scholarly journals The exterior gravitational potential of toroids

2020 ◽  
Vol 494 (4) ◽  
pp. 5825-5838
Author(s):  
J-M Huré ◽  
B Basillais ◽  
V Karas ◽  
A Trova ◽  
O Semerák
Keyword(s):  
Laplace Equation ◽  
Toroidal Shell ◽  
Gravitational Acceleration ◽  
Order Zero ◽  
Astrophysical Plasmas ◽  
Relative Precision ◽  
Circular Section ◽  
Inhomogeneous Bodies ◽  
Leading Term ◽  
Major Radius

ABSTRACT We perform a bivariate Taylor expansion of the axisymmetric Green function in order to determine the exterior potential of a static thin toroidal shell having a circular section, as given by the Laplace equation. This expansion, performed at the centre of the section, consists in an infinite series in the powers of the minor-to-major radius ratio e of the shell. It is appropriate for a solid, homogeneous torus, as well as for inhomogeneous bodies (the case of a core stratification is considered). We show that the leading term is identical to the potential of a loop having the same main radius and the same mass – this ‘similarity’ is shown to hold in the ${\cal O}(e^2)$ order. The series converges very well, especially close to the surface of the toroid where the average relative precision is ∼10−3 for e = 0.1 at order zero, and as low as a few 10−6 at second order. The Laplace equation is satisfied exactly in every order, so no extra density is induced by truncation. The gravitational acceleration, important in dynamical studies, is reproduced with the same accuracy. The technique also applies to the magnetic potential and field generated by azimuthal currents as met in terrestrial and astrophysical plasmas.

scholarly journals Measuring $\bar{g}$ with ${\rm AE\bar{g}IS}$, progress and perspectives

2014 ◽  
Vol 30 ◽  
pp. 1460262 ◽  
Author(s):  
D. Krasnický ◽  
S. Aghion ◽  
O. Ahlén ◽  
C. Amsler ◽  
A. Ariga ◽  
...  
Keyword(s):  
Production Method ◽  
Current Status ◽  
Gravity Measurement ◽  
Gravitational Acceleration ◽  
Short Term ◽  
Relative Precision ◽  
Weak Equivalence Principle ◽  
Experimental Apparatus ◽  
Antihydrogen Production ◽  
Near Future

[Formula: see text] experiment's main goal is to measure the local gravitational acceleration of antihydrogen [Formula: see text] and thus perform a direct test of the weak equivalence principle with antimatter. In the first phase of the experiment the aim is to measure [Formula: see text] with 1% relative precision. This paper presents the antihydrogen production method and a description of some components of the experiment, which are necessary for the gravity measurement. Current status of the [Formula: see text] experimental apparatus is presented and recent commissioning results with antiprotons are outlined. In conclusion we discuss the short-term goals of the [Formula: see text] collaboration that will pave the way for the first gravity measurement in the near future.

The Scanning Electron Microscopic Observation of the Vestibular Sensory Epithelia

1969 ◽  
Vol 27 ◽  
pp. 40-41
Author(s):  
D.J. Lim ◽  
W.C. Lane
Keyword(s):  
Semicircular Canals ◽  
Electron Microscopic Observation ◽  
Gravitational Acceleration ◽  
Electron Microscopic ◽  
Sensory Epithelia ◽  
Scanning Electron Microscopic ◽  
Vestibular Sensory Epithelia ◽  
And Function ◽  
Sand Piles ◽  
Active Investigation

The morphology and function of the vestibular sensory organs has been extensively studied during the last decade with the advent of electron microscopy and electrophysiology. The opening of the space age also accelerated active investigation in this area, since this organ is responsible for the sensation of balance and of linear, angular and gravitational acceleration.The vestibular sense organs are formed by the saccule, utricle and three ampullae of the semicircular canals. The maculae (sacculi and utriculi) have otolithic membranes on the top of the sensory epithelia. The otolithic membrane is formed by a layer of thick gelatin and sand-piles of calcium carbonate crystals (Fig.l).

