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 (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

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

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

Density Functional Theory of a Curved Liquid-Vapour Interface: Evaluation of the rigidity constants

It is argued that to arrive at a quantitative description of the surface tension of a liquid drop as a function of its inverse radius, it is necessary to include the bending rigidity k and Gaussian rigidity k_bar in its description. New formulas for k and k_bar in the context of density functional theory with a non-local, integral expression for the interaction between molecules are presented. These expressions are used to investigate the influence of the choice of Gibbs dividing surface and it is shown that for a one-component system, the equimolar surface has a special status in the sense that both k and k_bar are then the least sensitive to a change in the location of the dividing surface. Furthermore, the equimolar value for k corresponds to its maximum value and the equimolar value for k_bar corresponds to its minimum value. An explicit evaluation using a short-ranged interaction potential between molecules, shows that k is negative with a value around minus 0.5-1.0 kT and that k_bar is positive with a value which is a bit more than half the magnitude of k. Finally, for dispersion forces between molecules, we show that a term proportional to log(R)/R^2 replaces the rigidity constants and we determine the (universal) proportionality constants.Comment: 28 pages; 5 figures; accepted for publication in J. Phys.: Condens. Matter (2013

Testing the impact of diagenesis on the delta O-18 and delta C-13 of benthic foraminiferal calcite from a sediment burial depth transect in the equatorial Pacific

Stable oxygen and carbon isotope (δ18O and δ13C) values measured in foraminiferal calcite are one of the primary tools used in paleoceanography. Diagenetic recrystallisation of foraminiferal calcite can act to reset primary isotopic values but its effects are typically poorly quantified. Here we test the impact of early stage diagenesis on stable isotope records generated from a suite of drill sites in the equatorial Pacific Ocean recovered during Ocean Drilling Program (ODP) Leg 199 and Integrated Ocean Drilling Program (IODP) Expedition 320. Our selected sites form paleowater- and burial-depth transects, with excellent stratigraphic control allowing us to confidently correlate our records. We observe large inter-site differences in the preservation state of benthic foraminiferal calcite, implying very different recrystallisation histories, but negligible inter-site offsets in benthic δ18O and δ13C values. We infer that diagenetic alteration of benthic foraminiferal calcite (in sedimentary oozes) must predominantly occur at shallow burial depths (<100 m) where offsets in both the temperature and isotopic composition of waters in which the foraminifera calcified and pore-waters in which diagenesis occurs are small. Our results suggest that even extensive recrystallisation of benthic foraminiferal calcite results in minimal shifts from primary δ18O and δ13C values. This finding supports the long-held suspicion that diagenetic alteration of foraminiferal calcite is less problematic in benthic than in planktic foraminifera and that in deep–sea sediments routinely employed for palaeoceanographic studies benthic foraminifera are robust recorders of stable isotope values in the fossil record

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

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