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Performance sensitivity calculated by back substitution. Original Lyapunov equation differentiated two times with respect to parameter p. Each differential turns out to yield Lyapunov equation for first and second derivatives with respective to parameter p of steady-state covariance of state variables. Derivatives desired closed-loop performance sensitivities.
Automated multidisciplinary design of aircraft and other flight vehicles requires the optimization of complex performance objectives with respect to a number of design parameters and constraints. The effect of these independent design variables on the system performance criteria can be quantified in terms of sensitivity derivatives which must be calculated and propagated by the individual discipline simulation codes. Typical advanced CFD analysis codes do not provide such derivatives as part of a flow solution; these derivatives are very expensive to obtain by divided (finite) differences from perturbed solutions. It is shown that sensitivity derivatives can be obtained accurately and efficiently using the ADIFOR source translator for automatic differentiation. In particular, it is demonstrated that the 3-D, thin-layer Navier-Stokes, multigrid flow solver called TLNS3D is amenable to automatic differentiation in the forward mode even with its implicit iterative solution algorithm and complex turbulence modeling. It is significant that by using computational differentiation, consistent discrete nongeometric sensitivity derivatives have been obtained from an aerodynamic 3-D CFD code in a relatively short time, e.g., O(man-week) not O(man-year).
As a phase that travels through the crustal waveguide, Lg samples the velocity and attenuation structure of the crust. We have developed methods (Pasyanos et al., 2009a; Pasyanos et al., 2009b) to estimate Qp and Qs of the crust and upper mantle from the amplitudes of regional phases, and have applied it to a number of regions around the world, and over a broad frequency band (0.5 - 10 Hz). In prior attenuation modeling, Lg phase amplitudes are able to effectively distinguish the high Q (low attenuation) of old stable cratonic crust from the low Q (high attenuation) of more recently active tectonic regions. For a variety of purposes (e.g. waveform modeling, seismic hazard, etc.), it is useful to have more information on the depth-dependence of the Q structure in the crust. One obvious candidate for doing this is using the frequency-dependence information of Lg Q, in the manner of surface waves. Unfortunately, however, Lg samples the whole of the crust without much differentiation with respect to frequency that is characteristic of fundamental mode surface waves. Lg is generally thought to be the sum of supercritically reflected S-waves trapped in the crustal waveguide (e.g. Xie and Lay, 1994). The phase can also be modeled as a superposition of surface waves. At lower frequencies, it is primarily composed of fundamental and low-order surface waves, while at higher frequencies, it is comprised purely of many high-order surface waves. The low-order surface waves that comprise Lg in low frequency bands (< 1 Hz) are preferentially sensitive to shallow earth structure, such as sedimentary basins and upper crust, while high-order surface waves have a more homogenized sensitivity to the whole crust. Furthermore, at the lower frequencies, we might expect to see some differentiation in the sensitivity between early Lg (herein referred to as Lg1) and late Lg (referred to as Lg2) where the latter is comprised of lower-order surface waves and, hence, shallower structure. Therefore, we might expect to see the signature of shallow features, primarily the lower Q of sediments as compared to crystalline crust, at lower frequencies and in later arriving Lg amplitudes.
An airborne differential radiometer was demonstrated to be a sensitive, real-time detector of surface chlorophyll content in water bodies. The instrument continuously measures the difference in radiance between two wavelength bands, one centered near the maximum of the blue chlorophyll a absorption region and the other at a reference wavelength outside this region. Flights were made over fresh water lakes, marine waters, and an estuary, and the results were compared with 'ground truth' measurements of chlorophyll concentration. A correlation between output signal of the differential radiometer and the chlorophyll concentration was obtained. Examples of flight data are illustrated. Simultaneous airborne measurements of chlorophyll content and water temperature revealed that variations in chlorophyll are often associated with changes in temperature. Thus, simultaneous sensing of chlorophyll and temperature provides useful information for studies of marine food production, water pollution, and physical processes such as upwelling.
The addition of phase difference measurements to differential absorption experiments is shown to be both feasible and desirable. The phase information can provide a more sensitive measurement of electron density above about 75 km. The differential phase shift is only weakly dependent on collision frequency in this range, and so an accurate collision frequency profile is not a prerequisite. The differential phase shift and differential absorption measurements taken together can provide both electron density and collision frequency data from about 70 to 90 km.
