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At least 379 records · Page 21

Minimization of the vibration energy of thin-plate structure

An optimization method is proposed to reduce the vibration of thin plate structures. The method is based on a finite element shell analysis, a modal analysis, and a structural optimization method. In the finite element analysis, a triangular shell element with 18 dof is used. In the optimization, the overall vibration energy of the structure is adopted as the objective function, and it is minimized at the given exciting frequency by varying the thickness of the elements. The technique of modal analysis is used to derive the sensitivity of the vibration energy with respect to the design variables. The sensitivity is represented by the sensitivities of both eigenvalues and eigenvectors. The optimum value is computed by the gradient projection method and a unidimensional search procedure under the constraint condition of constant weight. A computer code, based on the proposed method, is developed and is applied to design problems using a beam and a plate as test cases. It is confirmed that the vibration energy is reduced at the given exciting frequency. For the beam excited by a frequency slightly less than the fundamental natural frequency, the optimized shape is close to the beam of uniform strength.

Inoue, Katsumi↗

Optimal control of coupled quantum systems based on the first-order Magnus expansion: Application to multiple dipole-dipole-coupled molecular rotors

This paper presents a method for performing approximate optimal control simulations for quantum systems with multiple coupled degrees of freedom. In this work, the time evolution is simulated using the first-order Magnus expansion in the interaction picture, where the couplings between different degrees of freedom are treated as the perturbation. A numerical implementation procedure is presented that leverages upon pairwise couplings and the separability of the zeroth-order time evolution operator to achieve a reduced computational cost, which is analyzed with respect to the number of degrees of freedom. The formulation is compatible with gradient-free methods to optimize the control field, and a stochastic hill climbing algorithm is adopted for this purpose. As illustrations, optimal control simulations are performed for systems of two and three dipole-dipole-coupled molecular rotors under the influence of a control field. For the two-rotor system, the field is optimized to achieve either orientation or entanglement objectives. For the three-rotor system, the field is optimized either to orient all three rotors in the same direction or to orient one rotor in a particular direction while the other two rotors point in the opposite direction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Improved image decompression for reduced transform coding artifacts

The perceived quality of images reconstructed from low bit rate compression is severely degraded by the appearance of transform coding artifacts. This paper proposes a method for producing higher quality reconstructed images based on a stochastic model for the image data. Quantization (scalar or vector) partitions the transform coefficient space and maps all points in a partition cell to a representative reconstruction point, usually taken as the centroid of the cell. The proposed image estimation technique selects the reconstruction point within the quantization partition cell which results in a reconstructed image which best fits a non-Gaussian Markov random field (MRF) image model. This approach results in a convex constrained optimization problem which can be solved iteratively. At each iteration, the gradient projection method is used to update the estimate based on the image model. In the transform domain, the resulting coefficient reconstruction points are projected to the particular quantization partition cells defined by the compressed image. Experimental results will be shown for images compressed using scalar quantization of block DCT and using vector quantization of subband wavelet transform. The proposed image decompression provides a reconstructed image with reduced visibility of transform coding artifacts and superior perceived quality.

