Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Differential”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,099 records · Page 61
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Dual-frequency (Ka-band and G-band) radar estimates of liquid water content profiles in shallow clouds

The profile of the liquid water content (LWC) in clouds provides fundamental information for understanding the internal structure of clouds, their radiative effects, propensity to precipitate, and degree of entrainment and mixing with the surrounding environment. In principle, differential absorption techniques based on coincident dual-frequency radar reflectivity observations have the potential to provide the LWC profile. Previous differential frequency radar reflectivity (DFR) efforts were challenged by the fact that the measurable differential attenuation for small quantities of LWC is usually comparable to the system measurement error. This typically renders the retrieval impractical, as the uncertainty can become many times greater than the retrieved value itself. Theoretically, this drawback can be mitigated following two interconnected approaches: (1) increasing the frequency separation between the dual-frequency radar system to measure greater differential attenuation and (2) increasing the radar operating frequency to reduce the instrument measurement random error. Our recently developed 239 GHz radar was deployed during the Eastern Pacific Cloud Aerosol Precipitation Experiment (EPCAPE) along with a variety of collocated remote sensing and in situ instruments. We have combined Ka-band (35 GHz) and G-band (239 GHz) observations to retrieve the LWC from more than 100 vertical profiles of shallow clouds with typical amounts of LWC smaller than 1 g m -3 . We theoretically and experimentally demonstrate that the Ka-band and G-band pair of frequencies offers at least a 65 % relative improvement in the LWC retrieval sensitivity compared to previous works reported in the literature using lower-frequency radars. This new technique provides a missing capability to determine the LWC in the challenging low liquid water path (LWP) range (< 200 g m -2 ) and suggests a way forward to characterize microphysical and dynamical processes more precisely in shallow clouds.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Dimming LED circuit augmenting DC/DC controller integrated circuit

Embodiments include systems, methods, and apparatuses for providing a dimming function in a single stage AC input light emitting diode (LED) driver with a controller that contains an on-chip error amplifier and an on-chip fixed reference voltage source coupled to a first input of the error amplifier. The controller controls a duty cycle of a switching transistor to cause a feedback voltage, applied to a first package input terminal, to match the reference voltage. To achieve a dimming function, a voltage across a current sense resistor in series with the LEDs is applied to a first input of a high gain differential amplifier, and a variable dimming control voltage is applied to a second input of the differential amplifier. The output of the differential amplifier is coupled to the first package input terminal. The differential amplifier input signals will be matched at the target LED current level.

Song, Zhengrong↗
DOE OSTI2024

Importance of Higher Fidelity Model Geometries during Optimization of Critical Experiments

PARADIGM, PARallel Approach of Differential and InteGral Measurements, is a cross-collaborative effort at Los Alamos National Laboratory between nuclear data theorists, differential and integral experimenters, as well as machine learning statisticians to tackle uncertainties in the intermediate region of 239 Pu. In essence, the idea behind PARADIGM is to remove the linear conceptualization of the nuclear data pipeline, shown in Figure 1, and replace it with a far more parallelized approach. The novel approach leverages machine learning to guide which differential measurements and integral experiments will result in the largest decrease in uncertain ties for a nuclide reaction pair in a given energy range. The concept builds off earlier work, EUCLID, which focused on the fast region of 239 Pu. The practical benefit of having evaluation, differential measurement, and integral experiment personnel in collaboration with machine learning is to represent the entire nuclear data in one snapshot. This enable large reduction in the time to deliver improved nuclear data, which using the PARADIGM approach could be done in 3 years. A general outline of PARADIGM and specific topics are available in other papers. The discussion here will pertain directly to the integral experiment design. More specifically, the process of taking a rough design and transforming it into a finalized neutronic model will be discussed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Selective Detection of Diglycolamide Diastereomers By Metal-Ligand Cluster Formation

