Circular Barrier Research Articles

Molecular dynamics calculation of the dielectric constant

Molecular dynamics simulation of a sample of a two-dimensional fluid of Stockmayer molecules (i.e. particles interacting via a central Lennard-Jones interaction plus a point dipole interaction) are reported. The dipolar interaction adopted is that required by two-dimensional electrostatics, so that the convergence problem is conserved. The sample (≈13 molecular diameters in size) is kept in vacuo by a steep circular potential barrier. It is first shown that for distances greater than 3 to 5 molecular diameters the macroscopic laws of electrostatics apply, by checking that the mean squared moment of an inner disc, as a function of the diameter of the disc, can be fitted with a single dielectric constant, which is thus determined. The Kirkwood correlation factor for an infinite sample is then evaluated. For highly polar systems, it is greater than unity. Also the radial vector correlation function h Δ(r), which describes the weight of in an expansion of the angle-dependent pair distribution f...

Rotating flow in a cylinder with a circular barrier on the bottom

The relative flow of a homogeneous, slightly viscous fluid in a rotating cylinder is induced by differential rotation of the bottom disk, on which a thin circular strip of small height is fixed. The axis of symmetry of the strip coincides with the rotation axis of the cylinder. At the strip a Stewartson layer exists which is partially free, partially attached to the strip. The structure of the Stewartson % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyramaaCa% aaleqabaWaaSGbaeaacaaIXaaabaGaaGinaaaaaaaaaa!3873!\[E^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} \]-layer (E being the Ekman number) is not affected by the height of the strip, but the % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyramaaCa% aaleqabaWaaSGbaeaacaaIXaaabaGaaG4maaaaaaaaaa!3872!\[E^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} \]-layer problem has to be solved in the two separate intervals. The fact that both solutions do not match at the strip edge necessitates the presence of an intermediate region that exhibits some characteristic features of an Ekman layer.

Steady state moisture flows in unsaturated soil containing a plane, isolated, impermeable barrier

A three-dimensional, axially symmetrical, steady state flow of moisture in an unsaturated soil has been analysed. The steady state infiltration is maintained by a constant flux across a circular disc on the horizontal soil surface. The flow encounters an obstacle in the form of a plane circular impermeable barrier of arbitrary radius. Except for this isolated barrier, at a given arbitrary depth, the rest of the soil is homogeneous and isotropic. The governing differential equation is linearized by assuming the hydraulic conductivity to be an exponential function of the pressure head. Techniques associated with dual integral equations constitute the basic tools that are employed in solving this problem. Explicit formulae and expressions are obtained for computing the solution for arbitrary values of the radius of the source, of the radius of the obstacle, and of the distance between them. Keeping the radius of the source as unity, the barrier radius and depth were varied in illustrative examples. Results are plotted in a series of figures. The concluding section briefly mentions relevance of such analysis to interpretation of field data on moisture contents or calculations of hydraulic conductivity. The problem of flow around an isolated disc in infinite space, with a uniform gravitational flow at large distances from this disc, can also be solved by the methods developed here. This has been done, and the results are plotted in a figure.

Moments of the first-passage time for a narrow-band process

The moments of the first-passage time of a narrow-band stochastic process produced by a linear oscillator excited by wide-band noise are presented for the case of a “safe” region defined by a circular barrier in the phase plane. As long as damping is small the moments produced will be approximately the same as those for the two-sided barrier problem. An iterative set of partial differential equations governing the moments, the first being the Pontriagin-Vitt equation for the mean first-passage time, are solved by using a Galerkin approximation. No restrictions are required on the barrier size.

An omnidirectional photometer of small dimensions

This omnidirectional photometer is intended for the measurement of daylight under grass swards; but the principle used in the instrument can be applied to measure the mean illumination at a point in other cases, for example, interior illumination. It consists of two small circular barrier layer cells, insulated from one another and mounted back to back, each being surmounted by a translucent diffusing hemispherical shell, diameter 5/8 in. The cell sensitivities are adjusted electrically to equality, the combined output being read on an indicating meter. Even for collimated light the response is uniform with orientation to better than ±5%.

