scholarly journals The electric or magnetic polarisation of a thin cylinder of finite length by a uniform field of force

1907 ◽  
Vol 79 (527) ◽  
pp. 31-42
Keyword(s):  
Finite Length ◽  
General Problem ◽  
Normal Component ◽  
Uniform Field ◽  
Electric Force ◽  
Central Section ◽  
Thin Cylinder ◽  
Method Of Solution ◽  
The Mean ◽  
Rod Of Finite Length

The problem to be considered is the calculation of the polarisation induced in a cylindrical rod of finite length by a uniform field of force parallel to its axis. The only formula previously given appears to be that of Green for the normal component of the polarity at the surface of the rod. In the following investigation the method of solution of the general problem of induction by series is used, and expressions are given in §§ 4 and 5 for the mean moment of the rod and the induction across the central section. It is assumed that the susceptibility of the rod is independent of the applied force; consequently the formulæ apply especially to a dielectric rod suspended in a uniform field of electric force, this being, in fact, the purpose for which the calculations were made.

Transient Heat Conduction in a Rod of Finite Length With Variable Thermal Properties

1960 ◽  
Vol 27 (4) ◽  
pp. 617-622 ◽  
Author(s):  
W. H. Chu ◽  
H. N. Abramson
Keyword(s):  
Thermal Properties ◽  
Heat Conduction ◽  
Finite Length ◽  
Thermophysical Properties ◽  
Numerical Procedure ◽  
Transient Heat Conduction ◽  
Theoretical Solution ◽  
Rod Of Finite Length

This paper presents a theoretical solution for transient heat conduction in a rod of finite length with variable thermal properties. A numerical procedure is developed and the results of one example are presented and compared with the corresponding solution for the case of constant properties. Application to the problem of determination of thermophysical properties is discussed briefly.

scholarly journals The diffusion and mobility of ions in a magnetic field

1912 ◽  
Vol 86 (590) ◽  
pp. 571-577 ◽  
Keyword(s):  
Magnetic Field ◽  
Free Path ◽  
Magnetic Force ◽  
Mean Free Path ◽  
Electric Force ◽  
Mobility Of Ions ◽  
The Mean ◽  
The Magnetic Field

1. When the motion of ions in a gas takes place in a magnetic field the rates of diffusion and the velocities due to an electric force may be determined by methods similar to those given in a previous paper. The effect of the magnetic field may be determined by considering the motion of each ion between collisions with molecules. The magnetic force causes the ions to be deflected in their free paths, and when no electric force is acting the paths are spirals, the axes being along the direction of the magnetic force. If H be the intensity of the magnetic field, e the charge, and m the mass of an ion, then the radius r of the spiral is mv /He, v being the velocity in the direction perpendicular to H. The distance that the ion travels in the interval between two collisions in a direction normal to the magnetic force is a chord of the circle of radius r . The average lengths of these chords may be reduced to any fraction of the projection of the mean free path in the direction of the magnetic force, so that the rate of diffusion of ions in the directions perpendicular to the magnetic force is less than the rate of diffusion in the direction of the force.

scholarly journals Stress systems in aeolotropic plates. II

1939 ◽  
Vol 173 (953) ◽  
pp. 173-192 ◽  
Keyword(s):  
Differential Equation ◽  
Plane Stress ◽  
Isotropic Material ◽  
Infinite Plate ◽  
Mean Values ◽  
Plane Plate ◽  
Method Of Solution ◽  
Stress Functions ◽  
The Mean ◽  
Fundamental Equations

1. Fundamental equations which can be applied to problems of generalized plane stress in any plane plate of aeolotropic material have been obtained by Huber (1938). When the material has two directions of symmetry at right angles in the plane of the plate the differential equation for the stress function simplifies, and in a previous paper by G. I. Taylor and the present writer (1939) a number of stress functions were obtained which satisfied this equation and also gave single-valued expressions for the mean values of the stresses and displacements. Some of these functions were used to solve the problem of an isolated force in an infinite plate. In the present paper formulae are obtained for generalized plane stress systems in an infinite aeolotropic strip and also in a semi-infinite plate which is bounded by one straight edge. In particular, a solution is given for the general problem of any force acting at any point either within or on the boundary of a strip or semi-infinite plate. The stresses due to any distribution of force over the strip or semi-infinite plate may be deduced by integration. The method of solution is similar to that used by Howland (1929) for stress systems in a strip of isotropic material and Howland’s results may be obtained from our general formulae by a limiting process. When a force acts on the boundary of a semi-infinite plate the stresses may be deduced from our general results. It is, however, easier to evaluate these stresses independently by considering the problem of an isolated force at the vertex of a wedge. This problem was actually solved by Michell (1900) for any aeolotropic plate whose moduluses are not functions of the distance from the vertex of the wedge, but we give a solution here using the methods and notation of this and our previous paper. For the case of a wedge with one straight boundary the results agree with those deduced from the general formulae for a force in a semi-infinite plate.

scholarly journals Mean flows generated by a progressing water wave packert

1981 ◽  
Vol 22 (3) ◽  
pp. 318-347 ◽  
Author(s):  
R. Grimshaw
Keyword(s):  
Wave Packet ◽  
Boundary Conditions ◽  
Finite Length ◽  
Water Wave ◽  
Wave Train ◽  
Mean Flow ◽  
The Mean

AbstractEquations are derived which describe the evolution of the mean flow generated by a progressing water wave packet. The effect of friction is included, and so the equations are subject to the boundary conditions first derived by Longuet-Higgins [10]. Solutions of the equations are obtained for a wave packet of finite length, and also for a uniform wave train. The latter solution is compared with experiments.

