scholarly journals XVII. The complete system of the periods of a hollow vortex ring

1895 ◽  
Vol 186 ◽  
pp. 603-619 ◽  
Keyword(s):  
Kinetic Theory ◽  
Vortex Ring ◽  
Cross Section ◽  
Steady Motion ◽  
Dynamical Theory ◽  
Vortex Theory ◽  
Wide Range ◽  
The Cross ◽  
Hollow Vortex ◽  
The Stability

According to the vortex theory of matter, atoms consist of vortex rings in an infinite perfect liquid, the æther. These rings may be either hollow or filled with otating liquid. The cross section of the hollow or rotating core is in the simplest ase small and the ring is circular. Such vortices have been investigated. It has been hown that they can exist, and that they are stable for certain types of deformation, in this paper the stability of the hollow vortex ring is investigated further, with a view to proving that it is stable for all small deformations of its surface. An attempt also made to make the vortex theory of matter agree with the kinetic theory of ases as regards the relation between the velocity and the energy of an atom. On he latter theory the energy of an atom varies as the square of its velocity, while on he former theory the energy decreases as the velocity increases. As the two theories liffer on a fundamental point, while the consequences of the kinetic theory agree over wide range with experiment, those of the vortex theory are likely to be in discrepancy therewith. However, no account has been taken of the electric change which an atom must hold if electrolysis is to be explained. This electrification will evidently alter the relation between the energy and the velocity. The nature of the change thus produced is here discussed for the case of a hollow vortex, the surface of which behaves as a conductor of electricity, a representation which is dynamically realised by the theory of a rotationally-elastic fluid æther developed in Mr. Larmor’s paper, “A Dynamical Theory of the Electric and Luminiferous Medium.” The small oscillations also are worked out with a view to the discussion of the stability of an electrified vortex. 2. The velocity of translation of the vortex in its steady motion is constant and perpendicular to its plane. By impressing on the whole liquid a velocity equal and opposite to this, the hollow is reduced to rest. Since the cross section of the hollow is small, any small length of it may be regarded as cylindrical. A cylindrical vortex must, by reason of symmetry, have its cross section a circle, so that the cross section of the hollow of the annular vortex is approximately circular, and the hollow itself approximately a tore.

scholarly journals III. The complete system of the periods of a hollow vortex ring

1895 ◽  
Vol 58 (347-352) ◽  
pp. 155-156 ◽  
Keyword(s):  
Vortex Ring ◽  
Cross Section ◽  
Electric Charge ◽  
Complete System ◽  
Steady Motion ◽  
Azimuth Angle ◽  
Axis Of Symmetry ◽  
Hollow Vortex ◽  
The Stability ◽  
Small Deformations

The author discusses the stability of a hollow annular vortex in an infinite perfect liquid, and also the effect of an electric charge on the steady motion and the stability of such a vortex. It is known that a hollow vortex ring (without electric charge) is stable for such small deformations as are symmetrical about the axis of symmetry of the ring, and for such as consist in displacement of the axis of the hollow without alteration of the size or shape of its cross section. This investigation shows that, in addition to the fluted and sinuous vibrations above referred to, the vortex is capable of beaded vibrations, in which the hollow is enlarged and contracted at regular intervals along its length, and also of vibration of a more general type, in which the displacement at any moment consists of waves on the surface of the hollow, of which the crests are circles parallel to the axis of the hollow, and the amplitude a sine or cosine of a multiple of the azimuth angle.

scholarly journals XX. The potential of an anchor ring.-Part II

1893 ◽  
Vol 184 ◽  
pp. 1041-1106 ◽  
Keyword(s):  
Vortex Ring ◽  
Cross Section ◽  
Steady Motion ◽  
Vortex Rings ◽  
Laplace’S Equation ◽  
Single Vortex ◽  
Laplace's Equation ◽  
The Stability ◽  
Work Done

This paper is a continuation of that at pp. 43-95 suprd , on “The Potential of an Anchor Bing.” In that paper the potential of an anchor ring was found at all external points; in this/its value is determined at internal points. The annular form of rotating gravitating fluid was also discussed in that paper; here the stability of such a ring is considered. In addition, the potential of a ring whose cross-section is elliptic, being of interest in connection with Saturn, is obtained. The similarity of the methods employed, as well as of the analysis, has led me to give in this paper also a determination of the steady motion of a single vortex-ring in an infinite fluid, and of several fine vortex rings on the same axis. In Section I. solutions of Laplace’s equation applicable to space inside an anchor ring are obtained. These results are applied to obtain the potential of a solid ring at internal points, and also of a distribution of matter on the surface of the ring. The work done in collecting the ring from infinity is obtained.