Four approaches to radio interferometric tracking of geosynchronous satellites are analyzed and compared. Quasar-based differential very-long-baseline interferometry, which requires a very sensitive receiver, can achieve meter-level position accuracy with a two-baseline system. Satellite-based differential VLBI gives somewhat lower accuracy with a compact, inexpensive receiver. Nondifferential VLBI, using less precise media and clock calibrations obtained by observing the GPS satellites, still gives 5-10 m position accuracy with two baselines. For a sufficiently inclined orbit, all interferometric approaches can yield six-component satellite state from a single baseline.
Enabling the computation of partial derivatives or sensitivities in production hydrocodes is beneficial for design, optimization, sensitivity analysis, and uncertainty quantification. Traditional finite difference approximations of these sensitivities are inefficient since convergence studies of the step size is required for each parameter of interest. For these reasons, HYPercomplex Automatic Differentiation (HYPAD) was implemented in the Eulerian hydrocode PAGOSA. HYPAD is analogous to forward-mode automatic differentiation except hypercomplex numbers (numbers with multiple imaginary parts) are used instead of dual numbers. Accurate partial derivatives can be computed of all state variables with respect to multiple input variables in a single run. The method was implemented using operator overloading to handle hypercomplex algebra. HYPAD was demonstrated and verified on Sod’s shock tube problem to compute derivatives of the state variables with respect to a material parameter, initial conditions, and geometry.
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.
Data-driven techniques for energy demand forecasting continue to emerge with promising impacts on distribution grid planning. However, the development of robust and generalizable machine learning models requires that representative high quality training data are available. Distributed energy resources have begun to embed intelligence, gathering large amounts of data on customer demand, behavior, and household devices that are connected to the grid. Though utilities aggregate meter-level demand data for load shaping, demand response, outage management, reliability planning, and billing applications, there lies an inherent privacy concern in sharing consumption data that may identify individual consumer behavioral patterns. Hence, while sharing the data is crucial, the private sensitive customer data must be safeguarded from being exposed or manipulated. In this study, we propose a roadmap for implementing a based privacy preserving framework to support the advancement of data-driven analytics in data-sensitive distributed energy resources environments. The roadmap incorporates federated learning–a distributed training framework, differential privacy–a statistical framework that provides guarantees to safeguard the leakage of sensitive data, secure multiparty computation and homomorphic encryption– techniques for encrypting model gradients and applying secure aggregation on the server. Moreover, we perform baseline experiments on the federated short-term load forecasting (STLF) task using open-source residential load profile datasets, offering insights into the challenges of integrating differential privacy into federated learning.
Manifesting chemical differences in individual rare earth (RE) element complexes is challenging due to the similar sizes of the tripositive cations and the corelike 4f shell. In this work, we disclose a new strategy for differentiating between similarly sized Dy 3+ and Y 3+ ions through a tailored photochemical reaction of their isostructural complexes in which the f-electron states of Dy 3+ act as an energy sink. Complexes RE(hfac) 3 (NMMO) 2 (RE = Dy (2-Dy) and Y (2-Y), hfac = hexafluoroacetylacetonate, and NMMO = N-methylmorpholine-N-oxide) showed variable rates of oxygen atom transfer (OAT) to triphenylphosphine under ultraviolet (UV) irradiation, as monitored by 1 H and 19 F NMR spectroscopies. Ultrafast transient absorption spectroscopy (TAS) identified the excited state(s) responsible for the photochemical OAT reaction or lack thereof. Competing sensitization pathways leading to excited-state deactivation in 2-Dy through energy transfer to the 4f electron manifold ultimately slows the OAT reaction at this metal cation. The measured rate differences between the open-shell Dy 3+ and closed-shell Y 3+ complexes demonstrate that using established principles of 4f ion sensitization may deliver new, selective modalities for differentiating the RE elements that do not depend on cation size.
