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Calibration of elastoplastic constitutive model parameters from full-field data with automatic differentiation-based sensitivities

Here, we present a framework for calibration of parameters in elastoplastic constitutive models that is based on the use of automatic differentiation (AD). The model calibration problem is posed as a partial differential equation-constrained optimization problem where a finite element (FE) model of the coupled equilibrium equation and constitutive model evolution equations serves as the constraint. The objective function quantifies the mismatch between the displacement predicted by the FE model and full-field digital image correlation data, and the optimization problem is solved using gradient-based optimization algorithms. Forward and adjoint sensitivities are used to compute the gradient at considerably less cost than its calculation from finite difference approximations. Through the use of AD, we need only to write the constraints in terms of AD objects, where all of the derivatives required for the forward and inverse problems are obtained by appropriately seeding and evaluating these quantities. We present three numerical examples that verify the correctness of the gradient, demonstrate the AD approach's parallel computation capabilities via application to a large-scale FE model, and highlight the formulation's ease of extensibility to other classes of constitutive models.

42 ENGINEERING↗

Tumor Radiation Therapy Creates Therapeutic Vaccine Responses to the Colorectal Cancer Antigen GUCY2C

Purpose: Radiation therapy (RT) is thought to produce clinical responses in cancer patients, not only through direct toxicity to cancer cells and supporting tumor stroma cells, but also through activation of immunologic effectors. More recently, RT has potentiated the local and systemic effects of cancer immunotherapy (IT). However, combination regimens that maximize immunologic and clinical efficacy remain undefined. Methods and Materials: We evaluated the impact of local RT on adenoviral-mediated vaccination against the colorectal cancer antigen GUCY2C (Ad5-GUCY2C) in a murine subcutaneous tumor model using mouse CT26 colon cancer cells (CT26-GUCY2C). Immune responses were assessed by ELISpot, and clinical responses were assessed by tumor size and incidence. Results: The specific sequence of tumor-directed RT preceding Ad5-GUCY2C IT transformed inactive therapeutic Ad5-GUCY2C vaccination into a curative vaccine. GUCY2C-specific T cell responses were amplified (P<.05), tumor eradication was maximized (P<.01), and tumor volumes were minimized (P<.001) in mice whose tumors were irradiated before, compared with after, Ad5-GUCY2C vaccination. The immunologic and antitumor efficacy of Ad5-GUCY2C was amplified comparably by unfractionated (8 Gy × 1), or biologically equivalent doses of fractionated (3.5 Gy × 3), RT. The antitumor effects of sequential RT and IT (RT-IT) depended on expression of GUCY2C by tumor cells and the adenoviral vaccine vector, and tumor volumes were inversely related to the magnitude of GUCY2C-specific T cell responses. Moreover, mice cured of CT26-GUCY2C tumors by RT-IT showed long-lasting antigen-dependent protection, resisting tumors formed by GUCY2C-expressing 4T1 breast cancer cells inoculated 50 days after CT26 cells. Conclusions: Optimal sequencing of RT and IT amplifies antigen-specific local and systemic immune responses, revealing novel acute and long-term therapeutic antitumor protection. These observations underscore the importance of modality sequence optimization before the initiation of clinical trials of RT and IT to maximize immune and antitumor responses.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Elastic robot control - Nonlinear inversion and linear stabilization

An approach to the control of elastic robot systems for space applications using inversion, servocompensation, and feedback stabilization is presented. For simplicity, a robot arm (PUMA type) with three rotational joints is considered. The third link is assumed to be elastic. Using an inversion algorithm, a nonlinear decoupling control law u(d) is derived such that in the closed-loop system independent control of joint angles by the three joint torquers is accomplished. For the stabilization of elastic oscillations, a linear feedback torquer control law u(s) is obtained applying linear quadratic optimization to the linearized arm model augmented with a servocompensator about the terminal state. Simulation results show that in spite of uncertainties in the payload and vehicle angular velocity, good joint angle control and damping of elastic oscillations are obtained with the torquer control law u = u(d) + u(s).

