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At least 955 records · Page 53

Asymptotic solution for heat convection-radiation equation

In this paper, we employ a new approximate analytical method called the optimal homotopy asymptotic method (OHAM) to solve steady state heat transfer problem in slabs. The heat transfer problem is modeled using nonlinear two-point boundary value problem. Using OHAM, we obtained the approximate analytical solution for dimensionless temperature with different values of a parameter ε. Further, the OHAM results for dimensionless temperature have been presented graphically and in tabular form. Comparison has been provided with existing results from the use of homotopy perturbation method, perturbation method and numerical method. For numerical results, we used Runge-Kutta Fehlberg fourth-fifth order method. It was found that OHAM produces better approximate analytical solutions than those which are obtained by homotopy perturbation and perturbation methods, in the sense of closer agreement with results obtained from the use of Runge-Kutta Fehlberg fourth-fifth order method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Soot Optical Property Study

Recent past studies of soot reaction processes in laminar premixed and nonpremixed flames generally have used the intrusive technique of thermophoretic sampling and analysis by transmission electron microscopy (TEM) to observe soot structure and obtain important fundamental information about soot particle properties, such as soot primary particle diameters, the rate of change of soot primary particle diameter as a function of time (or rate of soot surface growth or oxidation), the amount of soot particle reactive surface area per unit volume, the number of primary soot particles per unit volume, and the rate of formation of primary soot particles (or the rate of soot primary particle nucleation). Given the soot volume per unit volume of the flame (or the soot volume fraction), all these properties are readily found from a measurement of the soot primary particle diameter (which usually is nearly a constant for each location within a laminar flame). This approach is not possible within freely propagating flames, however, because soot properties at given positions in such flames vary relatively rapidly as a function of time in the soot formation and oxidation regions compared to the relatively lengthy sampling times needed to accumulate adequate soot samples and to minimize effects of soot collected on the sampling grid as it moves to and from the sampling position through other portions of the flame. Thus, nonintrusive optical methods must be used to find the soot primary particle diameters needed to define the soot surface reaction properties mentioned earlier. Unfortunately, approximate nonintrusive methods used during early studies of soot reaction properties in flames, found from laser scattering and absorption measurements analyzed assuming either Rayleigh scattering or Mie scattering from polydisperse effective soot particles having the same mass of soot as individual soot aggregates, have not been found to be an effective way to estimate the soot surface reaction area per unit volume. Thus, alternative nonintrusive optical methods of finding these properties must be sought, which was the objective of this phase of the investigation. The alternative method used here involves use of the Rayleigh-Debye-Gans-Polydisperse-Fractal-Aggregate (RDG-PFA) scattering approximation for soot aggregates in flames. Thus, the development of this method will be discussed next before describing its evaluation as a means of nonintrusively measuring soot primary particle diameters in soot-containing flames.

Aung, K. T.↗

Efficient eigensolution reanalysis of nonclassically damped structures

Effective methods of approximate eigensolution reanalysis of modified nonclassically damped structures are developed. For structures with passive or active discrete damping devices or with damping treatment, the system becomes nonproportionally damped and the computation of its dynamic responses may require the use of complex modes. For larger systems, the computation of complex modes is very expensive. Thus it is desirable to have approximate reanalysis techniques for the efficient evaluation of the effect of design changes. In recent years, the assumed mode reanalysis method was successfully applied to minimum weight design of undamped structures with natural frequency constraints. The accuracy of the assumed mode reanalysis method can be improved dramatically if the global approximation function includes the normal modes of the original system and their derivatives. This approach was demonstrated to be effective even for a system with shape changes. The approach used by Noor et al. for eigensolution reanalysis of undamped structures is extended to treat a nonclassically damped system.

Wang, Bo Ping↗

Well-Balanced Second-Order Convex Limiting Technique for Solving the Serre–Green–Naghdi Equations

In this article, we introduce a numerical method for approximating the dispersive Serre–Green–Naghdi equations with topography using continuous finite elements. The method is an extension of the hyperbolic relaxation technique introduced in Guermond et al. (J Comput Phys 450:110809, 2022). It is explicit, second-order accurate in space, third-order accurate in time, and is invariant-domain preserving. It is also well balanced and parameter free. Special attention is given to the convex limiting technique when physical source terms are added in the equations. The method is verified with academic benchmarks and validated by comparison with laboratory experimental data.

97 MATHEMATICS AND COMPUTING↗

Newton's method applied to finite-difference approximations for the steady-state compressible Navier-Stokes equations

Finite-difference approximations for steady-state compressible Navier-Stokes equations, whose two spatial dimensions are written in generalized curvilinear coordinates and strong conservation-law form, are presently solved by means of Newton's method in order to obtain a lifting-airfoil flow field under subsonic and transonnic conditions. In addition to ascertaining the computational requirements of an initial guess ensuring convergence and the degree of computational efficiency obtainable via the approximate Newton method's freezing of the Jacobian matrices, attention is given to the need for auxiliary methods assessing the temporal stability of steady-state solutions. It is demonstrated that nonunique solutions of the finite-difference equations are obtainable by Newton's method in conjunction with a continuation method.

