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At least 73 records · Page 4

Virtual element approximations of the time-fractional nonlinear convection-diffusion equation on polygonal meshes

We extend the Virtual Element Method to a two-dimensional unsteady nonlinear convection-diffusion equation characterized by a fractional-order derivative with respect to the time variable. Our methodology is based on three fundamental technical components: a fractional version of the Grunwald-Letnikov approximation, discrete maximal regularity, and the regularity theory associated with non-linearity. We prove the method's well-posedness, i.e., the approximate solution's existence and uniqueness to the time-fractional convection-diffusion equation with a Lipschitz nonlinear source term. The fully discrete scheme inherently maintains stability and consistency by leveraging the discrete maximal regularity and the energy projection operator. The convergence in the L 2 -norm and H 1 -norm to various mesh configurations is validated by numerical results, underlining the practical effectiveness of the proposed method.

97 MATHEMATICS AND COMPUTING

An Accurate SUPG-stabilized Continuous Galerkin Discretization for Anisotropic Heat Flux in Magnetic Confinement Fusion

We present a novel spatial discretization for the anisotropic heat conduction equation, aimed at improved accuracy at the high levels of anisotropy seen in a magnetized plasma, for example, for magnetic confinement fusion. The new discretization is based on a mixed formulation, introducing a form of the directional derivative along the magnetic field as an auxiliary variable and discretizing both the temperature and auxiliary fields in a continuous Galerkin (CG) space. Both the temperature and auxiliary variable equations are stabilized using the streamline upwind Petrov–Galerkin (SUPG) method, ensuring a better representation of the directional derivatives and therefore an overall more accurate solution. This approach can be seen as the CG-based version of our previous work (Wimmer, Southworth, Gregory, Tang, 2024), where we considered a mixed discontinuous Galerkin (DG) spatial discretization including DG-upwind stabilization. We prove consistency of the novel discretization, and demonstrate its improved accuracy over existing CG-based methods in test cases relevant to magnetic confinement fusion. This includes a long-run tokamak equilibrium sustainment scenario, demonstrating a 35% and 32% spurious heat loss for existing primal and mixed CG-based formulations versus 4% for our novel SUPG-stabilized discretization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

A prefiltering version of the Kalman filter with new numerical integration formulas for Riccati equations

A prefiltering version of the Kalman filter is derived for both discrete and continuous measurements. The derivation consists of determining a single discrete measurement that is equivalent to either a time segment of continuous measurements or a set of discrete measurements. This prefiltering version of the Kalman filter easily handles numerical problems associated with rapid transients and ill-conditioned Riccati matrices. Therefore, the derived technique for extrapolating the Riccati matrix from one time to the next constitutes a new set of integration formulas which alleviate ill-conditioning problems associated with continuous Riccati equations. Furthermore, since a time segment of continuous measurements is converted into a single discrete measurement, Potter's square root formulas can be used to update the state estimate and its error covariance matrix. Therefore, if having the state estimate and its error covariance matrix at discrete times is acceptable, the prefilter extends square root filtering with all its advantages, to continuous measurement problems.

Womble, M. E.

Finite difference solutions of the Euler equations in the vicinity of sharp edges

Attempts have been made to explain why finite difference solutions of the Euler equations can describe flows with large vortical structures around sharp-edged bodies. The present paper is concerned with the influence of a singular sharp edge on the truncation error for a set of discretized Euler equations. An analysis is conducted of the distribution of the truncation error of one finite difference approximation of the Euler equations near a sharp edge of a thin plate. The analysis leads to a determination of the size of the region of the neighborhood of such a singularity. Attention is given to the consistency of a discretization of the Euler equations, and numerical experiments.

Hartwich, P.-M.

Electromagnetic Scattering by Fully Ordered and Quasi-Random Rigid Particulate Samples

In this paper we have analyzed circumstances under which a rigid particulate sample can behave optically as a true discrete random medium consisting of particles randomly moving relative to each other during measurement. To this end, we applied the numerically exact superposition T-matrix method to model far-field scattering characteristics of fully ordered and quasi-randomly arranged rigid multiparticle groups in fixed and random orientations. We have shown that, in and of itself, averaging optical observables over movements of a rigid sample as a whole is insufficient unless it is combined with a quasi-random arrangement of the constituent particles in the sample. Otherwise, certain scattering effects typical of discrete random media (including some manifestations of coherent backscattering) may not be accurately replicated.

