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At least 289 records · Page 16

First Measurement of Differential Charged Current Quasielastic-like $\nu_\mu$–Argon Scattering Cross Sections In Kinematic Imbalance Variables With The MicroBooNE Detector

We report the first measurement of flux-integrated multi-differential cross sections for charged-current events with muon neutrinos scattering on argon with solely a muon and a single proton in the final state as a function of kinematic imbalance variables. The measurement was carried out using the Booster Neutrino Beam at Fermi National Accelerator Laboratory within the MicroBooNE Liquid Argon Time Projection Chamber detector with an exposure of 6.79 × 10 20 protons on target. Events were selected to enhance the contribution of charged-current mesonless interactions with one proton detected in the final state. The data discussed here are reported in terms of multidifferential cross sections in kinematic imbalance variables, which are generally sensitive to nuclear effects. The double-differential results in these variables can provide an excellent handle to disentagle specific nuclear aspects not easily isolated via single differential cross sections. Our results pave a path towards identifying regions of the phase-space where future interaction modeling development and Monte Carlo neutrino generator tuning efforts should concentrate. EVENT SELECTION Neutrino oscillation measurements aim to extract neutrino mixing angles, mass differences, the value of the chargeparity violating phase in the lepton sector, and to search for new physics beyond the Standard Model [1, 2]. For that to be achieved, an unprecedented understanding of neutrino-argon interactions is of utmost importance since a growing number of neutrino oscillation experiments employ Liquid Argon Time Projector Chamber (LArTPC) neutrino detectors [3–6]. The accuracy to which these experiments can extract neutrino oscillation parameters requires a good understanding of the neutrino energy. Experimentally, this energy is deduced from the measured kinetic energies of particles that are emitted following the neutrino interaction in the detector. The kinematic properties of such finalstate particles reflect complex dynamics due to nuclear and initial-state effects of the interaction [7]. However, certain categories of nuclear effects can be isolated by variables built specifically to characterize the degeneracy between such effects [8–10]. This note reports cross sections in kinematic variables sensitive to nuclear effects using events with one detected muon with momentum 0.1 < pµ < 1.2 GeV/c, and exactly one proton with 0.3 < pp < 1 GeV/c. This signal definition includes events with any number of protons below 300 MeV/c, neutrons at any momenta, and charged pions with momentum lower than 70 MeV/c. This choice is guided by the fact that their experimental signature of correlated muon-proton pairs is fairly straightforward to reconstruct [11–22]. Such events primarily originate from chargedcurrent (CC) neutrino-nucleon quasielastic (QE) scattering interactions where the neutrino removes a single intact nucleon from the nucleus without producing any additional particles. This definition can also include contributions from interactions that lead to the production of additional particles that are absent from the final state due to nuclear effects, such as pion absorption, or have momenta that are below the experimental detection threshold.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Towards reverse mode automatic differentiation of Kokkos-based codes

Derivative computation is a key component of optimization, sensitivity analysis, uncertainty quantification, and the solving of nonlinear problems. Automatic differentiation (AD) is a powerful technique for evaluating such derivatives, and in recent years, has been integrated into programming environments such as Jax, PyTorch, and TensorFlow to support derivative computations needed for training of machine learning models, facilitating wide-spread use of these technologies. The C++ language has become the de facto standard for scientific computing due to numerous factors, yet language complexity has made the wide-spread adoption of AD technologies for C++ difficult, hampering the incorporation of powerful differentiable programming approaches into C++ scientific simulations. This is exacerbated by the increasing emergence of architectures, such as GPUs, with limited memory capabilities and requiring massive thread-level concurrency. C++ AD tools must effectively use these environments to bring novel scientific simulations to next-generation DOE experimental and observational facilities. In this project, we investigated source transformation-based automatic differentiation using LLVM compiler infrastructure to automatically generate portable and efficient gradient computations of Kokkos-based code. We have demonstrated that our proposed strategy is feasible by investigating the usage of a prototype LLVM-based source transformation tool to generate gradients of simple functions made of sequences of simple Kokkos parallel regions. Speedups of up to 500x compared to Sacado were observed on NVIDIA V100 GPU.

97 MATHEMATICS AND COMPUTING↗

Lectures on Lie Group Analysis: Solving Differential Equations Using Symmetries

These notes are meant to be a supplemental reference for the beginner Lie Group Analyst. It is assumed that the reader has a basic concept of the fundamentals of Lie Group Theory (LGT), e.g. has seen the derivation of the infinitesimal generator and understands the mathematical meaning behind invariance. An excellent reference is Albright et al., “Symmetry Analysis of Differential Equations: A Primer,”. The reader is urged to read at least the first three chapters of that document to be able to follow the outset of Chapter 2 of this document. The reader should also have a general understanding of calculus, ordinary differential equations, and partial differential equations.

