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Instantaneous signals from coherent random sound field are summed and time delayed to avoid introducing vectorial addition errors. Resultant statistically independent signals are applied to spectrometer. Displayed sound pressure level is proportional to square root of sum of squares of sound pressure levels taken over frequency range of interest.
The global distribution of multi-kilometer (approx. 9 km) length scale 'roughness' (hereafter mesoscale roughness or MR) on Venus can be estimated from the Magellan global altimetry dataset (GxDR) and then compared with MR data derived for Earth from 5' ETOP5 data and for Mars (from USGS Mars DTM dataset). The mesoscale roughness parameter (MR) represents the RMS variance in meters of the actual planetary surface topography relative to the best fitting tangent plane defined on the basis of a 3x3 pixel sliding window. The best-fit plane was computed using a least-squares solution which minimizes delta H, the sum of the squares of the differences between the 9 local elevation values (H(sub i)), and the elevation of best-fit plane at the same grid location. Using the best-fit plane and delta H, we have computed the RMS 'roughness' var(delta R), where this parameter is always minimized on the basis of its calculation using least squares. We have called this 'ruggedness' parameter the Mesoscale Roughness (MR) because it is directly related to the high-frequency variance of topography after mesoscale slopes and tilts (i.e., for Venus, the baseline over which MR is computed (dx) is approx. 8.8 km and dx for Earth is approx. 9.3 km) are removed. As such, MR represents the degree to which a planetary surface is more rugged than approximately 10 km scale facets or tilts. It should not be confused with the radar 'RMS Roughness' parameter computed at 0.1 to 10 m length scales on the basis of the Magellan radar altimeter echo. We will use our MR parameter to investigate the global ruggedness properties of Venus as they relate to geological provinces and in comparison with the spatial pattern of MR for Earth and Mars.
Introduction: The probability of bone fracture during and after spaceflight is quantified to aid in mission planning, to determine required astronaut fitness standards and training requirements and to inform countermeasure research and design. Probability is quantified with a probabilistic modeling approach where distributions of model parameter values, instead of single deterministic values, capture the parameter variability within the astronaut population and fracture predictions are probability distributions with a mean value and an associated uncertainty. Because of this uncertainty, the model in its current state cannot discern an effect of countermeasures on fracture probability, for example between use and non-use of bisphosphonates or between spaceflight exercise performed with the Advanced Resistive Exercise Device (ARED) or on devices prior to installation of ARED on the International Space Station. This is thought to be due to the inability to measure key contributors to bone strength, for example, geometry and volumetric distributions of bone mass, with areal bone mineral density (BMD) measurement techniques. To further the applicability of model, we performed a parameter sensitivity study aimed at identifying those parameter uncertainties that most effect the model forecasts in order to determine what areas of the model needed enhancements for reducing uncertainty. Methods: The bone fracture risk model (BFxRM), originally published in (Nelson et al) is a probabilistic model that can assess the risk of astronaut bone fracture. This is accomplished by utilizing biomechanical models to assess the applied loads; utilizing models of spaceflight BMD loss in at-risk skeletal locations; quantifying bone strength through a relationship between areal BMD and bone failure load; and relating fracture risk index (FRI), the ratio of applied load to bone strength, to fracture probability. There are many factors associated with these calculations including environmental factors, factors associated with the fall event, mass and anthropometric values of the astronaut, BMD characteristics, characteristics of the relationship between BMD and bone strength and bone fracture characteristics. The uncertainty in these factors is captured through the use of parameter distributions and the fracture predictions are probability distributions with a mean value and an associated uncertainty. To determine parameter sensitivity, a correlation coefficient is found between the sample set of each model parameter and the calculated fracture probabilities. Each parameters contribution to the variance is found by squaring the correlation coefficients, dividing by the sum of the squared correlation coefficients, and multiplying by 100. Results: Sensitivity analyses of BFxRM simulations of preflight, 0 days post-flight and 365 days post-flight falls onto the hip revealed a subset of the twelve factors within the model which cause the most variation in the fracture predictions. These factors include the spring constant used in the hip biomechanical model, the midpoint FRI parameter within the equation used to convert FRI to fracture probability and preflight BMD values. Future work: Plans are underway to update the BFxRM by incorporating bone strength information from finite element models (FEM) into the bone strength portion of the BFxRM. Also, FEM bone strength information along with fracture outcome data will be incorporated into the FRI to fracture probability.