Radiative transfer

The Suzaku View of Highly Ionized Outflows in AGN: Statistical Detection and Global Absorber Properties - 1

We present the results of a new spectroscopic study of Fe K-band absorption in active galactic nuclei (AGN). Using data obtained from the Suzaku public archive we have performed a statistically driven blind search for Fe XXV Healpha and/or Fe XXVI Lyalpha absorption lines in a large sample of 51 Type 1.0−1.9 AGN. Through extensive Monte Carlo simulations we find that statistically significant absorption is detected at E greater than or approximately equal to 6.7 keV in 20/51 sources at the P(sub MC) greater than or equal tov 95 per cent level, which corresponds to approximately 40 per cent of the total sample. In all cases, individual absorption lines are detected independently and simultaneously amongst the two (or three) available X-ray imaging spectrometer detectors, which confirms the robustness of the line detections. The most frequently observed outflow phenomenology consists of two discrete absorption troughs corresponding to Fe XXV Healpha and Fe XXVI Lyalpha at a common velocity shift. From xstar fitting the mean column density and ionization parameter for the Fe K absorption components are log (N(sub H) per square centimeter)) is approximately equal to 23 and log (Xi/erg centimeter per second) is approximately equal to 4.5, respectively. Measured outflow velocities span a continuous range from less than1500 kilometers per second up to approximately100 000 kilometers per second, with mean and median values of approximately 0.1 c and approximately 0.056 c, respectively. The results of this work are consistent with those recently obtained using XMM-Newton and independently provides strong evidence for the existence of very highly ionized circumnuclear material in a significant fraction of both radio-quiet and radio-loud AGN in the local universe.

Gofford, Jason

Learning in stochastic neural networks for constraint satisfaction problems

Researchers describe a newly-developed artificial neural network algorithm for solving constraint satisfaction problems (CSPs) which includes a learning component that can significantly improve the performance of the network from run to run. The network, referred to as the Guarded Discrete Stochastic (GDS) network, is based on the discrete Hopfield network but differs from it primarily in that auxiliary networks (guards) are asymmetrically coupled to the main network to enforce certain types of constraints. Although the presence of asymmetric connections implies that the network may not converge, it was found that, for certain classes of problems, the network often quickly converges to find satisfactory solutions when they exist. The network can run efficiently on serial machines and can find solutions to very large problems (e.g., N-queens for N as large as 1024). One advantage of the network architecture is that network connection strengths need not be instantiated when the network is established: they are needed only when a participating neural element transitions from off to on. They have exploited this feature to devise a learning algorithm, based on consistency techniques for discrete CSPs, that updates the network biases and connection strengths and thus improves the network performance.

Johnston, Mark D.

Development of Position-Sensitive Magnetic Calorimeters for X-Ray Astronomy

Metallic magnetic calorimeters (MMC) are one of the most promising devices to provide very high energy resolution needed for future astronomical x-ray spectroscopy. MMC detectors can be built to large detector arrays having thousands of pixels. Position-sensitive magnetic (PoSM) microcalorimeters consist of multiple absorbers thermally coupled to one magnetic micro calorimeter. Each absorber element has a different thermal coupling to the MMC, resulting in a distribution of different pulse shapes and enabling position discrimination between the absorber elements. PoSMs therefore achieve the large focal plane area with fewer number of readout channels without compromising spatial sampling. Excellent performance of PoSMs was achieved by optimizing the designs of key parameters such as the thermal conductance among the absorbers, magnetic sensor, and heat sink, as well as the absorber heat capacities. Micro fab ri - cation techniques were developed to construct four-absorber PoSMs, in which each absorber consists of a two-layer composite of bismuth and gold. The energy resolution (FWHM full width at half maximum) was measured to be better than 5 eV at 6 keV x-rays for all four absorbers. Position determination was demonstrated with pulse-shape discrimination, as well as with pulse rise time. X-ray microcalorimeters are usually designed to thermalize as quickly as possible to avoid degradation in energy resolution from position dependence to the pulse shapes. Each pixel consists of an absorber and a temperature sensor, both decoupled from the cold bath through a weak thermal link. Each pixel requires a separate readout channel; for instance, with a SQUID (superconducting quantum interference device). For future astronomy missions where thousands to millions of resolution elements are required, having an individual SQUID readout channel for each pixel becomes difficult. One route to attaining these goals is a position-sensitive detector in which a large continuous or pixilated array of x-ray absorbers shares fewer numbers of temperature sensors. A means of discriminating the signals from different absorber positions, however, needs to be built into the device for each sensor. The design concept for the device is such that the shape of the temperature pulse with time depends on the location of the absorber. This inherent position sensitivity of the signal is then analyzed to determine the location of the event precisely, effectively yielding one device with many sub-pixels. With such devices, the total number of electronic channels required to read out a given number of pixels is significantly reduced. PoSMs were developed that consist of four discrete absorbers connected to a single magnetic sensor. The design concept can be extended to more than four absorbers per sensor. The thermal conductance between the sensor and each absorber is different by design and consequently, the pulse shapes are different depending upon which absorber the xrays are received, allowing position discrimination. A magnetic sensor was used in which a paramagnetic Au:Er temperature-sensitive material is located in a weak magnetic field. Deposition of energy from an x-ray photon causes an increase in temperature, which leads to a change of magnetization of the paramagnetic sensor, which is subsequently read out using a low noise dc-SQUID. The PoSM microcalorimeters are fully microfabricated: the Au:Er sensor is located above the meander, with a thin insulation gap in between. For this position-sensitive device, four electroplated absorbers are thermally linked to the sensor via heat links of different thermal conductance. One pixel is identical to that of a single-pixel design, consisting of an overhanging absorber fabricated directly on top of the sensor. It is therefore very strongly thermally coupled to it. The three other absorbers are supported directly on a silicon-nitride membrane. These absorbers are thermally coupled to the sensor via Ti (5 nm)/Au250 nm) metal links. The strength of the links is parameterized by the number of gold squares making up the link. For detector performance, experimentally different pulse-shapes were demonstrated with 6 keV x-rays, which clearly show different rise times for different absorber positions. For energy resolution measurement, the PoSM was operated at 32 mK with an applied field that was generated using a persistent current of 50 mA. Over the four pixels, energy resolution ranges from 4.4 to 4.7 eV were demonstrated.

