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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Strategies for Constructing and Operating DNA Origami Linear Actuators

Abstract Linear actuators are ubiquitous components at all scales of engineering. DNA nanotechnology offers a unique opportunity for bottom‐up assembly at the molecular scale, providing nanoscale precision with multiple methods for constructing and operating devices. In this paper, DNA origami linear actuators with up to 200 nm travel, based on a rail threading a topologically locked slider, are demonstrated. Two strategies, one‐ and two‐pot assembly, are demonstrated whereby the two components are folded from one or two DNA scaffold strands, respectively. In order to control the position of the slider on the rail, the rail and the inside of the slider are decorated with single‐stranded oligonucleotides with distinct sequences. Two positioning strategies, based on diffusion and capture of signaling strands, are used to link the slider reversibly to determined positions on the rail with high yield and precision. These machine components provide a basis for applications in molecular machinery and nanoscale manufacture including programmed chemical synthesis.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2015

Averaging and Linear Programming in Some Singularly Perturbed Problems of Optimal Control

The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon. We mostly focus on problems with time discounting criteria but a possibility of the extension of results to periodic optimization problems is discussed as well. Our consideration is based on earlier results on averaging of SP control systems and on linear programming formulations of optimal control problems. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with two numerical examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Approximating the linear response of physical chaos

Abstract Parametric derivatives of statistics are highly desired quantities in prediction, design optimization and uncertainty quantification. In the presence of chaos, the rigorous computation of these quantities is certainly possible, but mathematically complicated and computationally expensive. Based on Ruelle’s formalism, this paper shows that the sophisticated linear response algorithm can be dramatically simplified in higher-dimensional systems featuring statistical homogeneity in the physical space. We argue that the contribution of the SRB (Sinai–Ruelle–Bowen) measure gradient, which is an integral yet the most cumbersome part of the full algorithm, is negligible if the objective function is appropriately aligned with unstable manifolds. This abstract condition could potentially be satisfied by a vast family of real-world chaotic systems, regardless of the physical meaning and mathematical form of the objective function and perturbed parameter. We demonstrate several numerical examples that support these conclusions and that present the use and performance of a simplified linear response algorithm. In the numerical experiments, we consider physical models described by differential equations, including Lorenz 96 and Kuramoto–Sivashinsky.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Evaluation and comparison of an adaptive method technique for improved performance of linear Fresnel secondary designs

As a line-focus concentrating solar power (CSP) technology, linear Fresnel collectors have the potential to become a low-cost solution for electricity production and a variety of thermal energy applications. However, this technology often suffers from relatively low performance. A secondary reflector is a key component used to improve optical performance of a linear Fresnel collector. The shape of a secondary reflector is particularly critical in determining solar power captured by the absorber tube(s), and thus, the collector's optical performance. However, to the authors' knowledge, no well-established process existed to derive the optimal secondary shape prior to the development of a new adaptive method to optimize the secondary reflector shape. The new adaptive method does not assume any pre-defined analytical form; rather, it constitutes an optimum shape through an adaptive process by maximizing the energy collection onto the absorber tube. In this paper, the adaptive method is compared with popular secondary-reflector designs with respect to a collector's optical performance under various scenarios. For the first time, a comprehensive, in-depth comparison was conducted on all popular secondary designs for CSP applications. In conclusion, it is shown that the adaptive design exhibits the best optical performance.

14 SOLAR ENERGY↗
DOE OSTI2023

Incremental Interval Assignment by Integer Linear Algebra with Improvements

Interval Assignment (IA) is the problem of selecting the number of mesh edges (intervals) for each curve for conforming quad and hex meshing. The intervals x is fundamentally integer-valued. Many other approaches perform numerical optimization then convert a floating-point solution into an integer solution, which is slow and error prone. We avoid such steps: we start integer, and stay integer. Incremental Interval Assignment (IIA) uses integer linear algebra (Hermite normal form) to find an initial solution to the meshing constraints, satisfying the integer matrix equation Solving for reduced row echelon form provides integer vectors spanning the nullspace of A. Here we add vectors from the nullspace to improve the initial solution, maintaining Ax = b Heuristics find good integer linear combinations of nullspace vectors that provide strict improvement towards variable bounds or goals. IIA always produces an integer solution if one exists. In practice we usually achieve solutions close to the user goals, but there is no guarantee that the solution is optimal, nor even satisfies variable bounds, e.g. has positive intervals. We describe several algorithmic changes since first publication that tend to improve the final solution. The software is freely available.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Fast multiscale contrast independent preconditioners for linear elastic topology optimization problems