Large-scale self-consistent-field plus configuration-interaction calculations have been performed for the a 3Pi u and d 3Pi g states of C2. The theoretical potential curves are in good agreement with those found by a Klein-Dunham analysis of measured molecular constants in terms of shape and excitation energy. The sum of the squares of the theoretical transition moments between the states at 2.44 bohr is 4.12 a.u. which agrees with the results of shock tube measurements. The variation in the sum of the squares of the theoretical moments with internuclear separation agrees with the values of Danylewych and Nicholls (1974). Based on the data for C2 and mother molecules, it is suggested that CI calculations using near Hartree-Fock quality Slater basis sets produce highly reliable transition moments.
To estimate the degree of quantum entanglement of random pure states, it is crucial to understand the statistical behavior of entanglement indicators such as the von Neumann entropy, quantum purity, and entanglement capacity. These entanglement metrics are functions of the spectrum of density matrices, and their statistical behavior over different generic state ensembles have been intensively studied in the literature. As an alternative metric, in this work, we study the sum of the square root spectrum of density matrices, which is relevant to negativity and fidelity in quantum information processing. In particular, we derive the finite-size mean and variance formulas of the sum of the square root spectrum over the Bures–Hall ensemble, extending known results obtained recently over the Hilbert–Schmidt ensemble.
The sum of the squares of the electronic transition moments for the (E 1 Sigma +) - (X 1 Sigma +) band system of SiO has been determined from absorption measurements conducted in the reflected-shock region of a shock tube. The test gas produced by shock-heating a mixture of SiCl4, N2O, and Ar, and the spectra were recorded photographically in the 150-230-nm wavelength range. The values of the sum of the squares were determined by comparing the measured absorption spectra with those produced by a line-by-line synthetic spectrum calculation. The value so deduced at an r-centroid value of 3.0 bohr was 0.86 + or - 0.10 atomic unit.
Abstract not provided.
This paper investigates a problem on the steady-state, conduction-convection heat transfer process in cylindrical porous heat exchangers. The governing partial differential equations for the system are obtained using the energy conservation law. Solution of these equations and the concept of enthalpy lead to a new approach to prove a theorem that the sum of inverse squares of all the positive roots of the zero order Bessel function of the first kind equals to one-forth. As a corollary, it is shown that the sum of one over pth power (p greater than or equal to 2) of the roots converges to some constant.
This paper presents a methodology, along with applications to a grid type structure, for incorporating reliability considerations in the decision for actuator placement on large space structures. The method involves the minimization of a criterion that considers mission life and the reliability of the system components. It is assumed that the actuator gains are to be readjusted following failures, but their locations cannot be changed. The goal of the design is to suppress vibrations of the grid and the integral square of the grid modal amplitudes is used as a measure of performance of the control system. When reliability of the actuators is considered, a more pertinent measure is the expected value of the integral; that is, the sum of the squares of the modal amplitudes for each possible failure state considered, multiplied by the probability that the failure state will occur. For a given set of actuator locations, the optimal criterion may be graphed as a function of the ratio of the mean time to failure of the components and the design mission life or reservicing interval. The best location of the actuators is typically different for a short mission life than for a long one.
Equalization filters designed to minimize the mean square error between a delayed version of the original electrical signal and the equalized response at a point in a room have previously been investigated. In general, such a strategy degrades the response at positions in a room away from the equalization point. A method is presented for designing an equalization filter by adjusting the filter coefficients to minimize the sum of the squares of the errors between the equalized responses at multiple points in the room and delayed versions of the original, electrical signal. Such an equalization filter can give a more uniform frequency response over a greater volume of the enclosure than can the single point equalizer above. Computer simulation results are presented of equalizing the frequency responses from a loudspeaker to various typical ear positions, in a room with dimensions and acoustic damping typical of a car interior, using the two approaches outlined above. Adaptive filter algorithms, which can automatically adjust the coefficients of a digital equalization filter to achieve this minimization, will also be discussed.
A method and apparatus for directly measuring the time-averaged streamwise momentum in a turbulent stream use a probe which has total head response which varies as the cosine-squared of the angle of incidence. The probe has a nose with a slight indentation on its front face for providing the desired response. The method of making the probe incorporates unique design features. Another probe may be positioned in a side-by-side relationship to the first probe to provide a direct measurement of the total pressure. The difference between the two pressures yields the sum of the squares of the cross-stream components of the turbulence level.
