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At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

A unified view of hierarchy approach and formula of differentiation

The stochastic differential equation is a powerful tool for describing the dynamics of a dissipative system in which noise characterizes the influence of the environment. For the Ornstein-Uhlenbeck noise, both the formula of differentiation and the hierarchy approach provide efficient numerical simulations, with the stochastic differential equation transformed into a set of coupled, linear ordinary differential equations. We show that while these two deterministic schemes result in different sets of equations, they can be regarded as two representations of an underlying linear-dynamics. Moreover, by manipulating the involved Ornstein-Uhlenbeck noise, we propose a unified algorithm that may reduce to the hierarchy approach or the formula of differentiation in different limits. We further analyze the numerical performance of this algorithm and find that the hierarchy approach appears to be more efficient for our numerical model studies.

Yan, Yun-An (ORCID:000000031943459X)↗
DOE OSTI2013

INTERNAL-CYCLE VARIATION OF SOLAR DIFFERENTIAL ROTATION

The latitudinal distributions of the yearly mean rotation rates measured by Suzuki in 1998 and 2012 and Pulkkinen and Tuominen in 1998 are utilized to investigate internal-cycle variation of solar differential rotation. The rotation rate at the solar equator seems to have decreased since cycle 10 onward. The coefficient B of solar differential rotation, which represents the latitudinal gradient of rotation, is found to be smaller in the several years after the minimum of a solar cycle than in the several years after the maximum time of the cycle, and it peaks several years after the maximum time of the solar cycle. The internal-cycle variation of the solar rotation rates looks similar in profile to that of the coefficient B. A new explanation is proposed to address such a solar-cycle-related variation of the solar rotation rates. Weak magnetic fields may more effectively reflect differentiation at low latitudes with high rotation rates than at high latitudes with low rotation rates, and strong magnetic fields may more effectively repress differentiation at relatively low latitudes than at high latitudes. The internal-cycle variation is inferred as the result of both the latitudinal migration of the surface torsional pattern and the repression of strong magnetic activity in differentiation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Can we detect the stellar differential rotation of WASP-7 through the Rossiter–McLaughlin observations?

ABSTRACT The Rossiter–McLaughlin (RM) effect is the radial velocity signal generated when an object transits a rotating star. Stars rotate differentially and this affects the shape and amplitude of this signal, on a level that can no longer be ignored with precise spectrographs. Highly misaligned planets provide a unique opportunity to probe stellar differential rotation via the RM effect, as they cross several stellar latitudes. In this sense, WASP-7, and its hot Jupiter with a projected misalignment of ∼90°, is one of the most promising targets. The aim of this work is to understand if the stellar differential rotation is measurable through the RM signal for systems with a geometry similar to WASP-7. In this sense, we use a modified version of soap3.0 to explore the main hurdles that prevented the precise determination of the differential rotation of WASP-7. We also investigate whether the adoption of the next generation spectrographs, like ESPRESSO, would solve these issues. Additionally, we assess how instrumental and stellar noise influence this effect and the derived geometry of the system. We found that, for WASP-7, the white noise represents an important hurdle in the detection of the stellar differential rotation, and that a precision of at least 2 m s−1 or better is essential.

Serrano, L. M.↗
DOE OSTI2018

Differential Activity-Driven Instabilities in Biphasic Active Matter

Active stresses can cause instabilities in contractile gels and living tissues. Here we provide a generic hydrodynamic theory that treats these systems as a mixture of two phases of varying activity and different mechanical properties. We find that differential activity between the phases causes a uniform mixture to undergo a demixing instability. We follow the nonlinear evolution of the instability and characterize a phase diagram of the resulting patterns. Our study complements other instability mechanisms in mixtures driven by differential adhesion, differential diffusion, differential growth, and differential motion.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Decoupled Active and Reactive Power Control without PLL Requirement for Differential Buck Converter

This paper presents a decoupled active and reactive power control for the differential buck converter. This control does not require phase locked loop (PLL) for synchronization. Also, it achieves active and reactive power control in a simple single control loop structure. The differential buck converter has the capability to compensate the double line frequency power ripple without relying on additional hardware. Particularly, the Common Mode (CM) operation is used for active double line frequency power ripple absorption. Whereas, the Differential Mode (DM) operation is used as an active and reactive power exchanging port between the converter and the grid at the point of common coupling (PCC). The motivation behind this paper proposal are: (i) to avoid PLL induced instabilities, especially, when connecting the differential buck converter with weak grid, and (ii) direct active and reactive power control for the differential buck in a single loop control. The theoretical analyses are verified with a 5 kW converter with only 50 μF decoupling capacitor connected to a weak grid.

