Some heat-transfer problems inside an equilateral triangular region.
Linear heat transfer problems inside equitriangular region solved by integral transform series
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Ionospheric electron-density profiles with continuous gradients and underlying ionization corrections. I.
Ionospheric electron density profiles with continuous gradients and underlying ionization corrections, discussing integral transformation properties, integral equation inversion and second order lamination process
Paul, A. K.↗
Transformer with integral inductor
In accordance with one embodiment is a transformer with a core comprising a perimeter portion and central intervening portion. The central intervening portion is separated from the perimeter portion by air gaps, creating an opening on either side of the intervening portion. A primary winding and secondary winding are wound around the central intervening portion of the core. The primary winding is capable of electromagnetic interaction with the secondary winding. A pair of ferrite members arranged outward from a central axis of the central intervening portion of the core and increases a series inductance with the primary winding. In accordance with another aspect of the disclosure, each ferrite member may have an air gap associated with the core to facilitate heat dissipation from the transformer.
Rastogi, Sagar K.↗
Integrated Silicon Fourier Transform Spectrometer with Broad Bandwidth and Ultra‐High Resolution
An ultra-high resolution Fourier transform spectrometer (FTS) realized in silicon photonic platform that can operate with broad band, narrow band as well as a combination of broad band and narrow band signals is reported. The ultra-high resolution of the spectrometer is achieved by exploiting multiple techniques: a Michelson interferometer (MI) structure to increase the optical path delay (OPD), a hybrid waveguide design to reduce insertion loss, an optimized heater and air trenches to achieve higher thermal efficiency. Here, to further increase the OPD of the spectrometer to increase its resolution, a novel multiple interferometers approach is employed which combines balanced MI with N statically imbalanced MIs, thereby increasing the OPD of a single MI by factor of N + 1. An FTS spectrometer consisting of N = 2 such MIs is fabricated and experimentally characterized using unknown broad bandwidth input signal spectra of about 180 nm centered around 1550 nm, a narrow line laser input signal, and a combination of broad and narrow band signals demonstrating spectral resolution of about 0.16 nm.
Li, Ang↗
40 Ca transverse response function from coupled-cluster theory
Here, we present calculations of the 40 Ca transverse response function obtained from coupled-cluster theory used in conjunction with the Lorentz integral transform method. We employ nuclear forces derived at next-to-next-to leading order in chiral effective field theory with and without Δ degrees of freedom. We first benchmark this approach on the 4 He nucleus and compare both the transverse sum rule and the response function to earlier calculations based on different methods. As expected from the power counting of the chiral expansion of electromagnetic currents and from previous studies, our results retaining only one-body term underestimate the experimental data for 4 He by about 20%. However, when the method is applied to 40 Ca at the same order of the expansion, response functions do not lack strength and agree well with the world electron scattering data. We discuss various sources of theoretical uncertainties and comment on the comparison of our results with the available experiments.
39 ≤ A ≤ 58↗
An equitriangular transform and its application.
Method of finite integral transforms as format for employment of incomplete eigenfunctions, discussing application of equitriangular transform
BOUNDARY VALUE↗
A note on a broken layer in an orthotropic laminate composite
An orthotropic laminate composite containing a completely broken layer is considered. The problem is formulated in terms of integral transforms and then reduced to a singular integral equation which is solved numerically. The strength of stress singularity at the crack tip is determined from a characteristic equation which is obtained by studying the dominant part of the singular integral equation near the end points. The stress intensity factors are given for various material properties.
Arin, K.↗
A note on a broken layer in an orthotropic laminate composite
An orthotropic laminate composite containing a completely broken layer is considered. The problem is formulated in terms of integral transforms and then reduced to a singular integral equation which is solved numerically. The strength of stress singularity at the crack tip is determined from a characteristic equation which is obtained by studying the dominant part of the singular integral equation near the end points. The stress intensity factors are given for various material properties.
