The existence of a bending rigidity for a hard sphere liquid near a curved hard wall: Helfrich or Hadwiger?

In the context of Rosenfeld's Fundamental Measure Theory, we show that the bending rigidity is not equal to zero for a hard-sphere fluid in contact with a curved hard wall. The implication is that the Hadwiger Theorem does not hold in this case and the surface free energy is given by the Helfrich expansion instead. The value obtained for the bending rigidity is (1) an order of magnitude smaller than the bending constant associated with Gaussian curvature, (2) changes sign as a function of the fluid volume fraction, (3) is independent of the choice for the location of the hard wall.Comment: 19 pages, 5 figures, to appear in Physical Review

On the spectrum of fluctuations of a liquid surface: From the molecular scale to the macroscopic scale

We show that to account for the full spectrum of surface fluctuations from low scattering vector qd 1 (bulk-like fluctuations), one must take account of the interface's bending rigidity at intermediate scattering vector qd = 1, where d is the molecular diameter. A molecular model is presented to describe the bending correction to the capillary wave model for short-ranged and long-ranged interactions between molecules. We find that the bending rigidity is negative when the Gibbs equimolar surface is used to define the location of the fluctuating interface and that on approach to the critical point it vanishes proportionally to the interfacial tension. Both features are in agreement with Monte Carlo simulations of a phase-separated colloid-polymer system.Comment: 18 pages, 11 figures, accepted for publication in The Journal of Chemical Physic

On the spectrum of fluctuations of a liquid surface: From the molecular scale to the macroscopic scale

We show that to account for the full spectrum of surface fluctuations from low scattering vector qd << 1 (classical capillary wave theory) to high qd > 1 (bulk-like fluctuations), one must take account of the interface's bending rigidity at intermediate scattering vector qd = 1, where d is the molecular diameter. A molecular model is presented to describe the bending correction to the capillary wave model for short-ranged and long-ranged interactions between molecules. We find that the bending rigidity is negative when the Gibbs equimolar surface is used to define the location of the fluctuating interface and that on approach to the critical point it vanishes proportionally to the interfacial tension. Both features are in agreement with Monte Carlo simulations of a phase-separated colloid-polymer system.Comment: 18 pages, 11 figures, accepted for publication in The Journal of Chemical Physic

Lukan Easter Formation: Living out the Resurrection

(Excerpt) We will discuss two types of Easter formation in the early church, with Acts and Luke as guides to our Easter mystagogy. The topic is in one sense natural for a New Testament scholar, since all writers of the New Testament begin theologically from the resurrected Christ, because a Christian\u27s life-style (to use a modem shibboleth) is formed in the New Testament from the event of baptism, and because early Christian parenesis is essentially a realization of life under the Lordship of the Resurrected One. But it also brings some problems

The Lanczos potential for Weyl-candidate tensors exists only in four dimensions

We prove that a Lanczos potential L_abc for the Weyl candidate tensor W_abcd does not generally exist for dimensions higher than four. The technique is simply to assume the existence of such a potential in dimension n, and then check the integrability conditions for the assumed system of differential equations; if the integrability conditions yield another non-trivial differential system for L_abc and W_abcd, then this system's integrability conditions should be checked; and so on. When we find a non-trivial condition involving only W_abcd and its derivatives, then clearly Weyl candidate tensors failing to satisfy that condition cannot be written in terms of a Lanczos potential L_abc.Comment: 11 pages, LaTeX, Heavily revised April 200

Interplay between the Reactions to Light and to Gravity in Phycomyces

Sporangiophores of Phycomyces do not grow directly towards a horizontal beam of light, but equilibrate at an angle of about 30° above the horizontal. After describing several related observations, this paper suggests that the dioptric properties of an obliquely illuminated cylindrical lens, illustrated by a dummy cell, as well as a negative geotropic response, play major roles in determining the direction of growth. The shift of the equilibrium direction of growth towards the vertical, or a purely geotropic response, over a tenfold range of very low intensities (around 10^6 quanta/cm^2 sec., or 10^-13 watt/cm^2) has been studied, and an action spectrum made, measuring the quantum fluxes producing a standard intermediate equilibrium direction of growth at different wavelengths. This may differ from the action spectra at higher intensities in lacking conspicuous maxima from 370 to 490 mµ. However, in the ultraviolet it parallels the other spectra, although without showing the much higher quantum efficiency of ultraviolet relative to visible light previously noted. Possible interpretations are discussed

A local potential for the Weyl tensor in all dimensions

In all dimensions and arbitrary signature, we demonstrate the existence of a new local potential -- a double (2,3)-form -- for the Weyl curvature tensor, and more generally for all tensors with the symmetry properties of the Weyl curvature tensor. The classical four-dimensional Lanczos potential for a Weyl tensor -- a double (2,1)-form -- is proven to be a particular case of the new potential: its double dual.Comment: 7 pages; Late