Orourke, Thomas P.↗

Remote Radiation Sensing Using Aerial and Ground Platforms

Remote sensing of ionizing radiation has a significant role in waste management, nuclear material management and nonproliferation, and radiation safety. Robotic platforms can surpass the number of tasks that are achieved by humans. With this technique, the operator's radiation exposure can be decreased. Remote sensing allows for the evaluation and monitoring of radiological contamination. Gamma-ray and neutron sensors were integrated onto the robotic platforms. This approach allows for the radiation sensor data to be dynamically tracked and mapped thus enabling further analysis of the radiation flux in temporal and spatial domains. The goal is to complete scheduled tasks while the robot is being irradiated. To achieve this, electronic components must be shielded and radiation hardened. CZT Detector: Cadmium Zinc Telluride (CZT) detector technology has been a promising solution for gamma-ray and x-ray measurements. Detector data is transferred to the Odroid minicomputer that controls and powers the module via the USB. Robot Operating System (ROS) was utilized for data acquisition and data fusion. The Mariscotti method was employed for the spectrum analysis. A function was programmed in ROS for the automatic identification of photopeaks. CLYC Detector: A Cs{sub 2}LiYCl{sub 6}:Ce{sup 3+} (CLYC) detector was used for simultaneous medium-resolution gamma-ray measurements and neutron counting. A 2.54 cm diameter photomultiplier tube (PMT) was equipped with a high voltage supply and a miniature digitizer. Gamma-ray excitation: fast core-to-valence luminescence (CVL) with 1 ns decay constant, and prompt Ce{sup 3+} emission with 50 ns decay constant. Neutron excitation: slow cerium self-trapped excitation (Ce{sup 3+} STE), 1000 ns decay constant. Radiation Source Localization: Maximum Likelihood Estimation (MLE) and gradient-based methods were used to locate the position of a radiation source based on measured radiation intensities. Multi-Particle Transport Code FLUKA: Estimation of radiation damage of the electronic components is important in order to optimize the robot's operational time while it is irradiated. Displacement per atom (DPA) represents the radiation damage in materials exposed to the ionizing radiation. Various shielding layers of different thickness t were analyzed (< 5% statistical error). The model of the controller of the UAS was designed in FLUKA. Conclusion: CZT and CLYC detectors were integrated onto the robotic platforms. Radiation source localization and contour mapping using robotic platforms were studied. Functions for data analysis and fusion were developed in ROS. FLUKA code was utilized to analyze DPA values. Layers of low-density and high-density materials were used to shield the UAS electronics.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Pore-scale simulation of gas flow in microscopic permeable media with complex geometries

Lattice Boltzmann method (LBM) is an efficient tool to perform direct numerical simulation of gas flow in micro-size pores. Despite great advances in LBM and its use in describing gas flow in micro-size channels in slip and transitional flow regimes, exploring formulations that are able to capture flow behavior in domains with complex boundary geometries remains a challenging task. As a result, the impact of complexities in pore structures on gas flow may not be fully explored using LBM. In this study, we propose to use the combined bounce-back and Maxwellian diffusive reflection scheme to capture the slip velocity with a new set of slip coefficients. Optimal values of slip coefficients are determined using a gradient based method, where the results from the linearized Boltzmann equation is used as the reference solution. The proposed formulation is further validated against predictions from molecular dynamics simulation in the presence of complex geometries by introducing obstacles of different shapes in straight channels. LBM with the proposed boundary treatment is then used to investigate gas flow in a synthetic microscopic permeable medium. Here, results indicate that gas exhibits different flow configurations as Knudsen number varies, and apparent gas permeability appears to have up to a second-order dependency on the reciprocal mean pressure in slip and transitional flow regimes.

03 NATURAL GAS↗

Simulation toolkit for digital material characterization of large image-based microstructures

In this paper, an efficient image-based simulation toolkit for material characterization is presented, which is scalable to work from personal computers to workstations. The effective thermal conductivity, elasticity, and permeability are evaluated employing a computational homogenization framework based on the Finite Element Method (FEM). Two complementary open-source packages are presented: one developed in Python, which can convert digital images into voxel meshes (pyTomoviewer); the other developed in Julia, that can run numerical simulations to compute effective material properties (chpack). Also, a CUDA C version of chpack is provided (chfem_gpu). They were designed to deal with large multi-phase models, so strategies were devised to minimize their memory footprint, while avoiding a high toll on execution time. The voxel-based approach significantly simplifies the FEM meshes and allows efficient matrix-free implementations. In that sense, to handle large linear systems of equations, the element-by-element (EBE) technique is adopted, in conjunction with a low-memory implementation of the Preconditioned Conjugate Gradient (PCG) method. Finally, the code was thoroughly tested on an artificial geometry made of a square array of cylinders, for which analytical solutions exist, as well as on a real micro-tomographic reconstruction of FiberForm TM , a carbon preform commonly used in thermal protection systems.

