scholarly journals Measurement of the Radius of Metallic Plates Based on a Novel Finite Region Eigenfunction Expansion (FREE) Method

2020 ◽  
Author(s):  
Ruochen Huang ◽  
Mingyang Lu ◽  
Zhijie Zhang ◽  
Qian Zhao ◽  
Yuedong Xie ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Eigenfunction Expansion ◽  
Analytical Approach ◽  
Peak Frequency ◽  
Finite Region ◽  
Finite Radius ◽  
A Value ◽  
Wide Range ◽  
Frequency Feature ◽  
Tree Method

Eddy current based approaches have been investigated for a wide range of inspection applications. Dodd-Deeds model and the truncated region eigenfunction expansion (TREE) method are widely applied in various occasions, mostly for the cases that the sample is relatively larger than the radius of the sensor coil. The TREE method converts the integral expressions to the summation of many terms in the truncated region. In a recent work, the impedance of the co-axial air-cored sensor due to a plate of finite radius was calculated by the modified Dodd-Deeds analytical approach proposed by authors. In this paper, combining the modified analytical solution and the TREE method, a new finite region eigenfunction expansion (FREE) method is proposed. This method involves modifying its initial summation point from the first zero of the Bessel function to a value related to the radius of the plate, therefore makes it suitable for plate with finite dimensions. Experiments and simulations have been carried out and compared for the verification of the proposed method. Further, the planar size measurements of the metallic circular plate can be achieved by utilising the measured peak frequency feature.

scholarly journals Measurement of the Radius of Metallic Plates Based on a Novel Finite Region Eigenfunction Expansion (FREE) Method

2020 ◽  
Author(s):  
Ruochen Huang ◽  
Mingyang Lu ◽  
Wuliang Yin
Keyword(s):  
Analytical Solution ◽  
Eigenfunction Expansion ◽  
Analytical Approach ◽  
Peak Frequency ◽  
Finite Region ◽  
Finite Radius ◽  
A Value ◽  
Wide Range ◽  
Frequency Feature ◽  
Tree Method

Eddy current based approaches have been investigated for a wide range of inspection applications. Dodd-Deeds model and the truncated region eigenfunction expansion (TREE) method are widely applied in various occasions, mostly for the cases that the sample is relatively larger than the radius of the sensor coil. The TREE method converts the integral expressions to the summation of many terms in the truncated region. In a recent work, the impedance of the co-axial air-cored sensor due to a plate of finite radius was calculated by the modified Dodd-Deeds analytical approach proposed by authors. In this paper, combining the modified analytical solution and the TREE method, a new finite region eigenfunction expansion (FREE) method is proposed. This method involves modifying its initial summation point from the first zero of the Bessel function to a value related to the radius of the plate, therefore makes it suitable for plate with finite dimensions. Experiments and simulations have been carried out and compared for the verification of the proposed method. Further, the planar size measurements of the metallic circular plate can be achieved by utilising the measured peak frequency feature.

Path Integral Calculations of Particle Self-Energy and Effective Mass in Coulomb Systems

1997 ◽  
Vol 11 (04) ◽  
pp. 129-138 ◽  
Author(s):  
V. Sa-Yakanit ◽  
V. D. Lakhno ◽  
Klaus Haß
Keyword(s):  
Effective Mass ◽  
Path Integral ◽  
State Energy ◽  
Coulomb Systems ◽  
Integral Approach ◽  
Coupling Region ◽  
Self Energy ◽  
Consistent Approximation ◽  
A Value ◽  
Wide Range

The generalized path integral approach is applied to calculate the ground state energy and the effective mass of an electron-plasmon interacting system for a wide range of densities. It is shown that in the self-consistent approximation an abrupt transition between the weak coupling and the strong coupling region of interaction exists. The transition occurs at low electron densities according to a value of 418 for rs, when Wigner crystallization is possible. For densities of real metals, the electron bandwidth is calculated and a comparison with experimental results is given.

scholarly journals Framing the Values of Vernacular Architecture for a Value-Based Conservation: A Conceptual Framework

2021 ◽  
Vol 13 (9) ◽  
pp. 4974
Author(s):  
Obafemi A. P. Olukoya
Keyword(s):  
Vernacular Architecture ◽  
Conservation Strategy ◽  
Participatory Process ◽  
Value Assessment ◽  
A Value ◽  
Wide Range ◽  
Flexible Framework ◽  
Value Model ◽  
Contextual Values ◽  
Range Of Values