Arin, K.↗
Integrating biocatalysis with chemocatalysis for selective transformations
The integration of biocatalysis with chemocatalysis combines the excellent selectivity of the former with the robust reactivity of the latter and offers many advantages, such as lower cost, higher yield, enhanced selectivity, as well as less waste generation. Despite the challenge of incompatibilities between different classes of catalysts, recent advances in synthetic chemistry and biology provide ample opportunities for multistep cascade transformations that combine biocatalysis and chemocatalysis. In this research, we review recent progress in merging biocatalysis with chemocatalysis, highlighting selected examples of photo-/electricity-driven biotransformations and recently developed strategies for addressing the catalyst incompatibility issue.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
The Filtered Abel Transform and Its Application in Combustion Diagnostics
Many non-intrusive combustion diagnosis methods generate line-of-sight projections of a flame field. To reconstruct the spatial field of the measured properties, these projections need to be deconvoluted. When the spatial field is axisymmetric, commonly used deconvolution method include the Abel transforms, the onion peeling method and the two-dimensional Fourier transform method and its derivatives such as the filtered back projection methods. This paper proposes a new approach for performing the Abel transform method is developed, which possesses the exactness of the Abel transform and the flexibility of incorporating various filters in the reconstruction process. The Abel transform is an exact method and the simplest among these commonly used methods. It is evinced in this paper that all the exact reconstruction methods for axisymmetric distributions must be equivalent to the Abel transform because of its uniqueness and exactness. Detailed proof is presented to show that the two dimensional Fourier methods when applied to axisymmetric cases is identical to the Abel transform. Discrepancies among various reconstruction method stem from the different approximations made to perform numerical calculations. An equation relating the spectrum of a set of projection date to that of the corresponding spatial distribution is obtained, which shows that the spectrum of the projection is equal to the Abel transform of the spectrum of the corresponding spatial distribution. From the equation, if either the projection or the distribution is bandwidth limited, the other is also bandwidth limited, and both have the same bandwidth. If the two are not bandwidth limited, the Abel transform has a bias against low wave number components in most practical cases. This explains why the Abel transform and all exact deconvolution methods are sensitive to high wave number noises. The filtered Abel transform is based on the fact that the Abel transform of filtered projection data is equal to an integral transform of the original projection data with the kernel function being the Abel transform of the filtering function. The kernel function is independent of the projection data and can be obtained separately when the filtering function is selected. Users can select the best filtering function for a particular set of experimental data. When the kernal function is obtained, it can be used repeatedly to a number of projection data sets (rovs) from the same experiment. When an entire flame image that contains a large number of projection lines needs to be processed, the new approach significantly reduces computational effort in comparison with the conventional approach in which each projection data set is deconvoluted separately. Computer codes have been developed to perform the filter Abel transform for an entire flame field. Measured soot volume fraction data of a jet diffusion flame are processed as an example.
Simons, Stephen N.↗
Algorithms versus architectures for computational chemistry
The algorithms employed are computationally intensive and, as a result, increased performance (both algorithmic and architectural) is required to improve accuracy and to treat larger molecular systems. Several benchmark quantum chemistry codes are examined on a variety of architectures. While these codes are only a small portion of a typical quantum chemistry library, they illustrate many of the computationally intensive kernels and data manipulation requirements of some applications. Furthermore, understanding the performance of the existing algorithm on present and proposed supercomputers serves as a guide for future programs and algorithm development. The algorithms investigated are: (1) a sparse symmetric matrix vector product; (2) a four index integral transformation; and (3) the calculation of diatomic two electron Slater integrals. The vectorization strategies are examined for these algorithms for both the Cyber 205 and Cray XMP. In addition, multiprocessor implementations of the algorithms are looked at on the Cray XMP and on the MIT static data flow machine proposed by DENNIS.
Partridge, H.↗
Damage growth in composite laminates with interleaves
The influence of placing interleaves between fiber reinforced plies in multilayered composite laminates is investigated. The geometry of the composite is idealized as two dimensional, isotropic, linearly elastic media made of a damaged layer bonded between two half planes and separated by thin interleaves of low extensional and shear moduli. The damage in the layer is taken in the form of a symmetric crack perpendicular to the interface and may extend up to the interface. The case of an H-shaped crack in the form of a broken layer with delamination along the interface is also analyzed. The interleaves are modeled as distributed shear and tension springs. Fourier integral transform techniques are used to develop solutions in terms of singular integral equations. An asymptotic analysis of the integral equations based on Muskhelishvili's techniques reveals logarithmically singular axial stresses in the half plane at the crack tips for the broken layer. For the H shaped crack, similar singularities are found to exist in the axial stresses at the interface crack tips in the layer and the half plane. The solution of the equations is found numerically for the stresses and displacements by using the Hadamard's concept of direct differentiation of Cauchy integrals as well as Gaussian integration techniques.