Introduction (120 words): Differentiation of isomers using mass spectrometry is a challenge, as these species tend to produce ions of identical mass-to-charge ratio. Therefore, separation with mass spectrometry must rely on chemical differences between isomeric species. Separation of stereoisomers is especially challenging, as these species often have very similar chemistry. However, recent investigations of the solvent extraction behavior of diastereomers of diglycolamide molecules have shown that different stereoisomers can have significantly different lanthanide extraction efficiencies. These studies showed that the R,S stereoisomer of 2,2'-oxybis(N,N-dioctylpropanamide efficiently extracts lanthanides, while the S,S stereoisomer does not. Thus, gas-phase metal complexation may provide a pathway for differentiating these species using mass spectrometry. Methods (120 words): Europium, samarium, and holmium clusters with the R,S, and the S,S diastereomers of 2,2'-oxybis(N,N-didecylpropanamide (trivially tetradecyl diglycolamide, or mTDDGA) were generated in gas-phase using the electrospray ionization source of a Bruker (Billerica, MA, USA) micrOTOF-Q II quadrupole time-of-flight mass spectrometer. Solutions of aqueous lanthanide nitrate and diglycolamide ligands in 2-propanol were added to 50%:50% by volume acetonitrile:2-propanol to generate the spray solutions. Ligand concentration was maintained at approximately 6 µM, while lanthanide concentration was maintained at either 6 µM or 30 µM . High resolution, high mass accuracy spectra were recorded using the time-of-flight. Mass accuracy was ensured using external calibration with Agilent (Santa Clara, CA, USA) ESI-L Low Concentration tuning mix. Preliminary data (300 words): Electrospray of solutions containing only R,S-mTDDGA or S,S-m-TDDGA yield abundant peaks at m/z= 721.7, corresponding to [mTDDGA+H]+1, m/z = 743.7, corresponding to [mTDDGA+Na]+1, and m/z = 1464.4, corresponding to the sodium-bound dimer, [Na(mTDDGA)2]+1. Spray of solutions containing 6 µM europium (Eu) with 3 µM R,S-mTDDGA produced an abundant cluster ion with an isotopic envelope centered at m/z=772.0, corresponding to [Eu(R,S-mTDDGA)3]3+. Europium-containing cluster ions with isotopic envelopes apexing at m/z = 1012.3 and 1189.0 correspond to the [Eu(R,S-mTDDGA)4]3+ and [Eu(R,S-mTDDGA)5]3+ cluster ions, respectively. Protonated and sodiated R,S-mTDDGA are present as well, along with the sodium-bound dimer. In contrast, spray of solutions containing 6 µM europium (Eu) with 3 µM S,S-mTDDGA diastereomer yielded only protonated and sodiated ligand ions; no Eu- S,S-mTDDGA ions were present. This mirrors the solution-phase behavior, where the S,S diestereomer extracts lanthanides with significantly less efficiency than the R,S diestereomer. Experiments with holmium and samarium yielded the same results. Increasing the lanthanide concentration to 30 µM resulted in limited formation of lanthanide-S,S-mTDDGA clusters. However, the abundance of the [Ln(S,S-mTDDGA)3]3+ clusters remained low compared to the abundance of the protonated and sodiated ligand. Additionally, the abundance of the [Ln(R,S-mTDDGA)3]3+ cluster ion was significantly higher than that of the protonated and sodiated ligand in experiments with spray solutions containing 30 µM lanthanide with R,S-mTDDA, supporting the hypothesis that R,S-mTDDGA has a higher intrinsic affinity for the lanthanides than S,S-mTDDGA. Thus, the intrinsic complexation with lanthanides appears to offer a route to differentiate diglycolamide diestereomers in the gas-phase. Novelty (20): Stereoisomers can be differentiated in the gas phase by exploitation of differences in metal complexation chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Functional Data Analysis in Wearable Body Sensor Networks

Improving response time of indirect room-size calorimeters is still an outstanding problem in metabolic research. Accurate estimates of instantaneous rates of gaseous exchange require numerical differentiation of measured gaseousgas concentrations. We propose a new method to estimate the instantaneous gaseousgas exchange rates in indirect calorimetry. In contrast to the previously developed techniques, the method addresses the problem of differentiation of gaseous concentrations as an ill-posed problem. By applying the method of regularization, the problem of differentiation is converted into a well-posed problem resulting in smooth and consistent gaseous exchange rates. The validity of the method is tested on a large dataset of calorimeter experiments which included 313 human experiments along with 231 alcohol combustion experiments. It is demonstrated that the method is able to reliably differentiate between the “unphysiological” process of alcohol combustion and physiological variations produced by human metabolism. The method also allowed unraveling the previously unreported relative kinetics of O2 consumption and Respiratory Quotient (RQ) in humans. It was found that the kinetics of oxidative fuel selection lags behind the energy expenditure in humans exhibiting some sort of oxidative inertia. The time lag varies from 2-3 min up to 30 min, depending on particular individual. No such lag was found in alcohol combustion experiments. In addition to the relative kinetics of substrate oxidation, two statistical indexes reflecting variability of minute-by-minute RQ were estimated. The indexes were the RQ’s standard deviation and RQ’s first-order derivative. Both indexes showed statistically significant difference between human experiments and alcohol combustion experiments. We conclude that the proposed method can consistently extract physiologically-relevant information from noisy calorimetry data and the aforesaid information can provide additional insights into the mechanism of metabolic fuel selection in humans.

