Cylinder In Terms Research Articles

Added Mass of Two Cylinders

Expressions for the classical added-mass coefficients have been calculated for the case of two arbitrary circular cylinders using the dipolar coordinate system. These are then applied to calculate the three nonzero added-mass coefficients of two identical circular cylinders in terms of constants of Jacobian elliptic functions. A calculation procedure is also evolved for the case of two circular cylinders of different radii. Finally, these results are extended to the case of twin cylinders of arbitrary shape using a certain family of conformal mappings.

Ray tracing generalized cylinders

An algorithm is presented for ray tracing generalized cylinders, that is, objects defined by sweeping a two-dimensional contour along a three-dimensional trajectory. The contour can be any 'well-behaved' curve in the sense that it is continuous, and that the points where the tangent is horizontal or vertical can be determined, the trajectory can be any spline curve. First a definition is given of generalized cylinders in terms of the Frenet frame of the trajectory. Then the main problem in ray tracing these objects, the computation of the intersection points with a ray, is reduced to the problem of intersecting two two-dimensional curves. This problem is solved by a subdivision algorithm. The three-dimensional normal at the intersection point closest to the eye point, necessary to perform shading, is obtained by transforming the two-dimensional normal at the corresponding intersection point of the two two-dimensional curves. In this way it is possible to obtain highly realistic images for a very broad class of objects.

A Note on the Cooling of a Cylinder Entering a Fluid

A long cylinder enters a cooling fluid. An explicit expression is derived for the temperature distribution within the cylinder in terms of the radius of the cylinder, its speed, the diffusivity and the rate of heat loss into the fluid. Curves are given showing the steady temperature of the cylinder surface at the point of entry.

Multiple scattering of sound by correlated monolayers

Earlier results for scattering by random uncorrelated planar distributions, and by doubly periodic planar configurations of relatively arbitrary obstacles, are generalized to pair-correlated nonsymmetrical monolayers. The existing development for parallel cylinders in terms of the Zernike–Prins one-dimensional pair function p(x), is extended to analogous two-dimensional distributions specified by p(R) for aligned impenetrable disks. We obtain the average multiple scattered transmitted and reflected waves, and an energy conserving approximation of the differential scattering cross section per unit area. Simplified forms are developed to facilitate determing p by inverting measured data. Closed form low-frequency results are derived for identical ellipsoids aligned nonsymmetrically to the plane of centers, and the array multipole-coupling processes are discussed in terms of functions of p and their approximations.

Light scattering by tilted cylinders: properties of partial wave coefficients

We investigate relations among the partial-wave coefficients that describe scattering by infinite cylinders in terms of the parameters governing this process: the refractive index m, the size parameter x, and the tilting angle ϕ. We present a complete set of relations for nonabsorbing cylinders, and we discuss their physical significance in terms of the principles of reciprocity and energy conservation. In particular, we find that energy conservation for this nonspherical shape leads to additional constraints not present in the case of scattering by spheres.

Eddy currents in a conducting cylinder with a crack

We report calculations for the impedance of a long solenoid which surrounds a cylinder of conducting material containing a radial surface crack of constant depth. The calculation is accomplished by solving for the longitudinal ac magnetic field in the interior of the ’’cracked’’ cylinder in terms of an infinite series of cylindrical Bessel functions. All the coefficients in the series are determined in principle by boundary-condtion requirements and the most significant terms are obtained numerically by truncation of the series. The resulting impedance is calculated for a wide range of values of the ratios of crack depth to radius and radius to skin depth. The results are tabulated in a form useful for nondestructive testing purposes.

Optimal management of diffusion treatment of a viscoelastic cylinder in terms of acceptable concentration-dependent stresses

Optimal management of diffusion treatment of a viscoelastic cylinder in terms of acceptable concentration-dependent stresses

Transparency of pair-correlated, random distributions of small scatterers, with applications to the cornea.

We consider transmission through pair-correlated random distributions of lossless dielectric (globular, cylindrical, or plate-like) scatterers with length parameter a and average spacing small compared to wavelength. Each optical particle is centered in a tough adherent transparent coating whose outer surface (sphere, cylinder, or slab) has radius b smaller than or equal to a. The corresponding attenuation coefficients beta varies directly as WM involve an integral of the appropriate radial-distribution function. Using the scaled-particle equations of state and statistical-mechanics theorems, we evaluate WM explicitly as a rational function of the volume fraction W of the fluid of rigid b particles. We obtain betaM = betaO WM with betaO as the uncorrelated value; W3(W) for spheres decreases more rapidly with increasing W than W2 for cylinders, and W2 decreases faster than W1, the result for slabs. We apply the results for cylinders in terms of W2 to the problem of the transparency of the cornea (whose collagen fibers are the scatters), as posed by Maurice. The value W APPROXIMATELY 0.6 GIVES GOOD ACCORD WITH THE ESSENTIALS OF THE Data for the transparency of the normal cornea, and the opacity that results from swelling is accounted for by corresponding smaller values of W. Thus, the normal cornea is modeled as a very densely packed two-dimensional gas, with gas-particle (mechanical) radius about 60% greater than the fiber (optical) radius.