97 MATHEMATICS AND COMPUTING↗

Differentiable Multiphysics Codes: A Breakthrough Technology for Simulation and Computing

This document summarizes the findings of a strategic planning exercise commissioned by the Weapons Simulation and Computing, Computational Physics (WSC/CP) program at the Lawrence Livermore National Laboratory (LLNL) in FY24. During the year, the committee met with multiple stakeholder communities to gather input, opinions, suggestions and concerns which have been incorporated throughout this document. The key findings from this exercise are summarized: • The development of multiphysics modelling and simulation (mod/sim) codes and software technologies, their deployment on exascale compute platforms, and their broad adoption across the NNSA is a major success of the Advanced Simulation and Computing (ASC) program and the Exascale Computing Project (ECP). Sustained investment in these core technologies is essential. • Today’s state of the art involves running ensembles of O(100K) simulations to perform uncertainty quantification (UQ) and design studies using multiple statistical methods such as Bayesian optimization to understand sensitivities of our models and explore parameterized design spaces. Even with exascale computing, we are practically limited to O(10) parameters in these studies since the number of simulations required to sample the space scales exponentially with the number of design parameters. • The data from these simulation ensembles is increasingly being used to train machine learned (ML) surrogates (or reduced order models, ROMs) which can then be used for optimization or real time design exploration. However, the trained surrogates are still limited in the number of parameters they can represent due to the sampling limitations previously noted. • Augmenting our suite of integrated multiphysics simulation codes, both current and emerging, with the ability to compute gradients (solution derivatives) of arbitrary simulation outputs with respect to (some or all) simulation inputs would be a breakthrough technology, opening the door to a new era of efficient and automated inverse design based on verified and validated mod/sim capabilities. • This capability, which we refer to as differentiable multiphysics codes (DMCs), would revolutionize both UQ and optimization studies by breaking the curse of dimensionality that presently limits our “gradient-free” ensemble based computing approach. A similar breakthrough occurred in the AI/ML community once the ability to compute gradients of arbitrary loss functions using back-propagation became commonplace. Gradient information from the multiphysics codes can also be used to dramatically improve the efficiency and scale of training of ML/ROM surrogates for rapid assessments. • Achieving this in our suite of codes will be a grand challenge, similar to the amount of effort that was required to transition from CPU to GPU computing. It will require buy-in from the entire WSC/CP program and beyond, including all integrated codes, physics and engineering models, third-party library dependencies and performance portability abstractions. It will also require investment in research and development of numerical methods for computing adjoints of coupled physics across multiple adaptively refined moving meshes and of stochastic (Monte Carlo) and mesh free (SPH) methods. • New software and numerical techniques, largely pioneered by the AI/ML community, make this feasible. Chief among these is automatic differentiation (AD), the ability to employ AD at point-wise locations in a physics calculation (instead of traditional black-box approaches) and the ability to perform “back-propagation in time” (or reverse mode AD) for non-linear partial differential equations (PDEs). Fundamentally, the conclusion of this strategic planning exercise is that the time is right to undertake a large scale effort in WSC, centered on the existing integrated codes, to continue the natural evolution of mod/sim in the age of AI/ML. Instead of attempting to replace mod/sim with purely data driven AI/ML models, we believe the key to success is to integrate AI/ML by building on top of the decades of hard-won knowledge and the verified/validated multiphysics modelling capability that is the hallmark of the ASC program.

97 MATHEMATICS AND COMPUTING↗

High-precision quantum algorithms for partial differential equations

Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for linear ordinary differential equations are well established, the best previous quantum algorithms for linear partial differential equations (PDEs) have complexity poly(1/ϵ), where ϵ is the error tolerance. By developing quantum algorithms based on adaptive-order finite difference methods and spectral methods, we improve the complexity of quantum algorithms for linear PDEs to be poly(d,log(1/ϵ)), where d is the spatial dimension. Our algorithms apply high-precision quantum linear system algorithms to systems whose condition numbers and approximation errors we bound. We develop a finite difference algorithm for the Poisson equation and a spectral algorithm for more general second-order elliptic equations.

97 MATHEMATICS AND COMPUTING↗

Koopman-based Differentiable Predictive Control for the Dynamics-Aware Economic Dispatch Problem

The dynamics-aware economic dispatch (DED) problem embeds low-level generator dynamics and operational constraints to enable near real-time scheduling of generation units in a power network. DED produces a more dynamic supervisory control policy than traditional economic dispatch (T-ED) that reduces overall generation costs. However, the incorporation of differential equations that govern the system dynamics makes DED an optimization problem that is computationally prohibitive to solve. In this work, we present a new data-driven approach based on differentiable programming to efficiently obtain offline parametric solutions to the underlying DED problem. In particular, we employ the recently proposed differentiable predictive control (DPC) for offline learning of explicit neural control policies based on identified Koopman operator (KO) model of the system dynamics. We demonstrate the high solution quality and five orders of magnitude computational-time savings of the DPC method over the original optimization-based DED approach on a 9-bus test power grid network.