36 MATERIALS SCIENCE↗

Streaming Generalized Canonical Polyadic Tensor Decompositions

In this paper, we develop a method which we call OnlineGCP for computing the Generalized Canonical Polyadic (GCP) tensor decomposition of streaming data. GCP differs from traditional canonical polyadic (CP) tensor decompositions as it allows for arbitrary objective functions which the CP model attempts to minimize. This approach can provide better fits and more interpretable models when the observed tensor data is strongly non-Gaussian. In the streaming case, tensor data is gradually observed over time and the algorithm must incrementally update a GCP factorization with limited access to prior data. In this work, we extend the GCP formalism to the streaming context by deriving a GCP optimization problem to be solved as new tensor data is observed, formulate a tunable history term to balance reconstruction of recently observed data with data observed in the past, develop a scalable solution strategy based on segregated solves using stochastic gradient descent methods, describe a software implementation that provides performance and portability to contemporary CPU and GPU architectures and integrates with Matlab for enhanced usability, and demonstrate the utility and performance of the approach and software on several synthetic and real tensor data sets.

97 MATHEMATICS AND COMPUTING↗

Parallelization of the Physical-Space Statistical Analysis System (PSAS)

Atmospheric data assimilation is a method of combining observations with model forecasts to produce a more accurate description of the atmosphere than the observations or forecast alone can provide. Data assimilation plays an increasingly important role in the study of climate and atmospheric chemistry. The NASA Data Assimilation Office (DAO) has developed the Goddard Earth Observing System Data Assimilation System (GEOS DAS) to create assimilated datasets. The core computational components of the GEOS DAS include the GEOS General Circulation Model (GCM) and the Physical-space Statistical Analysis System (PSAS). The need for timely validation of scientific enhancements to the data assimilation system poses computational demands that are best met by distributed parallel software. PSAS is implemented in Fortran 90 using object-based design principles. The analysis portions of the code solve two equations. The first of these is the "innovation" equation, which is solved on the unstructured observation grid using a preconditioned conjugate gradient (CG) method. The "analysis" equation is a transformation from the observation grid back to a structured grid, and is solved by a direct matrix-vector multiplication. Use of a factored-operator formulation reduces the computational complexity of both the CG solver and the matrix-vector multiplication, rendering the matrix-vector multiplications as a successive product of operators on a vector. Sparsity is introduced to these operators by partitioning the observations using an icosahedral decomposition scheme. PSAS builds a large (approx. 128MB) run-time database of parameters used in the calculation of these operators. Implementing a message passing parallel computing paradigm into an existing yet developing computational system as complex as PSAS is nontrivial. One of the technical challenges is balancing the requirements for computational reproducibility with the need for high performance. The problem of computational reproducibility is well known in the parallel computing community. It is a requirement that the parallel code perform calculations in a fashion that will yield identical results on different configurations of processing elements on the same platform. In some cases this problem can be solved by sacrificing performance. Meeting this requirement and still achieving high performance is very difficult. Topics to be discussed include: current PSAS design and parallelization strategy; reproducibility issues; load balance vs. database memory demands, possible solutions to these problems.

Larson, J. W.↗

Reliable and Efficient Machine Learning (Final Technical Report)