While a growing number of researchers have provided series of tough critiques of the typology-led heritage value assessment over the recent years, the impacts have been constrained by the continued obsession with expanding the list of the predetermined value typologies rather than escaping its limitations. While these sustained debates have provided important insights, this article argues that operationalizing these predetermined ‘one-size-fits-all’ value typologies is symptomatic of a number of shortcomings, especially in the context of capturing the pluralities of values in contextualized heritage such as vernacular architecture. It also often undermines inclusivity and participation in the valuing processes. However, rather than simply rejecting the values-based paradigm, this article proposes a conceptual value assessment framework that is informed by the theorization of vernacular architecture as a contextualized heritage. The proposed Vernacular Value Model (VVM) puts forward the ‘when(s)’ and ‘how(s)’ of amalgamating both technical and normative processes to capture the range of contextual values present in built vernacular heritage. To this end, this article posits that by drawing on such a proposed flexible framework, the conservation strategy for built vernacular heritage can be propagated as an inclusive and participatory process which captures the wide range of values for a more sustainable practices for conservation.

MATHEMATICAL MODEL OF TWO-DIMENSIONAL LAYERED PRESSURE FLOW IN THE AUGER CHANNEL

2018 ◽  
Author(s):  
А.В. ГУКАСЯН ◽  
В.С. КОСАЧЕВ ◽  
Е.П. КОШЕВОЙ
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Cross Section ◽  
Dynamic Pressure ◽  
Two Dimensional ◽  
Flow Dynamic ◽  
Pressure Flow ◽  
Rectangular Channels ◽  
Wide Range ◽  
Pressure Characteristics

Получено аналитическое решение двумерного слоистого напорного течения в канале шнека, позволяющее моделировать расходно-напорные характеристики прямоугольных каналов шнековых прессов с учетом гидравлического сопротивления формующих устройств и рассчитывать расходно-напорные характеристики экструдеров в широком диапазоне геометрии витков как в поперечном сечении, так и по длине канала. Obtained the analytical solution of two-dimensional layered pressure flow in the screw channel, allow to simulate the flow-dynamic pressure characteristics of rectangular channels screw presses taking into account the hydraulic resistance of the forming device and calculate the mass flow-dynamic pressure characteristics of the extruders in a wide range of the geometry of the coils, as in its cross section and along the length of the channel.

scholarly journals Field-aligned chorus wave spectral power in Earth's outer radiation belt

2015 ◽  
Vol 33 (5) ◽  
pp. 583-597 ◽  
Author(s):  
H. Breuillard ◽  
O. Agapitov ◽  
A. Artemyev ◽  
E. A. Kronberg ◽  
S. E. Haaland ◽  
...  
Keyword(s):  
Pitch Angle ◽  
Radiation Belt ◽  
Spectral Power ◽  
Peak Frequency ◽  
Wave Power ◽  
Outer Radiation Belt ◽  
Substantial Impact ◽  
Wide Range ◽  
Frequency Variations ◽  
Chorus Wave

Abstract. Chorus-type whistler waves are one of the most intense electromagnetic waves generated naturally in the magnetosphere. These waves have a substantial impact on the radiation belt dynamics as they are thought to contribute to electron acceleration and losses into the ionosphere through resonant wave–particle interaction. Our study is devoted to the determination of chorus wave power distribution on frequency in a wide range of magnetic latitudes, from 0 to 40°. We use 10 years of magnetic and electric field wave power measured by STAFF-SA onboard Cluster spacecraft to model the initial (equatorial) chorus wave spectral power, as well as PEACE and RAPID measurements to model the properties of energetic electrons (~ 0.1–100 keV) in the outer radiation belt. The dependence of this distribution upon latitude obtained from Cluster STAFF-SA is then consistently reproduced along a certain L-shell range (4 ≤ L ≤ 6.5), employing WHAMP-based ray tracing simulations in hot plasma within a realistic inner magnetospheric model. We show here that, as latitude increases, the chorus peak frequency is globally shifted towards lower frequencies. Making use of our simulations, the peak frequency variations can be explained mostly in terms of wave damping and amplification, but also cross-L propagation. These results are in good agreement with previous studies of chorus wave spectral extent using data from different spacecraft (Cluster, POLAR and THEMIS). The chorus peak frequency variations are then employed to calculate the pitch angle and energy diffusion rates, resulting in more effective pitch angle electron scattering (electron lifetime is halved) but less effective acceleration. These peak frequency parameters can thus be used to improve the accuracy of diffusion coefficient calculations.