The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an adjoint analysis, which requires the numerical solution of large high-contrast linear elastic problems with features spanning several length scales. The size of the discretized problems forces the utilization of iterative linear solvers with solution time dependent on the quality of the preconditioner. The lack of clear separation between the scales, as well as the high-contrast, imposes severe challenges on the standard preconditioning techniques. Thus, here we propose new methods for the high-contrast elasticity equation with performance independent of the high-contrast and the multi-scale structure of the elasticity problem. The solvers are based on two-levels domain decomposition techniques with a carefully constructed coarse level to deal with the high-contrast and multi-scale nature of the problem. The construction utilizes spectral equivalence between scalar diffusion and each displacement block of the elasticity problems and, in contrast to previous solutions proposed in the literature, is able to select the appropriate dimension of the coarse space automatically. The new methods inherit the advantages of domain decomposition techniques, such as easy parallelization and scalability. Finally, the presented numerical experiments demonstrate the excellent performance of the proposed methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A coupling approach for linear elasticity problems with spatially non-coincident discretized interfaces

Here we present a new method for coupled linear elasticity problems whose finite element discretization may lead to spatially non-coincident discretized interfaces. Our approach combines the classical Dirichlet–Neumann coupling formulation with a new set of discretized interface conditions obtained through Taylor series expansions. We show that these conditions ensure linear consistency of the coupled finite element solution. We then formulate an iterative solution method for the coupled discrete system and apply the new coupling approach to two representative settings for which we also provide several numerical illustrations. The first setting is a mesh-tying problem in which both coupled structures have the same Lamé parameters whereas the second setting is an interface problem for which the Lamé parameters in the two coupled structures are different.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Scalable Preconditioning of Block-Structured Linear Algebra Systems using ADMM

In this paper, we study the solution of block-structured linear algebra systems arising in optimization by using iterative solution techniques. These systems are the core computational bottleneck of many problems of interest such as parameter estimation, optimal control, network optimization, and stochastic programming. Our approach uses a Krylov solver (GMRES) that is preconditioned with an alternating method of multipliers (ADMM). We show that this ADMM-GMRES approach overcomes well-known scalability issues of Schur complement decomposition in problems that exhibit a high degree of coupling. The effectiveness of the approach is demonstrated using linear systems that arise in stochastic optimal power flow problems and that contain up to 2 million total variables and 4,000 coupling variables. We find that ADMM-GMRES is nearly an order of magnitude faster than Schur complement decomposition. Moreover, we demonstrate that the approach is robust to the selection of the augmented Lagrangian penalty parameter, which is a key advantage over the direct use of ADMM.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Massively parallel and linear-scaling algorithm for second-order Moller–Plesset perturbation theory applied to the study of supramolecular wires

Here, we present a scalable cross-platform hybrid MPI/OpenMP/OpenACC implementation of the Divide–Expand–Consolidate (DEC) formalism with portable performance on heterogeneous HPC architectures. The Divide–Expand–Consolidate formalism is designed to reduce the steep computational scaling of conventional many-body methods employed in electronic structure theory to linear scaling, while providing a simple mechanism for controlling the error introduced by this approximation. Our massively parallel implementation of this general scheme has three levels of parallelism, being a hybrid of the loosely coupled task-based parallelization approach and the conventional MPI +X programming model, where X is either OpenMP or OpenACC. We demonstrate strong and weak scalability of this implementation on heterogeneous HPC systems, namely on the GPU-based Cray XK7 Titan supercomputer at the Oak Ridge National Laboratory. Using the “resolution of the identity second-order Moller–Plesset perturbation theory” (RI-MP2) as the physical model for simulating correlated electron motion, the linear-scaling DEC implementation is applied to 1-aza-adamantane-trione (AAT) supramolecular wires containing up to 40 monomers (2440 atoms, 6800 correlated electrons, 24 440 basis functions and 91 280 auxiliary functions). This represents the largest molecular system treated at the MP2 level of theory, demonstrating an efficient removal of the scaling wall pertinent to conventional quantum many-body methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Disjunctive linear separation conditions and mixed-integer formulations for aircraft conflict resolution

