Healthiness from Duality

Healthiness is a good old question in program logics that dates back to Dijkstra. It asks for an intrinsic characterization of those predicate transformers which arise as the (backward) interpretation of a certain class of programs. There are several results known for healthiness conditions: for deterministic programs, nondeterministic ones, probabilistic ones, etc. Building upon our previous works on so-called state-and-effect triangles, we contribute a unified categorical framework for investigating healthiness conditions. We find the framework to be centered around a dual adjunction induced by a dualizing object, together with our notion of relative Eilenberg-Moore algebra playing fundamental roles too. The latter notion seems interesting in its own right in the context of monads, Lawvere theories and enriched categories.Comment: 13 pages, Extended version with appendices of a paper accepted to LICS 201

Fluids of platelike particles near a hard wall

Fluids consisting of hard platelike particles near a hard wall are investigated using density functional theory. The density and orientational profiles as well as the surface tension and the excess coverage are determined and compared with those of a fluid of rodlike particles. Even for low densities slight orientational packing effects are found for the platelet fluid due to larger intermolecular interactions between platelets as compared with those between rods. A net depletion of platelets near the wall is exhibited by the excess coverage, whereas a change of sign of the excess coverage of hard-rod fluids is found upon increasing the bulk density.Comment: 6 pages, 9 figure

Theory of asymmetric non-additive binary hard-sphere mixtures

We show that the formal procedure of integrating out the degrees of freedom of the small spheres in a binary hard-sphere mixture works equally well for non-additive as it does for additive mixtures. For highly asymmetric mixtures (small size ratios) the resulting effective Hamiltonian of the one-component fluid of big spheres, which consists of an infinite number of many-body interactions, should be accurately approximated by truncating after the term describing the effective pair interaction. Using a density functional treatment developed originally for additive hard-sphere mixtures we determine the zero, one, and two-body contribution to the effective Hamiltonian. We demonstrate that even small degrees of positive or negative non-additivity have significant effect on the shape of the depletion potential. The second virial coefficient $B_2$, corresponding to the effective pair interaction between two big spheres, is found to be a sensitive measure of the effects of non-additivity. The variation of $B_2$ with the density of the small spheres shows significantly different behavior for additive, slightly positive and slightly negative non-additive mixtures. We discuss the possible repercussions of these results for the phase behavior of binary hard-sphere mixtures and suggest that measurements of $B_2$ might provide a means of determining the degree of non-additivity in real colloidal mixtures

On the Detectability of the Hydrogen 3-cm Fine Structure Line from the EoR

A soft ultraviolet radiation field, 10.2 eV < E <13.6 eV, that permeates neutral intergalactic gas during the Epoch of Reionization (EoR) excites the 2p (directly) and 2s (indirectly) states of atomic hydrogen. Because the 2s state is metastable, the lifetime of atoms in this level is relatively long, which may cause the 2s state to be overpopulated relative to the 2p state. It has recently been proposed that for this reason, neutral intergalactic atomic hydrogen gas may be detected in absorption in its 3-cm fine-structure line (2s_1/2 -> 2p_3/2) against the Cosmic Microwave Background out to very high redshifts. In particular, the optical depth in the fine-structure line through neutral intergalactic gas surrounding bright quasars during the EoR may reach tau~1e-5. The resulting surface brightness temperature of tens of micro K (in absorption) may be detectable with existing radio telescopes. Motivated by this exciting proposal, we perform a detailed analysis of the transfer of Lyman beta,gamma,delta,... radiation, and re-analyze the detectability of the fine-structure line in neutral intergalactic gas surrounding high-redshift quasars. We find that proper radiative transfer modeling causes the fine-structure absorption signature to be reduced tremendously to tau< 1e-10. We therefore conclude that neutral intergalactic gas during the EoR cannot reveal its presence in the 3-cm fine-structure line to existing radio telescopes.Comment: 7 pages, 4 figures, MNRAS in press; v2. some typos fixe

Purification, crystallization and preliminary X-ray crystallographic analysis of 3-ketosteroid Delta(1) -dehydrogenase from Rhodococcus erythropolis SQ1