Khan, Ahmad↗
DOE OSTI2013

Differential Power Processing for DC Systems

This paper introduces an approach to dc power delivery that reduces power loss by minimizing redundant energy conversion. Existing power distribution techniques tend to increase the number of cascaded conversion stages, which limits overall efficiency. Differential power processing enables independent load regulation, while processing only a small portion of the total load power. Bulk power conversion occurs once. Load voltage domains are connected in series, and differential converters act as controllable current sources to regulate intermediate nodes. This enables independent, low supply voltages, which can reduce system energy consumption, especially in digital circuits and solid-state lighting. Since differential voltage regulators process a fraction of the load power, decreased size, cost, and conversion losses are attainable. Under balanced load conditions, secondary differential converters do not process any power. This paper analyzes several differential power delivery architectures that can be applied to homogenous and heterogeneous loads at various levels: chip, board, blade, etc. A variety of operating conditions for a test system with four series voltage domains are examined in simulation and verified with experimental hardware. Results in a reference application show a 7-8% decrease in input power and 6-7 percentage points increase in overall conversion efficiency as compared to a conventional cascaded approach.

Shenoy, PS↗
DOE OSTI2018

An Optical Differentiator Based on a Three-Layer Structure with a W-Shaped Refractive Index Profile

An optical differentiator based on a three-layer resonant structure with a W-shaped refractive index profile is proposed. The differentiation operation is performed in reflection and is associated with the resonant excitation of an eigenmode of the structure localized in the central layer. The presented results of numerical simulations demonstrate the possibility of spatial differentiation of the transverse profile of an incident optical beam, temporal differentiation of the envelope of an incident optical beam, and simultaneous spatial and temporal differentiation with a high quality. The proposed structure can find applications in designing analog optical computing and optical information processing systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Differentiable Quantum Programming with Unbounded Loops

The emergence of variational quantum applications has led to the development of automatic differentiation techniques in quantum computing. Existing work has formulated differentiable quantum programming with bounded loops, providing a framework for scalable gradient calculation by quantum means for training quantum variational applications. However, promising parameterized quantum applications, e.g., quantum walk and unitary implementation, cannot be trained in the existing framework due to the natural involvement of unbounded loops. To fill in the gap, we provide the first differentiable quantum programming framework with unbounded loops, including a newly designed differentiation rule, code transformation, and their correctness proof. Technically, we introduce a randomized estimator for derivatives to deal with the infinite sum in the differentiation of unbounded loops, whose applicability in classical and probabilistic programming is also discussed. We implement our framework with Python and Q# and demonstrate a reasonable sample efficiency. Through extensive case studies, we showcase an exciting application of our framework in automatically identifying close-to-optimal parameters for several parameterized quantum applications.

Computer Science↗
DOE OSTI2019

Analysis of Differential Financial Impacts of LWR Load-Following Operations. Revision 1

