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At least 1,189 records · Page 66
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

Linearization Techniques for Controlled Piecewise Deterministic Markov Processes; Application to Zubov's Method

We aim at characterizing domains of attraction for controlled piecewise deterministic processes using an occupational measure formulation and Zubov's approach. Firstly, we provide linear programming (primal and dual) formulations of discounted, infinite horizon control problems for PDMPs. These formulations involve an infinite-dimensional set of probability measures and are obtained using viscosity solutions theory. Secondly, these tools allow to construct stabilizing measures and to avoid the assumption of stability under concatenation for controls. The domain of controllability is then characterized as some level set of a convenient solution of the associated Hamilton-Jacobi integral-differential equation. The theoretical results are applied to PDMPs associated to stochastic gene networks. Explicit computations are given for Cook's model for gene expression.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Conditions for the Solvability of the Linear Programming Formulation for Constrained Discounted Markov Decision Processes

We consider a discrete-time constrained discounted Markov decision process (MDP) with Borel state and action spaces, compact action sets, and lower semi-continuous cost functions. We introduce a set of hypotheses related to a positive weight function which allow us to consider cost functions that might not be bounded below by a constant, and which imply the solvability of the linear programming formulation of the constrained MDP. In particular, we establish the existence of a constrained optimal stationary policy. Our results are illustrated with an application to a fishery management problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Impulsive Control for Continuous-Time Markov Decision Processes: A Linear Programming Approach

In this paper, we investigate an optimization problem for continuous-time Markov decision processes with both impulsive and continuous controls. We consider the so-called constrained problem where the objective of the controller is to minimize a total expected discounted optimality criterion associated with a cost rate function while keeping other performance criteria of the same form, but associated with different cost rate functions, below some given bounds. Our model allows multiple impulses at the same time moment. The main objective of this work is to study the associated linear program defined on a space of measures including the occupation measures of the controlled process and to provide sufficient conditions to ensure the existence of an optimal control.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A New Proof That the Number of Linear Elastic Symmetries in Two Dimensions Is Four

In this work, we present an elementary and self-contained proof that there are exactly four symmetry classes of the elasticity tensor in two dimensions: oblique, rectangular, square, and isotropic. In two dimensions, orthogonal transformations are either reflections or rotations. The proof is based on identification of constraints imposed by reflections and rotations on the elasticity tensor, and it simply employs elementary tools from trigonometry, making the proof accessible to a broad audience. For completeness, we identify the sets of transformations (rotations and reflections) for each symmetry class and report the corresponding equations of motions in classical linear elasticity.

42 ENGINEERING↗
DOE OSTI2020

A Mixed Discontinuous Galerkin Method for Linear Elasticity with Strongly Imposed Symmetry

In this paper, we study a mixed discontinuous Galerkin (MDG) method to solve linear elasticity problem with arbitrary order discontinuous finite element spaces in d -dimension ( \(d=2,3\) ). This method uses polynomials of degree \(k+1\) for the stress and of degree k for the displacement ( \(k\ge 0\) ). The mixed DG scheme is proved to be well-posed under proper norms. Specifically, we prove that, for any \(k \ge 0\) , the \(H(\mathrm{div})\) -like error estimate for the stress and \(L^2\) error estimate for the displacement are optimal. We further establish the optimal \(L^2\) error estimate for the stress provided that the \({\mathcal {P}}_{k+2}-{\mathcal {P}}_{k+1}^{-1}\) Stokes pair is stable and \(k \ge d\) . Finally, we also provide numerical results of MDG showing that the orders of convergence are actually sharp.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Ir-192 radioisotope replacement with a hand-portable 1 MeV Ku-band electron linear accelerator

Although linear accelerators are used in many security, industrial and medical applications, the existing technologies are too large and expensive for several critical applications such as radioactive source replacement, field radiography and mobile cargo scanners. Here, one of the main requirements for these sources is to be highly portable to allow field operation. In response to this problem, RadiaBeam has designed a hand-portable 1 MeV X-ray source, scalable to higher energies, based on Ku-band split electron linac, that can be used for Ir-192 radioisotope replacement. In this paper, we present its multiphysics and engineering design studies, as well as an accelerating structure prototype along with RF measurements.