Modern scientific experiments generate massive amounts of data at a pace much faster than humans can manually analyze. While machine learning has revolutionized commercial data analysis (such as recommending movies or recognizing faces), applying these tools to complex scientific discovery is challenging because scientific answers must be precise, interpretable, and adhere to physical laws. The research under this project aims to develop new mathematical tools and computer algorithms specifically designed for scientific applications. Major progress has been made in automatically cleaning and deconstructing messy experimental data, analyzing the visual information of physical phenomena, determining the underlying physical variables, and providing rig orous mathematical analysis of interesting algorithms and concepts widely used in machine learning. This project addressed the critical gap between our ability to generate massive scientific data and our ability to extract interpretable information from it. We established mathematical foundations for Scientific Machine Learning (SciML) aimed at effective data analytics and automated discovery. Our work focused on three core objectives: (1) developing reliable feature extraction methods for dynamic high-dimensional data, (2) establishing mathematical foundations for discovering dynamics via neural networks, and (3) creating rigorous optimization techniques for these models. Key outcomes come from two fronts. On the practical side, they include the development of algorithms that significantly enhance the extraction of signals from field data, as well as the capability to handle situations that exhibit smooth variations or physical stretching due to temperature changes. They also include the creation of an automated framework for discovering fundamental state variables from raw experimental data, demonstrating the ability to identify intrinsic physical dimensions without prior knowledge of the governing laws. On the theoretical front, the research results in theoretical advances in Optimal Transport, a widely used notion in SciML, specifically regarding functions with fixed-size nodal sets, provide sharp bounds relevant to uncertainty quantification. Meanwhile, the outcomes also include the establishment of convergence theories for nonlocal gradient descent methods, enabling robust optimization with noisy data in high-dimensional settings commonly encountered in scientific modeling. The project also helps creating opportunities to train the next generation of researchers, equipping them with the necessary technical skills for today’s workplace and preparing them for future advances.

97 MATHEMATICS AND COMPUTING↗

Applications of Space-Filling-Curves to Cartesian Methods for CFD

The proposed paper presents a variety novel uses of Space-Filling-Curves (SFCs) for Cartesian mesh methods in 0. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, most are applicable on general body-fitted meshes -both structured and unstructured. We demonstrate the use of single O(N log N) SFC-based reordering to produce single-pass (O(N)) algorithms for mesh partitioning, multigrid coarsening, and inter-mesh interpolation. The intermesh interpolation operator has many practical applications including warm starts on modified geometry, or as an inter-grid transfer operator on remeshed regions in moving-body simulations. Exploiting the compact construction of these operators, we further show that these algorithms are highly amenable to parallelization. Examples using the SFC-based mesh partitioner show nearly linear speedup to 512 CPUs even when using multigrid as a smoother. Partition statistics are presented showing that the SFC partitions are, on-average, within 10% of ideal even with only around 50,000 cells in each subdomain. The inter-mesh interpolation operator also has linear asymptotic complexity and can be used to map a solution with N unknowns to another mesh with M unknowns with O(max(M,N)) operations. This capability is demonstrated both on moving-body simulations and in mapping solutions to perturbed meshes for finite-difference-based gradient design methods.

Aftosmis, Michael J.↗

Applications of Space-Filling-Curves to Cartesian Methods for CFD

This paper presents a variety of novel uses of space-filling-curves (SFCs) for Cartesian mesh methods in CFD. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, many are applicable on general body-fitted meshes-both structured and unstructured. We demonstrate the use of single theta(N log N) SFC-based reordering to produce single-pass (theta(N)) algorithms for mesh partitioning, multigrid coarsening, and inter-mesh interpolation. The intermesh interpolation operator has many practical applications including warm starts on modified geometry, or as an inter-grid transfer operator on remeshed regions in moving-body simulations Exploiting the compact construction of these operators, we further show that these algorithms are highly amenable to parallelization. Examples using the SFC-based mesh partitioner show nearly linear speedup to 640 CPUs even when using multigrid as a smoother. Partition statistics are presented showing that the SFC partitions are, on-average, within 15% of ideal even with only around 50,000 cells in each sub-domain. The inter-mesh interpolation operator also has linear asymptotic complexity and can be used to map a solution with N unknowns to another mesh with M unknowns with theta(M + N) operations. This capability is demonstrated both on moving-body simulations and in mapping solutions to perturbed meshes for control surface deflection or finite-difference-based gradient design methods.