This document reports the application of HERON (Holistic Energy Resource Optimization Network), a newly-developed RAVEN (Risk Analysis Virtual ENvironment) plugin for grid and capacity optimization, to a case study conducted in collaboration with Arizona Public Service (APS). The study is a work in progress; this report presents a description of current models and corresponding results for a particular consideration. APS is anticipating several operational challenges. The first is rapid growth of Variable Renewable Energy (VRE) sources such as wind and solar power providing energy to the grid in the APS service region. This creates challenges for baseload operation of the Palo Verde Generating Station (PVGS), a nuclear power plant co-owned and operated by APS. The second challenge for APS is a change in the cooling water acquisition contract with the Sub Regional Operating Group (SROG). The existing contract is expiring soon, and a renewal is only available for a significantly higher price of water. These two challenges represent a difficulty in maintaining profitability for PVGS as local area demand is highly fluctuant and water prices may increase. Furthermore, excess production at PVGS is currently traded on the Palo Verde energy Hub (PVH), which occasionally offers very low or negative locational marginal prices (LMP) for electricity. This analysis considers the potential benefits of occasional curtailment of PVGS as a method to mitigate unprofitable production hours. Similar to load following, optional daily curtailment would allow APS to elect curtailment of PVGS as low as 70% of its nominal operating level between the hours of 08:00 and 16:00 provided local area demand is met and it is profitable to do so. This document reports a stochastic differential analysis of the Net Present Value (NPV) of PVGS as operated by NPS as a result of optional curtailment operation. To model this differential case, HERON has been designed from previous efforts in this study as a generic tool to accelerate the design and execution of RAVEN workflows for technoeconomic analysis of grid energy systems. HERON leverages both RAVEN and the CashFlow plugin for RAVEN to stochastically explore or optimize a response surface with energy grid system production capacities as inputs and mean NPV as a goal function. HERON performs these evaluations by stochastically sampling market, weather, and demand events using RAVEN’s ARMA reduced-order model capability to generate boundary conditions for dispatch optimization. The algorithm performs the dispatch optimization for each of the synthetic scenarios. For this case, HERON designs workflows to simulate behavior of the PVH, wind, solar, and APS local area demand, and use these synthetic scenarios to stochastically evaluate the differential benefit of optional curtailment for each scenario. While this study finds optional curtailment to be a potential source of revenue, the magnitude of the differential NPV is sufficiently small that it is unlikely a priority for increasing the profitability of PVGS. Further, the differential NPV shrinks throughout the simulated years, suggesting the long-term benefit of such operation given current assumptions is negligible.

14 SOLAR ENERGY↗
DOE OSTI2021

Double-differential Measurements of Mesonless Charged-current Muon Neutrino Interactions on Argon with Final-State Protons using the MicroBooNE Detector

This note reports the first double-differential measurements of charged-current $ν_µ$ scattering on argon leading to final states containing zero mesons and one or more protons. This event topology (hereafter abbreviated as CC0$πNp$) is the most common at the neutrino energies typically produced by the Fermilab Booster Neutrino Beam. A detailed understanding of neutrino-argon scattering in the CC0$πNp$ channel is therefore crucial for the success of the precision neutrino oscillation analyses planned for the Short-Baseline Neutrino (SBN) program. This remains true for the upcoming Deep Underground Neutrino Experiment (DUNE), but the higher mean neutrino energy used there will ensure that more inelastic reaction modes, such as single pion production, will also play a major role. The analysis described in this note builds on a previous MicroBooNE study of the CC0$πNp$ channel which obtained the first single-differential cross-section measurements on an argon target. Since that foundational work, significant improvements have been made to MicroBooNE’s simulation software, event reconstruction algorithms, and procedure for calculating systematic uncertainties. When combined with a larger dataset (corresponding to a beam exposure of 6.79 × 10 20 protons-on-target versus 1.60 × 10 20 in Ref. [3]), these enhancements allow the important CC0$πNp$ channel to be studied in more detail. This note begins with a description of the data and simulation samples used as input to the analysis. Section 3 then defines the CC0$πNp$ signal event topology, and Section 4 describes a set of selection criteria designed to identify these events in MicroBooNE data. Binning schemes are then defined in Section 5 for two double-differential measurements of event rates. The first of these considers the momentum and scattering cosine of the outgoing muon, while the second reports the same observables for the leading proton, i.e., the final-state proton with the largest momentum. After a discussion of systematic uncertainties in Section 6, the note concludes by comparing the predictions of MicroBooNE Monte Carlo (MC) simulations to the measured double-differential distributions. These results will form the basis for a future extraction of flux-averaged double-differential CC0$πNp$ cross sections that will be immediately comparable to the theoretical predictions of multiple neutrino event generators. The selection described herein may also be used to study various other observables in CC0$πNp$ events, including those which are sensitive to correlations between leptonic and hadronic kinematics in the final state.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Differentially rotating white dwarfs. I. Regimes of internal rotation

Most viable models of Type Ia supernovae (SNe Ia) require the thermonuclear explosion of a carbon/oxygen white dwarf that has evolved in a binary system. Rotation could be an important aspect of any model for SNe Ia, whether single or double degenerate, with the white dwarf mass at, below, or above the Chandrasekhar limit. Differential rotation is specifically invoked in attempts to account for the apparent excess mass in the super-Chandrasekhar events. Some earlier work has suggested that only uniform rotation is consistent with the expected mechanisms of angular momentum transport in white dwarfs, while others have found pronounced differential rotation. We show that if the baroclinic instability is active in degenerate matter and the effects of magnetic fields are neglected, both nearly uniform rotation and strongly differential rotation are possible. We classify rotation regimes in terms of the Richardson number, Ri. At small values of Ri ⩽ 0.1, we find both the low-viscosity Zahn regime with a nonmonotonic angular velocity profile and a new differential rotation regime for which the viscosity is high and scales linearly with the shear, σ. Employment of Kelvin–Helmholtz viscosity alone yields differential rotation. Large values of Ri ≫ 1 produce a regime of nearly uniform rotation for which the baroclinic viscosity is of intermediate value and scales as σ{sup 3}. We discuss the gap in understanding of the behavior at intermediate values of Ri and how observations may constrain the rotation regimes attained by nature.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