Singh, S. N.↗

Latent uncertainties of the precalculated track Monte Carlo method

Purpose: While significant progress has been made in speeding up Monte Carlo (MC) dose calculation methods, they remain too time-consuming for the purpose of inverse planning. To achieve clinically usable calculation speeds, a precalculated Monte Carlo (PMC) algorithm for proton and electron transport was developed to run on graphics processing units (GPUs). The algorithm utilizes pregenerated particle track data from conventional MC codes for different materials such as water, bone, and lung to produce dose distributions in voxelized phantoms. While PMC methods have been described in the past, an explicit quantification of the latent uncertainty arising from the limited number of unique tracks in the pregenerated track bank is missing from the paper. With a proper uncertainty analysis, an optimal number of tracks in the pregenerated track bank can be selected for a desired dose calculation uncertainty. Methods: Particle tracks were pregenerated for electrons and protons using EGSnrc and GEANT4 and saved in a database. The PMC algorithm for track selection, rotation, and transport was implemented on the Compute Unified Device Architecture (CUDA) 4.0 programming framework. PMC dose distributions were calculated in a variety of media and compared to benchmark dose distributions simulated from the corresponding general-purpose MC codes in the same conditions. A latent uncertainty metric was defined and analysis was performed by varying the pregenerated track bank size and the number of simulated primary particle histories and comparing dose values to a “ground truth” benchmark dose distribution calculated to 0.04% average uncertainty in voxels with dose greater than 20% of D{sub max}. Efficiency metrics were calculated against benchmark MC codes on a single CPU core with no variance reduction. Results: Dose distributions generated using PMC and benchmark MC codes were compared and found to be within 2% of each other in voxels with dose values greater than 20% of the maximum dose. In proton calculations, a small (≤1 mm) distance-to-agreement error was observed at the Bragg peak. Latent uncertainty was characterized for electrons and found to follow a Poisson distribution with the number of unique tracks per energy. A track bank of 12 energies and 60000 unique tracks per pregenerated energy in water had a size of 2.4 GB and achieved a latent uncertainty of approximately 1% at an optimal efficiency gain over DOSXYZnrc. Larger track banks produced a lower latent uncertainty at the cost of increased memory consumption. Using an NVIDIA GTX 590, efficiency analysis showed a 807 × efficiency increase over DOSXYZnrc for 16 MeV electrons in water and 508 × for 16 MeV electrons in bone. Conclusions: The PMC method can calculate dose distributions for electrons and protons to a statistical uncertainty of 1% with a large efficiency gain over conventional MC codes. Before performing clinical dose calculations, models to calculate dose contributions from uncharged particles must be implemented. Following the successful implementation of these models, the PMC method will be evaluated as a candidate for inverse planning of modulated electron radiation therapy and scanned proton beams.

07 ISOTOPE AND RADIATION SOURCES↗

An efficient approach to ab initio Monte Carlo simulation

We present a Nested Markov chain Monte Carlo (NMC) scheme for building equilibrium averages based on accurate potentials such as density functional theory. Metropolis sampling of a reference system, defined by an inexpensive but approximate potential, was used to substantially decorrelate configurations at which the potential of interest was evaluated, thereby dramatically reducing the number needed to build ensemble averages at a given level of precision. The efficiency of this procedure was maximized on-the-fly through variation of the reference system thermodynamic state (characterized here by its inverse temperature β{sup 0}), which was otherwise unconstrained. Local density approximation results are presented for shocked states of argon at pressures from 4 to 60 GPa, where—depending on the quality of the reference system potential—acceptance probabilities were enhanced by factors of 1.2–28 relative to unoptimized NMC. The optimization procedure compensated strongly for reference potential shortcomings, as evidenced by significantly higher speedups when using a reference potential of lower quality. The efficiency of optimized NMC is shown to be competitive with that of standard ab initio molecular dynamics in the canonical ensemble.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Use of a New Analytical Model To Match Production Data and Identify Opportunities To Maximize Well Productivity in the Tuscaloosa Marine Shale Reservoir

