Approaching ultimate intrinsic SNR in a uniform spherical sample with finite arrays of loop coils

With the aid of classical statistical mechanics, a general expression for the static dielectric constant is derived. It is found, as in earlier work, that the dielectric constant is dependent upon the mean-square dipole moment of a macroscopic spherical sample of the substance. This mean-square moment is expanded as a series in powers of the mean molecular polarizability, and the terms proportional to the zero and first powers are evaluated in detail and in such a way that the long- and the short-range effects are separated. The former are determined with the aid of macroscopic arguments, so that a purely molecular theory remains. In the limit when short-range directional forces are zero, the formula reduces to the well-known Onsager equation. It is found that it is not in general legitimate to replace the surroundings of a macroscopic sample by a continuum having the bulk properties of the substance, and for this reason the approximate equation of Harris & Alder is found to lead to doubtful conclusions. The general equations are applied to the experimental data for water and other liquids, and the results are not unsatisfactory.

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Thomsen's parameters from p-wave measurements in a spherical sample‡

Geophysical Prospecting ◽

10.1111/j.1365-2478.2010.00917.x ◽

2010 ◽

Vol 60 (1) ◽

pp. 103-116 ◽

Cited By ~ 9

Author(s):

Andrej Bóna ◽

Dariush Nadri ◽

Miroslav Brajanovski

Keyword(s):

P Wave ◽

Wave Measurements ◽

Spherical Sample

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Pair distribution function analysis of X-ray diffraction from amorphous spheres in an asymmetric transmission geometry: application to a Zr58.5Cu15.6Ni12.8Al10.3Nb2.8glass

Journal of Applied Crystallography ◽

10.1107/s0021889813013162 ◽

2013 ◽

Vol 46 (4) ◽

pp. 999-1007 ◽

Cited By ~ 18

Author(s):

J. C. Bendert ◽

N. A. Mauro ◽

K. F. Kelton

Keyword(s):

Distribution Function ◽

Error Propagation ◽

Pair Distribution Function ◽

Function Analysis ◽

X Ray Diffraction ◽

Asymmetric Transmission ◽

X Ray ◽

Area Detector ◽

Spherical Sample ◽

Transmission Geometry

A method for the calculation of the pair distribution and structure functions from X-ray intensity data obtained with an area detector for an off-center incident X-ray beam on an amorphous sphere is presented. Error propagation for converting from the structure function to the pair distribution function is also described, including a summation series approach to treat the error from a high-qtruncation. A Zr58.5Cu15.6Ni12.8Al10.3Nb2.8glass (Vitreloy 106a) is used to demonstrate the techniques. In particular, the semi-analytical corrections presented to calculate the effects of secondary scatter within and asymmetric transmission through a spherical sample are verified.

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A spherical sample container for neutron powder diffractometry

Nuclear Instruments and Methods ◽

10.1016/0029-554x(78)90488-3 ◽

1978 ◽

Vol 151 (1-2) ◽

pp. 201-203

Author(s):

C. Riekel ◽

P. Convert ◽

G. Gobert ◽

C. Lazaro

Keyword(s):

Sample Container ◽

Spherical Sample

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Three-Dimensional High-Energy Electron Radiography Method for Static Mesoscale Samples Diagnostics

Applied Sciences ◽

10.3390/app9183764 ◽

2019 ◽

Vol 9 (18) ◽

pp. 3764

Author(s):

Quantang Zhao ◽

Yuanyuan Ma ◽

Jiahao Xiao ◽

Shuchun Cao ◽

Xiaokang Shen ◽

...

Keyword(s):

Three Dimensional ◽

High Energy ◽

Energy Electron ◽

New Method ◽

Reconstruction Method ◽

High Energy Electron ◽

Spherical Sample ◽

Internal Structures ◽

Dimensional Reconstruction ◽

Application Potential

In this paper, we propose a new method for static mesoscale sample diagnosis using three-dimensional radiography with high-energy electron radiography (HEER). The principle of three-dimensional high-energy electron radiography (TDHEER) is elucidated, and the feasibility of this method is confirmed by start-to-end simulation results. TDHEER is realized by combining HEER with the three-dimensional reconstruction method, by which more information about the samples can be attained, especially regarding the samples’ internal structures. With our study, the internal structures and the three-dimensional positions of the spherical sample are determined with a ~3 μm resolution. We believe that this new method enhances the HEER diagnostic capability and extends its application potential in mesoscale sciences.

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Large-Scale Shape Transformations of a Sphere Made of a Magnetoactive Elastomer

Polymers ◽

10.3390/polym12122933 ◽

2020 ◽

Vol 12 (12) ◽

pp. 2933

Author(s):

Oleg Stolbov ◽

Yuriy Raikher

Keyword(s):

Aspect Ratio ◽

Numerical Modelling ◽

Carbonyl Iron ◽

Applied Field ◽

Large Scale ◽

Ellipsoidal Approximation ◽

Spherical Sample ◽

Micron Size ◽

Ellipsoid Of Revolution ◽

Magnetoactive Elastomer

Magnetostriction effect, i.e., deformation under the action of a uniform applied field, is analyzed to detail for a spherical sample of a magnetoactive elastomer (MAE). A close analogy with the field-induced elongation of spherical ferrofluid droplets implies that similar characteristic effects viz. hysteresis stretching and transfiguration into a distinctively nonellipsoidal bodies, should be inherent to MAE objects as well. The absence until now of such studies seems to be due to very unfavorable conclusions which follow from the theoretical estimates, all of which are based on the assumption that a deformed sphere always retains the geometry of ellipsoid of revolution just changing its aspect ratio under field. Building up an adequate numerical modelling tool, we show that the ‘ellipsoidal’ approximation is misleading beginning right from the case of infinitesimal field strengths and strain increments. The results obtained show that the above-mentioned magnetodeformational effect should distinctively manifest itself in the objects made of quite ordinary MAEs, e.g., composites on the base of silicone cautchouc filled with micron-size carbonyl iron powder.

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