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Results for “Convex geometry”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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36 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Reliability-based hull geometry optimisation of a point-absorber wave energy converter with power take-off structural reliability objectives

Recent studies have focused on optimising wave energy converter (WEC) designs, maximising their power performance and techno-economic feasibility. Reliability has yet to be fully considered in these formulations, despite its impact on cost and performance. In this study, this gap is addressed by developing a reliability-based design optimisation framework for WEC hull geometries to explore the trade-off between power performance and power take-off (PTO) system damage equivalent loading (DEL). Optimised hull geometries for two sites are considered (from the centre of the North Sea and off the west coast of Norway), and two directions of motions (heave and surge). Results indicate that site characteristics affect the potential power production and DEL for an optimal WEC design. These are also affected by the direction of motion for power extraction, which also significantly changes optimal hull shape characteristics. Optimal surging WEC designs have edges facing oncoming wave directions, while heaving WECs have pointed bottoms, both to streamline movement. Larger, more convex WECs result in greater power production and DEL, while smaller, more concave WECs result in lesser power production and DEL. These findings underline the importance of considering WEC hull geometry in early design processes to optimise cost, power production, and reliability.

16 TIDAL AND WAVE POWER↗
DOE OSTI2024

A streamline coordinate analysis of a turbulent boundary layer subject to pressure gradients and curvature on the windward side of a bump

Direct numerical simulation (DNS) of a turbulent boundary layer over the Gaussian (Boeing) bump is performed. This boundary layer exhibits a series of adverse and favourable pressure gradients and convex and concave curvature effects before separating. These effects on turbulent boundary layers are characterised and compared with a lower-Reynolds-number flow over the same geometry. The momentum budgets are analysed in the streamline-aligned coordinate system upstream of the separation region. These momentum budgets allow the simplification of equations to facilitate an integral analysis. Integral-analysis-based approximations for Reynolds stresses in the inner and outer regions of the boundary layer are also formulated. The shear and wall-normal Reynolds stress profiles normalised by these approximations exhibit a better collapse compared with friction velocity and Zagarola–Smits normalisations in the strong favourable pressure gradient region and in the mild adverse pressure region that precedes it in this flow. Simplification of these Reynolds stress approximations along with results from the DNS are used to obtain semi-empirical approximations that are able to provide stress closure in terms of wall solution fields for the turbulent boundary layer under consideration.

42 ENGINEERING↗
DOE OSTI2020

The second-generation Shifted Boundary Method and its numerical analysis

Recently, the Shifted Boundary Method (SBM) was proposed within the class of unfitted (or immersed, or embedded) finite element methods. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we present enhanced variational SBM formulations for the Poisson and Stokes problems with improved flexibility and robustness. These simplified variational forms allow to relax some of the assumptions required by the mathematical proofs of stability and convergence of earlier implementations. First, we show that these new SBM implementations can be proved asymptotically stable and convergent even without the rather restrictive assumption that the inner product between the normals to the true and surrogate boundaries is positive. Second, we show that it is not necessary to introduce a stabilization term involving the tangential derivatives of the solution at Dirichlet boundaries, therefore avoiding the calibration of an additional stabilization parameter. Finally, we prove enhanced L 2 -estimates without the cumbersome assumption – of earlier proofs – that the surrogate domain is convex. Instead we rely on a conventional assumption that the boundary of the true domain is smooth, which can also be replaced by requiring convexity of the true domain. The aforementioned improvements open the way to a more general and efficient implementation of the Shifted Boundary Method, particularly in complex three-dimensional geometries. We complement these theoretical developments with numerical experiments in two and three dimensions.

42 ENGINEERING↗
DOE OSTI2022

Sub-keV design for the National Ignition Facility’s soft x-ray Opacity Spectrometer (OpSpec) and expansion plans for time-resolved measurements

When compared with the National Ignition Facility’s (NIF) original soft x-ray opacity spectrometer, which used a convex cylindrical design, an elliptically shaped design has helped to increase the signal-to-noise ratio and eliminated nearly all reflections from alternate crystal planes. The success of the elliptical geometry in the opacity experiments has driven a new elliptical geometry crystal with a spectral range covering 520–1100 eV. When coupled with the primary elliptical geometry, which spans 1000–2100 eV, the new sub-keV elliptical geometry helps to cover the full iron L-shell and major oxygen transitions important to solar opacity experimentation. The new design has been built and tested by using a Henke x-ray source and shows the desired spectral coverage. Additional plans are underway to expand these opacity measurements into a mode of time-resolved detection, ~1 ns gated, but considerations for the detector size and photometrics mean a crystal geometry redesign. Here, the new low-energy geometry, including preliminary results from the NIF opacity experiments, is presented along with the expansion plans into a time-resolved platform.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Area-Preserving Mapping of 3D Carotid Ultrasound Images Using Density-Equalizing Reference Map