In this paper, we address the aircraft conflict resolution problem in air traffic control. We introduce new mixed-integer programming formulations for aircraft conflict resolution with speed, heading and altitude control which are based on disjunctive linear separation conditions. We first examine the two-dimensional aircraft conflict resolution problem with speed and heading control represented as continuous decision variables. We show that the proposed disjunctive linear separation conditions are equivalent to the classical nonlinear conditions for aircraft separation. Further, we characterise conflict-free trajectories based on aircraft velocity bounds and propose a simple pre-processing algorithm to identify aircraft pairs which are either always conflict-free, or which cannot be separated using speed and heading control only. We then incorporate altitude control and propose a lexicographic optimisation formulation that aims to minimise the number of flight level changes before resolving outstanding conflicts via two-dimensional velocity control. The proposed mixed-integer programming formulations are nonconvex, and we propose convex relaxations, decomposition methods and constraint generation algorithms to solve the two-dimensional and lexicographic optimisation formulations to guaranteed optimality. Numerical experiments on four types of conflict resolution benchmarking instances are conducted to test the performance of the proposed mixed-integer formulations. Further, the proposed method is compared against two benchmarks based on state-of-the-art approaches for the aircraft conflict resolution problem. Our numerical results show that the proposed method largely outperforms both benchmarks in terms of runtime and is able to solve significantly more instances to global optimality.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Solution of the linear wave-particle kinetic equation for global modes of arbitrary frequency in a tokamak

The linear response of a plasma to perturbations of arbitrary frequency and wavelength is derived for any axisymmetric magnetized toroidal plasma. An explicit transformation to action-angle coordinates is achieved using orthogonal magnetic coordinates and the Littlejohn Lagrangian, establishing the validity of this result to arbitrary order in normalized Larmor radius. The global resonance condition for compressional modes is clarified in more detail than in previous works, confirming that the poloidal orbit-average of the cyclotron frequency gives the desired result at lowest order in Larmor radius. The global plasma response to the perturbation at each resonance is captured by a poloidal and gyroaverage of the perturbing potential. A “global gyroaveraging” of the potential is a natural by-product of this analysis which takes into account the changing of the magnetic field over an orbit. The resonance condition depends on two arbitrary integers which completely separately capture the effects poloidal non-uniformity and finite Larmor radius in generating sidebands. We learn that poloidal sidebands generated for compressional modes are dominated by the change in gyrofrequency over the orbit, which is very different to shear modes where the gyrofrequency only contributes via a finite Larmor radius effect. This increases the number of bounce harmonics required to compute the linear drive, giving a more complicated resonance map. An example calculation is given comparing resonance of shear and compressional modes in a published DIII-D case.

Compressional↗
DOE OSTI2014

Intraoperative Radiation Therapy in Early Breast Cancer Using a Linear Accelerator Outside of the Operative Suite: An “Image-Guided” Approach

Purpose: To present local control, complications, and cosmetic outcomes of intraoperative radiation therapy (IORT) for early breast cancer, as well as technical aspects related to the use of a nondedicated linear accelerator. Methods and Materials: This prospective trial began in May of 2004. Eligibility criteria were biopsy-proven breast-infiltrating ductal carcinoma, age >40 years, tumor <3 cm, and cN0. Exclusion criteria were in situ or lobular types, multicentricity, skin invasion, any contraindication for surgery and/or radiation therapy, sentinel lymph node involvement, metastasis, or another malignancy. Patients underwent classic quadrantectomy with intraoperative sentinel lymph node and margins evaluation. If both free, the patient was transferred from operative suite to linear accelerator room, and IORT was delivered (21 Gy). Primary endpoint: local recurrence (LR); secondary endpoints: toxicities and aesthetics. Quality assurance involved using a customized shield for chest wall protection, applying procedures to minimize infection caused by patient transportation, and using portal films to check collimator-shield alignment. Results: A total of 152 patients were included, with at least 1 year follow-up. Median age (range) was 58.3 (40-85.4) years, and median follow-up time was 50.7 (12-110.5) months. The likelihood of 5-year local recurrence was 3.7%. There were 3 deaths, 2 of which were cancer related. The Kaplan-Meier 5-year actuarial estimates of overall, disease-free, and local recurrence-free survivals were 97.8%, 92.5%, and 96.3%, respectively. The overall incidences of acute and late toxicities were 12.5% and 29.6%, respectively. Excellent, good, fair, and bad cosmetic results were observed in 76.9%, 15.8%, 4.3%, and 2.8% of patients, respectively. Most treatments were performed with a 5-cm collimator, and in 39.8% of the patients the electron-beam energy used was ≥12 MeV. All patients underwent portal film evaluation, and the shielding was repositioned in 39.9% of cases. No infection or anesthesia complications were observed. Conclusions: Local control with IORT was adequate, with low complication rates and good cosmetic outcomes. More than one-third of patients benefited from the “image-guidance” approach, and almost 40% benefited from the option of higher electron beam energies.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2015