Wave Propagation in Transversely Isotropic, Layered Cylinders

The propagation of infinite trains of symmetric harmonic waves traveling in infinitely long, right circular cylindrical shells is investigated on the basis of the three-dimensional theory of elasticity. The shells are assumed made of three concentric, transversely isotropic cylinders, each of different materials, bonded perfectly at their interfaces. The frequency equation is established by representing the displacement field in each cylinder in terms of potential functions and satisfying the Navier equations of motion and the boundary and interface conditions of the cylinder. The frequency equation has been programmed for numerical evaluation on an IBM 7044/7094 DCS computer, and the influence of the mechanical properties of the layers on the frequencies of the first few modes is investigated.

Diffusion and convection of heat from circular cylinders with known boundary conditions

AbstractThe problem of the diffusion and convection of heat in two-dimensional, incompressible flow past a circular cylinder is considered. Solutions are found for the temperature at any point exterior to the cylinder in terms of the boundary conditions on the surface and two particular boundary conditions are considered.

Circumferential Sound Pulses on Elastic Cylinders

We present a theoretical analysis of the diffraction of sound pulses on elastic cylinders in terms of circumferential waves. In particular, the speed of the pulse heads and the critical angles for entering and leaving the cylinder are obtained from causality arguments. Our conclusions are verified experimentally in the accompanying letter by Goodman et al.

Small Angle X-Ray Scattering from Randomly Oriented Cylinders of Arbitrary Cross Section

At the larger angles of the small-angle region, asymptotic expansions are the appropriate means of calculating the intensity of the small angle x-ray scattering from a sample of identical particles with uniform electron density and random position and orientation. Since other workers have previously shown that this intensity can be expressed as a Fourier integral transform involving a function characteristic of the size and shape of the particles, standard techniques for asymptotic expansion of Fourier integrals can be employed. In order to make a more general study than would be possible by consideration of particles with a single shape, right cylinders of arbitrary cross section have been chosen for this investigation. These generalized cylinders permit a fairly wide range of choice of particle shape and are well adapted to the study of both elongated and flattened particles. An integral has been developed which gives the characteristic function for the generalized cylinder in terms of the characteristic function of the two-dimensional cross section of the cylinder. As the asymptotic expressions for the scattered intensity depend quite critically on the discontinuities in derivatives of the characteristic function, a study has been made of these derivatives. An expression for the scattered intensity from rectangular parallepipeds has been calculated. A treatment of the limiting case of highly elongated cylinders is given.

Solid Angle Contour Integrals, Series, and Tables

The solid angle subtended at a point by any object is determined by the closed contour which outlines the ``visible'' boundary of the object from the point. By transformation of the double integral Ω=∫ ∫ sinθdθd[open phi] into a single integral over θ or [open phi] with limits determined by the contour and choice of axes, the solid angle may be simply represented in the important cases discussed as a contour integral. The integration has been carried out on the high-speed digital computer ORACLE at Oak Ridge National Laboratory. Solid angle tables have been prepared for the case of the circular disk and the entire finite right circular cylinder in terms of cylindrical coordinates. Each table contains in excess of 12 000 entries to six significant figures.

The dust-free space surrounding hot bodies

It is generally accepted that the dust-free space around hot bodies is due to the combined action of a radiometer force and an aerodynamic force caused by convection currents but no attempt has yet been made to derive a quantitative theory. Starting from the published work on the derivation of these forces a method has been evolved for equating them and the theory is worked out quantitatively for a vertical plate and for a horizontal cylinder in terms of temperature difference and the properties of the surrounding medium. The resulting relations are in good agreement with published experimental data.

Measurement of Impedance to Sound in Water

The method of measuring acoustic impedance by means of the interference of plane waves in a cylinder is not directly applicable to sound in water since it is impractical to obtain sufficient rigidity in the cylindrical walls to insure plane waves. A successful modification of the method was developed at the Massachusetts Institute of Technology by using pulsed signals in a cylinder several wave-lengths in diameter. There is a low frequency limitation to this scheme, which in this case is about 10 kc. With a view to extending the frequency range downward by using continuous waves (which are not plane), a theoretical investigation has been made of the steady-state sound fields in a long steel cylinder in terms of the wall thickness and the radius. The theoretical results have been checked by measurements of the distribution of sound pressure over cross sections and of the wave-lengths at various frequencies and for various tube terminations. It appears from the results of these investigations that the acoustic impedance of samples of materials or structures used as a termination of the tube can be reliably computed over a reasonable frequency range with a tube of practical dimensions.