Carotid atherosclerosis is a focal disease at the bifurcations of the carotid artery. To quantitatively monitor the local changes in the vessel-wall-plus-plaque thickness (VWT) and compare the VWT distributions for different patients or for the same patients at different ultrasound scanning sessions, a mapping technique is required to adjust for the geometric variability of different carotid artery models. In this work, we propose a novel method called density-equalizing reference map (DERM) for mapping 3D carotid surfaces to a standardized 2D carotid template, with an emphasis on preserving the local geometry of the carotid surface by minimizing the local area distortion. The initial map was generated by a previously described arc-length scaling (ALS) mapping method, which projects a 3D carotid surface onto a 2D non-convex L-shaped domain. A smooth and area-preserving flattened map was subsequently constructed by deforming the ALS map using the proposed algorithm that combines the density-equalizing map and the reference map techniques. This combination allows, for the first time, one-to-one mapping from a 3D surface to a standardized non-convex planar domain in an area-preserving manner. Evaluations using 20 carotid surface models show that the proposed method reduced the area distortion of the flattening maps by over 80% as compared to the ALS mapping method.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Size-Resolved Shape Evolution in Inorganic Nanocrystals Captured via High-Throughput Deep Learning-Driven Statistical Characterization

Precise size and shape control in nanocrystal synthesis is essential for utilizing nanocrystals in various industrial applications, such as catalysis, sensing, and energy conversion. However, traditional ensemble measurements often overlook the subtle size and shape distributions of individual nanocrystals, hindering the establishment of robust structure–property relationships. In this study, we uncover intricate shape evolutions and growth mechanisms in Co 3 O 4 nanocrystal synthesis at a subnanometer scale, enabled by deep-learning-assisted statistical characterization. By first controlling synthetic parameters such as cobalt precursor concentration and water amount then using high resolution electron microscopy imaging to identify the geometric features of individual nanocrystals, this study provides insights into the interplay between synthesis conditions and the sizedependent shape evolution in colloidal nanocrystals. Utilizing population-wide imaging data encompassing over 441,067 nanocrystals, we analyze their characteristics and elucidate previously unobserved size-resolved shape evolution. This high-throughput statistical analysis is essential for representing the entire population accurately and enables the study of the size dependency of growth regimes in shaping nanocrystals. Our findings provide experimental quantification of the growth regime transition based on the size of the crystals, specifically (i) for faceting and (ii) from thermodynamic to kinetic, as evidenced by transitions from convex to concave polyhedral crystals. Additionally, we introduce the concept of an “onset radius,” which describes the critical size thresholds at which these transitions occur. This discovery has implications beyond achieving nanocrystals with desired morphology; it enables finely tuned correlation between geometry and material properties, advancing the field of colloidal nanocrystal synthesis and its applications.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2026

From Points to Planes: A Workflow for Converting Three‐Dimensional Point Cloud Data Into Discrete Fracture Network Flow and Transport Models

We present the Point cLoud Algorithm for NEtwork Extraction of Discrete Fracture Networks (PLANE-DFN), a point cloud–based algorithm for automatic fracture network extraction designed to support discrete fracture network (DFN) modeling workflows. PLANE-DFN segments three-dimensional fracture planes from raw point cloud data using RANdom SAmple Consensus coupled with statistical outlier removal and density-based clustering to isolate individual fracture features. Each candidate plane is constrained against site-specific structural constraints based on strike and dip. After segmentation, each fracture is converted into a 2-D convex polygon suitable for meshing and simulation. The PLANE-DFN algorithm is validated by comparing geometric and flow and transport data against data from dfnWorks simulations with ensembles of plane-fit networks. We find that the flow and transport in plane-fit networks are comparable to dfnWorks-generated networks when realistic network geometry is maintained. The PLANE-DFN algorithm provides an automated and streamlined workflow to transform point clouds of data into DFN network geometry.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

System having blade segment with curved mounting geometry

A system includes a blade segment having a blade and a mounting segment coupled to the blade. Additionally, the mounting segment includes a first contact face and a second contact face, wherein the first and second contact face are concave with respect to a longitudinal axis of the blade segment. To reduce stresses within the mounting segment, the mounting segment further includes a lower face coupling the first contact face and the second contact face, wherein the lower face is convex across the longitudinal axis of the blade segment.