Bandler, SImon

An Integrated Computational Materials Engineering (ICME) Approach to Design Nonlinear Transition Zones Between Dissimilar Metals

Current approaches to designing graded transition joints (GTJs) between dissimilar metals often rely on linear changes in both composition profiles and thickness of each sublayer. This increases fabrication cost and may not be optimal with respect to residual stress or the formation of undesirable phases. Here, in this study, GTJs between P91 ferritic/martensitic steel and 347H austenitic stainless steel were designed using Integrated Computational Materials Engineering (ICME) principles with nonlinear composition and length profiles. Guided by inputs from classical mechanics and CALPHAD predictions of carbon chemical potential, a novel transition zone consisting of five discrete compositions was proposed, with the thickness of each sublayer varying according to a brachistochrone-inspired distribution. In addition to carbon potential gradients, CALPHAD was used to predict coefficients of thermal expansion, which were incorporated into finite element models to evaluate stress evolution. The proposed nonlinear design resulted in a smoother carbon potential gradient, lower carbon depletion at the P91 interface, and a comparable residual stress under long-term thermal exposure, compared to a conventional linear design using ten sublayers with equal thickness. This work introduces a brachistochrone-inspired distribution for GTJ design, offering a general framework for optimizing graded interfaces between dissimilar metals.

Directed Energy Deposition

Interim prediction method for fan and compressor source noise

A method is presented for interim use in assessing the noise generated by fans and compressors in turbojet and turbofan engines. One-third octave band sound pressure levels consisting of broadband, discrete tone, and combination-tone noise components are predicted. Spectral distributions and directivity variations are specified. The method is based on that developed by other investigators with modifications derived from an analysis of full-scale, single-stage fan data. Comparisons of predicted and measured noise performance are presented, and requirements for improving the method are discussed.

Heidmann, M. F.

Full-coverage film cooling heat transfer study: Summary of data for normal-hole injection and 30 deg slant-hole injection

Heat transfer to a full coverage film cooled turbulent boundary layer over a flat surface was studied. The surface consisted of a discrete hole test section containing 11 rows of holes spaced 5 diameters apart in a staggered array and an instrumented recovery region. Ten diameter spacing was also studied by plugging appropriate holes. Two test sections were used, one having holes normal to the surface and the other having holes angled 30 deg to the surface in the downstream direction. Stanton number data were obtained both in the full coverage region and in the downstream recovery region for a range of blowing ratios, or mass flux ratios, from 0 to 1.3. Initial conditions at the upstream edge of the blowing region were varied from 500 to 5000 for momentum thickness Reynolds number and from 100 to 1800 for enthalpy thickness Reynolds number. The range of Reynolds numbers based on hole diameter and mainstream velocity was 6000 to 22000. Initial boundary layer thicknesses range from 0.5 to 2.0 hole diameters. Air was used as the working fluid. The data were taken for the secondary injection temperature equal to the wall temperature and also equal to the mainstream temperature. Superposition was then used to obtain Stanton number as a continuous function of the injectant temperature. The heat transfer coefficient was defined on the basis of a mainstream-to-wall temperature difference. This definition permits direct comparison of performance between film cooling and transpiration cooling.

Crawford, M. E.

Infrared telescope on Spacelab 2

The infrared telescope (IRT) on Spacelab 2 which will be the first cryogenically cooled telescope operated from the Orbiter is discussed. Its objectives are to measure the induced environment about the Orbiter and to demonstrate the ability to manage a large volume of superfluid helium in space. The prime astrophysical objectives are to map extended sources of low surface brightness infrared emission, including the zodiacal light, the galactic plane, and extragalactic regions. The IRT design is described, including the f/4 15.2 cm highly baffled Herschelian telescope cooled to 8 K which may scan to within 35 deg of the sun. The focal plane cooled to 3 K consists of nine discrete photoconductors covering the wavelength of 4.5-120 microns in five bands, with a single stellar detector used for aspect determination. Overlapping scans, contiguous orbits, and a six degree per second scan rate permit rapid redundant coverage of 60 % of the sky.