Polycyclic aromatic hydrocarbons (PAHs) are ubiquitous environmental contaminants and are associated with human disease. Canonically, many PAHs induce toxicity via activation of the aryl hydrocarbon receptor (AHR) pathway. While the interaction between PAHs and the AHR is well-established, understanding which AHR-regulated transcriptional effects directly result in observable phenotypes and which are adaptive or benign is important to better understand PAH toxicity. Retene is a frequently detected PAH in environmental sampling and has been associated with AHR2-dependent developmental toxicity in zebrafish, though its mechanism of toxicity has not been fully elucidated. To interrogate transcriptional changes causally associated with retene toxicity, we conducted whole-animal RNA sequencing at 48 hours post-fertilization after exposure to eight retene concentrations. The concentrations were selected to produce effects ranging from no phenotype to mortality and malformations in 100% of animals at 5 days post-fertilization. We identified a concentration-response relationship between retene teratogenicity and differential gene expression in both number of DEGs and magnitude of expression change. Elevated expression of cyp1a at retene concentrations below the threshold for teratogenicity suggested that while cyp1a expression is a sensitive biomarker of AHR activation, it may be too sensitive to serve as a biomarker of AHR-dependent teratogenicity. Genes differentially expressed at only non-teratogenic concentrations were enriched for transforming growth factor-ß (TGF-ß) signaling pathway disruption while DEGs identified at only teratogenic concentrations were significantly enriched for response to xenobiotic stimulus and reduction-oxidation reaction activity. DEGs which spanned both non-teratogenic and teratogenic concentrations showed similar disrupted biological processes to those unique to teratogenic concentrations, indicating these processes were disrupted at low exposure concentrations. Gene co-expression network analysis identified several gene modules, including those associated with PAHs and AHR2 activation. One, Module 7, was strongly enriched for AHR2-associated genes and contained the strongest responses to retene. Benchmark concentration (BMC) of Module 7 genes identified a median BMC of 7.5 µM, nearly the highest retene concentration with no associated teratogenicity, supporting the hypothesis that Module 7 genes are largely responsible for retene toxicity.
An algorithm is developed to obtain the grid sensitivity with respect to design parameters for aerodynamic optimization. The procedure is advocating a novel (geometrical) parameterization using spline functions such as NURBS (Non-Uniform Rational B-Splines) for defining the wing-section geometry. An interactive algebraic grid generation technique, known as Two-Boundary Grid Generation (TBGG) is employed to generate C-type grids around wing-sections. The grid sensitivity of the domain with respect to geometric design parameters has been obtained by direct differentiation of the grid equations. A hybrid approach is proposed for more geometrically complex configurations such as a wing or fuselage. The aerodynamic sensitivity coefficients are obtained by direct differentiation of the compressible two-dimensional thin-layer Navier-Stokes equations. An optimization package has been introduced into the algorithm in order to optimize the wing-section surface. Results demonstrate a substantially improved design due to maximized lift/drag ratio of the wing-section.
An algorithm is developed to obtain the grid sensitivity with respect to design parameters for aerodynamic optimization. The procedure is advocating a novel (geometrical) parameterization using spline functions such as NURBS (Non-Uniform Rational B- Splines) for defining the airfoil geometry. An interactive algebraic grid generation technique is employed to generate C-type grids around airfoils. The grid sensitivity of the domain with respect to geometric design parameters has been obtained by direct differentiation of the grid equations. A hybrid approach is proposed for more geometrically complex configurations such as a wing or fuselage. The aerodynamic sensitivity coefficients are obtained by direct differentiation of the compressible two-dimensional thin-layer Navier-Stokes equations. An optimization package has been introduced into the algorithm in order to optimize the airfoil surface. Results demonstrate a substantially improved design due to maximized lift/drag ratio of the airfoil.
Here, we present a new software system PETSc TSAdjoint for first-order and second order adjoint sensitivity analysis of time-dependent nonlinear differential equations. The derivative calculation in PETSc TSAdjoint is essentially a high-level algorithmic differentiation process. The adjoint models are derived by differentiating the timestepping algorithms and implementing them based on the parallel infrastructure in PETSc. Full differentiation of the library code, including MPI routines, is avoided, and users do not need to derive their own adjoint models for their specific applications. PETSc TSAdjoint can compute the first-order derivative, that is, the gradient of a scalar functional, and the Hessian-vector product, which carries second-order derivative information, while requiring minimal input (a few callbacks) from the users. The adjoint model employs optimal checkpointing schemes in a manner that is transparent to users. Finally, usability, efficiency, and scalability are demonstrated through examples from a variety of applications.
