Effect of kinetic boundary conditions on the cross section of the scattering of an electromagnetic wave by a small metal particle

We analyze the transverse vibrations of a thin homogeneous beam which is symmetric with respect to the x-y and x-z planes. The cross section of the beam at x is assumed to have the form D(x)={(x,y,z)|x∈[0,1],y=xαy1,z=xβz1,(y1,z1)∈D1} where D1 is the cross section at x = 1. Expressions are obtained from which the eigenvalues and eigenfunctions can be easily found for 0 ≤ α < 2 and all combinations of clamped, hinged, guided, and free boundary conditions at both ends of the beam.

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Convective Heat Transfer in Elliptical Microchannels Under Slip Flow Regime and H1 Boundary Conditions

Journal of Heat Transfer ◽

10.1115/1.4032173 ◽

2015 ◽

Vol 138 (4) ◽

Cited By ~ 7

Author(s):

Pamela Vocale ◽

Gian Luca Morini ◽

Marco Spiga

Keyword(s):

Heat Transfer ◽

Nusselt Number ◽

Aspect Ratio ◽

Boundary Conditions ◽

Convective Heat Transfer ◽

Cross Section ◽

Convective Heat ◽

Slip Flow ◽

The Cross ◽

Cross Section Geometry

In this work, hydrodynamically and thermally fully developed gas flow through elliptical microchannels is numerically investigated. The Navier–Stokes and energy equations are solved by considering the first-order slip flow boundary conditions and by assuming that the wall heat flux is uniform in the axial direction, and the wall temperature is uniform in the peripheral direction (i.e., H1 boundary conditions). To take into account the microfabrication of the elliptical microchannels, different heated perimeter lengths are analyzed along the microchannel wetted perimeter. The influence of the cross section geometry on the convective heat transfer coefficient is also investigated by considering the most common values of the elliptic aspect ratio, from a practical point of view. The numerical results put in evidence that the Nusselt number is a decreasing function of the Knudsen number for all the considered configurations. On the contrary, the role of the cross section geometry in the convective heat transfer depends on the thermal boundary condition and on the rarefaction degree. With the aim to provide a useful tool for the designer, a correlation that allows evaluating the Nusselt number for any value of aspect ratio and for different working gases is proposed.

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Ranges of Backwater Curves in Lower Odra

Civil and Environmental Engineering Reports ◽

10.2478/ceer-2018-0048 ◽

2018 ◽

Vol 28 (4) ◽

pp. 25-35

Author(s):

Robert Mańko

Keyword(s):

Boundary Condition ◽

Boundary Conditions ◽

Cross Section ◽

River Network ◽

Hydrological Conditions ◽

Complicated System ◽

Odra River ◽

The Cross

Abstract In the paper, the backwater curve ranges at the mouth of the Odra River with changing boundary conditions were analysed. The aim of the study is to determine which boundary condition, i.e. stage of lower cross-section or flow in upper cross-section, has a greater impact on the formation of the backwater curve at the mouth of the Odra River. Due to the complicated system of the Lower Odra River network (Międzyodrze and Dabie Lake), the analysis takes into consideration a section of the Odra River from a weir in Widuchowa upwards, thereby accepting as an axiom that the cross-section in Widuchowa is within the range of sea impact, regardless of other hydrological conditions.

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Evaluating the Effect of Asymmetric Cross-section in Free Vibration and Bending Analysis Results of FG Sandwich Beam by Proposing Simple Efficient Element

Periodica Polytechnica Civil Engineering ◽

10.3311/ppci.17447 ◽

2021 ◽

Author(s):

Majid Yaghoobi ◽

Mohsen Sedaghatjo ◽

Reyhaneh Alizadeh ◽

Mohammad KARKON

Keyword(s):