King, Ethan↗

Site-Differentiated Iron–Sulfur Cluster Ligation Affects Flavin-Based Electron Bifurcation Activity

Electron bifurcation is an elegant mechanism of biological energy conversion that effectively couples three different physiologically relevant substrates. As such, enzymes that perform this function often play critical roles in modulating cellular redox metabolism. One such enzyme is NADH-dependent reduced-ferredoxin: NADP+ oxidoreductase (NfnSL), which couples the thermodynamically favorable reduction of NAD+ to drive the unfavorable reduction of ferredoxin from NADPH. The interaction of NfnSL with its substrates is constrained to strict stoichiometric conditions, which ensures minimal energy losses from non-productive intramolecular electron transfer reactions. However, the determinants for this are not well understood. One curious feature of NfnSL is that both initial acceptors of bifurcated electrons are unique iron–sulfur (FeS) clusters containing one non-cysteinyl ligand each. The biochemical impact and mechanistic roles of site-differentiated FeS ligands are enigmatic, despite their incidence in many redox active enzymes. Herein, we describe the biochemical study of wild-type NfnSL and a variant in which one of the site-differentiated ligands has been replaced with a cysteine. Results of dye-based steady-state kinetics experiments, substrate-binding measurements, biochemical activity assays, and assessments of electron distribution across the enzyme indicate that this site-differentiated ligand in NfnSL plays a role in maintaining fidelity of the coordinated reactions performed by the two electron transfer pathways. Given the commonality of these cofactors, our findings have broad implications beyond electron bifurcation and mechanistic biochemistry and may inform on means of modulating the redox balance of the cell for targeted metabolic engineering approaches.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Differential Accumulation of Misfolded Prion Strains in Natural Hosts of Prion Diseases

Prion diseases, also known as transmissible spongiform encephalopathies (TSEs), are a group of neurodegenerative protein misfolding diseases that invariably cause death. TSEs occur when the endogenous cellular prion protein (PrP C ) misfolds to form the pathological prion protein (PrP Sc ), which templates further conversion of PrP C to PrP Sc , accumulates, and initiates a cascade of pathologic processes in cells and tissues. Different strains of prion disease within a species are thought to arise from the differential misfolding of the prion protein and have different clinical phenotypes. Different strains of prion disease may also result in differential accumulation of PrP Sc in brain regions and tissues of natural hosts. Here, we review differential accumulation that occurs in the retinal ganglion cells, cerebellar cortex and white matter, and plexuses of the enteric nervous system in cattle with bovine spongiform encephalopathy, sheep and goats with scrapie, cervids with chronic wasting disease, and humans with prion diseases. By characterizing TSEs in their natural host, we can better understand the pathogenesis of different prion strains. This information is valuable in the pursuit of evaluating and discovering potential biomarkers and therapeutics for prion diseases.

59 BASIC BIOLOGICAL SCIENCES↗

A guide to the design of the virtual element methods for second- and fourth-order partial differential equations

Here we discuss the design and implementation details of two conforming virtual element methods for the numerical approximation of two partial differential equations that emerge in phase-field modeling of fracture propagation in elastic material. The two partial differential equations are: (i) a linear hyperbolic equation describing the momentum balance and (ii) a fourth-order elliptic equation modeling the damage of the material. Inspired by, we develop a new conforming VEM for the discretization of the two equations, which is implementation-friendly, i.e., different terms can be implemented by exploiting a single projection operator. We use C 0 and C 1 virtual elements for the second-and fourth-order partial differential equation, respectively. For both equations, we review the formulation of the virtual element approximation and discuss the details pertaining the implementation.

42 ENGINEERING↗

Ionospheric Studies with the Differential Doppler Technique

This report is essentially a review of the measurements related to the ionosphere utilizing the differential Doppler technique. A brief study of the theory is presented, in which the error incurred in measurements of ionospheric electron content, caused by the assumption of common-path propagation, is shown as a function of the zenith angle of observation for different values of the critical frequency foF2. Some measurements of electron densities, electron content, horizontal gradients, irregularities, and magnetic-storm effects are discussed. Comments are also made about the method of combining the differential Doppler with the Faraday rotation measurements to establish a necessary constant of integration in the measurements made with satellites. It is concluded that the differential Doppler technique, with harmonically related frequencies transmitted to or from rockets or satellites, can provide accurate information about the electron density or electron content of the medium, and that the knowledge of these quantities is valuable in understanding the morphology of the ionospheric processes.