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

A compute-bound formulation of Galerkin model reduction for linear time-invariant dynamical systems

This work aims to advance computational methods for projection-based reduced-order models (ROMs) of linear time-invariant (LTI) dynamical systems. For such systems, current practice relies on ROM formulations expressing the state as a rank-1 tensor (i.e., a vector), leading to computational kernels that are memory bandwidth bound and, therefore, ill-suited for scalable performance on modern architectures. This weakness can be particularly limiting when tackling many-query studies, where one needs to run a large number of simulations. This work introduces a reformulation, called rank-2 Galerkin, of the Galerkin ROM for LTI dynamical systems which converts the nature of the ROM problem from memory bandwidth to compute bound. We present the details of the formulation and its implementation, and demonstrate its utility through numerical experiments using, as a test case, the simulation of elastic seismic shear waves in an axisymmetric domain. We quantify and analyze performance and scaling results for varying numbers of threads and problem sizes. In conclusion, we present an end-to-end demonstration of using the rank-2 Galerkin ROM for a Monte Carlo sampling study. We show that the rank-2 Galerkin ROM is one order of magnitude more efficient than the rank-1 Galerkin ROM (the current practice) and about 970 times more efficient than the full-order model, while maintaining accuracy in both the mean and statistics of the field.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A mixed integer linear programming approach for the design of chemical process families

Tackling climate change goals requires widespread deployment of process technology variants across many decentralized sites with different geographical, environmental, and operational requirements. Conventional engineering approaches focus on unique designs for each installation (process variant), while missing opportunities for manufacturing standardization. Here, instead we seek to optimize a process platform of common unit designs while simultaneously designing an entire family of process variants that make use of that platform. This reduces engineering effort, deployment timelines, and manufacturing costs. We propose a nonlinear generalized disjunctive programming formulation and convert this to an efficient mixed-integer linear programming (MILP) formulation through discretization of the design space. We formulate our optimization in Pyomo with costing from IDAES, and we demonstrate the computational performance and solution quality on a water treatment desalination system from the PARETO framework and a carbon capture system built in Aspen Plus as part of CCSI2.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Effects of temperature and time on supercritical methanol Co-Liquefaction of rice straw and linear low-density polyethylene wastes

We report that biofuels are particularly attractive and play an increasingly important role in sustainable energy. However, biofuels originating from lignocellulosic biomass (LCB) are extremely challenging because of their low carbon content, low stability, and high oxygen content. This work evaluates the supercritical methanol (scMeOH) co-liquefaction of rice straw and linear low-density polyethylene (LLDPE) at temperature range of 240-340 °C for 0-2 h, to obtain hydrocarbons (HCs)-rich oil and carbon-rich solid product. Results show that reaction temperature dominated the yield and properties of products, but not the holding time. Among parameters tested, 30.07 wt% oil yield with 75.79% HCs content and 33.05 wt% oil yield with 70.91% HCs content were obtained at 300 °C for 1 h and 1.5 h, respectively. Simultaneously, the remaining solid products were still as high as 53.85 wt% with a carbon content of 79.59% and 48.28 wt% with carbon content of 81.34% under 300 °C for 1 h and 1.5 h, respectively. Ultimate analysis, FT-IR, TGA, and SEM show that solid products could be used as sustainable carbon resources, and solid fuel rather than soil amendment because of risk of micro plastic or adsorbent due to smooth surface without pores.

