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At least 325 records · Page 18

The CFL condition for spectral approximations to hyperbolic initial-boundary value problems

The stability of spectral approximations to scalar hyperbolic initial-boundary value problems with variable coefficients are studied. Time is discretized by explicit multi-level or Runge-Kutta methods of order less than or equal to 3 (forward Euler time differencing is included), and spatial discretizations are studied by spectral and pseudospectral approximations associated with the general family of Jacobi polynomials. It is proved that these fully explicit spectral approximations are stable provided their time-step, delta t, is restricted by the CFL-like condition, delta t less than Const. N(exp-2), where N equals the spatial number of degrees of freedom. We give two independent proofs of this result, depending on two different choices of approximate L(exp 2)-weighted norms. In both approaches, the proofs hinge on a certain inverse inequality interesting for its own sake. The result confirms the commonly held belief that the above CFL stability restriction, which is extensively used in practical implementations, guarantees the stability (and hence the convergence) of fully-explicit spectral approximations in the nonperiodic case.

Gottlieb, David↗

Proton-detected solid-state NMR spectroscopy of spin-1/2 nuclei with large chemical shift anisotropy

Constant-time (CT) dipolar heteronuclear multiple quantum coherence (D-HMQC) has previously been demonstrated as a method for proton detection of high-resolution wideline NMR spectra of spin-1/2 nuclei with large chemical shift anisotropy (CSA). However, 1 H transverse relaxation and t 1 -noise often reduce the sensitivity of D-HMQC experiments, preventing the theoretical gains in sensitivity provided by 1 H detection from being realized. In this paper, we demonstrate a series of improved pulse sequences for 1 H detection of spin-1/2 nuclei under fast MAS, with 195 Pt SSNMR experiments on cisplatin as an example. First, a t 1 -incrementation protocol for D-HMQC dubbed Arbitrary Indirect Dwell (AID) is demonstrated. AID allows the use of arbitrary, rotor asynchronous t 1 -increments, but removes the constant time period from CT D-HMQC, resulting in improved sensitivity by reducing transverse relaxation losses. Next, we show that short high-power adiabatic pulses (SHAPs), which efficiently invert broad MAS sideband manifolds, can be effectively incorporated into 1 H detected symmetry-based resonance echo double resonance (S-REDOR) and t 1 -noise eliminated (TONE) D-HMQC experiments. The S-REDOR experiments with SHAPs provide approximately double the dipolar dephasing, as compared to experiments with rectangular inversion pulses. We lastly show that sensitivity and resolution can be further enhanced with the use of swept excitation pulses as well as adiabatic magic angle turning (aMAT).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Eddy diffusivity operator in homogeneous isotropic turbulence

Here, we use the recently developed macroscopic forcing method to compute the scale-dependent eddy diffusivity characterizing ensemble-averaged scalar and momentum transport in incompressible homogeneous isotropic turbulence. For scales larger than the energy containing eddies, eddy diffusivity is found to be constant and consistent with the Boussinesq approximation. However, for small scales eddy diffusivity is found to vanish inversely proportional to the wave number. Behavior at all scales is reasonably captured by a nonlocal eddy diffusivity operator modeled as D/$\sqrt{I - l^2∇^2}$, where D is the eddy diffusivity in the Boussinesq limit, and l is a constant on the order of the large-eddy length. These results present a direct measurement of eddy diffusivity in turbulence with implications in turbulence modeling.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Particle size distributions from TRACER-MAP

Particle size distributions measured using a custom scanning mobility analyzer (SMPS) and a TSI, Inc. aerodynamic particle sizer (APS). The size distributions measured with the two instruments were merged during data inversion to produce a single distribution spanning a diameter range from approximately 19 nanometers to 15 micrometers. Size-dependent cloud condensation nuclei (CCN) activity measured with a CCN counter operated in parallel to the condensation particle counter in the SMPS are reported separately. The measurements were made from the Baylor University/University of Houston Mobile Air Quality Laboratory (MAQL) between July 5 and August 30, 2022 during the TRACER-MAP project. The trailer moved between five sites in the Houston regions as follows: Aldine: 7/5-7/8, 7/21-7/26, 8/15-8/24 University of Houston: 7/8-7/16, 8/8-8/15 San Jacinto monument: 7/16-7/21 Jones State Forest: 7/26-8/1; 8/24-8/30 AMF site in La Porte: 8/1-8/8