Anderson acceleration of the Jacobi iterative method: An efficient alternative to Krylov methods for large, sparse linear systems

We employ Anderson extrapolation to accelerate the classical Jacobi iterative method for large, sparse linear systems. Specifically, we utilize extrapolation at periodic intervals within the Jacobi iteration to develop the Alternating Anderson–Jacobi (AAJ) method. We verify the accuracy and efficacy of AAJ in a range of test cases, including nonsymmetric systems of equations. We demonstrate that AAJ possesses a favorable scaling with system size that is accompanied by a small prefactor, even in the absence of a preconditioner. In particular, we show that AAJ is able to accelerate the classical Jacobi iteration by over four orders of magnitude, with speed-ups that increase as the system gets larger. Moreover, we find that AAJ significantly outperforms the Generalized Minimal Residual (GMRES) method in the range of problems considered here, with the relative performance again improving with size of the system. As a result, the proposed method represents a simple yet efficient technique that is particularly attractive for large-scale parallel solutions of linear systems of equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Application of linear multifrequency-grey acceleration to preconditioned Krylov iterations for thermal radiation transport

The thermal radiative transfer (TRT) equations comprise a radiation equation coupled to the material internal energy equation. Linearization of these equations produces effective, thermally-redistributed scattering through absorption-reemission. In this paper, we investigate the effectiveness and efficiency of Linear-Multi-Frequency-Grey (LMFG) acceleration that has been reformulated for use as a preconditioner to Krylov iterative solution methods. We introduce two general frameworks, the scalar flux formulation (SFF) and the absorption rate formulation (ARF), and investigate their iterative properties in the absence and presence of true scattering. SFF has a group-dependent state size but may be formulated without inner iterations in the presence of scattering, while ARF has a group-independent state size but requires inner iterations when scattering is present. We compare and evaluate the computational cost and efficiency of LMFG applied to these two formulations using a direct solver for the preconditioners. Finally, this work is novel because the use of LMFG for the radiation transport equation, in conjunction with Krylov methods, involves special considerations not required for radiation diffusion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

A linearity preserving nodal variation limiting algorithm for continuous Galerkin discretization of ideal MHD equations

A stabilized continuous Galerkin (CG) method for magnetohydrodynamics (MHD) is presented herein. Ideal, compressible inviscid MHD equations are discretized in space on unstructured meshes using piecewise linear or bilinear finite element bases to get a semi-discrete scheme. Stabilization is then introduced to the semi-discrete method in a strategy that follows the algebraic flux correction paradigm. This involves adding some artificial diffusion to the high order, semi-discrete method and mass lumping in the time derivative term. The result is a low order method that provides local extremum diminishing properties for hyperbolic systems. The difference between the low order method and the high order method is scaled element-wise using a limiter and added to the low order scheme. The limiter is solution dependent and computed via an iterative linearity preserving nodal variation limiting strategy. The stabilization also involves an optional consistent background high order dissipation that reduces phase errors. The resulting stabilized scheme is a semi-discrete method that can be applied to inviscid shock MHD problems and may be even extended to resistive and viscous MHD problems. To satisfy the divergence free constraint of the MHD equations, we add parabolic divergence cleaning to the system. Various time integration methods can be used to discretize the scheme in time. We demonstrate the robustness of the scheme by solving several shock MHD problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

RandONets: Shallow networks with random projections for learning linear and nonlinear operators

Deep neural networks have been extensively used for the solution of both the forward and the inverse problem for dynamical systems. However, their implementation necessitates optimizing a high-dimensional space of parameters and hyperparameters. This fact, along with the requirement of substantial computational resources, pose a barrier to achieving high numerical accuracy, but also interpretability. Here, to address the above challenges, we present Random Projection-based Operator Networks (RandONets): shallow networks with random projections and tailor-made numerical analysis methods that learn accurately and fast linear and nonlinear operators. Building on previous works, we prove that RandOnets are universal approximators of linear and nonlinear operators. Due to their simplicity, RandONets provide a one-step transformation of the input space, facilitating interpretability. For the evaluation of their performance, we focus on operators of PDEs. We show, that RandONets outperform by several orders of magnitude, both in terms of numerical approximation accuracy and computational cost, the “vanilla” DeepONets. Hence, we believe that our method will trigger further developments in the field of scientific machine learning, for the development of new ‘’light”schemes that will provide high accuracy while reducing dramatically the computational cost. A MATLAB toolbox for RandONets, including demos, is available on GitHub at https://github.com/GianlucaFabiani/RandONets.