Aftosmis, M. J.↗

An extended variational method for the resistive wall mode in toroidal plasma confinement devices

The external-kink stability of a toroidal plasma surrounded by a rigid resistive wall is investigated. The well-known analysis of Haney and Freidberg is rigorously extended to allow for a wall that is sufficiently thick that the thin-shell approximation does not necessarily hold. A generalized Haney–Freidberg formula for the growth-rate of the resistive wall mode is obtained. Thick-wall effects do not change the marginal stability point of the mode but introduce an interesting asymmetry between growing and decaying modes. Growing modes have growth-rates that exceed those predicted by the original Haney–Freidberg formula. On the other hand, decaying modes have decay-rates that are less than those predicted by the original formula. The well-known Hu–Betti formula for the rotational stabilization of the resistive wall mode is also generalized to take thick-wall effects into account. Increasing wall thickness facilitates the rotational stabilization of the mode, because it decreases the critical toroidal electromagnetic torque that the wall must exert on the plasma. On the other hand, the real frequency of the mode at the marginal stability point increases with increasing wall thickness.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Tailoring the Electronic Structures and Spectral Properties of ZnO with Irradiation Defects Generated Under Intense Electronic Excitation: A Combined Experimental and DFT Approach

Here, the relationship between the composition of the internal defect states, spectral properties, and correlated electronic structures of wurtzite zinc oxide (ZnO) crystals under 645 MeV Xe 35+ irradiation is systematically investigated, employing experimental characterizations combined with first-principle calculations. Based on the ion irradiation-induced thermal expansion and relaxation processes, the high concentration of vacancy/interstitial defects produced from the transient disordered phase in molten track states trigger photoelectric changes, as follows: i) the generation of internal defect states effectively reduces the intrinsic bandgap (3.25 eV → 2.66 eV); ii) a large number of defective active sites inhibits the recombination between electron–hole pairs, causing dark conductance and photoconductance to increase with increasing damage levels until optimal fluence is achieved. Based on the density functional theory (DFT) with the GGA + U (GGA = generalized gradient approximation) method, the defective models associated with the different electronic structures, density of states, formation energy, and the nature of the chemical bonding are established. The narrowing of the bandgap observed experimentally and the enhancement of carrier concentration originating from the internal electron defect states are qualitatively verified, therefore laying the foundation for designing future nanoscale photoelectronic devices and microelectronics applications.

36 MATERIALS SCIENCE↗

Mechanisms of Complete Dissociation of CO 2 on Iron Clusters

Dissociation of CO 2 on iron clusters was studied by using semilocal density functional theory and basis sets of triple-zeta quality. Fe 2 , Fe 4 , and Fe 16 clusters were selected as the representative host clusters. When searching for isomers of Fe n CO 2 , n=2, 4 and 16 corresponding to carbon dioxide attachment to the host clusters, its reduction to O and CO, and to the complete dissociation, it was found that the total spin magnetic moments of the lowest energy states of the isomers are often quenched with respect to those of initial reagents Fe n +CO 2 . Dissociation pathways of the Fe 2 +CO 2 , Fe 4 +CO 2 , and Fe 16 +CO 2 reactions contain several transition states separated by the local minima states; therefore, a natural question is where do the spin flips occur? Since lifetimes of magnetically excited states were shown to be of the order of 100 fs, the search for the CO 2 dissociation pathways was performed under the assumption that magnetic deexcitation may occur at the intermediate local minima. Two dissociation pathways were obtained for each Fe n +CO 2 reaction using the gradient-based methods. It was found that the Fe 2 +CO 2 reaction is endothermic with respect to both reduction and complete dissociation of CO 2 , whereas the Fe 4 +CO 2 and Fe 16 +CO 2 reactions are exothermic to both reduction and complete dissociation of carbon dioxide. Finally, the CO 2 reduction was found to be more favorable than its complete dissociation in the Fe 4 case.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Response tailoring of elasto-plastic trusses

Abstract In this work we tailor the response of trusses loaded beyond their yield limit. The truss structures are modeled using finite strain theory and rate-independent elasto-plasticity. We design trusses with a tailored mechanical response that is between “elastic” and “elastic-ideal-plastic” subject to the volume constraint. The design updates are generated by the gradient-based Method of Moving Asymptotes (MMA) solver and the sensitivities of the response functions are computed using a path-dependent adjoint sensitivity analysis. The computations are performed in Matlab.