A note on the stability of a vortex ring of small cross-section

1974 ◽  
Vol 338 (1615) ◽  
pp. 535-537 ◽  
Keyword(s):  
Vortex Ring ◽  
Cross Section ◽  
Small Cross Section ◽  
Complete Discussion ◽  
Hollow Vortex ◽  
The Stability ◽  
Special Case

We show by considering the special case of a hollow vortex that the cut-off approximation cannot be used to give a complete discussion of stability. In particular we show that in this case the instability predicted by the cut-off approximation is spurious.

scholarly journals Optimization of Geometrical Parameters of Hollow-core Slabs by Formwork-free Shaping for Construction in Seismic Areas

2020 ◽  
Vol 8 (6) ◽  
pp. 4973-4977
Keyword(s):  
Cross Section ◽  
High Strength ◽  
Geometrical Parameters ◽  
Hollow Core ◽  
Constructive Solution ◽  
Industrial Buildings ◽  
Operational Load ◽  
Wide Range ◽  
Hollow Core Slab ◽  
The Cross

The building norms and standards of Uzbekistan on the reinforced concrete structures do not regulate the design of hollow-core slabs of formwork-free shaping, reinforced with prestressed wire reinforcement. The manufacturing technology of such slabs allows creating a wide range of products that increase the possibility of their use in various structural systems in residential, civil and industrial buildings, but in non-seismic areas only. The aim of this work is to develop a constructive solution for the cross section of a prestressed hollow-core floor slab of bench formwork-free shaping, reinforced with high-strength wire reinforcement, in order to create a wide range of products intended for construction in seismic areas. To achieve the goal, the problem of determining the optimal combination of height and configuration parameters of the cross section of such a slab is solved, meeting the normalized operational requirements and limitations of earthquake-resistant building standards. The main variable parameters are the height and the void degree of the section, characterized by the size and shape of voids. In calculating the cross-section of a hollow-core slab when substantiating the theoretical basis for the calculation, the cross section is reduced to the equivalent I-section. As a result of research, a constructive solution was developed for the slab cross section of the maximum parameter values (the span, operational load) set by the customer. The parameters of the slab cross-section are: the height 190 mm, the hollowness 38%, the height of the upper thickened flange (compared with the height of the lower flange) of the given section is 0.27h, the height of the lower flange is 0.17h, the reduced (total) thickness of all ribs “b” is 0.32 of the width of the upper flange. The voids in the section along the height of the slab are arranged asymmetrically. A patent for a utility model has been received for the proposed constructive solution of the slab cross section.

scholarly journals Optimized CNT-PDMS Flexible Composite for Attachable Health-Care Device

Sensors ◽  
2020 ◽  
Vol 20 (16) ◽  
pp. 4523 ◽  
Author(s):  
Jian Du ◽  
Li Wang ◽  
Yanbin Shi ◽  
Feng Zhang ◽  
Shiheng Hu ◽  
...  
Keyword(s):  
Composite Material ◽  
Percolation Threshold ◽  
Young’S Modulus ◽  
Cross Section ◽  
Young's Modulus ◽  
Large Strain ◽  
Weight Ratio ◽  
Linear Range ◽  
Wide Range ◽  
The Cross

The CNT-PDMS composite has been widely adopted in flexible devices due to its high elasticity, piezoresistivity, and biocompatibility. In a wide range of applications, CNT-PDMS composite sensors were used for resistive strain measurement. Accordingly, the percolation threshold 2%~4% of the CNT weight ratio in the CNT-PDMS composite was commonly selected, which is expected to achieve the optimized piezoresistive sensitivity. However, the linear range around the percolation threshold weight ratio (2%~4%) limits its application in a stable output of large strain (>20%). Therefore, comprehensive understanding of the electromechanical, mechanical, and electrical properties for the CNT-PDMS composite with different CNT weight ratios was expected. In this paper, a systematic study was conducted on the piezoresistivity, Young’s modulus, conductivity, impedance, and the cross-section morphology of different CNT weight ratios (1 to 10 wt%) of the CNT-PDMS composite material. It was experimentally observed that the piezo-resistive sensitivity of CNT-PDMS negatively correlated with the increase in the CNT weight ratio. However, the electrical conductivity, Young’s modulus, tensile strength, and the linear range of piezoresistive response of the CNT-PDMS composite positively correlated with the increase in CNT weight ratio. Furthermore, the mechanism of these phenomena was analyzed through the cross-section morphology of the CNT-PDMS composite material by using SEM imaging. From this analysis, a guideline was proposed for large strain (40%) measurement applications (e.g., motion monitoring of the human body of the finger, arm, foot, etc.), the CNT weight ratio 8 wt% was suggested to achieve the best piezoresistive sensitivity in the linear range.

scholarly journals Cross sections of electron collisions with noble gases atoms

2021 ◽  
pp. 11-16
Author(s):  
Rusudan Golyatina ◽  
Sergei Maiorov
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Noble Gas ◽  
Empirical Formulas ◽  
Electron Collisions ◽  
Wide Range ◽  
Analytical Formulas ◽  
The Cross ◽  
Approximation Coefficients ◽  
Ionization Cross Sections