Goree, James G.↗
Damage growth in composite laminates with interleaves
The influence of interleaves on the fracture behavior of laminated composites is investigated. The geometry of the composite consists of a cracked layer, bonded between two half-planes, which is separated by thin, low modulus, interleaves. The interleaves are modeled as uncoupled tension and shear springs. A stress analysis is carried out for a crack which may grow up to and spread along the interface. Integral transform techniques are used to develop the solution in terms of singular integral equations. An asymptotic analysis reveals logarithmic singularities in the critical stresses for the case of a broken layer. The equations are solved numerically and the effect of damage on critical stresses is studied. Initial results indicate that the interleaf gives a significant reduction in stresses in the adjacent regions and, if properly selected, should result in a more damage tolerant laminate.
Goree, James G.↗
On Certain Theoretical Developments Underlying the Hilbert-Huang Transform
One of the main traditional tools used in scientific and engineering data spectral analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). Both carry strong a-priori assumptions about the source data, such as being linear and stationary, and of satisfying the Dirichlet conditions. A recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT), proposes a novel approach to the solution for the nonlinear class of spectral analysis problems. Using a-posteriori data processing based on the Empirical Mode Decomposition (EMD) sifting process (algorithm), followed by the normalized Hilbert Transform of the decomposed data, the HHT allows spectral analysis of nonlinear and nonstationary data. The EMD sifting process results in a non-constrained decomposition of a source real-value data vector into a finite set of Intrinsic Mode Functions (IMF). These functions form a nearly orthogonal derived from the data (adaptive) basis. The IMFs can be further analyzed for spectrum content by using the classical Hilbert Transform. A new engineering spectral analysis tool using HHT has been developed at NASA GSFC, the HHT Data Processing System (HHT-DPS). As the HHT-DPS has been successfully used and commercialized, new applications pose additional questions about the theoretical basis behind the HHT and EMD algorithms. Why is the fastest changing component of a composite signal being sifted out first in the EMD sifting process? Why does the EMD sifting process seemingly converge and why does it converge rapidly? Does an IMF have a distinctive structure? Why are the IMFs nearly orthogonal? We address these questions and develop the initial theoretical background for the HHT. This will contribute to the development of new HHT processing options, such as real-time and 2-D processing using Field Programmable Gate Array (FPGA) computational resources,
Kizhner, Semion↗
A layered composite with a broken laminate
The problem of a laminate composite in the presence of a crack located normal to the bond lines is considered. Stress analysis of the limiting case when the crack extends to the bond lines is carried out. An integral transform technique is used to formulate the problem in terms of a singular integral equation. The power of stress singularity around the crack tip terminating at the interface is obtained using the above technique. The singular integral equation is solved numerically and the effect of material properties on the stress intensity factor is calculated.
Gupta, G. D.↗
A layered composite with a broken laminate.
The problem of a laminate composite in presence of a crack located normal to the bond lines is considered. Stress analysis of the limiting case when the crack extends to the bond lines is carried out. Integral transform technique is used to formulate the problem in terms of a singular integral equation from which the power of stress singularity around the crack tip terminating at the interface is obtained. The singular integral equation is solved numerically and the effect of material properties on the stress intensity factor is calculated.
Gupta, G. D.↗
On the Hilbert-Huang Transform Theoretical Developments
One of the main heritage tools used in scientific and engineering data spectrum analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). Both carry strong a-priori assumptions about the source data, such as linearity, of being stationary, and of satisfying the Dirichlet conditions. A recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT), proposes a novel approach to the solution for the nonlinear class of spectrum analysis problems. Using a-posteriori data processing based on the Empirical Mode Decomposition (EMD) sifting process (algorithm), followed by the normalized Hilbert Transform of the decomposition data, the HHT allows spectrum analysis of nonlinear and nonstationary data. The EMD sifting process results in a non-constrained decomposition of a source real value data vector into a finite set of Intrinsic Mode Functions (IMF). These functions form a near orthogonal adaptive basis, a basis that is derived from the data. The IMFs can be further analyzed for spectrum interpretation by the classical Hilbert Transform. A new engineering spectrum analysis tool using HHT has been developed at NASA GSFC, the HHT Data Processing System (HHT-DPS). As the HHT-DPS has been successfully used and commercialized, new applications post additional questions about the theoretical basis behind the HHT and EMD algorithms. Why is the fastest changing component of a composite signal being sifted out first in the EMD sifting process? Why does the EMD sifting process seemingly converge and why does it converge rapidly? Does an IMF have a distinctive structure? Why are the IMFs near orthogonal? We address these questions and develop the initial theoretical background for the HHT. This will contribute to the developments of new HHT processing options, such as real-time and 2-D processing using Field Programmable Array (FPGA) computational resources, enhanced HHT synthesis, and broaden the scope of HHT applications for signal processing.
Kizhner, Semion↗