54 ENVIRONMENTAL SCIENCES↗

Particle size distributions from TRACER-MAP

Particle size distributions measured using a custom scanning mobility analyzer (SMPS) and a TSI, Inc. aerodynamic particle sizer (APS). The size distributions measured with the two instruments were merged during data inversion to produce a single distribution spanning a diameter range from approximately 19 nanometers to 15 micrometers. Size-dependent cloud condensation nuclei (CCN) activity measured with a CCN counter operated in parallel to the condensation particle counter in the SMPS are reported separately. The measurements were made from the Baylor University/University of Houston Mobile Air Quality Laboratory (MAQL) between July 5 and August 30, 2022 during the TRACER-MAP project. The trailer moved between five sites in the Houston regions as follows: Aldine: 7/5-7/8, 7/21-7/26, 8/15-8/24 University of Houston: 7/8-7/16, 8/8-8/15 San Jacinto monument: 7/16-7/21 Jones State Forest: 7/26-8/1; 8/24-8/30 AMF site in La Porte: 8/1-8/8

54 ENVIRONMENTAL SCIENCES↗

Nozzle Free Jet Flows Within the Strong Curved Shock Regime

A study based on inviscid analysis was conducted to examine the flow field produced from a convergent-divergent nozzle when a strong curved shock occurs. It was found that a certain constraint is imposed on the flow solution of the problem which is the unique feature of the flow within this flow regime, and provides the reason why the inverse method of calculation cannot be employed for these problems. An approximate method was developed to calculate the flow field, and results were obtained for two-dimensional flows. Analysis and calculations were performed for flows with axial symmetry. It is shown that under certain conditions, the vorticity generated at the jet boundary may become infinite and the viscous effect becomes important. Under other conditions, the asymptotic free jet height as well as the corresponding shock geometry were determined.

Shih, Tso-Shin↗

Benchmark solutions for the galactic ion transport equations with spatial and energy coupling

In order to anticipate future space shielding requirements, NASA has initiated an effort to formulate computational methods to simulate radiation effects in space. As part of the program, numerical transport algorithms have been developed for the deterministic Boltzman equation describing galactic cosmic ray (GCR) interactions with matter. It thus becomes necessary to assess the accuracy of proposed deterministic algorithms. For this reason, analytical benchmark solutions to mathematically tractable galactic cosmic ray equations have recently been obtained. Even though these problems involve simplifying assumptions of the associated physics, they still contain the essential features of the basic transport processes. The solutions obtained are features of the basic transport processes. The solutions obtained are compared to results from numerical algorithms in order to ensure proper coding and to provide a measure of the accuracy of the numerical methods used in the algorithm. For the first time, mathematical methods have been applied to the galactic ion transport (GIT) equations in the straight ahead approximation with constant nuclear properties. The approach utilizes a Laplace transforms inversion yielding a closed form benchmark solution which is also computationally efficient.

Ganapol, Barry D.↗

Methods for local gravity field approximation

The most widely known modern method for estimating gravity field values from observed data is least-squares collocation. Its advantages are that it can make estimates at arbitrary locations based on irregularly spaced observations, and that it makes use of statistical information about errors in the input data while providing corresponding information about the quality of the output estimates. Disadvantages of collocation include the necessity of inverting square matrices of dimension equal to the number of data values and the need to assume covariance models for the gravity field and the data errors. Fourier methods are an important alternative to collocation; having the advantage of greater computational efficiency, but requiring data estimates to be on a regular grid and not using or providing statistical accuracy information. The GEOFAST algorithm is an implementation of collocation that achieves high computational efficiency by transforming the estimation equations into the frequency domain where an accurate approximation may be made to reduce the workload. The forward and inverse Fast Fourier Transforms (FFTs) are utilized. The accuracy and computational efficiency of the GEOFAST algorithm is demonstrated using two sets of synthetic gravity data: marine gravity for an ocean trench region including wavelengths longer than 200 km; and local land gravity containing wavelengths as short as 5 km. These results are discussed along with issues such as the advantages of first removing reference field models before carrying out the estimation algorithm.