60 - APPLIED LIFE SCIENCES↗
DOE OSTI2022

Learning generative neural networks with physics knowledge

Deep generative neural networks have enabled modeling complex distributions, but incorporating physics knowledge into the neural networks is still challenging and is at the core of current physics-based machine learning research. To this end, we propose a physics generative neural network (PhysGNN), a new class of generative neural networks for learning unknown distributions in a physical system described by partial differential equations (PDE). PhysGNN couples PDE systems with generative neural networks. It is a fully differentiable model that allows back-propagation of gradients through both numerical PDE solvers and generative neural networks, and is trained by minimizing the discrete Wasserstein distance between generated and observed probability distributions of the PDE outputs using the stochastic gradient descent method. Moreover, PhysGNN does not require adversarial training like standard generative neural networks, which offers better stability than adversarial training. We show that PhysGNN can learn complex distributions in stochastic inverse problems, where conventional methods such as maximum likelihood estimation and momentum matching methods may be inapplicable when little knowledge is known about the form of unknown distributions or the physical model is too complex. Furthermore, our method allows physics-based generative neural network training for learning complex distributions in the context of differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Loops of loops expansion in the amplituhedron

We study a novel geometric expansion for scattering amplitudes in the planar sector of $\mathcal{N}$ = 4 super Yang-Mills theory, in the context of the Amplituhedron which reproduces the all-loop integrand as a canonical differential form on the positive geometry. In a paper by Arkani-Hamed, Henn and one of the authors, it was shown that this result can be recast in terms of negative geometries with a certain hierarchy of loops (closed cycles) in the space of loop momenta, represented by lines in momentum twistor space. One can then calculate an all-loop order result in the approximation where only tree graphs in the space of all loops are considered. Furthermore, using differential equation methods, it is possible to calculate and resum integrated expressions and obtain strong coupling results. In this paper, we provide a more general framework for the ‘loops of loops’ expansion and outline a powerful method for the determination of differential forms for higher-order geometries. We solve the problem completely for graphs with one internal cycle, but the method can be used more generally for other geometries.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Hutchinson Trace Estimation for high-dimensional and high-order Physics-Informed Neural Networks

Physics-Informed Neural Networks (PINNs) have proven effective in solving partial differential equations (PDEs), especially when some data are available by seamlessly blending data and physics. However, extending PINNs to high-dimensional and even high-order PDEs encounters significant challenges due to the computational cost associated with automatic differentiation in the residual loss function calculation. Herein, we address the limitations of PINNs in handling high-dimensional and high-order PDEs by introducing the Hutchinson Trace Estimation (HTE) method. Starting with the second-order high-dimensional PDEs, which are ubiquitous in scientific computing, HTE is applied to transform the calculation of the entire Hessian matrix into a Hessian vector product (HVP). This approach not only alleviates the computational bottleneck via Taylor-mode automatic differentiation but also significantly reduces memory consumption from the Hessian matrix to an HVP’s scalar output. We further showcase HTE’s convergence to the original PINN loss and its unbiased behavior under specific conditions. Comparisons with the Stochastic Dimension Gradient Descent (SDGD) highlight the distinct advantages of HTE, particularly in scenarios with significant variability and variance among dimensions. We further extend the application of HTE to higher-order and higher-dimensional PDEs, specifically addressing the biharmonic equation. By employing tensor-vector products (TVP), HTE efficiently computes the colossal tensor associated with the fourth-order high-dimensional biharmonic equation, saving memory and enabling rapid computation. The effectiveness of HTE is illustrated through experimental setups, demonstrating comparable convergence rates with SDGD under memory and speed constraints. Additionally, HTE proves valuable in accelerating the Gradient-Enhanced PINN (gPINN) version as well as the Biharmonic equation. Overall, HTE opens up a new capability in scientific machine learning for tackling high-order and high-dimensional PDEs.