A New View on the Maximum Mass of Differentially Rotating Neutron Stars

We study the main astrophysical properties of differentially rotating neutron stars described as stationary and axisymmetric configurations of a moderately stiff Γ=2 polytropic fluid. The high level of accuracy and of stability of our relativistic multidomain pseudo-spectral code enables us to explore the whole solution space for broad ranges of the degree of differential rotation, but also of the stellar density and oblateness. Staying within an astrophysically motivated range of rotation profiles, we investigate the characteristics of neutron stars with maximal mass for all types of families of differentially rotating relativistic objects identified in a previous article. We find that the maximum mass depends on both the degree of differential rotation and the type of solution. It turns out that the maximum allowed mass can be up to 4 times higher than what it is for nonrotating stars with the same equation of state. Such values are obtained for a modest degree of differential rotation but for one of the newly discovered types of solutions. Since such configurations of stars are not that extreme, this result may have important consequences for the gravitational wave signal expected from coalescing neutron star binaries or from some supernova events.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling

Recent advances in differentiable modeling, a genre of physics-informed machine learning that trains neural networks (NNs) together with process-based equations, have shown promise in enhancing hydrological models' accuracy, interpretability, and knowledge-discovery potential. Current differentiable models are efficient for NN-based parameter regionalization, but the simple explicit numerical schemes paired with sequential calculations (operator splitting) can incur numerical errors whose impacts on models' representation power and learned parameters are not clear. Implicit schemes, however, cannot rely on automatic differentiation to calculate gradients due to potential issues of gradient vanishing and memory demand. Here we propose a “discretize-then-optimize” adjoint method to enable differentiable implicit numerical schemes for the first time for large-scale hydrological modeling. The adjoint model demonstrates comprehensively improved performance, with Kling–Gupta efficiency coefficients, peak-flow and low-flow metrics, and evapotranspiration that moderately surpass the already-competitive explicit model. Therefore, the previous sequential-calculation approach had a detrimental impact on the model's ability to represent hydrological dynamics. Furthermore, with a structural update that describes capillary rise, the adjoint model can better describe baseflow in arid regions and also produce low flows that outperform even pure machine learning methods such as long short-term memory networks. The adjoint model rectified some parameter distortions but did not alter spatial parameter distributions, demonstrating the robustness of regionalized parameterization. Despite higher computational expenses and modest improvements, the adjoint model's success removes the barrier for complex implicit schemes to enrich differentiable modeling in hydrology.

58 GEOSCIENCES↗
DOE OSTI2020

Logarithmic forms and differential equations for Feynman integrals

We describe in detail how a d log representation of Feynman integrals leads to simple differential equations. We derive these differential equations directly in loop momentum or embedding space making use of a localization trick and generalized unitarity. For the examples we study, the alphabet of the differential equation is related to special points in kinematic space, described by certain cut equations which encode the geometry of the Feynman integral. At one loop, we reproduce the motivic formulae described by Goncharov [1] that reappeared in the context of Feynman integrals in [2–4]. The d log representation allows us to generalize the differential equations to higher loops and motivates the study of certain mixed-dimension integrals.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2012

A Stochastic Maximum Principle for a Stochastic Differential Game of a Mean-Field Type