42 ENGINEERING↗
DOE OSTI2025

Multi-plane moment-of-fluid interface reconstruction in 3D

Moment-of-fluid (MOF) methods for interface reconstruction approximate the region occupied by material in each mesh element only through reference to its geometric moments. Here, we present a 3D MOF method that represents the material (POM) in each cell as the convex intersection of the cell and multiple half-spaces, each selected to minimize the least-squares error between computed moments of the approximated material and provided reference moments. This optimization problem is highly non-linear and non-convex, making the numerical result very sensitive to the initial guess. To create an effective initial guess in each cell, we construct an ellipsoid from 0th–2nd order reference moments such that its shape corresponds with that of the POM. Within this ellipsoid we inscribe a polyhedron, and initialize the minimization problem with the half-spaces defined by each of its faces. The inscribed polyhedron has minimally 4 faces, and using up to 3rd order moments permits optimization over up to 20 unknown values. We therefore define MOF methods that utilize 4, 5, or 6 half-spaces, correspondingly initialized with the faces of a single inscribed tetrahedron, triangular prism, or hexahedron. Stability of the non-linear optimization is further improved with a prepossessing step that normalizes the reference moments according to the axes of the reference ellipsoid. Using this approach, the non-linear least-squares solver reliably converges to a near-global minimum from a single initial guess. We demonstrate accuracy and robustness using single-cell and multi-cell examples over a wide spectrum of geometry. In particular, we demonstrate our ability to exactly reproduce several important and complex features defined by up to four half-spaces, such as corners, filaments, filament tips, and embedded material in the cell.

3D interface reconstruction↗
DOE OSTI2025

Temperature Field Reconstruction of Surfaces Heated Through Radiative Heat Transfer Using Convolutional Neural Networks

Microreactors could play a crucial role in decarbonizing our energy portfolio. However, their development and implementation come with specific challenges, particularly regarding cost. Due to their compact size and the harsh operational environment, collecting real-time data on reactor operation can be challenging. Many probe designs are unable to withstand extreme conditions (e.g., temperature, radiation) in the reactor. In this context, using convolutional neural networks (CNNs) can pave the way for developing a nonintrusive approach that relies solely on ex-core sensors. A well-trained physics-informed CNN can reconstruct the distribution of a given physical quantity over a domain using only a few sensors, allowing us to reconstruct the desired field distribution even in a limited space or complex geometries where a large array of sensors is impractical. In this work, we present the initial steps toward developing a real-time tool for monitoring the thermal behavior of nuclear reactor pressure vessels. Based on an experimental setup, a computational model using the Multiphysics Object-Oriented Simulation Environment (moose) framework was built, where the Ray Tracing and Heat Conduction modules were used to evaluate the temperature distribution over a convex metal surface heated through radiative heat transfer. This metal surface represents a section of a heated nuclear reactor vessel wall. The model also accounts for solid mechanics physics through the moose Solid Mechanics module. In situ experimental data, acquired from a Texas A&M facility, were used to validate the computational model. Part of the data generated by the moose model was used to train the convolutional neural network to reconstruct the vessel wall's outer surface temperature. The CNN generalization was then compared against the experimental and computational data.

Aldeia Machado, Luiz Carlos↗
DOE OSTI2020

Application of Koopman operator for model-based control of fracture propagation and proppant transport in hydraulic fracturing operation

