A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions
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This work presents a probabilistic scheme for solving semilinear nonlocal diffusion equations with volume constraints and integrable kernels. The nonlocal model of interest is defined by a time-dependent semilinear partial integro-differential equation (PIDE), in which the integro-differential operator consists of both local convection-diffusion and nonlocal diffusion operators. Here, our numerical scheme is based on the direct approximation of the nonlinear Feynman–Kac formula that establishes a link between nonlinear PIDEs and stochastic differential equations. The exploitation of the Feynman–Kac representation avoids solving dense linear systems arising from nonlocal operators. Compared with existing stochastic approaches, our method can achieve first-order convergence after balancing the temporal and spatial discretization errors, which is a significant improvement of existing probabilistic/stochastic methods for nonlocal diffusion problems. Error analysis of our numerical scheme is established. The effectiveness of our approach is shown in two numerical examples. The first example considers a three-dimensional nonlocal diffusion equation to numerically verify the error analysis results. The second example presents a physics problem motivated by the study of heat transport in magnetically confined fusion plasmas.
Purpose: Treatment plan optimization in multi-Co60 source focused radiotherapy with multiple isocenters is challenging, because dose distribution is normalized to maximum dose during optimization and evaluation. The objective functions are traditionally defined based on relative dosimetric distribution. This study presents an alternative absolute dose-volume constraint (ADC) based deterministic optimization framework (ADC-DOF). Methods: The initial isocenters are placed on the eroded target surface. Collimator size is chosen based on the area of 2D contour on corresponding axial slice. The isocenter spacing is determined by adjacent collimator sizes. The weights are optimized by minimizing the deviation from ADCs using the steepest descent technique. An iterative procedure is developed to reduce the number of isocenters, where the isocenter with lowest weight is removed without affecting plan quality. The ADC-DOF is compared with the genetic algorithm (GA) using the same arbitrary shaped target (254cc), with a 15mm margin ring structure representing normal tissues. Results: For ADC-DOF, the ADCs imposed on target and ring are (D100>10Gy, D50,10, 0<12Gy, 15Gy and 20Gy) and (D40<10Gy). The resulting D100, 50, 10, 0 and D40 are (9.9Gy, 12.0Gy, 14.1Gy and 16.2Gy) and (10.2Gy). The objectives of GA are to maximize 50% isodose target coverage (TC) while minimize the dose delivered to the ring structure, which results in 97% TC and 47.2% average dose in ring structure. For ADC-DOF (GA) techniques, 20 out of 38 (10 out of 12) initial isocenters are used in the final plan, and the computation time is 8.7s (412.2s) on an i5 computer. Conclusion: We have developed a new optimization technique using ADC and deterministic optimization. Compared with GA, ADC-DOF uses more isocenters but is faster and more robust, and achieves a better conformity. For future work, we will focus on developing a more effective mechanism for initial isocenter determination.
Drill rig parameter measurements are routinely used during deep well construction to monitor and guide drilling conditions for improved performance and reduced costs. While insightful into the drilling process, these measurements are of reduced value without a standard to aid in data evaluation and decision making. In the main body of this work (Volume 1), a method is demonstrated whereby rock reduction model constraints are used to interpret drilling response parameters; the method could be applied in real-time to improve decision-making in the field and to further discern technology performance during post-drilling evaluations. Drilling parameters are evaluated using laboratory-validated rock reduction models for predicting the phenomenological response of drag bits (Detournay and Defourny, 1992) in computational algorithms. The method presented has applicability to development of advanced analytics on future geothermal wells using real-time electronic data recording for improved performance and reduced drilling costs. A drilling cost model is also used to show the tradeoff between rate of penetration and bit life and the influence on interval drilling costs. Details of the bit specifications and performance are cataloged in an independent volume, documented under separate cover, for each of the four wells, and include Volume 2: Utah FORGE 16A(78)-32; Volume 3: Utah FORGE 56-32; Volume 4: Utah FORGE 78B-32 and Volume 5: Utah FORGE 16B(78)-32.
Drill rig parameter measurements are routinely used during deep well construction to monitor and guide drilling conditions for improved performance and reduced costs. While insightful into the drilling process, these measurements are of reduced value without a standard to aid in data evaluation and decision making. In the main body of this work (Volume 1), a method is demonstrated whereby rock reduction model constraints are used to interpret drilling response parameters; the method could be applied in real-time to improve decision-making in the field and to further discern technology performance during post-drilling evaluations. Drilling parameters are evaluated using laboratory-validated rock reduction models for predicting the phenomenological response of drag bits (Detournay and Defourny, 1992) in computational algorithms. The method presented has applicability to development of advanced analytics on future geothermal wells using real-time electronic data recording for improved performance and reduced drilling costs. A drilling cost model is also used to show the tradeoff between rate of penetration and bit life and the influence on interval drilling costs. Details of the bit specifications and performance are cataloged in an independent volume, documented under separate cover, for each of the four wells, and include Volume 2: Utah FORGE 16A(78)-32; Volume 3: Utah FORGE 56-32; Volume 4: Utah FORGE 78B-32 and Volume 5: Utah FORGE 16B(78)-32.