Interpretable machine learning↗
DOE OSTI2016

Accuracy evaluation of the optical surface monitoring system on EDGE linear accelerator in a phantom study

Frameless stereotactic radiosurgery (SRS) requires dedicated systems to monitor the patient position during the treatment to avoid target underdosage due to involuntary shift. The optical surface monitoring system (OSMS) is here evaluated in a phantom-based study. The new EDGE linear accelerator from Varian (Varian, Palo Alto, CA) integrates, for cranial lesions, the common cone beam computed tomography (CBCT) and kV-MV portal images to the optical surface monitoring system (OSMS), a device able to detect real-time patient's face movements in all 6 couch axes (vertical, longitudinal, lateral, rotation along the vertical axis, pitch, and roll). We have evaluated the OSMS imaging capability in checking the phantoms' position and monitoring its motion. With this aim, a home-made cranial phantom was developed to evaluate the OSMS accuracy in 4 different experiments: (1) comparison with CBCT in isocenter location, (2) capability to recognize predefined shifts up to 2° or 3 cm, (3) evaluation at different couch angles, (4) ability to properly reconstruct the surface when the linac gantry visually block one of the cameras. The OSMS system showed, with a phantom, to be accurate for positioning in respect to the CBCT imaging system with differences of 0.6 ± 0.3 mm for linear vector displacement, with a maximum rotational inaccuracy of 0.3°. OSMS presented an accuracy of 0.3 mm for displacement up to 1 cm and 1°, and 0.5 mm for larger displacements. Different couch angles (45° and 90°) induced a mean vector uncertainty < 0.4 mm. Coverage of 1 camera produced an uncertainty < 0.5 mm. Translations and rotations of a phantom can be accurately detect with the optical surface detector system.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2016

Optimal technique of linear accelerator–based stereotactic radiosurgery for tumors adjacent to brainstem

Stereotactic radiosurgery (SRS) is a well-established technique that is replacing whole-brain irradiation in the treatment of intracranial lesions, which leads to better preservation of brain functions, and therefore a better quality of life for the patient. There are several available forms of linear accelerator (LINAC)–based SRS, and the goal of the present study is to identify which of these techniques is best (as evaluated by dosimetric outcomes statistically) when the target is located adjacent to brainstem. We collected the records of 17 patients with lesions close to the brainstem who had previously been treated with single-fraction radiosurgery. In all, 5 different lesion catalogs were collected, and the patients were divided into 2 distance groups—1 consisting of 7 patients with a target-to-brainstem distance of less than 0.5 cm, and the other of 10 patients with a target-to-brainstem distance of ≥ 0.5 and < 1 cm. Comparison was then made among the following 3 types of LINAC-based radiosurgery: dynamic conformal arcs (DCA), intensity-modulated radiosurgery (IMRS), and volumetric modulated arc radiotherapy (VMAT). All techniques included multiple noncoplanar beams or arcs with or without intensity-modulated delivery. The volume of gross tumor volume (GTV) ranged from 0.2 cm{sup 3} to 21.9 cm{sup 3}. Regarding the dose homogeneity index (HI{sub ICRU}) and conformity index (CI{sub ICRU}) were without significant difference between techniques statistically. However, the average CI{sub ICRU} = 1.09 ± 0.56 achieved by VMAT was the best of the 3 techniques. Moreover, notable improvement in gradient index (GI) was observed when VMAT was used (0.74 ± 0.13), and this result was significantly better than those achieved by the 2 other techniques (p < 0.05). For V{sub 4} {sub Gy} of brainstem, both VMAT (2.5%) and IMRS (2.7%) were significantly lower than DCA (4.9%), both at the p < 0.05 level. Regarding V{sub 2} {sub Gy} of normal brain, VMAT plans had attained 6.4 ± 5%; this was significantly better (p < 0.05) than either DCA or IMRS plans, at 9.2 ± 7% and 8.2 ± 6%, respectively. Owing to the multiple arc or beam planning designs of IMRS and VMAT, both of these techniques required higher MU delivery than DCA, with the averages being twice as high (p < 0.05). If linear accelerator is only 1 modality can to establish for SRS treatment. Based on statistical evidence retrospectively, we recommend VMAT as the optimal technique for delivering treatment to tumors adjacent to brainstem.

61 RADIATION PROTECTION AND DOSIMETRY↗