CONTRIBUTION OF DRIFT AND DIFFUSION TO WATER CAPACITY DEIONIZATION

Drift and diffusion of ions in a cavity having the shape of oblate ellipsoid of revolution are considered. The obtained approximate relationship, between the time of drift and diffusion filling of deep cavity with ions, contains the applied voltage and the ratio of cavity size to the distance between electrodes. It shows that in the performed experiments with the device for water capacitive deionization the filling of electrodes by ions was carried out, mainly, due to diffusion.

The Sheet of Giants: Unusual properties of the Milky Way’s immediate neighbourhood

ABSTRACT We quantify the shape and overdensity of the galaxy distribution in the ‘Local Sheet’ within a sphere of R = 8 Mpc and compare these properties with the expectations of the ΛCDM model. We measure ellipsoidal axis ratios of c/a ≈ 0.16 and b/a ≈ 0.79, indicating that the distribution of galaxies in the Local Volume can be approximated by a flattened oblate ellipsoid, consistent with the ‘sheet’-like configuration noted in previous studies. In contrast with previous estimates that the Local Sheet has a density close to average, we find that the number density of faint and bright galaxies in the Local Volume is ≈1.7 and ≈5.2 times denser, respectively, than the mean number density of galaxies of the same luminosity. Comparison with simulations shows that the number density contrasts of bright and faint galaxies within 8 Mpc alone make the Local Volume a ≈2.5 σ outlier in the ΛCDM cosmology. Our results indicate that the cosmic neighbourhood of the Milky Way may be unusual for galaxies of similar luminosity. The impact of the peculiar properties of our neighbourhood on the properties of the Milky Way and other nearby galaxies is not yet understood and warrants further study.

An approximation of geodesic circle passing through three points on an ellipsoid

In this paper we present an approximation method for a geodesic circle passing through three points on an oblate ellipsoid. Our method uses a prolate ellipsoid passing through the three points, and the new approximation curve is the intersection of the oblate and prolate ellipsoids, which can be obtained algebraically without iterations. The advantage of our approximation method is that it yields a significantly smaller approximation error. Compared to the plane section curve passing through the three points on the oblate ellipse, our method reduces the approximation error by at least 98\hspace{0.1667em}\% when the radii of geodesic circles are 100 km∼1000 km on the surface of the Earth. We illustrate the results using numerical examples.

Reversible morphological changes of assembled supramolecular amphiphiles triggered by pH-modulated host–guest interactions

Acid–base modulated host–guest binding at the micellar–water interface triggers reversible oblate ellipsoid-to-lamellar morphological transitions revealing the relationship between and morphology.

Solutions to the ellipsoidal Clairaut constant and the inverse geodetic problem by numerical integration

We derive computational formulas for determining the Clairaut constant, i.e. the cosine of the maximum latitude of the geodesic arc, from two given points on the oblate ellipsoid of revolution. In all cases the Clairaut constant is unique. The inverse geodetic problem on the ellipsoid is to determine the geodesic arc between and the azimuths of the arc at the given points. We present the solution for the fixed Clairaut constant. If the given points are not(nearly) antipodal, each azimuth and location of the geodesic is unique, while for the fixed points in the ”antipodal region”, roughly within 36”.2 from the antipode, there are two geodesics mirrored in the equator and with complementary azimuths at each point. In the special case with the given points located at the poles of the ellipsoid, all meridians are geodesics. The special role played by the Clairaut constant and the numerical integration make this method different from others available in the literature.