Drill rig parameter measurements are routinely used during deep well construction to monitor and guide drilling conditions for improved performance and reduced costs. While insightful into the drilling process, these measurements are of reduced value without a standard to aid in data evaluation and decision making. In the main body of this work (Volume 1), a method is demonstrated whereby rock reduction model constraints are used to interpret drilling response parameters; the method could be applied in real-time to improve decision-making in the field and to further discern technology performance during post-drilling evaluations. Drilling parameters are evaluated using laboratory-validated rock reduction models for predicting the phenomenological response of drag bits (Detournay and Defourny, 1992) in computational algorithms. The method presented has applicability to development of advanced analytics on future geothermal wells using real-time electronic data recording for improved performance and reduced drilling costs. A drilling cost model is also used to show the tradeoff between rate of penetration and bit life and the influence on interval drilling costs. Details of the bit specifications and performance are cataloged in an independent volume, documented under separate cover, for each of the four wells, and include Volume 2: Utah FORGE 16A(78)-32; Volume 3: Utah FORGE 56-32; Volume 4: Utah FORGE 78B-32 and Volume 5: Utah FORGE 16B(78)-32.
Drill rig parameter measurements are routinely used during deep well construction to monitor and guide drilling conditions for improved performance and reduced costs. While insightful into the drilling process, these measurements are of reduced value without a standard to aid in data evaluation and decision making. In the main body of this work (Volume 1), a method is demonstrated whereby rock reduction model constraints are used to interpret drilling response parameters; the method could be applied in real-time to improve decision-making in the field and to further discern technology performance during post-drilling evaluations. Drilling parameters are evaluated using laboratory-validated rock reduction models for predicting the phenomenological response of drag bits (Detournay and Defourny, 1992) in computational algorithms. The method presented has applicability to development of advanced analytics on future geothermal wells using real-time electronic data recording for improved performance and reduced drilling costs. A drilling cost model is also used to show the tradeoff between rate of penetration and bit life and the influence on interval drilling costs. Details of the bit specifications and performance are cataloged in an independent volume, documented under separate cover, for each of the four wells, and include Volume 2: Utah FORGE 16A(78)-32; Volume 3: Utah FORGE 56-32; Volume 4: Utah FORGE 78B-32 and Volume 5: Utah FORGE 16B(78)-32.
A finite element program is presented for computer-automated, minimum weight design of elastic structures with constraints on stresses (including local instability criteria) and displacements. Volume 1 of the report contains the theoretical and user's manual of the program. Sample problems and the listing of the program are included in Volumes 2 and 3. The element subroutines are organized so as to facilitate additions and changes by the user. As a result, a relatively minor programming effort would be required to make DESAP 1 into a special purpose program to handle the user's specific design requirements and failure criteria.
DESAP 2 is described as a finite element program for computer-automated, minimum weight design of elastic structures with constraints on stresses (including local instability criteria) and buckling loads. No limits are placed on the number of load conditions for stress-constrained design, but only one of these load conditions can be chosen as the potential buckling load. A substantial portion of DESAP 2, particularly the analysis of the prebuckling state, is derived from the SOLID SAP finite element program. The stress-constrained design is based on the classical stress ratio method, which drives the design towards a fully stressed state. The constraints on the buckling load are handled by solving the appropriate optimality criterion by successive iterations. During each iteration, the element sizes determined by the stress ratio method are used as the minimum size constraints. The element subroutines are organized in a manner that permits the user to make additions and changes with a minimal programming effort. Consequently, DESAP 2 can readily be changed into a special-purpose program to handle the user's specific design requirements and failure criteria.
This paper describes the design of a passive isolation system using D-struts (Registered TradeMark) to isolate an optical payload from aircraft-borne jitter with challenging stroke per volume requirements. It discusses the use of viscoelastic-coated D-struts® that meet the customer performance and outgassing specification, NASA-1124. The result was a relatively soft isolation system, (where the first mode was 13 Hz), with each individual strut capable of withstanding loads on the order of magnitude of 623 N (140 lbf), weighing less than 910 g (2 lbm), fitting in a volume 5.1 cm (2 inches) in diameter and 12-cm (4.7-inches) long and capable of performing up to 1000 Hz without nonlinearities.