Curse of dimensionality↗
DOE OSTI2025

Constrained or unconstrained? Neural-network-based equation discovery from data

Throughout many fields, practitioners often rely on differential equations to model systems. Yet, for many applications, the theoretical derivation of such equations and/or the accurate resolution of their solutions may be intractable. Instead, recently developed methods, including those based on parameter estimation, operator subset selection, and neural networks, allow for the data-driven discovery of both ordinary and partial differential equations (PDEs), on a spectrum of interpretability. The success of these strategies is often contingent upon the correct identification of representative equations from noisy observations of state variables and, as importantly and intertwined with that, the mathematical strategies utilized to enforce those equations. Specifically, the latter has been commonly addressed via unconstrained optimization strategies. Representing the PDE as a neural network, we propose to discover the PDE (or the associated operator) by solving a constrained optimization problem and using an intermediate state representation similar to a physics-informed neural network (PINN). The objective function of this constrained optimization problem promotes matching the data, while the constraints require that the discovered PDE is satisfied at a number of spatial collocation points. We present a penalty method and a widely used trust-region barrier method to solve this constrained optimization problem, and we compare these methods on numerical examples. Our results on several example problems demonstrate that the latter constrained method outperforms the penalty method, particularly for higher noise levels or fewer collocation points. This work motivates further exploration into using sophisticated constrained optimization methods in scientific machine learning, as opposed to their commonly used, penalty-method or unconstrained counterparts. For both of these methods, we solve these discovered neural network PDEs with classical methods, such as finite difference methods, as opposed to PINNs-type methods relying on automatic differentiation. Here, we briefly highlight how simultaneously fitting the data while discovering the PDE improves the robustness to noise and other small, yet crucial, implementation details.

Data-driven discovery↗
DOE OSTI2022

Physics constrained learning for data-driven inverse modeling from sparse observations

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that measures the discrepancy between predictions and observations in some chosen norm. This loss function often includes the PDE constraints as a penalty term when only sparse observations are available. As a result, the PDE is only satisfied approximately by the solution. However, the penalty term typically slows down the convergence of the optimizer for stiff problems. We present a new approach that trains the embedded DNNs while numerically satisfying the PDE constraints. We develop an algorithm that enables differentiating both explicit and implicit numerical solvers in reverse-mode automatic differentiation. This allows the gradients of the DNNs and the PDE solvers to be computed in a unified framework. We demonstrate that our approach enjoys faster convergence and better stability in relatively stiff problems compared to the penalty method. Furthermore, our approach allows for the potential to solve and accelerate a wide range of data-driven inverse modeling, where the physical constraints are described by PDEs and need to be satisfied accurately.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A gradient-based deep neural network model for simulating multiphase flow in porous media

We report simulation of multiphase flow in porous media is crucial for the effective management of subsurface energy and environment-related activities. The numerical simulators used for modeling such processes rely on spatial and temporal discretization of the governing mass and energy balance partial-differential equations (PDEs) into algebraic systems via finite-difference/volume/element methods. These simulators usually require dedicated software development and maintenance, and suffer low efficiency from a runtime and memory standpoint for problems with multi-scale heterogeneity, coupled-physics processes or fluids with complex phase behavior. Therefore, developing cost-effective, data-driven models can become a practical choice, and in this work, we choose deep learning approaches as they can handle high dimensional data and accurately predict state variables with strong nonlinearity. In this paper, we describe a gradient-based deep neural network (GDNN) constrained by the physics related to multiphase flow in porous media. We tackle the nonlinearity of flow in porous media induced by rock heterogeneity, fluid properties, and fluid-rock interactions by decomposing the nonlinear PDEs into a dictionary of elementary differential operators. We use a combination of operators to handle rock spatial heterogeneity and fluid flow by advection. Since the augmented differential operators are inherently related to the physics of fluid flow, we treat them as first principles prior knowledge to regularize the GDNN training. We use the example of pressure management at geologic CO 2 storage sites, where CO 2 is injected in saline aquifers and brine is produced, and apply GDNN to construct a predictive model that is trained with physics-based simulation data and emulates the physics process. We demonstrate that GDNN can effectively predict the nonlinear patterns of subsurface responses, including the temporal and spatial evolution of the pressure and saturation plumes. We also successfully extend the GDNN to convolutional neural network (CNN), namely gradient-based CNN (GCNN), and validate its capability to improve the prediction accuracy. GDNN has great potential to tackle challenging problems that are governed by highly nonlinear physics and enable the development of data-driven models with higher fidelity.