09 BIOMASS FUELS↗
DOE OSTI2022

Application of Box-Behnken design in optimizing product properties of supercritical methanol co -liquefaction of rice straw and linear low-density polyethylene

We report co-processing of plastic and biomass wastes to produce high-quality fuel has been attracting considerable interest in energy recovery. This work employed Box-Behnken Design (BBD) to optimize yield and properties of oil from supercritical methanol (scMeOH) co-liquefaction of rice straw (RS) and linear low-density polyethylene (LLDPE). Three independent variables of reaction temperature (270, 300, and 330°C), holding time (60, 90, and 120 mins), and RS/LLDPE mass ratio (0.15, 0.50, and 0.85) were selected for experiments. A maximum oil yield of 34.17 wt% was achieved at 303°C, 96 mins, and RS/LLDPE ratio of 0.59 according to BBD. Temperature and RS/LLDPE ratio dominated the oil yield and synergistic effects during co-liquefaction, whereas time was an insignificant factor. Optimum oil from co-liquefaction contained substantial hydrocarbons content of 32.91% compared to that from single RS-derived oil of 7.77%. Solid product obtained at the optimum condition could be used as solid fuel, due to its relatively high HHV of 43.08 MJ/kg compared to the other solid fuels (13.90–32.14 MJ/kg). This work provides a deep understanding of the co-processing of solid biomass and plastic wastes.

09 BIOMASS FUELS↗
DOE OSTI2025

Alternative mixed integer linear programming optimization for joint job scheduling and data allocation in grid computing

This paper presents a novel approach to the joint optimization of job scheduling and data allocation in grid computing environments. We formulate this joint optimization problem as a mixed integer quadratically constrained program. To tackle the nonlinearity in the constraint, we alternatively fix a subset of decision variables and optimize the remaining ones via Mixed Integer Linear Programming (MILP). We solve the MILP problem at each iteration via an off-the-shelf MILP solver. Our experimental results show that our method significantly outperforms existing heuristic methods, employing either independent optimization or joint optimization strategies. We have also verified the generalization ability of our method over grid environments with various sizes and its high robustness to the algorithm setting.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Tuning successive linear programming to solve AC optimal power flow problem for large networks

Successive linear programming (SLP) is a practical approach for solving large-scale nonlinear optimization problems. Alternating current optimal power flow (ACOPF) is no exception, particularly the large size of real-world networks. However, in order to achieve tractability, it is essential to tune the SLP algorithm presented in the literature. This paper presents a modified SLP algorithm to solve the ACOPF problem, specified by the U.S. Department of Energy’s (DOE) Grid Optimization (GO) Competition Challenge 1, within strict time limits. The algorithm first finds a near-optimal solution for the relaxed problem (i.e., Stage 1). Then, it finds a feasible solution in the proximity of the near-optimal solution (i.e., Stage 2 and Stage 3). The numerical experiments on test cases ranging from 500-bus to 30,000-bus systems show that the algorithm is tractable. Here the results show that our proposed algorithm is tractable and can solve more than 80% of test cases faster than the well-known Interior Point Method while significantly reduce the number of iterations required to solve ACOPF. The number of iterations is considered an important factor in the examination of tractability which can drastically reduce the computational time required within each iteration.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2012

Factors Predictive of Symptomatic Radiation Injury After Linear Accelerator-Based Stereotactic Radiosurgery for Intracerebral Arteriovenous Malformations