Sailor, R. V.↗

Axions and SN 1987A: Axion trapping

If an axion of mass between about 10(exp -3) and 10 eV exists, axion emission would have significantly affected the cooling of the nascent neutron star associated with SN 1987A. For an axion of mass greater than about 10(exp -2) eV axions would, like neutrinos, have a mean-free path that is smaller than the size of a neutron star, and thus would become trapped and radiated from an axion sphere. The trapping regime is treated by using numerical models of the initial cooling of a hot neutron star that incorporate a diffusion approximation for axion-energy transport. The axion opacity due to inverse nucleon-nucleon, axion bremsstrahlung is computed; and then the numerical models are used to calculate the integrated axion luminosity, the temperature of the axion sphere, and the effect of axion emission on the neutrino bursts detected by the Kamiokande II (KII) and Irvine-Michigan-Brookhaven (IMB) water-Cherenkov detectors. The larger the axion mass, the stronger the trapping and the smaller the axion luminosity. The estimate of the axion mass is confirmed above which trapping is so strong that axion emission does not significantly affect the neutrino burst. Based upon the neutrino-burst duration - the most sensitive barometer of axion cooling - it is concluded that for an axion mass greater than about 3 eV axion emission would not have had a significant effect on the neutrino bursts detected by KII and IMB. It is strongly suggested that an axion with mass in the interval 10(exp -3) to 3 eV is excluded by the observation of neutrinos from SN 1987A.

Burrows, Adam↗

Robust inverse kinematics using damped least squares with dynamic weighting

This paper presents a general method for calculating the inverse kinematics with singularity and joint limit robustness for both redundant and non-redundant serial-link manipulators. Damped least squares inverse of the Jacobian is used with dynamic weighting matrices in approximating the solution. This reduces specific joint differential vectors. The algorithm gives an exact solution away from the singularities and joint limits, and an approximate solution at or near the singularities and/or joint limits. The procedure is here implemented for a six d.o.f. teleoperator and a well behaved slave manipulator resulted under teleoperational control.

Schinstock, D. E.↗

Very long baseline IPS observations of the solar wind speed in the fast polar streams

Observations of intensity scintillation (IPS) with two or more spaced antennas have been widely used to measure the solar wind velocity. Such methods are particularly valuable in regions which spacecraft have not yet penetrated, but they are also very useful in improving the spatial temporal sampling of the solar wind, even in regions where spacecraft data are available. The principle of the measurement is to measure the time delay tau(sub d) between the scintillations observed with an antenna baseline b. The velocity estimate is just V = b/tau(sub d). The error in estimation of the time delay delta tau(sub d) is independent of the baseline length, thus the error in the velocity estimate delta V given by delta(V)/V approximately equals to (delta tau(sub d))/tau(sub d) is inversely proportional to tau(sub d) and hence to b. However the use of a long baseline b has a less obvious advantage; it provides a means for separating fast and slow contributions when both are present in the scattering region. Here we will present recent observations made using the large cylinder antenna at Ooty in the Nilgiri Hills of South India, and one of the 45 m dishes of GMRT near Pune in West-Central India. The baseline of 900 km is, by a considerable margin, the longest ever used for IPS and provides excellent velocity resolution. These results compared with the ULYSSES observations and other IPS measurements made closer to the sun with higher frequency instruments such as EISCAT and the VLBA will provide a precise measure of the velocity profile of the fast north-polar stream.

Rao, A. Pramesh↗

Analytic approximations to the modon dispersion relation

Three explicit analytic approximations are given to the modon dispersion relation developed by Flierl et al. (1980) to describe Gulf Stream rings and related phenomena in the oceans and atmosphere. The solutions are in the form of k(q), and are developed in the form of a power series in q for small q, an inverse power series in 1/q for large q, and a two-point Pade approximant. The low order Pade approximant is shown to yield a solution for the dispersion relation with a maximum relative error for the lowest branch of the function equal to one in 700 in the q interval zero to infinity.

Boyd, J. P.↗

System Identification for Nonlinear Control Using Neural Networks

An approach to incorporating artificial neural networks in nonlinear, adaptive control systems is described. The controller contains three principal elements: a nonlinear inverse dynamic control law whose coefficients depend on a comprehensive model of the plant, a neural network that models system dynamics, and a state estimator whose outputs drive the control law and train the neural network. Attention is focused on the system identification task, which combines an extended Kalman filter with generalized spline function approximation. Continual learning is possible during normal operation, without taking the system off line for specialized training. Nonlinear inverse dynamic control requires smooth derivatives as well as function estimates, imposing stringent goals on the approximating technique.