Consideration is given to the analysis of data on the cross sections of elastic and inelastic col-lisions of electrons with noble gas atoms. The transport (diffusion) cross section, the excita-tion and ionization cross sections are studied. For the selected sets of experimental and theo-retical data, optimal analytical formulas are found and approximation coefficients are select-ed for them. The obtained semi-empirical formulas allow us to reproduce the cross section values in a wide range of collision energies from 0.001 to 10000 eV with an accuracy of sev-eral percent.

scholarly journals Numerical simulation of cutting layer in internal corners milling

Mechanik ◽  
2019 ◽  
Vol 92 (7) ◽  
pp. 412-414
Author(s):  
Jan Burek ◽  
Rafał Flejszar ◽  
Barbara Jamuła
Keyword(s):  
Numerical Simulation ◽  
Numerical Model ◽  
Cross Section ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Cross Section Area ◽  
Section Area ◽  
The Cross ◽  
The Stability

The analytical and numerical model of the cross-section of the machined layer in the process of milling of concave rounding is presented. Simulation tests were carried out to determine the cross-sectional area of the cutting layer. A strategy has been developed that allows to increase the stability of the cross-section area of the cutting layer when the mill enters the inner corner area.

scholarly journals CRITERION OF MINIMUMMATERIAL CONSUMPTIONOF FLANGE OF I-SHAPED BAR WITH A VARIATION IN ITS THICKNESS ANDOUTLINE OF THE WIDTH, WITH RESTRICTION TO THE VALUE OF THE CRITICALFORCE OR RESTRICTIONTO THE VALUE OF THEFIRSTNATURAL FREQUENCY INTWO PRINCIPAL PLANESO

2018 ◽  
Vol 14 (2) ◽  
pp. 96-108
Author(s):  
Leonid S. Lyakhovich ◽  
Pavel A. Akimov ◽  
Boris A. Tukhfatullin
Keyword(s):  
Natural Frequency ◽  
Cross Section ◽  
Critical Force ◽  
Principal Plane ◽  
Material Consumption ◽  
The Cross ◽  
The Stability

We have already presented original criterion of minimum material consumption within the design of the outline of the width of the I-shaped bar and the stability constraints or restriction to the value of the first natu­ral frequency in one principal plane of inertia of the cross-section. This paper is devoted in its turn to a criterion for the minimum material capacity of the I-shaped bar with a variation in its thickness and outline of the width, with restrictions to the value of the critical force or restriction to the value of the first natural frequency in two principal planes of inertia of the section

Influence of the Steel Channel Shaped Shear Connectors on the Stability of the Simply Supported Steel Bridge without the Intermediate Bracing System in the Construction Stage

2021 ◽  
Vol 879 ◽  
pp. 151-168
Author(s):  
Van Khai Nguyen ◽  
Nghia Dai Van ◽  
Van Tuong Khanh Vo ◽  
Rin Anh Nguyen ◽  
Phuc Gia Nguyen ◽  
...  
Keyword(s):  
Cross Section ◽  
Steel Plate ◽  
Moment Of Inertia ◽  
Steel Bridge ◽  
Bridge Structure ◽  
Shear Connectors ◽  
The Cross ◽  
The Stability ◽  
The Moment ◽  
Main Girder

Steel bridge structure without intermediate bracing system (IBS) has been widely used in several countries and one of them is Japan. In this type of structure, the main steel girder is not reinforced by the stiffeners. The stiffness of the main girder is enhanced with steel plate directly welded to the top flange of the main girder, forming the “beams–system”. The reinforced concrete deck slab with the set of main girder and steel plate works compositely through steel shear connectors whose shape is C (channel) or I character. As for steel bridge structures, the main role of shear connectors is shear resistance between the concrete deck slab and steel girder plate in the exploitation stage. However, previous research has shown that the density of shear connectors influences on the stability as well as the stiffness of the bridge structure. Therefore, it has approved that this appurtenance is able to not only have the ability of shear resistance but also enhance the stiffness of the steel bridge structure which is particularly surveyed with the type of especial bridge structure – the steel bridge structure without IBS. Hence, the shear connectors in this kind of bridge structure are deliberately researched as an extra role in the construction stage. The following factors of the channel shape shear connectors would be researched for evaluating their impacting level on the stability of the special steel bridge structure: the properties (the length and the moment of inertia of the cross-section) and the density on the steel plate. Through the analysis of impacting level to the stability of three mentioned factors (the length and density of the shear connectors; the moment of inertia of the cross-section), the expected result is as following: 1) The minimum density of shear connectors is proposed. 2) The influence of the moment of inertia of the cross-section, the density, and the length on the stability is quite clear. 3) As for the economy, the optimal designed range among three factors is also suggested.

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