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At least 1,747 records · Page 97
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Adaptive mesh refinement in stress-constrained topology optimization

We present a topology structural optimization framework with adaptive mesh refinement and stress-constraints. Finite element approximation and geometry representation benefit from such refinement by enabling more accurate stress field predictions and greater resolution of the optimal structural boundaries. We combine a volume fraction filter to impose a minimum design feature size, the RAMP penalization to generate “black-and-white designs” and a RAMP-like stress definition to resolve the “stress singularity problem.” Regions with stress concentrations dominate the optimized design. As such, rigorous simulations are required to accurately approximate the stress field. To achieve this goal, we invoke a threshold operation and mesh refinement during the optimization. We do so in an optimal fashion, by applying adaptive mesh refinement techniques that use error indicators to refine and coarsen the mesh as needed. In this way, we obtain more accurate simulations and greater resolution of the design domain. We present results in two dimensions to demonstrate the efficiency of our method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

A computational investigation of the finite-time blow-up of the 3D incompressible Euler equations based on the Voigt regularization

We report the results of a computational investigation of two blow-up criteria for the 3D incompressible Euler equations. One criterion was proven in a previous work, and a related criterion is proved here. These criteria are based on an inviscid regularization of the Euler equations known as the 3D Euler-Voigt equations, which are known to be globally well-posed. Moreover, simulations of the 3D Euler-Voigt equations also require less resolution than simulations of the 3D Euler equations for xed values of the regularization parameter α > 0. Therefore, the new blow-up criteria allow one to gain information about possible singularity formation in the 3D Euler equations indirectly; namely, by simulating the better-behaved 3D Euler-Voigt equations. The new criteria are only known to be suficient for blow-up. Therefore, to test the robustness of the inviscid-regularization approach, we also investigate analogous criteria for blow-up of the 1D Burgers equation, where blow-up is well-known to occur.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Interior energy error estimates for the weak Galerkin finite element method

Consider the Poisson equation in a polytopal domain ΩRC d (d=2,3) as the model problem. In this paper, we study interior energy error estimates for the weak Galerkin finite element approximation to elliptic boundary value problems. In particular, we show that the interior error in the energy norm is bounded by three components: the best local approximation error, the error in negative norms, and the trace error on the element boundaries. This implies that the interior convergence rate can be polluted by solution singularities on the domain boundary, even when the solution is smooth in the interior region. Numerical results are reported to support the theoretical findings. Lastly, to the best of our knowledge, this is the first local energy error analysis that applies to general meshes consisting of polytopal elements and hanging nodes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Conservative numerical schemes with optimal dispersive wave relations: Part I. Derivation and analysis

An energy-conserving and an energy-and-enstrophy conserving numerical schemes are derived by approximating the Hamiltonian formulation of the inviscid shallow water flows based on the vorticity-divergence variables. These schemes also conserve the first-order moments such as mass and vorticity, as usual. The conservative properties of the schemes stem from the skew-symmetry and singularities of the Poisson brackets, which are carefully retained in the discrete approximations. Here, the schemes operate on unstructured orthogonal dual meshes, over bounded or unbounded domains, and they are also shown to possess the same optimal dispersive wave relations as those of the Z-grid scheme, which is a consequence of the use of the vorticity and divergence variables.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

Umbral moonshine and K3 surfaces

Recently, 23 cases of umbral moonshine, relating mock modular forms and finite groups, have been discovered in the context of the 23 even unimodular Niemeier lattices. One of the 23 cases in fact coincides with the so-called Mathieu moonshine, discovered in the context of K3 non-linear sigma models. In this paper we establish a uniform relation between all 23 cases of umbral moonshine and K3 sigma models, and thereby take a first step in placing umbral moonshine into a geometric and physical context. In addition, this is achieved by relating the ADE root systems of the Niemeier lattices to the ADE du Val singularities that a K3 surface can develop, and the configuration of smooth rational curves in their resolutions. A geometric interpretation of our results is given in terms of the marking of K3 surfaces by Niemeier lattices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

On the Trotter Error in Many-body Quantum Dynamics with Coulomb Potentials

Efficient simulation of many-body quantum systems is central to advances in physics, chemistry, and quantum computing, with a key question being whether the simulation cost scales polynomially with the system size. Here, in this work, we analyze many-body quantum systems with Coulomb interactions, which are fundamental to electronic and molecular systems. We prove that Trotterization for such unbounded Hamiltonians achieves a 1/4-order convergence rate, with explicit polynomial dependence on the number of particles. The result holds for all initial wavefunctions in the domain of the Hamiltonian, and the 1/4-order convergence rate is optimal, as previous work has numerically demonstrated that it can be saturated by a specific initial ground state. The main challenges arise from the many-body structure and the singular nature of the Coulomb potential. Our proof strategy differs from prior state-of-the-art Trotter analyses, addressing both difficulties in a unified framework. Our analysis treats the Coulomb potential as an unbounded operator without modification or regularization, and does not rely on spatial discretization, making it compatible with both first- and second-quantized circuit constructions.