The sum of the squares of the electronic transition moments for the A 1 Pi - X 1 Sigma + band system of SiO has been determined from absorption measurements conducted in the reflected-shock region of a shock tube. The test gas was produced by shock-heating a mixture of N2O, SiCl4, and Ar, and the spectra were recorded photographically in the 260-290-nm wavelength range. The values of the sum as a function of internuclear distance between 2.8 and 3.3 Bohr were determined by comparing the measured absorption spectrum with that produced by a line-by-line synthetic-spectrum calculation which accounted for instrumental broadening. The value of the sum so deduced at an internuclear distance of 3.0 Bohr was 1.0 + or - 0.3 atomic units.
If the Peccei-Quinn field containing the QCD axion undergoes rotations in the early universe, the dimension-five operator responsible for neutrino masses can generate a lepton asymmetry that ultimately gives rise to the observed baryon asymmetry of the Universe. This lepto-axiogenesis scenario requires a flat potential for the radial direction of the Peccei-Quinn field, naturally realized in supersymmetric models. We carefully compute the efficiency of this mechanism for the Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) and Kim-Shifman-Vainshtein-Zakharov (KSVZ) axion models and place lower bounds on the masses of scalar superpartners required to reproduce the observed baryon asymmetry. For the KSVZ model, we find an efficiency for generation of the asymmetry six times larger than the previously extant computation after including scattering channels involving superpartners. In this case, the superpartner scale should be above 30 TeV for a domain wall number of one; the lower bound weakens for larger domain wall numbers. We find that the superpartner mass scale may also be as low as ~ 30 TeV for the DFSZ model. In all cases, the lower bound on the superpartner masses is inversely proportional to the sum of the squares of the neutrino masses and so can strengthen as the upper bound on the neutrino mass improves. We identify the parameter space where the axion rotation can simultaneously produce axion dark matter via kinetic misalignment; in this case it is possible to put an upper bound of order PeV on the masses of scalar superpartners.
A search for long-lived heavy neutrinos (N) in the decays of B mesons produced in proton-proton collisions at $ \sqrt{s} $ = 13 TeV is presented. The data sample corresponds to an integrated luminosity of 41.6 fb$^{−1}$ collected in 2018 by the CMS experiment at the CERN LHC, using a dedicated data stream that enhances the number of recorded events containing B mesons. The search probes heavy neutrinos with masses in the range 1 < m$_{N}$ < 3 GeV and decay lengths in the range 10$^{−2}$ < cτ$_{N}$ < 10$^{4}$ mm, where τ$_{N}$ is the N proper mean lifetime. Signal events are defined by the signature B → ℓ$_{B}$NX; N → ℓ$^{±}$π$^{∓}$, where the leptons ℓ$_{B}$ and ℓ can be either a muon or an electron, provided that at least one of them is a muon. The hadronic recoil system, X, is treated inclusively and is not reconstructed. No significant excess of events over the standard model background is observed in any of the ℓ$^{±}$π$^{∓}$ invariant mass distributions. Limits at 95% confidence level on the sum of the squares of the mixing amplitudes between heavy and light neutrinos, |V$_{N}$|$^{2}$, and on cτ$_{N}$ are obtained in different mixing scenarios for both Majorana and Dirac-like N particles. The most stringent upper limit |V$_{N}$|$^{2}$ < 2.0 × 10$^{−5}$ is obtained at m$_{N}$ = 1.95 GeV for the Majorana case where N mixes exclusively with muon neutrinos. The limits on |V$_{N}$|$^{2}$ for masses 1 < m$_{N}$ < 1.7 GeV are the most stringent from a collider experiment to date.[graphic not available: see fulltext]
For fused magnesia smelting processes, the proportional-integral-derivative (PID) controller is difficult to regulate the smelting currents within desired ranges due to unexpected variations of the dynamics caused by material feeding operations. To solve this problem, we first proposed its dynamic model composed of a linear model and an uncertain nonlinear dynamic system that describes the unknown time-varying dynamics of nonlinearity and strong couplings among controlled variables. Then, using the accurately calculated value of the uncertain part at the previous sampling time instant and the tracking error that reflects the influence of its change rate, we developed a feedforward and a one-step optimal control to obtain two signal compensators to eliminate the impact of frequent variations of the uncertainties. For the compensators, we proposed a weight selection method to minimize the sum of the squared tracking error with ensured closed-loop stability. Based on the abovementioned modeling and control structure, we finally developed a novel adaptive PID controller augmented with signal compensators to control the whole process. Industrial applications have shown that the proposed method can always keep the tracking error and the control input within their targeted ranges, leading to a significantly reduced energy consumption per ton and increased fused magnesia production.
