Cutoff frequencies of eccentric waveguides.
Point matching method, solving boundary value problem in uniform cylindrical waveguide with inserted conductor within conducting tube
CYLINDRICAL SHELL↗
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Magnetohydrodynamical equilibria with current singularities and continuous rotational transform
We revisit the Hahm–Kulsrud–Taylor (HKT) problem, a classic prototype problem for studying resonant magnetic perturbations and 3D magnetohydrodynamical equilibria. We employ the boundary-layer techniques developed by Rosenbluth, Dagazian, and Rutherford (RDR) for the internal m = 1 kink instability, while addressing the subtle difference in the matching procedure for the HKT problem. Pedagogically, the essence of RDR's approach becomes more transparent in the reduced slab geometry of the HKT problem. We then compare the boundary-layer solution, which yields a current singularity at the resonant surface, to the numerical solution obtained using a flux-preserving Grad–Shafranov solver. The remarkable agreement between the solutions demonstrates the validity and universality of RDR's approach. Additionally, we show that RDR's approach consistently preserves the rotational transform, which hence stays continuous, contrary to a recent claim that RDR's solution contains a discontinuity in the rotational transform.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
The Statistical Consulting Center for Astronomy (SCCA)
The process by which raw astronomical data acquisition is transformed into scientifically meaningful results and interpretation typically involves many statistical steps. Traditional astronomy limits itself to a narrow range of old and familiar statistical methods: means and standard deviations; least-squares methods like chi(sup 2) minimization; and simple nonparametric procedures such as the Kolmogorov-Smirnov tests. These tools are often inadequate for the complex problems and datasets under investigations, and recent years have witnessed an increased usage of maximum-likelihood, survival analysis, multivariate analysis, wavelet and advanced time-series methods. The Statistical Consulting Center for Astronomy (SCCA) assisted astronomers with the use of sophisticated tools, and to match these tools with specific problems. The SCCA operated with two professors of statistics and a professor of astronomy working together. Questions were received by e-mail, and were discussed in detail with the questioner. Summaries of those questions and answers leading to new approaches were posted on the Web (www.state.psu.edu/ mga/SCCA). In addition to serving individual astronomers, the SCCA established a Web site for general use that provides hypertext links to selected on-line public-domain statistical software and services. The StatCodes site (www.astro.psu.edu/statcodes) provides over 200 links in the areas of: Bayesian statistics; censored and truncated data; correlation and regression, density estimation and smoothing, general statistics packages and information; image analysis; interactive Web tools; multivariate analysis; multivariate clustering and classification; nonparametric analysis; software written by astronomers; spatial statistics; statistical distributions; time series analysis; and visualization tools. StatCodes has received a remarkable high and constant hit rate of 250 hits/week (over 10,000/year) since its inception in mid-1997. It is of interest to scientists both within and outside of astronomy. The most popular sections are multivariate techniques, image analysis, and time series analysis. Hundreds of copies of the ASURV, SLOPES and CENS-TAU codes developed by SCCA scientists were also downloaded from the StatCodes site. In addition to formal SCCA duties, SCCA scientists continued a variety of related activities in astrostatistics, including refereeing of statistically oriented papers submitted to the Astrophysical Journal, talks in meetings including Feigelson's talk to science journalists entitled "The reemergence of astrostatistics" at the American Association for the Advancement of Science meeting, and published papers of astrostatistical content.
Akritas, Michael↗
Towards Automatically Matching Security Advisories to CPEs: String Similarity-based Vendor Matching
When a vulnerability is reported by the National Vulnerability Database (NVD), affected products are listed in the structured Common Platform Enumeration (CPE) format. Unfortunately, if the vulnerability is in a software library (e.g., Log4j), it will not include CPEs for each product containing that library. In these cases, security operators need to manually read the vendor's or third-party security advisories to see if their product is affected. However, these advisories do not report affected products in a structured format, which prevents automated processing, This paper makes the first effort towards automatically constructing structured CPEs for the vulnerable products in a non-NVD security advisory from the unstructured data in the advisory. Since this is a very challenging problem, this paper specifically focuses on the initial but key step of matching the un-structured vendor names in security advisories to the structured vendor representations in the standard CPE format. We explore the feasibility of using string similarity to solve the problem. The basic idea is to compare a vendor name from the non-NVD advisory with each vendor in the official CPE dictionary. The CPE vendor with the highest similarity score to the advisory's vendor will be considered as the match. We first conduct an experimental, comparative study of multiple mainstream string similarity metrics for this matching problem. To improve the performance, we then design a new string similarity metric that is adapted from an existing metric by weighing different tokens in the advisory's vendor name differently.