Fang, Di [Duke Univ., Durham, NC (United States)]↗
DOE OSTI2017

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solution of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

The Management of Cephalic Arch Stenosis in Arteriovenous Fistulas for Hemodialysis: A Systematic Review

AimTo conduct a systematic review of management of current cephalic arch stenosis (CAS) and associated outcomes in the context of dysfunctional hemodialysis access.Materials and MethodsPubMed, Web of Science, and Cochrane Library were searched to retrieve literature on the management of CAS. Studies had to focus on management of access stenosis solely in the cephalic arch. Case reports and literature reviews were excluded. Studies were categorized by intervention, and primary and secondary patency data were compiled. Studies were aggregated, and meta-analyses were performed where possible.ResultsNine papers satisfied the aforementioned criteria: five were retrospective studies and four were prospective studies. CAS management strategies have included percutaneous transluminal balloon angioplasty (PTA), peripheral cutting balloons, surgical cephalic vein transpositions, bare stents, and stent grafts. Reporting strategies varied between studies. Meta-analyses showed that results were variable even within studies using the same modality, particularly for PTA.ConclusionNo singular, definitive management strategy exists for CAS. Current studies are limited by being primarily single-center retrospective trials featuring heterogenous patient populations, interventions, and endpoints. Priorities for future studies should include larger randomized trials, more uniform management strategies and endpoints, and a longer duration of follow-up.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2015

The fragile-to-strong dynamical crossover and the system viscoelasticity in attractive glass forming colloids

The dynamical arrest phenomena of an adhesive hard-sphere (AHS) colloid, L64-D 2O system has been investigated by using calorimetry and the complex shear modulus. This system is characterized by a rich temperature (T) and volume fraction ($\phi$) phase diagram with a percolation line (PT). According to the mode-coupling theory (MCT), a cusp-like singularity and two glassy phases, one attractive (AG) and one repulsive (RG), are supposed to coexist in the phase diagram. The MCT scaling laws used to study the shear viscosity with $\phi$ and T as control parameters propose the existence of fragile-to-strong dynamic crossover (FSDC) analogous to that observed in molecular supercooled liquid glass formers. The measured critical values of the control parameters, coincident with the PT line, where the clustering process generates the AG phase, define the FSDC locus. This is in agreement with the extended mode-coupling theory that takes into account both cage and inter-cluster hopping effects. Here, we demonstrate, by considering the frequency dependence of the complex moduli, that there is the onset of a system viscoelasticity as an effect of the clustering accompanying the FSDC. We will reveal as the measured frequency-dependent complex moduli satisfy the scaling relations predicted by the scalar elasticity percolation theory and well account for the system evolution toward the glass transition process.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Mallat Scattering Transformation based surrogate for Magnetohydrodynamics

Abstract A Machine and Deep Learning (MLDL) methodology is developed and applied to give a high fidelity, fast surrogate for 2D resistive MagnetoHydroDynamic (MHD) simulations of Magnetic Liner Inertial Fusion (MagLIF) implosions. The resistive MHD code is used to generate an ensemble of implosions with different liner aspect ratios, initial gas preheat temperatures (that is, different adiabats), and different liner perturbations. The liner density and magnetic field as functions of x , y , and z were generated. The Mallat Scattering Transformation (MST) is taken of the logarithm of both fields and a Principal Components Analysis (PCA) is done on the logarithm of the MST of both fields. The fields are projected onto the PCA vectors and a small number of these PCA vector components are kept. Singular Value Decompositions of the cross correlation of the input parameters to the output logarithm of the MST of the fields, and of the cross correlation of the SVD vector components to the PCA vector components are done. This allows the identification of the PCA vectors vis-a-vis the input parameters. Finally, a Multi Layer Perceptron (MLP) neural network with ReLU activation and a simple three layer encoder/decoder architecture is trained on this dataset to predict the PCA vector components of the fields as a function of time. Details of the implosion, stagnation, and the disassembly are well captured. Examination of the PCA vectors and a permutation importance analysis of the MLP show definitive evidence of an inverse turbulent cascade into a dipole emergent behavior. The orientation of the dipole is set by the initial liner perturbation. The analysis is repeated with a version of the MST which includes phase, called Wavelet Phase Harmonics (WPH). While WPH do not give the physical insight of the MST, they can and are inverted to give field configurations as a function of time, including field-to-field correlations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Three-dimensional nonlocal anisotropic elasticity: a generalized continuum theory of Ångström-mechanics