Stengel, Robert F.↗

The Global Methane Budget 2000-2012

The global methane (CH4) budget is becoming an increasingly important component for managing realistic pathways to mitigate climate change. This relevance, due to a shorter atmospheric lifetime and a stronger warming potential than carbon dioxide, is challenged by the still unexplained changes of atmospheric CH4 over the past decade. Emissions and concentrations of CH4 are continuing to increase, making CH4 the second most important human-induced greenhouse gas after carbon dioxide. Two major difficulties in reducing uncertainties come from the large variety of diffusive CH4 sources that overlap geographically, and from the destruction of CH4 by the very short-lived hydroxyl radical (OH). To address these difficulties, we have established a consortium of multi-disciplinary scientists under the umbrella of the Global Carbon Project to synthesize and stimulate research on the methane cycle, and producing regular (approximately biennial) updates of the global methane budget. This consortium includes atmospheric physicists and chemists, biogeochemists of surface and marine emissions, and socio-economists who study anthropogenic emissions. Following Kirschke et al. (2013), we propose here the first version of a living review paper that integrates results of top-down studies (exploiting atmospheric observations within an atmospheric inverse-modeling framework) and bottom-up models, inventories and data-driven approaches (including process-based models for estimating land surface emissions and atmospheric chemistry, and inventories for anthropogenic emissions, data-driven extrapolations).For the 2003-2012 decade, global methane emissions are estimated by top-down inversions at 558 TgCH4 yr(exp -1), range 540-568. About 60 of global emissions are anthropogenic (range 50-65%). Since 2010, the bottom-up global emission inventories have been closer to methane emissions in the most carbon-intensive Representative Concentrations Pathway (RCP8.5) and higher than all other RCP scenarios. Bottom-up approaches suggest larger global emissions (736 TgCH4 yr(exp -1), range 596-884) mostly because of larger natural emissions from individual sources such as inland waters, natural wetlands and geological sources. Considering the atmospheric constraints on the top-down budget, it is likely that some of the individual emissions reported by the bottom-up approaches are overestimated, leading to too large global emissions. Latitudinal data from top-down emissions indicate a predominance of tropical emissions (approximately 64% of the global budget, less than 30deg N) as compared to mid (approximately 32%, 30-60deg N) and high northern latitudes (approximately 4%, 60-90deg N). Top-down inversions consistently infer lower emissions in China (approximately 58 TgCH4 yr(exp -1), range 51-72, minus14% ) and higher emissions in Africa (86 TgCH4 yr(exp -1), range 73-108, plus 19% ) than bottom-up values used as prior estimates. Overall, uncertainties for anthropogenic emissions appear smaller than those from natural sources, and the uncertainties on source categories appear larger for top-down inversions than for bottom-up inventories and models. The most important source of uncertainty on the methane budget is attributable to emissions from wetland and other inland waters. We show that the wetland extent could contribute 30-40% on the estimated range for wetland emissions. Other priorities for improving the methane budget include the following: (i) the development of process-based models for inland-water emissions, (ii) the intensification of methane observations at local scale (flux measurements) to constrain bottom-up land surface models, and at regional scale (surface networks and satellites) to constrain top-down inversions, (iii) improvements in the estimation of atmospheric loss by OH, and (iv) improvements of the transport models integrated in top-down inversions. The data presented here can be downloaded from the Carbon Dioxide Information Analysis Center (http://doi.org/10.3334/CDIAC/GLOBAL_ METHANE_BUDGET_2016_V1.1) and the Global Carbon Project.