scholarly journals The effect of enriched cyclopoid copepods on the coloration and feeding rate of Betta splendens

2021 ◽  
Vol 869 (1) ◽  
pp. 012007
Author(s):  
A Yuslan ◽  
N Nasir ◽  
H Suhaimi ◽  
A Arshad ◽  
N W Rasdi
Keyword(s):  
Rice Bran ◽  
Feeding Rate ◽  
Effective Means ◽  
B Value ◽  
Proximate Analysis ◽  
Betta Splendens ◽  
A Value ◽  
Wide Range ◽  
Significant Difference ◽  
L Value

Abstract Copepods with a wide range of sizes, species, and nutritional compositions are preferred as live food for rearing of Betta splendens larvae. This research focuses on evaluating the efficiency of copepod enrichment diets in improving the coloration and feeding rate of B. splendens. Copepod were enriched with Chlorella sp. (T1), capsicum (T2), mixed vegetable (carrot + spinach), (T3), yeast (T4) and rice bran (T5) in 24 hours prior the feeding tests. As a result, proximate analysis of enriched-copepods showed that T1 (70.88±0.41) has highest protein content and T5 (22.01±0.59) has the highest lipid content. The specific growth rate and survival rate of B. splendens was highest in the treatment T1 (2.56±0.07%; 91.11±1.92%) and followed closely by T3 (2.49±0.51%; 85.55±8.39%). Feeding rate, T3 (70.08±3.88%) presented highest rate compared to other treatments. The different enrichment diets used were significantly impact the coloration test on body of L* value (P=0.001, P<0.05), T3 (66.11±3.60) appeared darker in color in contrast to others. As for a* value, the coloration was not impacted with the use of different enrichment on copepods (P=0.158, P>0.05) was detected for T1 (2.84±0.73) that gave a redder shade than other treatments did. T3 (2.40±0.30) exerted a more yellowish shade than the rest for b* value with a significant difference (P=0.015, P<0.05). The current study demonstrates that, rice bran, capsicum and mixed vegetable enrichment (carrot and spinach) have the potential to be an effective means of increasing B. splendens coloring and feeding rate. This potential diet can be further used as a substitution to artificial foods in producing sustainable culture of ornamental fish in the aquaculture industry.

scholarly journals Gaussian Circular 2D FIR Filters Designed Using Analytical Approach

2020 ◽  
Vol 16 ◽  
Keyword(s):  
Analytical Approach ◽  
Design Procedure ◽  
Peak Frequency ◽  
Fir Filters ◽  
Chebyshev Series ◽  
Analytical Design ◽  
Frequency Transformation ◽  
Low Pass ◽  
Band Pass ◽  
2D Fir Filters

This paper proposes an analytical design procedure for a particular class of 2D filters, namelyGaussian-shaped, circularly-symmetric FIR filters. We approach both low-pass and band-pass circular filters,which are adjustable in selectivity and peak frequency. The design starts from a given 1D Gaussian prototypefilter, approximated using the Chebyshev series. A frequency transformation is applied to derive the circularfilter. Several design examples are provided for both types of filters. The filters designed through this methodare efficient, their frequency response results in a factored or nested form, convenient for implementation.

scholarly journals Analytical solution for residual stress and strain preserved in anisotropic inclusion entrapped in an isotropic host

Solid Earth ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 817-833
Author(s):  
Xin Zhong ◽  
Marcin Dabrowski ◽  
Bjørn Jamtveit
Keyword(s):  
Residual Stress ◽  
Aspect Ratio ◽  
Analytical Solution ◽  
Strain State ◽  
Spherical Inclusion ◽  
Raman Shift ◽  
Stress And Strain ◽  
Wide Range ◽  
Inclusion Shape ◽  
Diamond Inclusions