We construct a stochastic maximum principle (SMP) which provides necessary conditions for the existence of Nash equilibria in a certain form of N-agent stochastic differential game (SDG) of a mean-field type. The information structure considered for the SDG is of a possible asymmetric and partial type. To prove our SMP we take an approach based on spike-variations and adjoint representation techniques, analogous to that of S. Peng (SIAM J. Control Optim. 28(4):966-979, 1990) in the optimal stochastic control context. In our proof we apply adjoint representation procedures at three points. The first-order adjoint processes are defined as solutions to certain mean-field backward stochastic differential equations, and second-order adjoint processes of a first type are defined as solutions to certain backward stochastic differential equations. Second-order adjoint processes of a second type are defined as solutions of certain backward stochastic equations of a type that we introduce in this paper, and which we term conditional mean-field backward stochastic differential equations. From the resulting representations, we show that the terms relating to these second-order adjoint processes of the second type are of an order such that they do not appear in our final SMP equations. A comparable situation exists in an article by R. Buckdahn, B. Djehiche, and J. Li (Appl. Math. Optim. 64(2):197-216, 2011) that constructs a SMP for a mean-field type optimal stochastic control problem; however, the approach we take of using these second-order adjoint processes of a second type to deal with the type of terms that we refer to as the second form of quadratic-type terms represents an alternative to a development, to our setting, of the approach used in their article for their analogous type of term.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Prym Differentials on Variable Tori

We consider multiplicative functions and Prym differentials on variable tori. We prove counterparts of the theorem on the total sum of residues for Prym differentials of any integer order on tori. As a consequence, reciprocity laws are proved. We construct elementary Prym differentials of all kinds with any integer order which holomorphically depend on the moduli of tori and characters. We derive an analogue of the Appell decomposition formula for functions with characters. We also study vector bundles of Prym differentials of any integer order over the product of Teichmueller spaces for a torus and a group of characters.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Forced expression of NR4A3 induced the differentiation of human neuroblastoma-derived NB1 cells

Nuclear receptor subfamily 4, group A, member 3 (NR4A3) is a member of the NR4A subgroup of orphan nuclear receptors, implicated in the regulation of diverse biological functions, including metabolism, angiogenesis, inflammation, cell proliferation, and apoptosis. Although many reports have suggested the involvement of NR4A3 in the development and/or progression of tumors, its role varies among tumor types. Previously, we reported that DNA hypomethylation at NR4A3 exon 3 is associated with lower survival rate of neuroblastoma (NB) patients. As hypomethylation of this region results in reduced expression of NR4A3, our observations suggested that NR4A3 functions as a tumor suppressor in NB. However, the exact mechanisms underlying its functions have not been clarified. In the present study, we analyzed public databases and showed that reduced NR4A3 expression was associated with shorter survival period of NB in two out of three datasets. An in vitro study revealed that forced expression of NR4A3 in human NB-derived cell line NB1 resulted in elongation of neurites along with overexpression of GAP43, one of the differentiation markers of NB. On the other hand, siRNA-mediated knockdown of NR4A3 suppressed the expression level of GAP43. Interestingly, the forced expression of NR4A3 induced only the GAP43 but not the other molecules involved in NB cell differentiation, such as MYCN, TRKA, and PHOX2B. These results indicated that NR4A3 directly activates the expression of GAP43 and induces differentiated phenotypes of NB cells, without affecting the upstream signals regulating GAP43 expression and NB differentiation.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2025

Differentiable hybrid neural network approach for enhancing reactor dynamics simulations

Reactor dynamics simulations provide essential insights into the time-dependent behavior of nuclear reactors under various operating conditions. However, high-fidelity simulations can be computationally intensive, requiring significant computational resources. Here, to address this challenge, this study employs a differentiable hybrid model that utilizes neural networks as a corrector to enhance the performance of a low-fidelity simulation, aligning its predictions with those of a high-fidelity simulation. Low-fidelity and high-fidelity simulations were obtained by adjusting the mesh size in the System Dynamics Analysis Tool. The differentiable hybrid model was trained in two approaches: time-step-wise and sequence-wise. It was then applied to simulate various transients in a molten salt reactor. Its performance was evaluated by comparing its responses to transients against those of the high-fidelity simulation. An additional approach was performed using a data-driven model to correct the low-fidelity simulation. In comparison, the differentiable hybrid model showed significant improvements in transient prediction, effectively addressing the limitations of the low-fidelity simulations. The results highlighted the robustness of the differentiable hybrid model in both training approaches. It delivered simulations that were at least 3.8 times faster than high-fidelity models. In the time-step-wise approach, it achieved at least a 39% improvement in accuracy. In the sequence-wise approach, it showed at least an 81% accuracy improvement over the full transient. This approach offers a promising path for improving computational efficiency without compromising accuracy in nuclear reactor simulations, making it suitable for real-time digital twin applications.

42 - ENGINEERING↗