Free Vibration ◽

Boundary Conditions ◽

Cross Section ◽

Timoshenko Beam ◽

Equilibrium Equation ◽

Vertical Displacement ◽

Asymmetric Effect ◽

Bending Analysis ◽

Different Boundary Conditions ◽

The Cross

In this paper, the asymmetric effect of the cross-section on the free vibration and bending analysis of FG sandwich beams are evaluated. For this purpose, a simple, efficient element is formulated. The new element is created based on the Timoshenko beam theory. The third- and second-order polynomials will be used for vertical displacement and rotation fields, respectively. The proposed formulation will be written based on satisfying the equilibrium equation. Satisfying the equilibrium equation of the Timoshenko beam, in addition to increasing element efficiency, will reduce the number of nodal unknowns. Several benchmark tests with different boundary conditions are used for thin and thick beams to prove the efficiency of the proposed element. The responses of the good elements of other researchers have been used for comparison. Numerical tests prove the rapid convergence rate and high accuracy of the proposed element in free vibration and bending analysis of the beams with various cross-section types and different boundary conditions. The pinned-sliding support conditions for the beam are used to evaluate the asymmetric effect of the cross-section. The use of asymmetric cross-sections creates additional axial displacements and intensifies the deflection of the beam under the lateral load. By increasing the asymmetry, the additional axial displacement and vertical displacement increase. These additional deflections for thin beams are more than thick ones. Also, asymmetry results in increasing the natural frequencies of beams. In the free vibration analysis, the effect of asymmetry on thick beams is more than thin ones.

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Current density distribution within a small metal particle in an electromagnetic wave field

Optics and Spectroscopy ◽

10.1134/s0030400x08100159 ◽

2008 ◽

Vol 105 (4) ◽

pp. 611-616 ◽

Cited By ~ 2

Author(s):

I. O. Moiseev ◽

A. A. Yushkanov ◽

Yu. I. Yalamov

Keyword(s):

Electromagnetic Wave ◽

Density Distribution ◽

Wave Field ◽

Current Density ◽

Metal Particle ◽

Current Density Distribution ◽

Electromagnetic Wave Field ◽

Small Metal Particle

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The Impact of Boundary Conditions on the Response of NiMnGa Samples in Actuation and Power Harvesting Applications

Volume 1: Development and Characterization of Multifunctional Materials; Modeling, Simulation and Control of Adaptive Systems; Integrated System Design and Implementation ◽

10.1115/smasis2013-3234 ◽

2013 ◽

Cited By ~ 1

Author(s):

Isaac Nelson ◽

Constantin Ciocanel ◽

Doug LaMaster ◽

Heidi Feigenbaum

Keyword(s):

Magnetic Field ◽

Boundary Conditions ◽

Cross Section ◽

Effective Length ◽

Power Harvesting ◽

Simply Supported ◽

Voltage Output ◽

The Cross ◽

The Difference ◽

The Impact

Magnetic shape memory alloys (MSMAs) are materials that can display up to 10% recoverable strain in response to the application of a magnetic field or compressive mechanical stress. The magnetomechanical response of the material makes MSMAs suitable for applications such as actuation, sensing, and power harvesting. While the magnetomechanical response of the material has been extensively investigated to date, there is no report in the literature on the effect of the boundary conditions (BCs) on its response. The response of MSMAs is primarily driven by the reorientation of internal martensite variants, in conjunction with rotation of magnetization vectors, and domain wall motion. During the reorientation process a change in material’s magnetization occurs. For sensing and power harvesting applications, a pick-up coil may be used to convert this change in magnetization into an electric potential/voltage. To date, it has been confirmed experimentally that, according to Faraday’s law of induction, the magnitude of the output voltage depends on the number of turns of the pick-up coil, the amplitude of the reorientation strain, the magnitude and direction of the biased magnetic field, and the frequency at which the reorientation occurs. However, to our knowledge, no study has been carried out to investigate the effect of the BCs on the voltage output. This paper examines the effect of the BCs on the material’s magnetomechanical response, as well as on the corresponding voltage output. Three BCs are considered in the performed experiments: i) simply supported, ii) clamped, and iii) mixed (i.e. one end clamped and one end guided). The difference observed in the magnetomechanical response of the material, between the tested BCs, is attributed to the local effects caused by the grips (particularly the clamped and mixed conditions) and by the rotation of the specimen within the grips (in the simply supported condition). The latter is facilitated by the difference between the cross section of the specimen and the cross section of the cavity receiving the sample and by the larger effective length of the specimen in this case.