IONOSPHERE↗

Solution of differential equations by application of transformation groups

Report applies transformation groups to the solution of systems of ordinary differential equations and partial differential equations. Lies theorem finds an integrating factor for appropriate invariance group or groups can be found and can be extended to partial differential equations.

Driskell, C. N., Jr.↗

Eclipse and noneclipse differential photoelectron flux.

Differential photoelectron flux in the energy range of 3 to 50 eV has been measured in the lower ionosphere both during the March 7, 1970, solar eclipse and during a period 24 hours earlier. The two measurements were made with identical retarding potential analyzers carried on Nike-Apache rocket flights to a peak altitude of approximately 180 km. The differential electron flux spectrum within totality on the eclipse flight had the same shape but was a factor of 10 smaller in magnitude than that measured on the control day at altitudes between 120 and 180 km, an expected result for an eclipse function decreasing to 1/10 at totality. The differential flux spectrum measured in full sun has the same general energy dependence as that reported by Doering et al. (1970) but is larger by a factor of 2 to 10, depending on altitude.

Knudsen, W. C.↗

Determination of flow areas for series-parallel compartment venting to satisfy pressure differential requirements.

A unique method for solving the design problem of determining the areas required to meet an imposed pressure differential limit is presented. The associated analytical technique for determining the transient pressure differentials in a multicompartment series-parallel connected system is also presented. In an effort to verify the results obtained by using the analytical methods presented, a test was conducted using a seven compartment system. It was found in the investigations that a computer program based on the analytical model described can determine the pressure, temperature, pressure differentials, and mass flow rates into and out of each compartment at subsonic or sonic velocities.

Kirby, C. E.↗

Phase jitter in a differential phase experiment.

Austin (1971) had concluded that, because of the 'phase jitter,' the differential phase experiment is useful over a more limited height range than the differential absorption experiment. Several observations are presented to show that this conclusion is premature. It is pointed out that the logical basis of the differential absorption experiment also requires that the O- and X-mode echoes, at a given time, come from the same irregularities. Austin's calculations are believed to contain a systematic error above 80 km.

Tanenbaum, B. S.↗

PLZT block data composers operated in differential phase mode

The use of PLZT ceramics with the 7/65/35 composition in block data composer (BDC) input devices for holographic memory systems has previously been described for operation in the strain biased, scattering, and edge effect modes. A new and promising mode of BDC operation is the differential phase mode in which each element of a matrix array BDC acts as a phase modulator. The phase modulation results from a phase difference in the optical path length between the electrically poled and depoled states of the PLZT. It is shown that a PLZT BDC can be used as a matrix-type phase modulator to record and process digital data by the differential phase mode in a holographic recording/processing system with readout contrast ratios of between 10:1 and 15:1. The differential phase mode has the advantages that strain bias is not required and that the thickness and strain variations in the PLZT are cancelled out.

Drake, M. D.↗

Lunar baselines and libration from differential VLBI observations of ALSEPs

Differential very-long-baseline interferometric observations of signals from Apollo Lunar Surface Experiment Package telemetry transmitters will yield the relative projected positions of the transmitters with uncertainty of only 1-3 m, set mainly by uncertainty of the lunar ephemeris. Noise and systematic instrumental errors which in the past affected similar observations have been reduced to the equivalent of a few centimeters on the lunar surface by the development of a new type of differential receiver. Continued observations should yield a determination of the motion of the moon about its center of mass with uncertainty less than 1 sec of selenocentric arc. Improvements (by other means) in our knowledge of the moon's orbital motion would allow a further order-of-magnitude refinement in the libration and relative position results obtainable by differential VLBI.

Counselman, C. C., III↗

A result on differential inequalities and its application to higher order trajectory derivatives

A result on differential inequalities is obtained by considering the adjoint differential equation of the variational equation of the right side of the inequality. The main theorem is proved using basic results on differentiability of solutions with respect to initial conditions. The result is then applied to the problem of determining solution behavior using comparison techniques.

Gunderson, R. W.↗

Effect of varying differentiator frequency response on recorded peak dP/dt

Dogs were used to study the effects of varying the differentiator cutoff frequency on the recorded peak first derivative of left ventricular pressure with respect to time (dP/dt), using high-precision solid-state pressure transducers and recording equipment. In canine hearts with a basic periodicity of 1 to 3 Hz, the differentiator frequency response required to record an accurate peak dP/dt is found to be influenced by the value of peak dP/dt. At peak dP/dt ranging from 1500 to 9000 mm Hg/sec (200 and 1200 kPa/sec), a differentiator cutoff frequency of at least 90 Hz was required to record accurately peak dP/dt.

Barry, W. H.↗