems has as its specific goal research on optical computing architectures suitable for use at the highest possible speeds. The program can be targeted toward exploiting the time domain because other programs in the Center are pursuing research on parallel optical systems, exploiting optical interconnection and optical devices and materials. Using a general purpose computing architecture as the focus, we are developing design techniques, tools and architecture for operation at the speed of light limit. Experimental work is being done with the somewhat low speed components currently available but with architectures which will scale up in speed as faster devices are developed. The design algorithms and tools developed for a general purpose, stored program computer are being applied to other systems such as optimally controlled optical communication networks.

Jordan, Harry F.↗

Scalable Optical-Fiber Communication Networks

Scalable arbitrary fiber extension network (SAFEnet) is conceptual fiber-optic communication network passing digital signals among variety of computers and input/output devices at rates from 200 Mb/s to more than 100 Gb/s. Intended for use with very-high-speed computers and other data-processing and communication systems in which message-passing delays must be kept short. Inherent flexibility makes it possible to match performance of network to computers by optimizing configuration of interconnections. In addition, interconnections made redundant to provide tolerance to faults.

Chow, Edward T.↗

Mississippi State University Center for Air Sea Technology FY95 Research Program

The Mississippi State University (MSU) Center for Air Sea Technology (CAST) evolved from the Institute for Naval Oceanography's (INO) Experimental Center for Mesoscale Ocean Prediction (ECMOP) which was started in 1989. MSU CAST subsequently began operation on 1 October 1992 under an Office of Naval Research (ONR) two-year grant which ended on 30 September 1994. In FY95 MSU CAST was successful in obtaining five additional research grants from ONR, as well as several other research contracts from the Naval Oceanographic Office via NASA, the Naval Research Laboratory, the Army Corps of Engineers, and private industry. In the past, MSU CAST technical research and development has produced tools, systems, techniques, and procedures that improve efficiency and overcome deficiency for both the operational and research communities residing with the Department of Defense, private industry, and university ocean modeling community. We continued this effort with the following thrust areas: to develop advanced methodologies and tools for model evaluation, validation and visualization, both oceanographic and atmospheric; to develop a system-level capability for conducting temporally and ; spatially scaled ocean simulations driven by or are responsive to ocean models, and take into consideration coupling to atmospheric models; to continue the existing oceanographic/atmospheric data management task with emphasis on distributed databases in a network environment, with database optimization and standardization, including use of Mosaic and World Wide Web (WWW) access; and to implement a high performance parallel computing technology for CAST ocean models

Yeske, Lanny↗

Microreactor System Design for a NASA In Situ Propellant Production Plant on Mars

The NASA In Situ Resource Utilization (ISRU) program is planning near-term missions to Mars that will include chemical processes for converting the carbon dioxide (CO2) and possibly water from the Martian environment to propellants, oxygen, and other useful chemicals. The use of indigenous resources reduces the size and weight of the payloads from Earth significantly, representing enormous cost savings that make human exploration of Mars affordable. Extraterrestrial chemical processing plants will need to be compact, lightweight, highly efficient under reduced gravity, and extraordinarily reliable for long periods. Microchemical and thermal systems represent capability for dramatic reduction in size and weight, while offering high reliability through massive parallelization. In situ propellant production (ISPP), one aspect of the ISRU program, involves collecting and pressurizing atmospheric CO2, conversion reactions, chemical separations, heat exchangers, and cryogenic storage. A preliminary system design of an ISPP plant based on microtechnology has demonstrated significant size, weight, and energy efficiency gains over the current NASA baseline. Energy management is a strong driver for Mars-based processes, not only because energy is a scarce resource, but because heat rejection is problematic; the low pressure environment makes convective heat transfer ineffective. Energy efficiency gains are largely achieved in the microchemical plant through extensive heat recuperation and energy cascading, which has a small size and weight penalty because the added micro heat exchangers are small. This leads to additional size and weight gains by reducing the required area of waste heat radiators. The microtechnology-based ISPP plant is described in detail, including aspects of pinch analysis for optimizing the heat exchanger network. Three options for thermochemical compression Of CO2 from the Martian atmosphere, adsorption, absorption, and cryogenic freezing, are presented, as well as three options for water decomposition, low temperature electrolysis, high temperature electrolysis, and thermochemical decomposition. Other elements of the plant include Sabatier and reverse water gas shift reactors, water recovery, chemical separations, and cryogenic storage. Data are presented supporting preliminary sizing of components, and results of the system design are compared to the existing NASA baseline that is based on conventional technologies.

TeGrotenhuis, W. E.↗

Communal Sensor Network for Adaptive Noise Reduction in Aircraft Engine Nacelles

Emergent behavior, a subject of much research in biology, sociology, and economics, is a foundational element of Complex Systems Science and is apropos in the design of sensor network systems. To demonstrate engineering for emergent behavior, a novel approach in the design of a sensor/actuator network is presented maintaining optimal noise attenuation as an adaptation to changing acoustic conditions. Rather than use the conventional approach where sensors are managed by a central controller, this new paradigm uses a biomimetic model where sensor/actuators cooperate as a community of autonomous organisms, sharing with neighbors to control impedance based on local information. From the combination of all individual actions, an optimal attenuation emerges for the global system.

Jones, Kennie H.↗