McClanahan, Kylie↗
Physics-embedded inverse analysis with algorithmic differentiation for the earth’s subsurface
Abstract Inverse analysis has been utilized to understand unknown underground geological properties by matching the observational data with simulators. To overcome the underconstrained nature of inverse problems and achieve good performance, an approach is presented with embedded physics and a technique known as algorithmic differentiation. We use a physics-embedded generative model, which takes statistically simple parameters as input and outputs subsurface properties (e.g., permeability or P-wave velocity), that embeds physical knowledge of the subsurface properties into inverse analysis and improves its performance. We tested the application of this approach on four geologic problems: two heterogeneous hydraulic conductivity fields, a hydraulic fracture network, and a seismic inversion for P-wave velocity. This physics-embedded inverse analysis approach consistently characterizes these geological problems accurately. Furthermore, the excellent performance in matching the observational data demonstrates the reliability of the proposed method. Moreover, the application of algorithmic differentiation makes this an easy and fast approach to inverse analysis when dealing with complicated geological structures.
54 ENVIRONMENTAL SCIENCES↗
Radiative interactions in multi-dimensional chemically reacting flows using Monte Carlo simulations
The Monte Carlo method (MCM) is applied to analyze radiative heat transfer in nongray gases. The nongray model employed is based on the statistical narrow band model with an exponential-tailed inverse intensity distribution. The amount and transfer of the emitted radiative energy in a finite volume element within a medium are considered in an exact manner. The spectral correlation between transmittances of two different segments of the same path in a medium makes the statistical relationship different from the conventional relationship, which only provides the non-correlated results for nongray methods is discussed. Validation of the Monte Carlo formulations is conducted by comparing results of this method of other solutions. In order to further establish the validity of the MCM, a relatively simple problem of radiative interactions in laminar parallel plate flows is considered. One-dimensional correlated Monte Carlo formulations are applied to investigate radiative heat transfer. The nongray Monte Carlo solutions are also obtained for the same problem and they also essentially match the available analytical solutions. the exact correlated and non-correlated Monte Carlo formulations are very complicated for multi-dimensional systems. However, by introducing the assumption of an infinitesimal volume element, the approximate correlated and non-correlated formulations are obtained which are much simpler than the exact formulations. Consideration of different problems and comparison of different solutions reveal that the approximate and exact correlated solutions agree very well, and so do the approximate and exact non-correlated solutions. However, the two non-correlated solutions have no physical meaning because they significantly differ from the correlated solutions. An accurate prediction of radiative heat transfer in any nongray and multi-dimensional system is possible by using the approximate correlated formulations. Radiative interactions are investigated in chemically reacting compressible flows of premixed hydrogen and air in an expanding nozzle. The governing equations are based on the fully elliptic Navier-Stokes equations. Chemical reaction mechanisms were described by a finite rate chemistry model. The correlated Monte Carlo method developed earlier was employed to simulate multi-dimensional radiative heat transfer. Results obtained demonstrate that radiative effects on the flowfield are minimal but radiative effects on the wall heat transfer are significant. Extensive parametric studies are conducted to investigate the effects of equivalence ratio, wall temperature, inlet flow temperature, and nozzle size on the radiative and conductive wall fluxes.