Koch, D.

Multiple Alfven wave reflections excited by Io Origin of the Jovian decametric arcs

The recent Voyager radio astronomy measurements near Jupiter show that the Jovian decametric radiation consists of numerous discrete features called decametric arcs which are observed at all Jovian longitudes. It is generally believed that these arcs are produced by an interaction of Io with the Jovian magnetosphere. In this paper we propose that the large number of decametric arcs is caused by multiple reflections of a standing Alfven wave current system excited by Io. Estimates of the reflection coefficient at the ionosphere and other damping processes show that a large number of reflections can occur, with the Alfven wave current system possibly extending completely around Jupiter. This source geometry can account for a number of otherwise puzzling characteristics of the Jovian decametric radiations,

Gurnett, D. A.

A multilevel control approach for a modular structured space platform

A three axis mathematical representation of a modular assembled space platform consisting of interconnected discrete masses, including a deployable truss module, was derived for digital computer simulation. The platform attitude control system as developed to provide multilevel control utilizing the Gauss-Seidel second level formulation along with an extended form of linear quadratic regulator techniques. The objectives of the multilevel control are to decouple the space platform's spatial axes and to accommodate the modification of the platform's configuration for each of the decoupled axes.

Chichester, F. D.

Harmonic structure of Pc 3-4 pulsations

Power spectra of magnetic pulsations observed at synchronous orbit by the ATS 6 satellite often show several spectral peaks simultaneously. Such pulsations, called harmonic events because of the nearly constant separation between successive peaks, are continuously observed in the dayside in the Pc 3-4 frequency range (6.6-100 mHz). The harmonic events are seen clearly only in the east-west magnetic field component. The spectral peaks are regularly spaced with a typical minimum separation of 14 mHz in the morning gradually decreasing to 10 mHz in the afternoon. In the dynamic spectra of harmonic events, the fundamental mode is usually absent. In addition, the relative amplitudes of the higher harmonics depend on the magnetic latitude. These observed features can be explained by a standing Alfven wave consisting of many discrete harmonic frequencies. A statistical analysis of power spectra demonstrates that at least 10-30% of Pc 3 pulsations can be classified as harmonic events. For a selected event on August 7, 1975, the plasma mass density at the synchronous orbit is estimated to be 3-8 hydrogen mass/cu cm.

Takahashi, K.

Andrean examples of mega-geomorphology themes

Geomorphic (or physiographic) provinces have been a well known and useful method of regional landform classification for a century. Every earth scientist will recognize a phrase such as Appalachian Plateau or Southern Rocky Mountains as defining a discrete region of consistent geologic structure that has experienced a similar interval of erosion by a similar process or set of processes. The geomorphic provinces formalized in the United States by Fenneman in the 1920's continue to be highly satisfactory even though some boundaries were only vaguely drawn. Mosaics of LANDSAT images illustrate better than any earlier maps the validity and coherence of Fenneman's provinces. The concept of geomorphic provinces has been used subconsciously or intuitively, to describe the relief of the ocean floor and the topography of the Moon and other planets.

Bloom, A. L.

Simulation of double layers in a model auroral circuit with nonlinear impedance

A reduced circuit description of the U-shaped potential structure of a discrete auroral arc, consisting of the flank transmission line plus parallel-electric-field region, is used to provide the boundary condition for one-dimensional simulations of the double-layer evolution. The model yields asymptotic scalings of the double-layer potential, as a function of an anomalous transport coefficient alpha and of the perpendicular length scale l(a) of the arc. The arc potential phi(DL) scales approximately linearly with alpha, and for alpha fixed phi (DL) about l(a) to the z power. Using parameters appropriate to the auroral zone acceleration region, potentials of phi (DPL) 10 kV scale to projected ionospheric dimensions of about 1 km, with power flows of the order of magnitude of substorm dissipation rates.

Smith, R. A.

A four-layer model for the heat budget of homogeneous land surfaces

The present model envisions the heat balance of a homogeneous land surface in terms of available energy, a set of driving potentials, and parameters for the physical state of the soil and vegetation. Two unique features of the model are: (1) the expression of the interaction of evaporation from the soil and from foliage by changes in the value of the saturation vapor pressure deficit of air in the canopy (the conclusions of this interaction being consistent with field observations); and (2) the treatment of sensible and latent heat exchange between the atmosphere and a soil consisting of two discrete layers.

Choudhury, B. J.