Purpose: To investigate predictive factors in the development of symptomatic radiation injury after treatment with linear accelerator-based stereotactic radiosurgery for intracerebral arteriovenous malformations and relate the findings to the conclusions drawn by Quantitative Analysis of Normal Tissue Effects in the Clinic (QUANTEC). Methods and Materials: Archived plans for 73 patients who were treated at the British Columbia Cancer Agency were studied. Actuarial estimates of freedom from radiation injury were calculated using the Kaplan-Meier method. Univariate and multivariate Cox proportional hazards models were used for analysis of incidence of radiation injury. Log-rank test was used to search for dosimetric parameters associated with freedom from radiation injury. Results: Symptomatic radiation injury was exhibited by 14 of 73 patients (19.2%). Actuarial rate of symptomatic radiation injury was 23.0% at 4 years. Most patients (78.5%) had mild to moderate deficits according to Common Terminology Criteria for Adverse Events, version 4.0. On univariate analysis, lesion volume and diameter, dose to isocenter, and a V{sub x} for doses {>=}8 Gy showed statistical significance. Only lesion diameter showed statistical significance (p < 0.05) in a multivariate model. According to the log-rank test, AVM volumes >5 cm{sup 3} and diameters >30 mm were significantly associated with the risk of radiation injury (p < 0.01). The V{sub 12} also showed strong association with the incidence of radiation injury. Actuarial incidence of radiation injury was 16.8% if V{sub 12} was <28 cm{sup 3} and 53.2% if >28 cm{sup 3} (log-rank test, p = 0.001). Conclusions: This study confirms that the risk of developing symptomatic radiation injury after radiosurgery is related to lesion diameter and volume and irradiated volume. Results suggest a higher tolerance than proposed by QUANTEC. The widely differing findings reported in the literature, however, raise considerable uncertainties.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2012

The Use of Photon Beams of a Flattening Filter-free Linear Accelerator for Hypofractionated Volumetric Modulated Arc Therapy in Localized Prostate Cancer

Purpose: To evaluate the potential usage of flattening filter-free (FFF) photon beams in the treatment of prostate cancer. Methods and Materials: Volumetric-modulated arc therapy (VMAT) treatment planning was performed for 7 patients using TrueBeam{sup Registered-Sign} linear accelerator and photon beams with (X6, X10) and without (X6FFF, X10FFF) flattening filter. Prescribed dose was 19 Multiplication-Sign 3 Gy = 57 Gy. One or two 360 Degree-Sign arcs with dose rate of 600 MU/min for flattened beams, and 1,200 MU/min for FFF beams were used. Results: No difference was detected between the four beams in PTV coverage, conformity, and homogeneity. Mean body dose and body volume receiving 50% of the prescribed dose decreased with increasing mean energy (r{sup 2} = 0.8275, p < 0.01). X6FFF delivered 3.6% more dose compared with the X6 (p < 0.01). X10FFF delivered 3.0% (p < 0.01), and the X10 5.8% (p < 0.01) less mean body dose compared with X6. There was a significant increase in the mean dose to the rectum for the X10 compared with X6 (2.6%, p < 0.01). Mean dose to the bladder increased by 1.3% for X6FFF and decreased by 2.3% for X10FFF. Using a single arc and FFF, treatment time was reduced by 35% (2 SD = 10%). Conclusion: FFF beams resulted in dose distributions similar to flattened beams. X10FFF beam provided the best solution, sparing rectum and bladder and minimizing whole-body dose. FFF beams lead to a time efficient treatment delivery, particularly when combined with hypofractionated VMAT.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2014

Linear Accelerator-Based Radiosurgery Alone for Arteriovenous Malformation: More Than 12 Years of Observation

Purpose: Although radiosurgery is an accepted treatment method for intracranial arteriovenous malformations (AVMs), its long-term therapeutic effects have not been sufficiently evaluated, and many reports of long-term observations are from gamma-knife facilities. Furthermore, there are few reported results of treatment using only linear accelerator (LINAC)-based radiosurgery (LBRS). Methods and Materials: Over a period of more than 12 years, we followed the long-term results of LBRS treatment performed in 51 AVM patients. Results: The actuarial obliteration rates, after a single radiosurgery session, at 3, 5, 10, and 15 years were 46.9%, 54.0%, 64.4%, and 68.0%, respectively; when subsequent radiosurgeries were included, the rates were 46.9%, 61.3%, 74.2%, and 90.3%, respectively. Obliteration rates were significantly related to target volumes ≥4 cm{sup 3}, marginal doses ≥12 Gy, Spetzler-Martin grades (1 vs other), and AVM scores ≥1.5; multivariate analyses revealed a significant difference for target volumes ≥4 cm{sup 3}. The postprocedural actuarial symptomatic radiation injury rates, after a single radiation surgery session, at 5, 10, and 15 years were 12.3%, 16.8%, and 19.1%, respectively. Volumes ≥4 cm{sup 3}, location (lobular or other), AVM scores ≥1.5, and the number of radiosurgery were related to radiation injury incidence; multivariate analyses revealed significant differences associated with volumes ≥4 cm{sup 3} and location (lobular or other). Conclusions: Positive results can be obtained with LBRS when performed with a target volume ≤4 cm{sup 3}, an AVM score ≤1.5, and ≥12 Gy radiation. Bleeding and radiation injuries may appear even 10 years after treatment, necessitating long-term observation.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2017