This work explores the application of the recently developed Koopman operator approach for model identification and feedback control of a hydraulic fracturing process. Controlling fracture propagation and proppant transport with precision is a challenge due in large part to the difficulty of constructing approximate models that accurately capture the characteristic moving boundary and highly-coupled dynamics exhibited by the process. Koopman operator theory is particularly attractive here as it offers a way to explicitly construct linear representations for even highly nonlinear dynamics. The method is data-driven and relies on lifting the states to an infinite-dimensional space of functions called observables where the dynamics are governed by a linear Koopman operator. Here this work considers two problems: (a) fracture geometry control, and (b) proppant concentration control. In both cases, an approximate linear model of the corresponding dynamics is constructed and used to design a model predictive controller (MPC). The manuscript shows that in the case of highly nonlinear dynamics, as observed in the proppant concentration, use of canonical functions in the observable basis fails. In such cases, a priori system knowledge can be leveraged to choose the required basis. The numerical experiments demonstrate that the Koopman linear model shows excellent agreement with the real system and successfully achieves the desired target values maximizing the oil and gas productivity. Additionally, due to its linear structure, the Koopman models allow convex MPC formulations that avoid any issues associated with nonlinear optimization.

42 ENGINEERING↗
DOE OSTI2022

Geometric prior of multi-resolution yielding manifolds and the local closest point projection for nearly non-smooth plasticity

Elastoplasticity models often introduce a scalar-valued yield function to implicitly represent the boundary between elastic and plastic material states. Here this paper introduces a new alternative where the yield envelope is represented by a manifold of which the topology and the geometry are learned from a set of data points in a parametric space (e.g. principal stress space, π-plane). Here, deep geometric learning enables us to reconstruct a highly complex yield envelope by breaking it down into multiple coordinate charts. The global atlas that consists of these coordinate charts in return allows us to represent the yield surface via multiple overlapping patches, each with a specific local parametrization. This setup provides several advantages over the classical implicit function representation approach. For instance, the availability of coordinate charts enables us to introduce an alternative stress integration algorithm where the trial stress may project directly on a local patch and hence circumvent the issues related to non-smoothness and the lack of convexity of yield surfaces. Meanwhile, the local parametric approach also enables us to predict hardening/softening locally in the parametric space, even without complete knowledge of the yield surface. Comparisons between the classical yield function approach on the non-smooth plasticity and anisotropic cam-clay plasticity model are provided to demonstrate the capacity of the models for highly precise yield surface and the feasibility of the implementation of the learned model in the local stress integration algorithm.

42 ENGINEERING↗
DOE OSTI2021

A Multi-Objective Bayesian Optimization Approach Using the Weighted Tchebycheff Method

Abstract Bayesian optimization (BO) is a low-cost global optimization tool for expensive black-box objective functions, where we learn from prior evaluated designs, update a posterior surrogate Gaussian process model, and select new designs for future evaluation using an acquisition function. This research focuses upon developing a BO model with multiple black-box objective functions. In the standard multi-objective (MO) optimization problem, the weighted Tchebycheff method is efficiently used to find both convex and non-convex Pareto frontiers. This approach requires knowledge of utopia values before we start optimization. However, in the BO framework, since the functions are expensive to evaluate, it is very expensive to obtain the utopia values as a prior knowledge. Therefore, in this paper, we develop a MO-BO framework where we calibrate with multiple linear regression (MLR) models to estimate the utopia value for each objective as a function of design input variables; the models are updated iteratively with sampled training data from the proposed MO-BO. These iteratively estimated mean utopia values are used to formulate the weighted Tchebycheff MO acquisition function. The proposed approach is implemented in two numerical test examples and one engineering design problem of optimizing thin tube geometries under constant loading of temperature and pressure, with minimizing the risk of creep-fatigue failure and design cost, along with risk-based and manufacturing constraints. Finally, the model accuracy with frequentist, Bayesian and without MLR-based calibration are compared to true Pareto solutions.

Engineering↗
DOE OSTI2021

Scattering amplitudes and simple canonical forms for simple polytopes

We provide an efficient recursive formula to compute the canonical forms of arbitrary d-dimensional simple polytopes, which are convex polytopes such that every vertex lies precisely on d facets. For illustration purposes, we explicitly derive recursive formulae for the canonical forms of Stokes polytopes, which play a similar role for a theory with quartic interaction as the Associahedron does in planar bi-adjoint φ 3 theory. As a by-product, our formula also suggests a new way to obtain the full planar amplitude in φ 4 theory by taking suitable limits of the canonical forms of constituent Stokes polytopes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Covariant bit threads