The low productivity of the oil wells in the Tuscaloosa Marine Shale (TMS) Trend, located in Louisiana and Mississippi, is a mystery. Production data from 55 wells in the TMS Trend were analyzed to identify possible means of enhancing well productivity. The -1/2 slope in a log–log plot for reservoir linear flow (RLF) was observed for some wells, but not all, and the -1 slope for boundary–dominated flow (BDF) has not been seen in the past 5 years of production. The behavior of the TMS wells is attributed to the ultralow permeability of the TMS matrix and the decline of fracture conductivity, both of which delay the BDF. On the basis of the concept of the distance of investigation, derived from the radius–of–investigation concept, the matrix permeability of the seven TMS wells was estimated to be between 34 and 65 nd, with an average of 51 nd. A new mathematical model for production decline of multifractured horizontal wells was developed taking into consideration the time–dependent fracture conductivity during the BDF period. This model fits TMS–well production data, with an average error of 6.12% and an R2 value of 0.96. Assuming constant matrix permeability, fitting the new model to the production data in the BDF period gives a rate of fracture–conductivity decline of between 0.20 and 0.74% per month. The new mathematical model reveals opportunities to optimize well completion to enhance well productivity in the TMS Trend. For a given amount of fracture proppant allocated to a well, the shortest possible fracture spacing should be used to maximize well productivity. If the number of fractures is fixed as a constraint of well completion design, well productivity is inversely proportional to the square root of fracture spacing (i.e., if the fracture spacing is shortened by fourfold, well productivity is expected to double). If the horizontal wellbore length is fixed as a constraint of well completion, well productivity is inversely proportional to fracture spacing (i.e., if the fracture spacing is shortened by 50%, well productivity is expected to double).

Engineering↗

Robust torque control of an elastic robotic arm based on invertibility and feedback stabilization

An approach to the control of elastic robotic systems for space applications using inversion, servocompensation, and feedback stabilization is presented. For simplicity, a robot arm (PUMA-type) with three rotational joints is considered. The third link is assumed to be elastic. Using an inversion algorithm, a nonlinear decoupling control law, u sub d, is derived such that in the closed loop system, independent control of joint angles by the three joint torquers is accomplished. For the stabilization of elastic oscillations, a linear feedback torquer control law, u sub s, is obtained applying linear quadratic optimization to the linearized arm model augmented with a servocompensator about the terminal state. Simulation results show that, in spite of uncertainties in the payload and vehicle angular velocity, good joint angle control and damping of elastic oscillations are obtained with the torquer control law u = u sub d + u sub s.

Singh, S. N.↗

Particle Segregation in a Flowing Suspension Subject to High-Gradient Strong Electric Fields

The widespread use of electro-hydrodynamic devices and processes emphasizes a critical need for developing a comprehensive predictive theory capable of improving our fundamental understanding of the behavior of a suspension subject to an AC electric field and shear, and of facilitating the design and optimization of such devices. The currently favored approach to the qualitative interpretation of the AC field driven manipulation of suspensions is based on a model which considers only the force exerted on a single particle by an external field and neglects the field-induced and hydrodynamic interparticle interactions both being inversely proportional to the interparticle distance raised to the power three. On the other hand, the purpose of the field-induced separation is to concentrate particles in certain regions of a device. This clearly raises the fundamental question regarding the extent to which we can neglect these slow decaying electrical and hydrodynamic collective interactions and rely on the predictions of a single-particle model. Another important issue that still remains open is how to characterize the polarization of a particle exposed to a strong electric field. The presentation will address both these questions. Experiments were conducted in a parallel-plate channel in which a 10(exp -3) (v/v) suspension of heavy, positively polarized Al2O3 spheres was exposed to an AC field under conditions such that the field lines were arranged in the channel cross-section perpendicular to the streamlines of the main flow. To reduce the effects of the gravitational settling of the particles, the channel was slowly rotated (4 rpm) around a horizontal axis. Following the application of a high-gradient strong AC field (approx. kV/mm), the particles were found to move towards both the high-voltage (HV) and grounded (GR) electrodes and to form 'bristles' along their edges.