42 ENGINEERING↗
DOE OSTI2026

Performance evaluation of neutron noise analysis in detecting special nuclear materials

Reliable and rapid inspection techniques play a vital role in preventing illicit trafficking of special nuclear materials. Active interrogation systems using neutrons produced by portable, high-flux deuterium-deuterium or deuterium-tritium neutron generators are being actively developed as a secondary scanning tool for this purpose. In this study, a neutron noise analysis-based approach for detecting unshielded and shielded special nuclear materials by using a pulsed deuterium-tritium neutron generator was evaluated. Here, this approach analyzes the fluctuation of neutron counts. Its performance was quantified with regard to time-to-detection to achieve a minimum probability of detection of 99% and a probability of false alarm of less than 1% considering various amounts of special nuclear materials and different shielding configurations. It was demonstrated that this approach could detect 17 uranium slugs in 5 s given a neutron generator yield of 8.1 × 10 7 n/s. These slugs could be detected within a reasonable time frame (200 s) when they were shielded by 10.16 cm of high-density polyethylene. The results obtained using the neutron noise analysis approach were compared with those obtained using the commonly used differential die-away analysis technique, a sensitive technique for detecting the presence of fissile materials by utilizing the prompt fission neutrons produced when the source neutrons from a neutron generator are completely diminished. For example, the time to detect 2 unshielded uranium slugs was 2.1 s when using the differential die-away analysis technique; it increased to 93 s for the neutron noise analysis approach. Although the noise analysis-based approach exhibits an overall performance which is not as good as that of differential die-away, neutron noise provides an alternative method for effective detection of special nuclear materials.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Loss of MBD2 affects early T cell development by inhibiting the WNT signaling pathway

Highlights: • MBD2 deficiency resulted in retardation of T cell differentiation at the DN3 stage. • Decreased proliferative capacity and increased apoptosis were detected in Mbd2{sup −/−} DN thymocytes. • MBD2 affects early T cell development by regulating the expression of key genes of WNT pathway. DNA methylation alters the expression of certain genes without any alteration to the DNA sequence and is a dynamic process during normal hematopoietic differentiation. As an epigenetic regulator, methyl-CpG-binding domain protein 2 (MBD2) is an important member of the MBD protein family and is acknowledged as a “reader” of DNA methylation. We used a mouse model to study the effects of MBD2 on the early development of T cells. Here, we found that MBD2 deficiency led to retardation of T cell differentiation at the DN3 stage. Meanwhile, decreased proliferative capacity and increased apoptosis were detected in Mbd2{sup −/−} DN thymocytes. Furthermore, we found the WNT pathway was significantly down-regulated in Mbd2{sup −/−} DN thymocytes: DKK1 (Dickkopf-1) expression was significantly increased, while TCF7 (transcription factor 7) and c-MYC were down-regulated. Thus, these findings established that MBD2 acted as a dominant regulator to imprint DN T cell development via the WNT pathway.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Tbx18-positive cells-derived myofibroblasts contribute to renal interstitial fibrosis via transforming growth factor-β signaling

It has been demonstrated that the T-box family transcription factor 18 (Tbx18) -positive cells give rise to renal mesenchymal cells and contribute to the development of the urinary system. However, it is unclear whether Tbx18-positive cells are the origin of the myofibroblasts during renal fibrosis. The present study aimed to determine the contribution of Tbx18-positive cells in kidney fibrosis and their underlying mechanism. We show that Tbx18-positive cells contribute to the development of the urinary system, especially renal fibroblasts. Following unilateral ureteral obstruction (UUO), genetic fate tracing results demonstrated that Tbx18-positive cells not only proliferate but also expand and differentiate into fibroblasts and myofibroblasts, indicating that they may act as profibrotic progenitors. Cell culture results suggest that transforming growth factor (TGF)-β promotes Tbx18-positive cells differentiation into myofibroblasts and assist their contribution to kidney fibrosis. Overall, the present study demonstrated that Tbx18-positive cells may act as profibrotic progenitor cells in a pathological condition of UUO-induced injury. Moreover, TGF-β may play a role in differentiation of Tbx18-positive cells into myofibroblasts in kidney fibrosis. These findings may provide a potential target on Tbx18-positive myofibroblast progenitors in the treatment of renal fibrosis.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Practical Considerations for Understanding Surface Reaction Mechanisms Involved in Heterogeneous Catalysis