We derive several new reformulations of the Hubeny-Rangamani-Takayanagi covariant holographic entanglement entropy formula. These include: (1) a minimax formula, which involves finding a maximal-area achronal surface on a timelike hypersurface homologous to D(A) (the boundary causal domain of the region A whose entropy we are calculating) and minimizing over the hypersurface; (2) a max V-flow formula, in which we maximize the flux through D(A) of a divergenceless bulk 1-form V subject to an upper bound on its norm that is non-local in time; and (3) a min U-flow formula, in which we minimize the flux over a bulk Cauchy slice of a divergenceless timelike 1-form U subject to a lower bound on its norm that is non-local in space. The two flow formulas define convex programs and are related to each other by Lagrange duality. For each program, the optimal configurations dynamically find the HRT surface and the entanglement wedges of A and its complement. The V-flow formula is the covariant version of the Freedman-Headrick bit thread reformulation of the Ryu-Takayanagi formula. We also introduce a measure-theoretic concept of a “thread distribution”, and explain how Riemannian flows, V-flows, and U-flows can be expressed in terms of thread distributions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

End-exclusion zones in strongly stretched, molten polymer brushes of arbitrary shape

Theories of strongly stretched polymer brushes, particularly the parabolic brush theory, are valuable for providing analytically tractable predictions for the thermodynamic behavior of surface-grafted polymers in a wide range of settings. Furthermore, the parabolic brush limit fails to describe polymers grafted to convex curved substrates, such as the surfaces of spherical nanoparticles or the interfaces of strongly segregated block copolymers. It has previously been shown that strongly stretched curved brushes require a boundary layer devoid of free chain ends, requiring modifications of the theoretical analysis. While this “end-exclusion zone” has been successfully incorporated into the descriptions of brushes grafted onto the outer surfaces of cylinders and spheres, the behavior of brushes on surfaces of arbitrary curvature has not yet been studied. We present a formulation of the strong-stretching theory for molten brushes on the surfaces of arbitrary curvature and identify four distinct regimes of interest for which brushes are predicted to possess end-exclusion zones, notably including regimes of positive mean curvature but negative Gaussian curvature. Through numerical solutions of the strong-stretching brush equations, we report predicted scaling of the size of the end-exclusion zone, the chain end distribution, the chain polarization, and the free energy of stretching with mean and Gaussian surface curvatures. Through these results, we present a comprehensive picture of how the brush geometry influences the end-exclusion zones and exact strong-stretching free energies, which can be applied, for example, to model the full spectrum of brush geometries encountered in block copolymer melt assembly.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Concavity-based local erosion and sphere-size-based local dilation applied to lithium-ion battery electrode microstructures for particle identification

Performance metrics of lithium-ion batteries can be extracted from the analysis of electrode microstructures nanoscale imaging. The characterization workflow can involve a challenging particle identification, or instance segmentation, step. In this work, we propose a new identification method based on an original transformation: a sphere-size-based local dilation followed by a concavity-based local erosion, that is local morphology closing. The new transformation is much more efficient than the global morphology closing, with correct identification achieved with only 1.7 % dilation volume and 2.6 % erosion volume on a test geometry, compared to 39.2 % and more than 50 %, respectively, with its global counterpart. The new method has been then benchmarked versus other identification algorithms (watershed and pseudo coulomb repulsive field) on a real electrode microstructure with equal or better segmentation achieved.

25 ENERGY STORAGE↗
DOE OSTI2026

Statistics of base polytopes in F-theory

We propose a new statistical ensemble of toric bases for elliptic Calabi-Yaus used in F-theory models, by focusing on only the convex hull of the base, i.e., the base polytope. This physically motivated coarse-graining greatly simplifies the combinatorial complexity of the part of the 4d F-theory landscape with toric bases. We develop a Monte Carlo approach that randomly samples the base polytopes within fixed boxes, with proper statistical weights. We first apply the algorithm to the set of 2d base polytopes, generating an enlarged set of toric 2d bases that include certain types of codimension-two (4,6) points, and we validate our approach against exact numbers. We then explore the set of 3d base polytopes which fit in a set of “maximal” 3d boxes, and estimate the total number of inequivalent 3d base polytopes to be 10 85 –10 90 . We provide statistical data such as the distribution of non-Higgsable gauge groups on these bases. Amusingly, a similar method can also be applied to generate reflexive polytopes in various dimensions. In both the reflexive and base polytope cases, the number of relevant polytopes obeys a Gaussian distribution as a function of the number of vertices, which can be understood in terms of other results on random polytopes in the math literature.

Differential and algebraic geometry↗