In this paper, based on Eringen’s theory of nonlocal anisotropic elasticity, the three-dimensional nonlocal anisotropic elasticity of generalized Helmholtz type is developed. The derivation of a new three-dimensional nonlocal anisotropic kernel, which is the Green function of the three-dimensional anisotropic Helmholtz equation, enables to capture anisotropic length scale effects by means of a length scale tensor, which is a symmetric tensor of rank two. The derived nonlocal kernel function possesses up to six internal characteristic lengths on the Ångström-scale. The presented theory of nonlocal elasticity possesses the appropriate property to be a generalized continuum theory of Ångström-mechanics, since the range of its validity and applicability is up to the Ångström-scale. The connection between the theory of nonlocal anisotropic elasticity and lattice theory is established. The tensor function of nonlocal elastic moduli as well as the nonlocal kernel function is given in terms of the Hessian matrix in the lattice approach. In the framework of the considered theory, the modeling of dislocations in anisotropic materials taking into consideration anisotropic dislocation core effects is presented. Important dislocation key formulas, namely the anisotropic Peach–Koehler stress formula, the Peach–Koehler force and the anisotropic Blin’s formula, are derived. A major tool used in deriving the expression of anisotropic Blin’s formula is Kirchner’s so-called FF-tensor, which is here generalized toward nonlocal anisotropic elasticity. The main feature and advantage of the derived fields, compared with the corresponding ones in classical anisotropic elasticity, is that they are free of singularities. Numerical applications to straight dislocations in bcc Fe are given, revealing the ability and advantage of the considered theory to describe adequately nonsingular anisotropic stress and self-energy fields capturing the effects of anisotropy on the Ångström-scale.

42 ENGINEERING↗
DOE OSTI2022

Numerical algorithms for water waves with background flow over obstacles and topography

Abstract We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a periodic, multiply connected fluid domain that includes stationary obstacles and variable bottom topography. One approach is formulated in terms of the surface velocity potential while the other evolves the vortex sheet strength. Both methods employ layer potentials in the form of periodized Cauchy integrals to compute the normal velocity of the free surface, are compatible with arbitrary parameterizations of the free surface and boundaries, and allow for circulation around each obstacle, which leads to multiple-valued velocity potentials but single-valued stream functions. We prove that the resulting second-kind Fredholm integral equations are invertible, possibly after a physically motivated finite-rank correction. In an angle-arclength setting, we show how to avoid curve reconstruction errors that are incompatible with spatial periodicity. We use the proposed methods to study gravity-capillary waves generated by flow around several elliptical obstacles above a flat or variable bottom boundary. In each case, the free surface eventually self-intersects in a splash singularity or collides with a boundary. We also show how to evaluate the velocity and pressure with spectral accuracy throughout the fluid, including near the free surface and solid boundaries. To assess the accuracy of the time evolution, we monitor energy conservation and the decay of Fourier modes and compare the numerical results of the two methods to each other. We implement several solvers for the discretized linear systems and compare their performance. The fastest approach employs a graphics processing unit (GPU) to construct the matrices and carry out iterations of the generalized minimal residual method (GMRES).

Ambrose, David M.↗
DOE OSTI2018

Risk-Informed Analysis of Accidents at Reactor Facilities with VVER

An accident with ‘rupture of steam line’ as the initial event was studied for a reactor facility with VVER-1000. A computational analysis was performed of different flow scenarios of an accident with singular and multiple failures of the safety systems. The realization probability and the consequences were evaluated for each accident sequence. The consequences of the accidents are ranked and the most instructive combinations of failures of systems and blockings are determined from the standpoint of risk. The presented method is based on multivariate calculations and an integrated combination of deterministic and probabilistic approaches to safety validation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2016