Liu, Jiwen↗
Optimal Power Management of Battery Energy Storage Systems via Ensemble Kalman Inversion
Optimal power management of battery energy storage systems (BESS) is crucial for their safe and efficient operation. Numerical optimization techniques are frequently utilized to solve the optimal power management problems. However, these techniques often fall short of delivering real-time solutions for large-scale BESS due to their computational complexity. To address this issue, this paper proposes a computationally efficient approach. We introduce a new set of decision variables called power-sharing ratios corresponding to each cell, indicating their allocated power share from the output power demand. We then formulate an optimal power management problem to minimize the system-wide power losses while ensuring compliance with safety, balancing, and power supply-demand match constraints. To efficiently solve this problem, a parametrized control policy is designed and leveraged to transform the optimal power management problem into a parameter estimation problem. We then implement the ensemble Kalman inversion to estimate the optimal parameter set. The proposed approach significantly reduces computational requirements due to 1) the much lower dimensionality of the decision parameters and 2) the estimation treatment of the optimal power management problem. Finally, we conduct extensive simulations to validate the effectiveness of the proposed approach. The results show promise in accuracy and computation time compared with explored numerical optimization techniques.
Farakhor, Amir↗
Identification of Leakage Spectra from Neutron Activation in Glass/Cherenkov Detectors - Paper 96
Oak Ridge National Laboratory has developed a new detector system concept that can be deployed in major US cities to identify the leakage spectrum of a nuclear weapon detonation. The detector is based on a small piece of glass that has been doped with an element that has a high activation cross section and creates a radioactive activation product with a reasonable length half-life. The decay of the activation product(s) after exposure creates Cherenkov light which can propagate to a photomultiplier and can be turned into a count-rate signal. The signal from each glass in each detector in a city can be individually analyzed to determine the amount of activation products produced in the initial exposure. Several activation products can be determined in a single glass if the half-lives are not the same. With a known source location and a detailed 3D model of a city, neutron transport simulations can be made by using a library of known sources to predict the activation amounts each source would have made in the glass detectors. A simple comparison of the measured activation amounts and the predicted activation amounts can identify the source spectrum contained in the library that is the best match. Choosing dopants with a large range in the threshold energy for the activation reactions can help to differentiate the spectra in the library. The method of matching the measured activation amounts to the predicted activation amounts to identify the source spectrum is similar to the analysis used for the passive Activation Foil Integrated Detector System (AFIDS), also developed at Oak Ridge National Laboratory. In AFIDS, wires or foils of known mass and isotopic composition are deployed before and then collected after exposure. Counting gammas in a nearby laboratory determines the activation amounts. The glass/Cherenkov system is active - it uses a battery-powered detector to count flashes of Cherenkov light and to communicate its count rates to a remote location for further analysis. Work has been performed in several areas, including glass making, automated detection and communication systems and software tools for analysis of the signal and source spectrum identification. Bell and Boatner have developed phosphate glasses that incorporate elements with high capture cross sections, and Hayward has simulated the response with Geant4 and measured the response with isotopic gamma sources. This paper will focus on the software tools for determining the activation amounts from the Cherenkov count-rate signal and finding the best matching source spectrum. A test problem in an urban environment is used to demonstrate the potential of a spectrum identification system using neutron activation. The analysis methods developed to identify the neutron leakage spectra from Cherenkov light given off by neutron activation in doped glasses work well. The calculation used to unfold the count-rate information into the number of actual activation products uses robust algorithms that can also compute associated uncertainties. These uncertainties and the known uncertainties of the glass tube material compositions are incorporated into the matching analysis to determine which of the source spectra in the library best matches the measured activation data. Any measurement method used to identify a neutron source spectrum relies at some point on a comparison against known sources; no identification method is definitive. Detection systems measure some physical aspect of the source, not its serial number. Many systems measure the physical aspect to determine that the source has some property, and then leave it to experts to determine which potential sources share that property. The analysis system presented here incorporates the comparison into the analysis itself. The statistical tests show which of the known library sources match the measured data the best and whether that match is a good match. If the best match still does not fit the measured data well (a very high χ{sup 2} value), that indicates the true source is not one of the sources in the library. This is still valuable information for decision makers. (authors)
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
A photogrammetric solution to a particular problem
A closed-form mathematical solution to the classical photogrammetric problem is presented. Although quite general, the solution is more applicable to problems in which the image-space conjugates are very difficult to match but one of the elements of the pair is not. Additionally, observations are made that should make the solution to the general problem of automatic matching less computationally intensive. This approach was used to analyze flow visualization data for the F-18 High Alpha Research Vehicle. The conditions for this analysis were less than ideal for image-to-object-space transformation.