Experimental Platform for Ultra-high Dose Rate FLASH Irradiation of Small Animals Using a Clinical Linear Accelerator

Purpose: A key factor limiting the effectiveness of radiation therapy is normal tissue toxicity, and recent preclinical data have shown that ultra-high dose rate irradiation (>50 Gy/s, “FLASH”) potentially mitigates this effect. However, research in this field has been strongly limited by the availability of FLASH irradiators suitable for small animal experiments. We present a simple methodologic approach for FLASH electron small animal irradiation with a clinically available linear accelerator (LINAC). Methods and Materials: We investigated the FLASH irradiation potential of a Varian Clinac 21EX in both clinical mode and after tuning of the LINAC. We performed detailed FLUKA Monte Carlo and experimental dosimetric characterization at multiple experimental locations within the LINAC head. Results: Average dose rates of ≤74 Gy/s were achieved in clinical mode, and the dose rate after tuning exceeded 900 Gy/s. We obtained 220 Gy/s at 1-cm depth for a >4-cm field size with 90% homogeneity throughout a 2-cm-thick volume. Conclusions: We present an approach for using a clinical LINAC for FLASH irradiation. We obtained dose rates exceeding 200 Gy/s after simple tuning of the LINAC, with excellent dosimetric properties for small animal experiments. This will allow for increased availability of FLASH irradiation to the general research community.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2026

Goal-oriented real-time Bayesian inference for linear autonomous dynamical systems with application to digital twins for tsunami early warning

We present a goal-oriented framework for constructing digital twins with the following properties: (1) they employ discretizations of high-fidelity partial differential equation (PDE) models governed by autonomous dynamical systems, leading to large-scale forward problems; (2) they solve a linear inverse problem to assimilate observational data to infer uncertain model components followed by a forward prediction of the evolving dynamics; and (3) the entire end-to-end, data-to-inference-to-prediction computation is carried out without approximation and in real time through a Bayesian framework that rigorously accounts for uncertainties. Several challenges must be overcome to realize this framework, including the large scale of the forward problem, the high dimensionality of the parameter space, and for a class of problems including those we target, the slow decay of the singular values of the parameter-to-observable map. Here we introduce a methodology to overcome these challenges by exploiting the autonomous structure of the forward model to decompose the solution of the inverse problem into a one-time-only offline phase in which the PDE model is solved a limited number of times (equal to the number of sensors), and an online phase that maps well onto GPUs and computes the parameter inference and prediction of quantities of interest in real time, given observational data. Our ultimate goal is to apply this framework to construct digital twins for subduction zones, including Cascadia, to provide early warning for tsunamis generated by megathrust earthquakes. To this end, we demonstrate how our methodology can be used to employ seafloor pressure observations, along with the coupled acoustic–gravity wave equations, to infer the earthquake-induced spatiotemporal seafloor motion (discretized with $\mathscr{O}$ (10 9 ) parameters) and forward predict the tsunami propagation. We present results of an end-to-end inference, prediction, and uncertainty quantification for a representative test problem with $\mathscr{O}$ (10 8 ) inversion parameters for which goal-oriented Bayesian inference is accomplished exactly and in real time, that is, in a matter of seconds.

97 MATHEMATICS AND COMPUTING↗