We report thatpProbing is a general technique that is used to reduce the variance of the Hutchinson stochastic estimator for the trace of the inverse of a large, sparse matrix A. The variance of the estimator is the sum of the squares of the off-diagonal elements of A -1 . Therefore, this technique computes probing vectors that when used in the estimator annihilate the largest off-diagonal elements. For matrices that display decay of the magnitude of |A$^{-1}_{ij}$| with the graph distance between nodes i and j, this is achieved through graph coloring of increasing powers A k . Equivalently, when a matrix stems from a lattice discretization, it is computationally beneficial to find a distance-k coloring of the lattice. Previously, a hierarchical coloring was proposed so that k can be increased at runtime as needed without discarding previous work. In this work, we study probing for the more general problem of computing the trace of a permutation of A -1 , say PA -1 . The motivation comes from lattice quantum chromodynamics (QCD), where we need to construct “disconnected diagrams” to extract flavor-separated generalized parton functions. In lattice QCD, where the matrix has a four-dimensional toroidal lattice structure, these nonlocal operators correspond to a PA -1 , where P is the permutation relating to some displacement $\vec{p}$ in one or more dimensions. We focus on a single dimension displacement (p), but our methods are general. We show that probing on A k or (PA) k does not annihilate the largest magnitude elements. To resolve this issue, our displacement-based probing works on PA k using a new coloring scheme that works directly on appropriately displaced neighborhoods on the lattice. We prove lower bounds on the number of colors needed and study the effect of this scheme on variance reduction, both theoretically and experimentally on a real-world lattice QCD calculation. We achieve orders of magnitude speedup over the unprobed or the naively probed methods.
Uncertainty analyses are an important part of calibrations and testing. They allow researchers insight on how to reduce and mitigate errors in testing. Each device used in testing introduces error in a system, as well as other sources such as environmental conditions, electronics, analog to digital, and random errors. Each source is carefully examined to identify how much error it introduces to a system. These sources are then combined using various methods of uncertainty calculations. To verify and validate software, a manual calculation is required to ensure the software is performing as intended. Using Excel to verify the calculations, we can identify discrepancies within the software. The root of the sum of the squares uncertainty (RSS) is used to find the combined uncertainty of a device at one and two standard deviations of the mean. Calibrations on accelerometers are performed using a vibration system along with a back-toback reference accelerometer. The vibration system takes a reference point at 100Hz frequency at 10g amplitude. The sensitivities are collected at each dialed in frequency. The sensitivity of the device represents the electrical output of the UUT (mV, pC, etc.) per unit of acceleration (g). The full history of sensitivities of selected accelerometers are used to find the averaged, standard deviation, and uncertainty of the device at each frequency tested. The uncertainty calculations from excel and the software are then compared.
Calculations of annual energy production (AEP) from a wind power plant – whether based on preconstruction or operational data – are critical for wind plant financial transactions. The uncertainty in the AEP calculation is especially important in quantifying risk and is a key factor in determining financing terms. A popular industry practice is to assume that different uncertainty components within an AEP calculation are uncorrelated and can therefore be combined as the sum of their squares. We assess the practical validity of this assumption for operational-based uncertainty by performing operational AEP estimates for more than 470 wind plants in the United States, mostly in simple terrain. We apply a Monte Carlo approach to quantify uncertainty in five categories: revenue meter data, wind speed data, regression relationship between density-corrected wind speed (from reanalysis data) and measured wind power, length of long-term-correction data set, and future interannual variability. We identify correlations between categories by comparing the results across all 470 wind plants. We observe a positive correlation between interannual variability and the linearized long-term correction; a negative correlation between wind resource interannual variability and linear regression; and a positive correlation between reference wind speed uncertainty and linear regression. Then, we contrast total operational AEP uncertainty values calculated by omitting and considering correlations between the uncertainty components. We quantify that ignoring these correlations leads to an underestimation of total AEP uncertainty of, on average, 0.1% and as large as 0.5% for specific sites. Although these are not large increases, these would still impact wind plant financing rates; further, we expect these values to increase for wind plants in complex terrain. Based on these results, we conclude that correlations between the identified uncertainty components should be considered when computing the total AEP uncertainty.