Saunois, Marielle↗

Sequential ensemble transform for Bayesian inverse problems

In this work, we present the Sequential Ensemble Transform (SET) method, an approach for generating approximate samples from a Bayesian posterior distribution. The method explores the posterior distribution by solving a sequence of discrete optimal transport problems to produce a series of transport plans which map prior samples to posterior samples. We prove that the sequence of Dirac mixture distributions produced by the SET method converges weakly to the true posterior as the sample size approaches infinity. Furthermore, our numerical results indicate that, when compared to standard Sequential Monte Carlo (SMC) methods, the SET approach is more robust to the choice of Markov mutation kernels and requires less computational efforts to reach a similar accuracy when used to explore complex posterior distributions. Finally, we describe adaptive schemes that allow to completely automate the use of the SET method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Low-Current, Xenon Orificed Hollow Cathode Performance for In-Space Applications

An experimental investigation of the operating characteristics of 3.2-mm diameter orificed hollow cathodes was conducted to examine low current and low flow rate operation. Cathode power was minimized with an orifice aspect ratio of approximately one and the use of an enclosed keeper. Cathode flow rate requirements were proportional to orifice diameter and the inverse of the orifice length. The minimum power consumption in diode mode was 10-W, and the minimum mass flow rate required for spot-mode emission was approximately 0.08-mg/s. Cathode temperature profiles were obtained using an imaging radiometer and conduction was found to be the dominant heat transfer mechanism from the cathode tube. Orifice plate temperatures were found to be weakly dependent upon the flow rate and strongly dependent upon the current.

Domonkos, Matthew T.↗

SGD-Net: Efficient Model-Based Deep Learning with Theoretical Guarantees

Deep unfolding networks have recently gained popularity for solving imaging inverse problems. However, the computational and memory complexity of data-consistency layers within traditional deep unfolding networks scales with the number of measurements, limiting their applicability to large-scale imaging inverse problems. We propose SGD-Net as a new methodology for improving the efficiency of deep unfolding through stochastic approximations of the data-consistency layers. Our theoretical analysis shows that SGD-Net can be trained to approximate batch deep unfolding networks to an arbitrary precision. Our simulations on intensity diffraction tomography and sparse-view computed tomography show that SGD-Net can match the performance of the traditional batch network at a fraction of training and testing complexity.Deep unfolding networks have recently gained popularity for solving imaging inverse problems. However, the computational and memory complexity of data-consistency layers within traditional deep unfolding networks scales with the number of measurements, limiting their applicability to large-scale imaging inverse problems. We propose SGD-Net as a new methodology for improving the efficiency of deep unfolding through stochastic approximations of the data-consistency layers. Our theoretical analysis shows that SGD-Net can be trained to approximate batch deep unfolding networks to an arbitrary precision. Our simulations on intensity diffraction tomography and sparse-view computed tomography show that SGD-Net can match the performance of the traditional batch network at a fraction of training and testing complexity.

97 MATHEMATICS AND COMPUTING↗

Permeate fluxes from desalination of brines and produced waters: A reactive transport modeling study

The increasing interest in the use of membrane systems to desalinate inland brackish water, agricultural drainage, and industrially produced wastewater demands improved means of predicting desalination system performance under variable feedwater compositions. The interaction among water flow, solute transport, and chemical composition in these systems impacts permeate flux evolution. Here, an established multicomponent reactive transport simulator that accounts for these coupled processes is applied to compute osmotic pressure and permeate fluxes in reverse osmosis (RO) systems. The model is first validated by predicting permeate fluxes for a set of benchtop crossflow experiments subject to a range of feed flow rates and compositions, under fouling and non-fouling conditions. Results compare favorably with measured data that show that solutions with similar total dissolved solids concentrations but different compositions result in different permeate fluxes. The model is then applied to predict permeate fluxes from the desalination of produced waters using a commercial spiral wound RO module. For NaCl-dominant brines, at total dissolved salt concentrations (TDS) below about 70 g/L, permeate fluxes are inversely proportional to water mole fraction as the latter is a reasonable approximation of water activity (i.e. ideal mixing). In the case of Ca–Cl-, Na–CO3- and Na–SO4-dominant brines below about 70 g/L TDS, this relationship does not hold as well and tends to overpredict osmotic pressure and thus underpredict permeate fluxes. However, the opposite becomes true at higher TDS values for typical produced waters. The scaling potential of these waters is also computed by allowing the precipitation of minerals above their saturation limit on the RO membrane. This work demonstrates how reactive transport models developed for the analysis of waters from geological systems can be extended to improve process design, optimization, and control in desalination systems from produced waters and beyond.

Molins, Sergi↗