Acrivos, Andreas↗

Development of Multi-Sensor Global Cloud and Radiance Composites for Earth Radiation Budget Monitoring from DSCOVR

The Deep Space Climate Observatory (DSCOVR) enables analysis of the daytime Earth radiation budget via the onboard Earth Polychromatic Imaging Camera (EPIC) and National Institute of Standards and Technology Advanced Radiometer (NISTAR). Radiance observations and cloud property retrievals from low earth orbit and geostationary satellite imagers have to be co-located with EPIC pixels to provide scene identification in order to select anisotropic directional models needed to calculate shortwave and longwave fluxes. A new algorithm is proposed for optimal merging of selected radiances and cloud properties derived from multiple satellite imagers to obtain seamless global hourly composites at 5-kilometer resolution. An aggregated rating is employed to incorporate several factors and to select the best observation at the time nearest to the EPIC measurement. Spatial accuracy is improved using inverse mapping with gradient search during reprojection and bicubic interpolation for pixel resampling. The composite data are subsequently remapped into EPIC-view domain by convolving composite pixels with the EPIC point spread function (PSF) defined with a half-pixel accuracy. PSF-weighted average radiances and cloud properties are computed separately for each cloud phase. The algorithm has demonstrated contiguous global coverage for any requested time of day with a temporal lag of under 2 hours in over 95 percent of the globe.

Khlopenkov, Konstantin↗

Predicting Dynamic-to-Static Correction Factor from Petrophysical Data and Chemostratigraphy using Unsupervised Machine Learning

Estimating static mechanical properties of stratigraphic layers is critical for optimizing subsurface engineering applications. To estimate dynamic-to-static correction factor F ds (static-to-dynamic Young’s modulus ratio) across the Caney shale interval in Oklahoma, USA, we integrated triaxial test measurements and petrophysical data, including well logs and X-ray fluorescence (XRF) using unsupervised machine learning (ML). We used a novel workflow that includes principal component analysis (PCA) to reduce data set dimensionality of well logs and XRF data sets—both separately and combined—creating three scenarios, and later applied inverse distance weighting (IDW) to derive F ds profiles for these scenarios. Furthermore, we applied K-means clustering on each scenario to predict depositional facies, and built a stiffness zonation profile through chemostratigraphic analysis of the terrigenous elements to validate the predicted F ds . The predicted F ds profile from each scenario using the PCA-IDW method was compared with the constant F ds approach from our previous study by calculating the root mean square error (RMSE). The combined data sets scenario yielded the lowest RMSE value of 0.113, while the RMSE values for the well logs and XRF scenarios were 0.131 and 0.129, respectively. In addition, the predicted F ds from the XRF scenario well-matched the stiffness zonation from the chemostratigraphic analysis that was built using the optimized K-means clustering of nine clusters for that scenario. These methods and findings offer a valuable tool for refining lithological classification and improving the F ds profile, potentially enhancing drilling and stimulation strategies for subsurface energy engineering applications.

clastic rock↗

nPINNs: Nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications

Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integro-differential equations with sparse, noisy, unstructured, and multifidelity data. PINNs incorporate all available information, including governing equations (reflecting physical laws), initial-boundary conditions, and observations of quantities of interest, into a loss function to be minimized, thus recasting the original problem into an optimization problem. In this paper, we extend PINNs to parameter and function inference for integral equations such as nonlocal Poisson and nonlocal turbulence models, and we refer to them as nonlocal PINNs (nPINNs). The contribution of the paper is three-fold. First, we propose a unified nonlocal Laplace operator, which converges to the classical Laplacian as one of the operator parameters, the nonlocal interaction radius $\delta$ goes to zero, and to the fractional Laplacian as $\delta$ goes to infinity. This universal operator forms a super-set of classical Laplacian and fractional Laplacian operators and, thus, has the potential to fit a broad spectrum of data sets. We also provide theoretical convergence rates with respect to $\delta$ and verify them via numerical experiments. Second, we use nPINNs to estimate the two parameters, $\delta$ and $\alpha$, characterizing the kernel of the unified operator. The strong non-convexity of the loss function yielding multiple (good) local minima reveals the occurrence of the operator mimicking phenomenon, that is, different pairs of estimated parameters could produce multiple solutions of comparable accuracy. Third, we propose another nonlocal operator with spatially variable order $\alpha(y)$, which is more suitable for modeling turbulent Couette flow. Our results show that nPINNs can jointly infer this function as well as $\delta$. More importantly, these parameters exhibit a universal behavior with respect to the Reynolds number, a finding that contributes to our understanding of nonlocal interactions in wall-bounded turbulence.