Hedgley, David R., Jr.↗
Scaling a discrete structural model to match measured modal frequencies
The structure modification problem, where the computer model of a structure is to be upgraded on the basis of experimental measurements of normal mode frequencies, is approached by the modal energy concept. The modes for correlation with test data are selected on the basis of relative strain energy participation. The resulting procedure can be viewed as an extension of White's (1972) method. Its advantage lies in that both the number and choice of structural parameters to be varied in the modification are arbitrary.
Taylor, J. E.↗
A Measure Approximation for Distributionally Robust PDE-Constrained Optimization Problems
In numerous applications, scientists and engineers acquire varied forms of data that partially characterize the inputs to an underlying physical system. This data is then used to inform decisions such as controls and designs. Consequently, it is critical that the resulting control or design is robust to the inherent uncertainties associated with the unknown probabilistic characterization of the model inputs. Here in this work, we consider optimal control and design problems constrained by partial differential equations with uncertain inputs. We do not assume a known probabilistic model for the inputs, but rather we formulate the problem as a distributionally robust optimization problem where the outer minimization problem determines the control or design, while the inner maximization problem determines the worst-case probability measure that matches desired characteristics of the data. We analyze the inner maximization problem in the space of measures and introduce a novel measure approximation technique, based on the approximation of continuous functions, to discretize the unknown probability measure. Finally, we prove consistency of our approximated min-max problem and conclude with numerical results.
54 ENVIRONMENTAL SCIENCES↗
The Power of Pausing: Advancing Understanding of Thermalization in Experimental Quantum Annealers
We investigate alternative annealing schedules on the current generation of quantum annealing hardware (the D-Wave 2000Q), which includes the use of forward and reverse annealing with an- intermediate pause. This work provides new insights into the inner workings of these devices (and quantum devices in general), particular into how thermal effects govern the system dynamics. We show that a pause mid-way through the anneal can cause a dramatic change in the output distribution, and we provide evidence suggesting thermalization is indeed occurring during such a pause. We demonstrate that upon pausing the system in a narrow region shortly after the minimum gap, the probability of successfully finding the ground state of the problem Hamiltonian can be increased by several orders of magnitude. We relate this effect to relaxation (i.e. thermalization) after diabatic and thermal excitations that occur in the region near to the minimum gap. For a set of large-scale problems of up to 500 qubits, we demonstrate that the distribution returned from the annealer very closely matches a (classical) Boltzmann distribution of the problem Hamiltonian, albeit one with a temperature at least 1.5 times higher than the (effective) temperature of the device. Moreover, we show that larger problems are more likely to thermalize to a classical Boltzmann distribution.
Marshall, Jeffrey↗
TESTING CONVERGENCE FOR GLOBAL ACCRETION DISKS
Global disk simulations provide a powerful tool for investigating accretion and the underlying magnetohydrodynamic turbulence driven by magneto-rotational instability (MRI). Using them to accurately predict quantities such as stress, accretion rate, and surface brightness profile requires that purely numerical effects, arising from both resolution and algorithm, be understood and controlled. We use the flux-conservative Athena code to conduct a series of experiments on disks having a variety of magnetic topologies to determine what constitutes adequate resolution. We develop and apply several resolution metrics: (Q{sub z} ) and (Q{sub {phi}}), the ratio of the grid zone size to the characteristic MRI wavelength, {alpha}{sub mag}, the ratio of the Maxwell stress to the magnetic pressure, and / , the ratio of radial to toroidal magnetic field energy. For the initial conditions considered here, adequate resolution is characterized by (Q{sub z} ) {>=} 15, (Q{sub {phi}}) {>=} 20, {alpha}{sub mag} Almost-Equal-To 0.45, and / {approx}0.2. These values are associated with {>=}35 zones per scaleheight H, a result consistent with shearing box simulations. Numerical algorithm is also important. Use of the Harten-Lax-van Leer-Einfeldt flux solver or second-order interpolation can significantly degrade the effective resolution compared to the Harten-Lax-van Leer discontinuities flux solver and third-order interpolation. Resolution at this standard can be achieved only with large numbers of grid zones, arranged in a fashion that matches the symmetries of the problem and the scientific goals of the simulation. Without it, however, quantitative measures important to predictions of observables are subject to large systematic errors.