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A New Approach to the Demonstration of Oxidase-Localization Using Tannic Acid Or Catechin

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100073933 ◽

1973 ◽

Vol 31 ◽

pp. 698-699

Author(s):

V. Mizuhira ◽

Y. Futaesaku

Keyword(s):

Cross Section ◽

Tannic Acid ◽

Elastic Fiber ◽

The Other ◽

New Approach ◽

Tissue Block ◽

Active Reaction ◽

The Cross

Previously we reported that tannic acid is a very effective fixative for proteins including polypeptides. Especially, in the cross section of microtubules, thirteen submits in A-tubule and eleven in B-tubule could be observed very clearly. An elastic fiber could be demonstrated very clearly, as an electron opaque, homogeneous fiber. However, tannic acid did not penetrate into the deep portion of the tissue-block. So we tried Catechin. This shows almost the same chemical natures as that of proteins, as tannic acid. Moreover, we thought that catechin should have two active-reaction sites, one is phenol,and the other is catechole. Catechole site should react with osmium, to make Os- black. Phenol-site should react with peroxidase existing perhydroxide.

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Electron Microscopy of the Shape of Small Metal Particles

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100079024 ◽

1977 ◽

Vol 35 ◽

pp. 300-301

Author(s):

M. Jose Yacaman

Keyword(s):

Electron Microscopy ◽

Metal Particle ◽

Field Experiments ◽

Size Range ◽

Dark Field ◽

Metal Particles ◽

Bragg Condition ◽

Crystal Particle ◽

Small Metal Particle ◽

Small Metal Particles

In the Study of small metal particles the shape is a very Important parameter. Using electron microscopy Ino and Owaga(l) have studied the shape of twinned particles of gold. In that work electron diffraction and contrast (dark field) experiments were used to produce models of a crystal particle. In this work we report a method which can give direct information about the shape of an small metal particle in the amstrong- size range with high resolution. The diffraction pattern of a sample containing small metal particles contains in general several systematic and non- systematic reflections and a two-beam condition can not be used in practice. However a N-beam condition produces a reduced extinction distance. On the other hand if a beam is out of the bragg condition the effective extinction distance is even more reduced.

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Energy Distribution in Electron Beams

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100096096 ◽

1972 ◽

Vol 30 ◽

pp. 568-569

Author(s):

Tamotsu Ohno

Keyword(s):

Electron Beam ◽

Energy Distribution ◽

Cross Section ◽

Integral Curve ◽

Electron Beams ◽

Electron Gun ◽

Angular Divergence ◽

Apparent Increase ◽

Integral Width ◽

The Cross

The energy distribution in an electron; beam from an electron gun provided with a biased Wehnelt cylinder was measured by a retarding potential analyser. All the measurements were carried out with a beam of small angular divergence (<3xl0-4 rad) to eliminate the apparent increase of energy width as pointed out by Ichinokawa.The cross section of the beam from a gun with a tungsten hairpin cathode varies as shown in Fig.1a with the bias voltage Vg. The central part of the beam was analysed. An example of the integral curve as well as the energy spectrum is shown in Fig.2. The integral width of the spectrum ΔEi varies with Vg as shown in Fig.1b The width ΔEi is smaller than the Maxwellian width near the cut-off. As |Vg| is decreased, ΔEi increases beyond the Maxwellian width, reaches a maximum and then decreases. Note that the cross section of the beam enlarges with decreasing |Vg|.

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