97 MATHEMATICS AND COMPUTING↗

Direct evidence for a pressure-induced nodal superconducting gap in the Ba 0.65 Rb 0.35 Fe 2 As 2 superconductor

The superconducting gap structure in iron-based high-temperature superconductors (Fe-HTSs) is non-universal. Contrasting with other unconventional superconductors, in the Fe-HTSs both d-wave and extended s-wave pairing symmetries are close in energy. Probing the proximity between these very different superconducting states and identifying experimental parameters that can tune them is of central interest. Here we report high-pressure muon spin rotation experiments on the temperature-dependent magnetic penetration depth in the optimally doped nodeless s-wave Fe-HTS Ba 0.65 Rb 0.35 Fe 2 As 2 . Upon pressure, a strong decrease of the penetration depth in the zero-temperature limit is observed, while the superconducting transition temperature remains nearly constant. More importantly, the low-temperature behaviour of the inverse-squared magnetic penetration depth, which is a direct measure of the superfluid density, changes qualitatively from an exponential saturation at zero pressure to a linear-in-temperature behaviour at higher pressures, indicating that hydrostatic pressure promotes the appearance of nodes in the superconducting gap.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications

Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integro-differential equations with sparse, noisy, unstructured, and multifidelity data. PINNs incorporate all available information, including governing equations (reflecting physical laws), initial-boundary conditions, and observations of quantities of interest, into a loss function to be minimized, thus recasting the original problem into an optimization problem. In this paper, we extend PINNs to parameter and function inference for integral equations such as nonlocal Poisson and nonlocal turbulence models, and we refer to them as nonlocal PINNs (nPINNs). The contribution of the paper is three-fold. First, we propose a unified nonlocal Laplace operator, which converges to the classical Laplacian as one of the operator parameters, the nonlocal interaction radius δ goes to zero, and to the fractional Laplacian as δ goes to infinity. This universal operator forms a super-set of classical Laplacian and fractional Laplacian operators and, thus, has the potential to fit a broad spectrum of data sets. We provide theoretical convergence rates with respect to δ and verify them via numerical experiments. Second, we use nPINNs to estimate the two parameters, δ and α, characterizing the kernel of the unified operator. The strong non-convexity of the loss function yielding multiple (good) local minima reveals the occurrence of the operator mimicking phenomenon, that is, different pairs of estimated parameters could produce multiple solutions of comparable accuracy. Third, we propose another nonlocal operator with spatially variable order α(γ), which is more suitable for modeling turbulent Couette flow. Our results show that nPINNs can jointly infer this function as well as δ. More importantly, these parameters exhibit a universal behavior with respect to the Reynolds number, a finding that contributes to our understanding of nonlocal interactions in wall-bounded turbulence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Combined linear theory/impact theory method for analysis and design of high speed configurations

Pressure distributions on a wing body at Mach 4.63 are calculated. The combined theory is shown to give improved predictions over either linear theory or impact theory alone. The combined theory is also applied in the inverse design mode to calculate optimum camber slopes at Mach 4.63. Comparisons with optimum camber slopes obtained from unmodified linear theory show large differences. Analysis of the results indicate that the combined theory correctly predicts the effect of thickness on the loading distributions at high Mach numbers, and that finite thickness wings optimized at high Mach numbers using unmodified linear theory will not achieve the minimum drag characteristics for which they are designed.