79 ASTRONOMY AND ASTROPHYSICS↗
Digital approximation of continuous-data control systems by point-by-point state comparison
This paper presents a point-by-point state comparison method of approximating a continuous-data system by a sampled-data system. The problem is to attempt the matching of the states of the two systems at the sampling instants. A partial matching has to be conducted if the systems have more states than controls. A weighting matrix is used to regulate the partial matching and weights placed on each state. The digital approximation is affected by use of forward gain E(T) and feedback gain G(T) in the sampled-data system. It is shown that, in general, these gains can be approximated by truncated Taylor series expansions. An illustrative example is given using the one-axis dynamics of the Skylab satellite.
Kuo, B. C.↗
Urban development applications project. Urban technology transfer study
Technology transfer is defined along with reasons for attempting to transfer technology. Topics discussed include theoretical models, stages of the innovation model, communication process model, behavior of industrial organizations, problem identification, technology search and match, establishment of a market mechanism, applications engineering, commercialization, and management of technology transfer.
Source record↗
Magnetocentrifugally driven flows from young stars and disks. 2: Formulation of the dynamical problem
We formulate the dynamical problem of a cool wind centrifugally driven from the magnetic interface of a young star and an adjoining Keplerian disk. We examine the situation for mildly accreting T Tauri stars that rotate slowly as well as rapidly accreting protostars that rotate near break-up. In both cases a wind can be driven from a small X-region just outside the stellar magnetopause, where the field lines assume an open geometry and are rooted to material that rotates at an angular speed equal both to the local Keplerian value and to the stellar angular speed. Assuming axial symmetry for the ideal magnetohydrodynamic flow, which requires us to postpone asking how the (lightly ionized) gas is loaded onto field lines, we can formally integrate all the governing equations analytically except for a partial equation that describes how streamlines spread in the meridional plane. Apart from the difficulty of dealing with PDEs of mixed type, finding the functional forms of the conserved quantities along streamlines - the ratio beta of magnetic field to mass flux, the specific energy H of the fluid in the rotating frame, and the total specific angular momentum J carried in the matter and the field - constitutes a standard difficulty in this kind of (Grad-Shafranov) formalism. Fortunately, because the ratio of the thermal speed of the mass-loss regions to the Keplerian speed of rotation of the interface constitutes a small parameter epsilon, we can attack the overall problem by the method of matched asymptotic expansions. This procedure leads to a natural and systematic technique for obtaining the relevant functional dependences of beta, H, and J. Moreover, we are able to solve analytically for the properties of the flow emergent from the small transsonic region driven by gas pressure without having to specify the detailed form of any of the conserved functions, beta, H, and J. This analytical solution provides inner boundary conditions for the numerical computation in a companion paper by Najita & Shu of the larger region where the main acceleration to terminal speeds occurs.
Shu, Frank H.↗
Matching Crystal Structures Atom-to-Atom
Finding an optimal match between two different crystal structures underpins many important materials science problems, including describing solid-solid phase transitions and developing models for interface and grain boundary structures. Here, we formulate the matching of crystals as an optimization problem where the goal is to find the alignment and the atom-to-atom map that minimize a given cost function such as the Euclidean distance between the atoms. We construct an algorithm that directly solves this problem for large finite portions of the crystals and retrieves the periodicity of the match subsequently. We demonstrate its capacity to describe transformation pathways between known polymorphs and to reproduce experimentally realized structures of semi-coherent interfaces. Additionally, from our findings, we define a rigorous metric for measuring distances between crystal structures that can be used to properly quantify their geometric (Euclidean) closeness.
36 MATERIALS SCIENCE↗
Analysis of an entrainment model of the jet in a crossflow
A theoretical model has been proposed for the problem of a round jet in an incompressible cross-flow. The method of matched asymptotic expansions has been applied to this problem. For the solution to the flow problem in the inner region, the re-entrant wake flow model was used with the re-entrant flow representing the fluid entrained by the jet. Higher order corrections are obtained in terms of this basic solution. The perturbation terms in the outer region was found to be a line distribution of doublets and sources. The line distribution of sources represents the combined effect of the entrainment and the displacement.
Chang, H. S.↗