Bailey, Harry E.↗

Time accuracy and the use of implicit methods

Some of the approximations used to make implicit methods more efficient and practical for the solution of the Euler and Navier-Stokes equations are addressed. In particular, approximate factorizations, diagonalizations, and linearization approximations are reviewed and categorized. A subiteration correction scheme commonly in use at present is introduced, improved, demonstrated, and analyzed. This scheme is used to produce a second-order accurate, more robust implicit method for unsteady flow computations. The subiteration approach can be employed to recover time accuracy without increasing computational time (in most cases producing substantial savings).

Pulliam, Thomas H.↗

Deep Koopman operators for causal discovery

Causal discovery aims to identify cause-effect mechanisms for better scientific understanding, explainable decision-making, and more accurate modeling. Standard statistical frameworks, such as Granger causality, lack the ability to quantify causal relationships in nonlinear dynamics due to the presence of complex feedback mechanisms, timescale mixing, and nonstationarity. Thus, applying these methods to study causal dynamics in real-world systems, such as the Earth, is a major challenge. Addressing this shortcoming, we leverage deep learning and a Koopman operator-theoretic formalism to present a class of causal discovery algorithms. Kausal uses deep Koopman operator methods to approximate nonlinear dynamics in a linearized vector space in which traditional causal inference methods such as Granger causality can be more easily applied. Our idealized experiments demonstrate Kausal’s superior ability in discovering and characterizing causal signals compared to existing deep learning and non-deep learning state-of-the-art approaches. Finally, the successful identification of major El Niño and La Niña events in observations showcases Kausal’s skill to handle real-world applications.

54 ENVIRONMENTAL SCIENCES↗

Supervised Learning for Distribution Secondary Systems Modeling: Improving Solar Interconnection Processes

The current interconnection process and hosting capacity analysis for distributed energy resources (DERs), such as photovoltaics (PV) and battery energy storage systems, are based on analyzing grid network constraints (voltage and thermal) using only medium-voltage distribution network models. This is because most utilities do not have secondary low-voltage system models that connect service transformers and residential customers. This is important because in many cases the main impact of interconnecting DERs could occur on the low-voltage distribution systems. This paper proposes a supervised learning method to approximate local secondary models to improve the interconnection process. The proposed supervised learning method includes a decision tree model that predicts the secondary topology and a logistic regression model that predicts conductor types. The case studies demonstrate the benefits of including secondary low-voltage circuits in the interconnection process. We report the proposed modeling methodology is readily scalable and thus can reduce the cost and effort of PV interconnection for the industry and stakeholders.

14 SOLAR ENERGY↗

Alternating direction implicit methods for parabolic equations with a mixed derivative

Alternating direction implicit (ADI) schemes for two-dimensional parabolic equations with a mixed derivative are constructed by using the class of all A sub 0-stable linear two-step methods in conjunction with the method of approximation factorization. The mixed derivative is treated with an explicit two-step method which is compatible with an implicit A sub 0-stable method. The parameter space for which the resulting ADI schemes are second order accurate and unconditionally stable is determined. Some numerical examples are given.

Beam, R. M.↗

Alternating direction implicit methods for parabolic equations with a mixed derivative

Alternating direction implicit (ADI) schemes for two-dimensional parabolic equations with a mixed derivative are constructed by using the class of all A(0)-stable linear two-step methods in conjunction with the method of approximate factorization. The mixed derivative is treated with an explicit two-step method which is compatible with an implicit A(0)-stable method. The parameter space for which the resulting ADI schemes are second-order accurate and unconditionally stable is determined. Some numerical examples are given.

Beam, R. M.↗

An Analytical Method of Estimating Turbine Performance

A method is developed by which the performance of a turbine over a range of operating conditions can be analytically estimated from the blade angles and flow areas. In order to use the method, certain coefficients that determine the weight flow and friction losses must be approximated. The method is used to calculate the performance of the single-stage turbine of a commercial aircraft gas-turbine engine and the calculated performance is compared with the performance indicated by experimental data. For the turbine of the typical example, the assumed pressure losses and turning angles give a calculated performance that represents the trends of the experimental performance with reasonable accuracy. The exact agreement between analytical performance and experimental performance is contingent upon the proper selection of the blading-loss parameter. A variation of blading-loss parameter from 0.3 to 0.5 includes most of the experimental data from the turbine investigated.

Kochendorfer, Fred D↗

First MEM task IRMEO in IRAF

The first task for image restoration using the Maximum Entropy Method (MEM) in IRAF, called IRMEO, is described. The underlining algorithm is the approximate Newton method for optimization. The basic input images and parameters for deconvolution are described in some detail. Results of preliminary tests, including the number of iterations, required CPU time on a variety of computers, and deconvolved images are reported and compared with those from other deconvolution methods. The merits and limitations of this task are pointed out. The possible development of better MEM tasks on the basis of IRMEO is also discussed.