Atomic Imaging of Crystals using Large-Angle Electron Scattering in STEM

1990 ◽  
Vol 48 (1) ◽  
pp. 74-75
Author(s):  
D.E. Jesson ◽  
S. J. Pennycook
Keyword(s):  
Wave Function ◽  
Electron Scattering ◽  
Numerical Solutions ◽  
Large Angle ◽  
Real Space ◽  
High Angle ◽  
Analytical Treatment ◽  
Order Zero ◽  
Experimental Conditions ◽  
Ewald Sphere

It is well known that conventional atomic resolution electron microscopy is a coherent imaging process best interpreted in reciprocal space using contrast transfer function theory. This is because the equivalent real space interpretation involving a convolution between the exit face wave function and the instrumental response is difficult to visualize. Furthermore, the crystal wave function is not simply related to the projected crystal potential, except under a very restrictive set of experimental conditions, making image simulation an essential part of image interpretation. In this paper we present a different conceptual approach to the atomic imaging of crystals based on incoherent imaging theory. Using a real-space analysis of electron scattering to a high-angle annular detector, it is shown how the STEM imaging process can be partitioned into components parallel and perpendicular to the relevant low index zone-axis.It has become customary to describe STEM imaging using the analytical treatment developed by Cowley. However, the convenient assumption of a phase object (which neglects the curvature of the Ewald sphere) fails rapidly for large scattering angles, even in very thin crystals. Thus, to avoid unpredictive numerical solutions, it would seem more appropriate to apply pseudo-kinematic theory to the treatment of the weak high angle signal. Diffraction to medium order zero-layer reflections is most important compared with thermal diffuse scattering in very thin crystals (<5nm). The electron wave function ψ(R,z) at a depth z and transverse coordinate R due to a phase aberrated surface probe function P(R-RO) located at RO is then well described by the channeling approximation;

Analysis of the effects of seismic interference on the measurement results of gravitational acceleration by ballistic laser gravimeters

2020 ◽  
Vol 0 (1) ◽  
pp. 51-61
Author(s):  
Олександр Іванович Вінніченко ◽  
Павло Іванович Неєжмаков ◽  
Анатолій Васильович Омельченко ◽  
Олексій Валерійович Федоров ◽  
Володимир Федорович Болюх
Keyword(s):  
Gravitational Acceleration ◽  
Measurement Results

Improvement Of Free Convection From Three horizontal Finned Cylinders Fixed Between Two Walls

2018 ◽  
Vol 6 (2) ◽  
pp. 98-114 ◽  
Author(s):  
Hassan K. Abdullah ◽  
Haneen H. Rahman
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Prandtl Number ◽  
Convection Heat Transfer ◽  
Constant Heat Flux ◽  
Heat Fluxes ◽  
Head Orientation ◽  
Outer Diameter ◽  
Gravitational Acceleration ◽  
Convection Heat

Improvement of  free convection heat transfer from three finned cylinders arranged at a triangle shape fixed between two walls has been investigated in this study. Three mild steel finned cylinders fixed between two walls from Pyrex glass have been used as a test rig. It has been changed the spacing between the cylinders (X/D=1,2,3 & S/D=2,4,6) and the head orientation of a triangle to the top under constant heat flux values (38, 254, 660, 1268) W/m2 and compare with case of three finned cylinders arranged in vertical array in line fixed between two wall. The experiments are carried for Rayleigh number (Ra) from (15x103 to 14 x104 ) and Prandtl  number from (0.706-0.714 ). The results indicated an increase in Nu with increasing Ra for all cylinders. Furthermore,hx and Nu increased proportionally with the increasing of cylinder spacings for all heat fluxes. Also the experimental results show the case of triangle arrangement is improvement the heat transfer more than case of vertical arrangement. Heat transfer dimensionless correlating equation is also proposed.              Nomeclature: Ax: surface area(m2), T∞: surrounding temperature(k), D: the outer diameter of fin (m), Kf: the thermal conductivity for air at film temperature(W/m.k), hx: Local convection heat transfer(W/m2.k),  Gravitational acceleration(m/s2), I: Electric current (Amp), Nu: Nusselt number, Pr: Prandtl number

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