Abstract. Raman elastic thermobarometry has recently been applied in many petrological studies to recover the pressure and temperature (P–T) conditions of mineral inclusion entrapment. Existing modelling methods in petrology either adopt an assumption of a spherical, isotropic inclusion embedded in an isotropic, infinite host or use numerical techniques such as the finite-element method to simulate the residual stress and strain state preserved in the non-spherical anisotropic inclusions. Here, we use the Eshelby solution to develop an analytical framework for calculating the residual stress and strain state of an elastically anisotropic, ellipsoidal inclusion in an infinite, isotropic host. The analytical solution is applicable to any class of inclusion symmetry and an arbitrary inclusion aspect ratio. Explicit expressions are derived for some symmetry classes, including tetragonal, hexagonal, and trigonal. The effect of changing the aspect ratio on residual stress is investigated, including quartz, zircon, rutile, apatite, and diamond inclusions in garnet host. Quartz is demonstrated to be the least affected, while rutile is the most affected. For prolate quartz inclusion (c axis longer than a axis), the effect of varying the aspect ratio on Raman shift is demonstrated to be insignificant. When c/a=5, only ca. 0.3 cm−1 wavenumber variation is induced as compared to the spherical inclusion shape. For oblate quartz inclusions, the effect is more significant, when c/a=0.5, ca. 0.8 cm−1 wavenumber variation for the 464 cm−1 band is induced compared to the reference spherical inclusion case. We also show that it is possible to fit an effective ellipsoid to obtain a proxy for the averaged residual stress or strain within a faceted inclusion. The difference between the volumetrically averaged stress of a faceted inclusion and the analytically calculated stress from the best-fitted effective ellipsoid is calculated to obtain the root-mean-square deviation (RMSD) for quartz, zircon, rutile, apatite, and diamond inclusions in garnet host. Based on the results of 500 randomly generated (a wide range of aspect ratio and random crystallographic orientation) faceted inclusions, we show that the volumetrically averaged stress serves as an excellent stress measure and the associated RMSD is less than 2 %, except for diamond, which has a systematically higher RMSD (ca. 8 %). This expands the applicability of the analytical solution for any arbitrary inclusion shape in practical Raman measurements.

Comparison Between Empirical and Numerical Labyrinth Flow Correlations

1987 ◽  
Author(s):  
H. Zimmermann ◽  
K. H. Wolff
Keyword(s):  
Analytical Approach ◽  
Test Results ◽  
Wide Range ◽  
Loss Coefficients

An improved analytical approach for the correlation of labyrinth flow is put forward. This method modifies the standard labyrinth characteristics in a way, that the first fin has individual loss coefficients. The comparison with test results is very satisfactory for a wide range of geometries.

NUMERICAL SOLUTIONS OF SMOLUCHOWSKI'S EQUATIONS FOR THE COAGULATION OF UNCHARGED AEROSOLS

1965 ◽  
Vol 43 (8) ◽  
pp. 2312-2318 ◽  
Author(s):  
J. M. Beeckmans
Keyword(s):  
Particle Size ◽  
Numerical Solutions ◽  
Coagulation Factor ◽  
Dispersion Parameter ◽  
Particle Size Range ◽  
Mean Particle Size ◽  
A Value ◽  
Wide Range ◽  
Differential Sedimentation ◽  
Smoluchowski’S Equation

Smoluchowski's equations for the coagulation of uncharged aerosol particles were programmed for solution by electronic computer. Terms representing differential sedimentation, turbulence, and mean aggregate density in solid aerosols were included. The effect of heterogeneity in the particle-size distribution of the aerosols on their rate of coagulation was illustrated by means of a slip-corrected coagulation factor Fc, which assumes a value of unity in all non-turbulent homogeneous aerosols. Curves of Fc vs. σg, the geometrical standard deviation, were calculated for aerosols of various mean particle-size. The effects due to turbulence, and to differential sedimentation, were illustrated in a similar manner. It was also found that the process of coagulation gives rise to a degree of dispersion which is independent of the original dispersion parameter, and depends only slightly on the mean particle-size of the aerosol over a wide range of particle-sizes. In the particle-size range in which differential sedimentation is inappreciable, the relatively constant value of the dispersion parameter implies that heterogeneous aerosols must obey the simplified integrated form of Smoluchowski's equation, which is applicable to homogeneous aerosols. The coagulation constant exceeds that predicted by the simple theory by about 10% for liquid aerosols of 0.1 μ or less.

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