Effect of Transverse and Longitudinal Surface Waviness on the Operation of Journal Bearings

1972 ◽  
Vol 14 (3) ◽  
pp. 168-172 ◽  
Author(s):  
P. Shelly ◽  
C. Ettles
Keyword(s):  
High Speed ◽  
Load Capacity ◽  
Surface Waviness ◽  
Machining Processes ◽  
Finishing Process ◽  
Oil Flow ◽  
Method Of Solution ◽  
The Mean ◽  
Effect Of Surface ◽  
Bearing Friction

An analysis is made to evaluate the effect of surface finish produced by the two final machining processes of high speed aero boring and broaching. A finite difference method of solution is used in which the number of waves superimposed on the basic geometry is successively increased. A strong asymptotic trend was found for all bearing characteristics beyond a relatively small number of waves. It is found that the load capacity compared to a smooth bearing is reduced for both processes if the surface waviness is included as an addition to the film height. If the film thickness is assumed to extend to the mean wave height, the load capacity is increased. The effect of surface waviness becomes more pronounced at higher eccentricities or as the amplitude of the waviness is increased. The variation of bearing friction and oil flow is shown. It is concluded that neither finishing process would have a serious deleterious effect on journal bearing performance.

scholarly journals A Comparison Theorem for Stability of Linear Stochastic Implicit Difference Equations of Index-1

2020 ◽  
Vol 36 (3) ◽  
Author(s):  
Nguyen Hong Son
Keyword(s):  
Comparison Theorem ◽  
Difference Equations ◽  
Mean Square ◽  
Mean Square Stability ◽  
Method Of Solution ◽  
The Mean ◽  
Definition Of

In this paper we study linear stochastic implicit difference equations (LSIDEs for short) of index-1. We give a definition of solution and introduce an index-1 concept for these equations. The mean square stability of LSIDEs is studied by using the method of solution evaluation. An example is given to illustrate the obtained results.

Translating Solitons of the Mean Curvature Flow Asymptotic to Hyperplanes in ℝn+1

2018 ◽  
Vol 2020 (24) ◽  
pp. 10114-10153 ◽  
Author(s):  
Eddygledson S Gama ◽  
Francisco Martín
Keyword(s):  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Normal Component ◽  
Vertical Cylinder ◽  
Curvature Flow ◽  
Grim Reaper ◽  
The Family ◽  
The Mean ◽  
Translating Solitons

Abstract A translating soliton is a hypersurface $M$ in ${\mathbb{R}}^{n+1}$ such that the family $M_t= M- t \,\mathbf e_{n+1}$ is a mean curvature flow, that is, such that normal component of the velocity at each point is equal to the mean curvature at that point $\mathbf{H}=\mathbf e_{n+1}^{\perp }.$ In this paper we obtain a characterization of hyperplanes that are parallel to the velocity and the family of tilted grim reaper cylinders as the only translating solitons in $\mathbb{R}^{n+1}$ that are $C^1$-asymptotic to two half-hyperplanes outside a non-vertical cylinder. This result was proven for translators in $\mathbb{R}^3$ by the 2nd author, Perez-Garcia, Savas-Halilaj, and Smoczyk under the additional hypotheses that the genus of the surface was locally bounded and the cylinder was perpendicular to the translating velocity.

Free Surface Flow over Obstacles at Subcritical Froude Numbers

1978 ◽  
Vol 5 (2) ◽  
pp. 89-94
Author(s):  
J.S.C. Tong ◽  
I.G. Currie
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Finite Length ◽  
Theoretical Approach ◽  
Wave Train ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Horizontal Surface ◽  
Lee Waves ◽  
The Mean

Experiments were carried out on free-surface flow over obstacles of finite length. The obstacles were located on the otherwise horizontal surface which contained the free-surface flow. The Froude number in each case was subcritical and resulted in a train of lee waves on the surface, downstream of the obstacles. The results confirm the predicted phenomenon of ‘upstream influence’ – that the mean upstream depth and the mean downstream depth should differ. Serious discrepancies between the observed results and the results from existing theories are noted, however. Not only is the amplitude of the lee waves at variance with the theory, but the phasing of the wave train, relative to the obstacle, is different. An alternative theoretical approach is proposed, the results from which are in much better agreement with the observed results.

Effect of a Simulated Free Surface on the Wake of a Slender Body

1986 ◽  
Vol 30 (04) ◽  
pp. 242-255
Author(s):  
P. Mitra ◽  
W. Neu ◽  
J. Schetz
Keyword(s):  
Free Surface ◽  
Turbulent Flow ◽  
Normal Component ◽  
Image Plane ◽  
Axisymmetric Body ◽  
Transverse Component ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Flow Measurements ◽  
The Mean

Turbulent flow measurements were performed in the wake of a slender axisymmetric body in the presence of a flat plate strut and an image plane crudely representing the "rigid lid" approximation to a free surface. The tests were performed in a wind tunnel at a nominal Reynolds number of 6.0 ⨯ 105. A Yawhead probe was used for the mean flow measurements, and a Constant Temperature Anemometer System with an x-wire probe was used to obtain the turbulent flow characteristics. The presence of the image plane was found to increase the velocity defect and the static pressure as the image plane was approached. A redistribution among the various components of velocity fluctuations was noted near the image plane. The transverse component was enhanced at the expense of the normal component. The image plane also was found to influence the magnitudes and radial spread of turbulence intensities and Reynolds stresses. Some interactions between the wake of the axisymmetric body and that of the plate strut were observed. Overall, the mean velocities and the turbulence quantities indicated symmetry about the image plane throughout the wake.

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