Brooke, D.↗

Understanding the Origin of Negative Temperature Dependence and Activity of N-Coordinated Cobalt Sites During Ethylene Dimerization

The on-demand production of short-chain linear alpha olefins (LAOs; C4-C8) via C2H4 dimerization and oligomerization is industrially attractive, prompting extensive research on designing active, selective, and stable catalysts for industrial use. Cobalt supported on ammoniated carbon (Co(NH3)x/C) catalysts have shown remarkable activity and selectivity in this process. However, critical aspects such as the active phase, active site structure, the role of the catalyst support, cobalt loading effects, and the inverse correlation of the reaction rate with temperature remain inadequately understood. This study systematically explores these factors using a combination of steady-state differential catalytic tests, in situ molecular characterization including diffuse reflectance UV-Vis (DR-UV-Vis), Infrared, and Raman spectroscopies, and ex situ X-ray diffraction (XRD) and high annular aberration-corrected dark field transmission electron microscopy (HAADF-STEM). Various supports (SiO2, Al2O3, NH4-ZSM-5, g-C3N4, and C) and cobalt loadings (1.0-3.0 Co nm-2) were studied to determine the optimal catalyst composition and identify the active phase and sites. Carbon-supported catalysts uniquely produce C4-8 LAOs during C2H4 dimerization, with site-time-yield remaining constant (~10-3 s-1) for 1.0-4.0 Co nm-2 at prolonged reaction times (24-48?h time-on-stream). At higher loadings of 6.0 Co nm-2, the formation of crystalline CoO and Co3O4 phases reduces catalytic activity and LAO selectivity. Our findings show that active catalysts lack crystalline cobalt oxides and instead feature dispersed Co2+ sites, tetra-coordinated to a mix of N/NH3 and O/H2O ligands, which catalyze C2H4 dimerization via the Cossee-Arlman mechanism, exhibiting 1st order dependence on C2H4 concentration. The observed inverse rate-temperature correlation is attributed to compensation effects (i.e., presence of Cremer-Constable relationship) linked to changes in adsorption enthalpic and entropic factors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Optimal sensing on an asymmetric exceptional surface

We study the connection between exceptional points (EPs) and optimal parameter estimation, in a simple system consisting of two counterpropagating traveling wave modes in a microring resonator. The unknown parameter to be estimated is the strength of a perturbing cross-coupling between the two modes. Partially reflecting the output of one mode into the other creates a non-Hermitian Hamiltonian that exhibits a family of EPs, creating an exceptional surface (ES). We use a fully quantum treatment of field inputs and noise sources to obtain a quantitative bound on the estimation error by calculating the quantum Fisher information (QFI) in the output fields, whose inverse gives the Cramér-Rao lower bound on the mean-squared error of any unbiased estimator. We determine the bounds for two input states, namely, a semiclassical coherent state and a highly nonclassical NOON state. We find that the QFI is enhanced in the presence of an EP for both of these input states and that both states can saturate the Cramér-Rao bound. We then identify idealized yet experimentally feasible measurements that achieve the minimum bound for these two input states. We also investigate how the QFI changes for parameter values that do not lie on the ES, finding that these can have a larger QFI, suggesting alternative routes to optimize the parameter estimation for this problem.

Exceptional points↗

Optimization of Time-Dependent Particle Tracing Using Tetrahedral Decomposition

An efficient algorithm is presented for computing particle paths, streak lines and time lines in time-dependent flows with moving curvilinear grids. The integration, velocity interpolation and step-size control are all performed in physical space which avoids the need to transform the velocity field into computational space. This leads to higher accuracy because there are no Jacobian matrix approximations or expensive matrix inversions. Integration accuracy is maintained using an adaptive step-size control scheme which is regulated by the path line curvature. The problem of cell-searching, point location and interpolation in physical space is simplified by decomposing hexahedral cells into tetrahedral cells. This enables the point location to be done analytically and substantially faster than with a Newton-Raphson iterative method. Results presented show this algorithm is up to six times faster than particle tracers which operate on hexahedral cells yet produces almost identical particle trajectories.

Kenwright, David↗