Time-dependent density-functional theory is mathematically formulated through nonlinear coupled time-dependent three-dimensional partial differential equations, and it is natural to expect a strong sensitivity of its solutions to variations of the initial conditions, akin to the butterfly effect ubiquitous in classical dynamics. Since the Schrödinger equation for an interacting many-body system is, however, linear and mathematically the exact equations of the density-functional theory reproduce the corresponding one-body properties, it would follow that the Lyapunov exponents are also vanishing within a density-functional theory framework. Whether for realistic implementations of the time-dependent density-functional theory the question of the absence of the butterfly effect and whether the dynamics provided is indeed a predictable theory was never discussed. At the same time, since the time-dependent density-functional theory is a unique tool allowing us to study the nonequilibrium dynamics of strongly interacting many-fermion systems, the question of predictability of this theoretical framework is of paramount importance. Here our analysis, for a number of quantum superfluid many-body systems (unitary Fermi gas, nuclear fission, and heavy-ion collisions) with a classical equivalent number of degrees of freedom O(10 10 ) and larger, suggests that its maximum Lyapunov exponents are negligible for all practical purposes.
Measurements of the inclusive and differential fiducial cross sections for the Higgs boson production in the H → ZZ → 4ℓ (ℓ = e, μ) decay channel are presented. The results are obtained from the analysis of proton-proton collision data recorded by the CMS experiment at the CERN LHC at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb$^{−1}$. The measured inclusive fiducial cross section is 2.73 ± 0.26 fb, in agreement with the standard model expectation of 2.86 ± 0.1 fb. Differential cross sections are measured as a function of several kinematic observables sensitive to the Higgs boson production and decay to four leptons. A set of double-differential measurements is also performed, yielding a comprehensive characterization of the four leptons final state. Constraints on the Higgs boson trilinear coupling and on the bottom and charm quark coupling modifiers are derived from its transverse momentum distribution. All results are consistent with theoretical predictions from the standard model.
The technique of implicit differentiation has been used in combination with linearized lifting-surface theory to derive analytical expressions for aerodynamic sensitivities (i.e., rates of change of lifting pressures with respect to general changes in aircraft geometry, including planform variations) for steady or oscillating planar or nonplanar lifting surfaces in subsonic, sonic, or supersonic flow. The geometric perturbation is defined in terms of a single variable, and the user need only provide simple expressions or similar means for defining the continuous or discontinuous global or local perturbation of interest. Example expressions are given for perturbations of the sweep, taper, and aspect ratio of a wing with trapezoidal semispan planform. In addition to direct computational use, the analytical method presented here should provide benchmark criteria for assessing the accuracy of aerodynamic sensitivities obtained by approximate methods such as finite geometry perturbation and differencing. The present process appears to be readily adaptable to more general surface-panel methods.
The emergent contaminant family, per- and poly-fluorinated alkyl substances (PFAS) has gained research attention due to their widespread detection and stability within the environment. Despite the growing amount of research on perfluorooctanesulfonic acid (PFOS) and perfluoro-n-octanoic acid (PFOA) in aquatic organisms, investigations detailing behavioral and physiological effects of aquatic organisms exposed to a mixture of PFAS analytes in the wild have been limited. The objective of this study was to evaluate the potential behavioral and histological effects of environmental exposure to PFAS compounds within multiple trophic levels of aquatic ecosystems. The current study investigates effects of environmentally relevant PFAS concentration exposures in crayfish (Faxonius immunis, F. rusticus, F. virilis) and bluegill (Lepomis macrochirus) sourced from four water bodies in Northern Michigan. Antipredator response and foraging behavioral assays were used to investigate potential effects on crayfish; a swimming speed behavioral assay and liver and gill histology analysis were used to investigate potential effects on fish. Linear mixed model and multiple regression analyses resulted in significant relationships between tissue accumulation levels of long chain PFAS compounds and crayfish foraging and fish critical swimming speed responses. Crayfish foraging decreased and fish critical swim speeds increased with PFAS exposure which may lead to energetic and population concerns. Antipredator response in crayfish and liver and gill histology in fish were not significantly related to PFAS tissue or water concentrations. The sensitivity of crayfish and bluegill behavior contributes to the growing body of research regarding the differential toxicity of short-chain and long-chain PFAS compounds. The sensitivity of some aquatic organism behaviors to PFAS accumulated in tissue may have implications for PFAS transfer and alterations to ecosystem functioning; based on the results of this field study, further laboratory research is recommended to further evaluate these relationships.