Acquiring useful knowledge about the active site(s) of a catalyst, nature of reactant–catalyst interactions, nature of reactive intermediates, rate-determining step, reaction rate orders that affect various process parameters, and reaction mechanism as a whole is exceedingly challenging. This is especially true in the case of heterogeneous catalysts due to the complexity of the nature of surface active sites and their nonstatic behavior. Here, we present our perspective on differentiating between various surface reaction mechanisms in light of pioneering studies by leaders in the field, with the aim of clarifying some of the confusion associated with these complex mechanisms, especially the Eley–Rideal mechanism. Using bibliometric analysis, we identify and discuss the following four reactions that most commonly invoke the Eley– Rideal mechanism: H 2 activation, CO oxidation, esterification of alcohols by acids, and selective catalytic reduction (SCR) of NO x with NH 3 . Our analysis of studies utilizing well-suited experimental and computational methodologies for differentiating surface reaction mechanisms suggests that the above-mentioned four reactions do not occur via the Eley–Rideal mechanism. Instead, each reaction occurs via the Langmuir–Hinshelwood mechanism with nonidealities present. Lastly, we highlight practical considerations regarding select experimental (characterization methods and differential kinetics) and computational modeling that we believe can provide useful insights to accurately discern between the various possible reaction mechanisms in heterogeneous catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

A tale of two planets: Disparate evolutionary models for Mars inferred from radiogenic isotope compositions of Martian meteorites

The radiogenic isotopic compositions of basaltic Martian meteorites (shergottites) and clinopyroxene/olivine cumulate meteorites (nakhlite/chassignites) are used to define the global evolution of Mars. However, the two main groups of meteorites demonstrate that their sources underwent divergent styles of magmatic evolution. The shergottites portray a planet that differentiated ~4.52 billion years ago via solidification of a magma ocean, producing incompatible element-depleted and -enriched reservoirs that remained isolated until melt production. In contrast, the reservoir from which the nakhlite/chassignites derive may have formed earlier, produced melts that fractionated Sm/Nd and Hf/W differently, was compositionally less variable, and experienced a significantly more complex history following primordial differentiation than the shergottite sources. The disparate histories recorded by these two groups of meteorites elucidate important questions that could be addressed by acquiring additional samples. Obtaining samples that shared the isotopic systematics of the shergottites would provide confidence that extrapolating the primordial differentiation history of Mars from shergottite radiogenic isotope systematics is reasonable. Returned samples from Mars will also constrain the physical locations of the meteorite source regions, providing insights into the general structure of the Martian mantle. In addition, they will help constrain the phases present in the martian mantle during melting and the conditions under which they are stable. Finally, identifying an evolved lithology that satisfies the geochemical and isotopic constraints placed on the incompatible element-enriched endmember observed in the shergottites would define the nature of magmatic evolution on Mars and whether it is more akin to processes on the Earth or the Moon.

Mars↗
DOE OSTI2021

On the Symmetry of Blast Waves

This paper presents a brief historical review of G. I. Taylor’s solution of the point blast wave problem which was applied to the Trinity test of the first atomic bomb. Lie group symmetry techniques (also referred to throughout this paper as geometric techniques) are used to derive Taylor’s famous two-fifths law that relates the position of a blast wave to the time after the explosion and the total energy released. The theory of exterior differential systems is combined with the method of characteristics to demonstrate that the solution of the blast wave problem is directly related to the basic relationships that exist between the symmetry (or geometry) and the physics of wave propagation through the equations of motion. The point blast wave model is cast in terms of two exterior differential systems, and both systems are shown to be integrable with local solutions for the velocity, pressure, and density along curves in space and time behind the blast wave. This work is dedicated to the memory of Professor Roy Axford, who introduced many of his students to the topic of symmetry analysis of differential equations.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2025

Harnessing the power of gradient-based simulations for multi-objective optimization in particle accelerators

Abstract Particle accelerator operation requires simultaneous optimization of multiple objectives. Multi-objective optimization (MOO) is particularly challenging due to trade-offs between the objectives. Evolutionary algorithms, such as genetic algorithms (GAs), have been leveraged for many optimization problems, however, they do not apply to complex control problems by design. This paper demonstrates the power of differentiability for solving MOO problems in particle accelerators using a deep differentiable reinforcement learning (DDRL) algorithm. We compare the DDRL algorithm with model-free reinforcement learning (MFRL), GA, and Bayesian optimization (BO) for simultaneous optimization of heat load and trip rates in the continuous electron beam accelerator facility. The underlying problem enforces strict constraints on both individual states and actions as well as cumulative (global) constraints on energy requirements of the beam. Using historical accelerator data, we develop a physics-based surrogate model which is differentiable and allows for back-propagation of gradients. The results are evaluated in the form of a Pareto-front with two objectives. We show that the DDRL outperforms MFRL, BO, and GA on high dimensional problems.

43 PARTICLE ACCELERATORS↗