42 ENGINEERING↗

On the Sampling-Based Computation of Nash Equilibria Under Uncertainty via the Nikaido–Isoda Function

We consider the computation of an equilibrium of a stochastic Nash equilibrium problem, where the player objectives are assumed to be L 0 -Lipschitz continuous and convex, given rival decisions with convex and closed player-specific feasibility sets. To address this problem, we consider minimizing a suitably defined value function defined using the Nikaido–Isoda function. Such an avenue does not necessitate either monotonicity properties of the concatenated gradient map or potentiality requirements on the game but does require a suitable regularity requirement under which a stationary point is a Nash equilibrium. We design and analyze a sampling-enabled projected-gradient-response method, reliant on inexact resolution of a player-level best-response subproblem. Here, by deriving suitable Lipschitzian guarantees on the value function, we derive both asymptotic guarantees for the sequence of generated iterates as well as rate and complexity guarantees for computing a stationary point by appropriate choices of the sampling rate and inexactness sequence.

Nikaido-Isoda function↗

Learning generative neural networks with physics knowledge

Deep generative neural networks have enabled modeling complex distributions, but incorporating physics knowledge into the neural networks is still challenging and is at the core of current physics-based machine learning research. To this end, we propose a physics generative neural network (PhysGNN), a new class of generative neural networks for learning unknown distributions in a physical system described by partial differential equations (PDE). PhysGNN couples PDE systems with generative neural networks. It is a fully differentiable model that allows back-propagation of gradients through both numerical PDE solvers and generative neural networks, and is trained by minimizing the discrete Wasserstein distance between generated and observed probability distributions of the PDE outputs using the stochastic gradient descent method. Moreover, PhysGNN does not require adversarial training like standard generative neural networks, which offers better stability than adversarial training. We show that PhysGNN can learn complex distributions in stochastic inverse problems, where conventional methods such as maximum likelihood estimation and momentum matching methods may be inapplicable when little knowledge is known about the form of unknown distributions or the physical model is too complex. Furthermore, our method allows physics-based generative neural network training for learning complex distributions in the context of differential equations.

97 MATHEMATICS AND COMPUTING↗

Bayesian inference of heterogeneous epidemic models: Application to COVID-19 spread accounting for long-term care facilities

Here we propose a high dimensional Bayesian inference framework for learning heterogeneous dynamics of a COVID-19 model, with a specific application to the dynamics and severity of COVID-19 inside and outside long-term care (LTC) facilities. We develop a heterogeneous compartmental model that accounts for the heterogeneity of the time-varying spread and severity of COVID-19 inside and outside LTC facilities, which is characterized by time-dependent stochastic processes and time-independent parameters in ~ 1500 dimensions after discretization. To infer these parameters, we use reported data on the number of confirmed, hospitalized, and deceased cases with suitable post-processing in both a deterministic inversion approach with appropriate regularization as a first step, followed by Bayesian inversion with proper prior distributions. To address the curse of dimensionality and the ill-posedness of the high-dimensional inference problem, we propose use of a dimension-independent projected Stein variational gradient descent method, and demonstrate the intrinsic low-dimensionality of the inverse problem. We present inference results with quantified uncertainties for both New Jersey and Texas, which experienced different epidemic phases and patterns. Moreover, we also present forecasting and validation results based on the empirical posterior samples of our inference for the future trajectory of COVID-19.

42 ENGINEERING↗