Two-dimensional Flow around a Circular Barrier in a Rotating Spherical Shell

An experiment has been recently set up in the hydrodynamics laboratory to study the flow of fluid around a circular barrier. In a rotating spherical shell of liquid, a small cylindrical obstacle is moved zonally in mid-latitudes and observations are made of the resulting perturbed flow. If the flow relative to the obstacle is westerly, a strong anticyclonic circulation is set up faround the barrier and wave motions exist around the globe. When the basic flow is easterly with the same relative speed, no circulation is found, but the wake is very long and broad and the fluid in it has little motion relative to the obstacle. When viewed with respect to the shell, the obstacle moving eastward creates a strong westerly jet at its latitude.

Two-dimensional Flow around a Circular Barrier in a Rotating Spherical Shell

An experiment has been recently set up in the hydrodynamics laboratory to study the flow of fluid around a circular barrier. In a rotating spherical shell of liquid, a small cylindrical obstacle is moved zonally in mid-latitudes and observations are made of the resulting perturbed flow. If the flow relative to the obstacle is westerly, a strong anticyclonic circulation is set up faround the barrier and wave motions exist around the globe. When the basic flow is easterly with the same relative speed, no circulation is found, but the wake is very long and broad and the fluid in it has little motion relative to the obstacle. When viewed with respect to the shell, the obstacle moving eastward creates a strong westerly jet at its latitude.

GEOLOGY OF THE WALLIS ISLANDS

The Wallis Islands comprise Uvea, the main island, and 22 islets enclosed by or lying upon a nearly circular barrier reef about 200 miles west of the Samoan group in the Southern Pacific Ocean. The highest point in the group, about 470 feet above sea level, and several crater lakes exist on Uvea Island. The high islands are composed of olivine basaltic lavas and pyroclastics, except for one cinder cone and its associated flows of oligoclase andesite on Uvea Island. The low islands either are composed of calcareous sand or are erosional remnants of tuff cones and lava domes. Uvea Island was built by the coalescence of lava flows from 19 volcanic vents. The vents comprise 15 flat shield-shaped lava cones, 3 consolidated ash cones, and 1 cinder cone. Except for two Recent lava cones barely covered with soil, the bulk of the island is composed of deeply weathered middle Pleistocene(?) volcanics. Lavas of intermediate age do not exist. Limestone ejecta in the tuff cones indicate that the whole group is built on a submerged reef, probably about 180 feet below sea level. This reef presumably rests on a Tertiary basaltic volcano. Definite evidence of emerged shore lines at 25 and 5 feet above mean sea level exists, as well as evidence suggestive of higher stands.

Resistance to a barrier in the shape of an arc of a circle

Comparatively little progress in the solution of the problem of discontinuous fluid motion past a curved barrier was made until Levi-Civita formulated a method of transforming that part of the barrier which is in contact with the moving fluid into a semi-circle in an Argand diagram. This, indeed, was the starting point of much work of interest and importance. Useful accounts of the problem of motion past any barrier, together with extensions, are given by Cisotti and Brillouin. Leaving out of account such barriers as are made up of one or more planes, problems which can be solved by the older methods based on Schwartz-Christoffel transformations, the only applications of Levi-Civita’s method to curved barriers seem to be that made by Brillouin in the paper referred to, and those made by S. Brodetsky in 1922. The work of Brillouin. however, and that of other investigators are essentially backward processes, in which a likely expression is written down and the streaming motion implied, as well as the shape of the boundary, are investigated. A more direct attack is obtained by suitably choosing the coefficients in Levi-Civita’s general formula, and arriving at the solution for a given curved barrier by a series of steps in successive approximation. The solution of the problem for a circular barrier placed symmetrically in the streaming fluid has been obtained in this manner by S. Brodetsky. The object of this paper is to solve the problem of the circular barrier placed in any position in the streaming fluid, subject to the condition, however, that neither of the ends of the barrier are in the “dead” fluid— i. e ., the radius of curvature of the free stream line is zero at each end. This immediately restricts the barrier, if convex to the streaming fluid, to be of angular extent less than 110·2°.