Wu, Nailong↗

Comparison of techniques for approximating ocean bottom topography in a wave-refraction computer model

A study of the effects of using different methods for approximating bottom topography in a wave-refraction computer model was conducted. Approximation techniques involving quadratic least squares, cubic least squares, and constrained bicubic polynomial interpolation were compared for computed wave patterns and parameters in the region of Saco Bay, Maine. Although substantial local differences can be attributed to use of the different approximation techniques, results indicated that overall computed wave patterns and parameter distributions were quite similar.

Poole, L. R.↗

Computed Tomography by Combining Transmission and Scatter Radiography Methods

In 2015, approximately 13 billion tons of freight was transported in the US, roughly 40 tons per person. 40% of all freight on a ton-mile basis will be transported by railroads. Class I railroads have approximately 140,000 miles (224,000 km) of railroad track across the country. Approximately 3,200 crossties per mile secure the rails at the proper gauge, transmit loads to the ballast, and prevent lateral and longitudinal shifting. Wood crossties can fail in many ways including rotting, breaking, cracking, and splitting. Developing new technologies to inspect these crossties are necessary to help maintain and ensure safe railroad operations. The Georgetown Railroad Equipment Company partnered with the University of Florida to develop the Aurora Xi X-ray backscatter inspection system. This system generates 2D backscatter images at 25 mph to detect weakness in wood crossties long before the internal degradation is visible on the tie surface. The railroad industry has a need for a high-speed high resolution 3D inspection method to inspect approximately 20 million newly fabricated railroad crossties per year. Currently new ties are not radiographically inspected to reject internal flaws and verify that rot prevention treatments have adequately penetrated into the crosstie. Current spiral scan computed tomography (CT) systems are not designed for the 100 cm/s to 400 cm/s speed of a wood crosstie production line. Building on the technology developed for the 2D Aurora Xi system, a new 3D fan-beam inspection system and CT method is being developed. A previous scatter CT method by Arsenault and Hussein required moving the Xray source to many positions, averaging the X-ray spectra, and ignoring the Compton scatter change of energy. The proposed design and method combines transmission and scatter radiography in all directions without moving or rotating the X-ray sources or detectors. (authors)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Expectation propagation for nonlinear inverse problems – with an application to electrical impedance tomography

In this paper, we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the Bayesian formulation of nonlinear inverse problems. It is capable of efficiently delivering reliable estimates of the posterior mean and covariance, thereby providing an inverse solution together with quantified uncertainties. Some theoretical properties of the iterative algorithm are discussed, and the efficient implementation for an important class of problems of projection type is described. The method is illustrated with one typical nonlinear inverse problem, electrical impedance tomography with complete electrode model, under sparsity constraints. Numerical results for real experimental data are presented, and compared with that by Markov chain Monte Carlo. The results indicate that the method is accurate and computationally very efficient.

97 MATHEMATICS AND COMPUTING↗

Variational principles with Padé approximants for tearing mode analysis

Tearing modes occur in several distinct physical regimes, and it is often important to compute the inner layer response for these modes with various effects. There is a need for an approximate and efficient method of solving the inner layer equations in all these regimes. In this paper, we introduce a method of solving the inner layer equations based on using a variational principle with Padé approximants. For all the regimes considered, the main layer equations to be solved are inhomogeneous, and Padé approximants give a convenient and efficient method of satisfying the correct asymptotic behavior at the edge of the layer. Results using this variational principle—Padé approximant method in three of these regimes is presented. These regimes are the constant-ψ resistive-inertial (RI) regime, the constant-ψ viscoresistive regime, and the non-constant-ψ inviscid tearing regime. The last regime includes the constant-ψ RI regime and the inertial regime. The results show that reasonable accuracy can be obtained very efficiently with Padé approximants having a small number of parameters.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Hybrid Finite Element--Spectral Method for the Fractional Laplacian: Approximation Theory and Efficient Solver

Here, a numerical scheme is presented for approximating fractional order Poisson problems in two and three dimensions. The scheme is based on reformulating the original problem posed over $\Omega$ on the extruded domain $\mathcal{C}=\Omega\times[0,\infty)$ following. The resulting degenerate elliptic integer order PDE is then approximated using a hybrid FEM-spectral scheme. Finite elements are used in the direction parallel to the problem domain $\Omega$, and an appropriate spectral method is used in the extruded direction. The spectral part of the scheme requires that we approximate the true eigenvalues of the integer order Laplacian over $\Omega$. We derive an a priori error estimate which takes account of the error arising from using an approximation in place of the true eigenvalues. We further present a strategy for choosing approximations of the eigenvalues based on Weyl's law and finite element discretizations of the eigenvalue problem. The system of linear algebraic equations arising from the hybrid FEM-spectral scheme is decomposed into blocks which can be solved effectively using standard iterative solvers such as multigrid and conjugate gradient. Numerical examples in two and three dimensions suggest that the approach is quasi-optimal in terms of complexity.

97 MATHEMATICS AND COMPUTING↗

Methods of the Galerkin type

Optimal approximations, weighted residuals method, and linear and nonlinear applications of methods of Galerkin type with proof of convergence

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