3-Ketosteroid Delta(1)-dehydrogenase plays a crucial role in the early steps of steroid degradation by introducing a double bond between the C1 and C2 atoms of the A-ring of its 3-ketosteroid substrates. The 3-ketosteroid Delta(1)-dehydrogenase from Rhodococcus erythropolis SQ1, a 56 kDa flavoprotein, was crystallized using the sitting-drop vapour-diffusion method at room temperature. The crystals grew in various buffers over a wide pH range (from pH 5.5 to 10.5), but the best crystallization condition consisted of 2%(nu/nu) PEG 400, 0.1 M HEPES pH 7.5, 2.0 M ammonium sulfate. A native crystal diffracted X-rays to 2.0 angstrom resolution. It belonged to the primitive orthorhombic space group P2(1)2(1)2(1), with unit-cell parameters a = 107.4, b = 131.6, c = 363.2 angstrom, and contained eight molecules in the asymmetric unit. The initial structure of the enzyme was solved using multi-wavelength anomalous dispersion (MAD) data collected from a Pt-derivatized crystal

Phase behavior of hard spheres confined between parallel hard plates: Manipulation of colloidal crystal structures by confinement

We study the phase behavior of hard spheres confined between two parallel hard plates using extensive computer simulations. We determine the full equilibrium phase diagram for arbitrary densities and plate separations from one to five hard-sphere diameters using free energy calculations. We find a first-order fluid-solid transition, which corresponds to either capillary freezing or melting depending on the plate separation. The coexisting solid phase consists of crystalline layers with either triangular or square symmetry. Increasing the plate separation, we find a sequence of crystal structures from n triangular to (n+1) square to (n+1) triangular, where n is the number of crystal layers, in agreement with experiments on colloids. At high densities, the transition between square to triangular phases are intervened by intermediate structures, e.g., prism, buckled, and rhombic phases.Comment: 9 pages, 4 figures. Accepted for publication in J. Phys.: Condens. Matte

Phase behaviour of charged colloidal sphere dispersions with added polymer chains

We study the stability of mixtures of highly screened repulsive charged spheres and non-adsorbing ideal polymer chains in a common solvent using free volume theory. The effective interaction between charged colloids in an aqueous salt solution is described by a screened-Coulomb pair potential, which supplements the pure hard-sphere interaction. The ideal polymer chains are treated as spheres that are excluded from the colloids by a hard-core interaction, whereas the interaction between two ideal chains is set to zero. In addition, we investigate the phase behaviour of charged colloid-polymer mixtures in computer simulations, using the two-body (Asakura-Oosawa pair potential) approximation to the effective one-component Hamiltonian of the charged colloids. Both our results obtained from simulations and from free volume theory show similar trends. We find that the screened-Coulomb repulsion counteracts the effect of the effective polymer-mediated attraction. For mixtures of small polymers and relatively large charged colloidal spheres, the fluid-crystal transition shifts to significantly larger polymer concentrations with increasing range of the screened-Coulomb repulsion. For relatively large polymers, the effect of the screened-Coulomb repulsion is weaker. The resulting fluid-fluid binodal is only slightly shifted towards larger polymer concentrations upon increasing the range of the screened-Coulomb repulsion. In conclusion, our results show that the miscibility of dispersions containing charged colloids and neutral non-adsorbing polymers increases, upon increasing the range of the screened-Coulomb repulsion, or upon lowering the salt concentration, especially when the polymers are small compared to the colloids.Comment: 25 pages,13 figures, accepted for publication on J.Phys.:Condens. Matte

Sedimentation of binary mixtures of like- and oppositely charged colloids: the primitive model or effective pair potentials?

We study sedimentation equilibrium of low-salt suspensions of binary mixtures of charged colloids, both by Monte Carlo simulations of an effective colloids-only system and by Poisson-Boltzmann theory of a colloid-ion mixture. We show that the theoretically predicted lifting and layering effect, which involves the entropy of the screening ions and a spontaneous macroscopic electric field [J. Zwanikken and R. van Roij, Europhys. Lett. {\bf 71}, 480 (2005)], can also be understood on the basis of an effective colloid-only system with pairwise screened-Coulomb interactions. We consider, by theory and by simulation, both repelling like-charged colloids and attracting oppositely charged colloids, and we find a re-entrant lifting and layering phenomenon when the charge ratio of the colloids varies from large positive through zero to large negative values