Tensile cracking of a brittle conformal coating on a rough substrate

This note examines the effect of interfacial roughness on the initiation and growth of channel cracks in a brittle film. A conformal film with cusp-like surface flaws that replicate the substrate roughness is investigated. This type of surface flaw is relatively severe in the sense that stress diverges as the cusp-tip is approached (i.e., there is a power-law stress singularity). For the geometry and range of film properties considered, the analysis suggests that smoothing the substrate could substantially increase the film’s resistance to the formation of the through-the-thickness cracks that precede channel cracking. Furthermore, smoothing the substrate’s surface has a relatively modest effect on the film stress needed to propagate a channel crack.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Toward memory-efficient melt pool monitoring: a classification framework using event-based imaging and sparse sensing technique

Vision sensors like CMOS and CCD cameras are often used for in-process monitoring of melt pools in laser-based additive and welding processes, but they require transferring large amounts of data and computational processing resources. Event-based neuromorphic imagery, on the other hand, detects only the change in pixel intensity, thus potentially reducing the data amount and latency. With an event imager, this study develops a framework for melt pool condition classification, including image construction, time scale selection, optimal pixel selection, and sparse classification, to achieve a highly memory-efficient scheme. These are based on sparse sensing techniques with singular value decomposition (SVD) and QR pivoting, the two fundamental matrix transformations for linear dimensionality reduction. The framework is then validated by classifying a controlled experiment by exciting various mode shapes of liquid gallium pools of varying depths (3, 6, and 8 mm). At 200 pixels, the classifier can reach overall accuracy of 75%, while at 2000 pixels (0.013% of the total possible pixels), the accuracy is nearly 90% (89.86%). At the same number of pixels, random selection can only achieve 46% and 67%, respectively. The memory savings of the sparsely sampled event data compared to a conventional imager is about 500 times. In addition to performance, implementation and limitations of the framework are also discussed.

42 ENGINEERING↗
DOE OSTI2022

CUPID: The Next-Generation Neutrinoless Double Beta Decay Experiment

We report CUPID is a next-generation tonne-scale bolometric neutrinoless double beta decay experiment that will probe the Majorana nature of neutrinos and discover lepton number violation in case of observation of this singular process. CUPID will be built on experience, expertise and lessons learned in CUORE and will be installed in the current CUORE infra-structure in the Gran Sasso underground laboratory. The CUPID detector technology, successfully tested in the CUPID-Mo experiment, is based on scintillating bolometers of Li 2 MoO 4 enriched in the isotope of interest 100 Mo. In order to achieve its ambitious science goals, the CUPID collaboration aims to reduce the backgrounds in the region of interest by a factor 100 with respect to CUORE. This performance will be achieved by introducing the high efficient α/β discrimination demonstrated by the CUPID-0 and CUPID-Mo experiments, and using a high transition energy double beta decay nucleus such as 100 Mo to minimize the impact of the gamma background. CUPID will consist of about 1500 hybrid heat-light detectors for a total isotope mass of 250 kg. The CUPID scientific reach is supported by a detailed and safe background model based on CUORE, CUPID-Mo and CUPID-0 results. The required performances have already been demonstrated and will be presented.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

A Local Macroscopic Conservative (LoMaC) Low Rank Tensor Method for the Vlasov Dynamics

Abstract In this paper, we propose a novel Local Macroscopic Conservative (LoMaC) low rank tensor method for simulating the Vlasov-Poisson (VP) system. The LoMaC property refers to the exact local conservation of macroscopic mass, momentum and energy at the discrete level. This is a follow-up work of our previous development of a conservative low rank tensor approach for Vlasov dynamics ( arXiv:2201.10397 ). In that work, we applied a low rank tensor method with a conservative singular value decomposition to the high dimensional VP system to mitigate the curse of dimensionality, while maintaining the local conservation of mass and momentum. However, energy conservation is not guaranteed, which is a critical property to avoid unphysical plasma self-heating or cooling. The new ingredient in the LoMaC low rank tensor algorithm is that we simultaneously evolve the macroscopic conservation laws of mass, momentum and energy using a flux-difference form with kinetic flux vector splitting; then the LoMaC property is realized by projecting the low rank kinetic solution onto a subspace that shares the same macroscopic observables by a conservative orthogonal projection. The algorithm is extended to the high dimensional problems by hierarchical Tuck decomposition of solution tensors and a corresponding conservative projection algorithm. Extensive numerical tests on the VP system are showcased for the algorithm’s efficacy.

Guo, Wei↗