Purpose: Determine equivalent Organ at Risk (OAR) tolerance dose (TD) constraints for MV x-rays and particle therapy. Methods: Equivalent TD estimates for MV x-rays are determined from an isoeffect, regression-analysis of published and in-house constraints for various fractionation schedules (n fractions). The analysis yields an estimate of (α/β) for an OAR. To determine equivalent particle therapy constraints, the MV x-ray TD(n) values are divided by the RBE for DSB induction (RBE{sub DSB}) or cell survival (RBE{sub S}). Estimates of (RBE{sub DSB}) are computed using the Monte Carlo Damage Simulation, and estimates of RBES are computed using the Repair-Misrepair-Fixation (RMF) model. A research build of the RayStation™ treatment planning system implementing the above model is used to estimate (RBE{sub DSB}) for OARs of interest in 16 proton therapy patient plans (head and neck, thorax, prostate and brain). Results: The analysis gives an (α/β) estimate of about 20 Gy for the trachea and heart and 2–4 Gy for the esophagus, spine, and brachial plexus. Extrapolation of MV x-ray constraints (n = 1) to fast neutrons using RBE{sub DSB} = 2.7 are in excellent agreement with clinical experience (n = 10 to 20). When conventional (n > 30) x-ray treatments are used as the reference radiation, fast neutron RBE increased to a maximum of 6. For comparison to a constant RBE of 1.1, the RayStation™ analysis gave estimates of proton RBE{sub DSB} from 1.03 to 1.33 for OARs of interest. Conclusion: The presented system of models is a convenient formalism to synthesize from multiple sources of information a set of self-consistent plan constraints for MV x-ray and hadron therapy treatments. Estimates of RBE{sub DSB} from the RayStation™ analysis differ substantially from 1.1 and vary among patients and treatment sites. A treatment planning system that incorporates patient and anatomy-specific corrections in proton RBE would create opportunities to increase the therapeutic ratio. The research build of the RayStation used in the study was made available to the University of Washington free of charge. RaySearch Laboratories did not provide any monetary support for the reported studies.
For abstract, see N77-18469.
For abstract, see N77-18469.
For abstract, see N77-18472.
For abstract, see N77-18472.
Background: Following the success of Artemis I, NASA is preparing for human extended duration missions. Ongoing efforts are focused on mitigating mission-related risks, including those affecting crew health and performance. Communication latency, logistics of resupply and time frame of medical evacuation are barriers to provision of healthcare for these missions, especially with respect to constraints in mass, volume, and crew training. An in-depth assessment of medical risks, capabilities and resources for a specific mission design is necessary to determine an optimal balance that maximizes likelihood of mission success. Overview: IMPACT (Informed Mission Planning via Analysis of Complex Tradespaces) is a dynamic tool designed to estimate medical risk and outcomes for a specific mission design. In its current iteration, a list of medical conditions selected based on likelihood of occurrence and/or consequence was linked to a set of clinical capabilities and resources necessary for diagnosis and management. A probabilistic risk analysis tool was then used to identify and estimate the likelihood and consequence of risks through the following outcome metrics: loss of crew life (inflight mortality due to medical conditions), need for medical evacuation (return to definitive care), and crew disability (task time affected based on how medical conditions influence the ability to perform specific exploration mission crew tasks). Finally, the model’s optimization algorithm provides recommendations for medical capabilities that maximize risk mitigation relative to mass and volume constraints. In the Spring of 2023, IMPACT was utilized to estimate outcome metrics for a design reference mission that would be representative of an extended duration Artemis mission. Notional data generated were then used to determine a recommended set of medical capabilities and resources relative to user-defined mass and volume constraints. A multidisciplinary team has also been updating IMPACT to strengthen the model’s fidelity. Figure 1 shows how updates to outcome metric inputs for the conditions resulted in different capability and resource allocation recommendations. Discussion: This presentation will discuss the IMPACT tool and share the latest data generated for a representative extended duration Artemis mission. Efforts to improve the fidelity of data generated by the model’s algorithm will also be discussed.
Background: Following the success of Artemis I, NASA is preparing for human extended duration missions. Ongoing efforts are focused on mitigating mission-related risks, including those affecting crew health and performance. Communication latency, logistics of resupply and time frame of medical evacuation are barriers to provision of healthcare for these missions, especially with respect to constraints in mass, volume, and crew training. An in-depth assessment of medical risks, capabilities and resources for a specific mission design is necessary to determine an optimal balance that maximizes likelihood of mission success. Overview: IMPACT (Informed Mission Planning via Analysis of Complex Tradespaces) is a dynamic tool designed to estimate medical risk and outcomes for a specific mission design. In its current iteration, a list of medical conditions selected based on likelihood of occurrence and/or consequence was linked to a set of clinical capabilities and resources necessary for diagnosis and management. A probabilistic risk analysis tool was then used to identify and estimate the likelihood and consequence of risks through the following outcome metrics: loss of crew life (inflight mortality due to medical conditions), need for medical evacuation (return to definitive care), and crew disability (task time affected based on how medical conditions influence the ability to perform specific exploration mission crew tasks). Finally, the model’s optimization algorithm provides recommendations for medical capabilities that maximize risk mitigation relative to mass and volume constraints. In the Spring of 2023, IMPACT was utilized to estimate outcome metrics for a design reference mission that would be representative of an extended duration Artemis mission. Notional data generated were then used to determine a recommended set of medical capabilities and resources relative to user-defined mass and volume constraints. A multidisciplinary team has also been updating IMPACT to strengthen the model’s fidelity. Figure 1 shows how updates to outcome metric inputs for the conditions resulted in different capability and resource allocation recommendations. Discussion: This presentation will discuss the IMPACT tool and share the latest data generated for a representative extended duration Artemis mission. Efforts to improve the fidelity of data generated by the model’s algorithm will also be discussed.
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