Negations and contrapositions of complete lattices

AbstractWe introduce the negation CL of a complete lattice L as the concept lattice of the complementary context (TL, ML, ≰), formed by the join-irreducible elements as objects and the meet-irreducible elements as attributes. We show that the double negation CCL is always order-embeddable in L, and that for finite lattices, the sequence (CnL)nϵω runs into a ‘flip-flop’ (i.e., CnL ⋍ Cn + 2 L for some n). Using vertical sums, we provide constructions of lattices which are isomorphic or dually isomorphic to their own negation. The only finite distributive examples among such ‘self-negative’ or ‘self-contrapositive’ lattices are vertical sums of four-element Boolean lattices. Explicitly, we determine all self-negative and all self-contrapositive lattices with less than 11 points

Coulometry and Calorimetry of Electric Double Layer Formation in Porous Electrodes

Coulometric measurements on salt-water-immersed nanoporous carbon electrodes reveal, at a fixed voltage, a charge decrease with increasing temperature. During far-out-of-equilibrium charging of these electrodes, calorimetry indicates the production of both irreversible Joule heat and reversible heat, the latter being associated with entropy changes during electric double layer (EDL) formation in the nanopores. These measurements grant experimental access --for the first time-- to the entropic contribution of the grand potential; for our electrodes, this amounts to roughly 25% of the total grand potential energy cost of EDL formation at large applied potentials, in contrast with point-charge model calculations that predict 100%. The coulometric and calorimetric experiments show a consistent picture of the role of heat and temperature in EDL formation and provide hitherto unused information to test against EDL models.Comment: 11 pages, 10 figure

A Proof of Tarski’s Fixed Point Theorem by Application of Galois Connections

Two examples of Galois connections and their dual forms are considered. One of them is applied to formulate a criterion when a given subset of a complete lattice forms a complete lattice. The second, closely related to the first, is used to prove in a short way the Knaster-Tarski’s fixed point theore

Coupling of Josephson flux-flow oscillators to an external RC load

We investigate by numerical simulations the behavior of the power dissipated in a resistive load capacitively coupled to a Josephson flux flow oscillator and compare the results to those obtained for a d.c. coupled purely resistive load. Assuming realistic values for the parameters R and C, both in the high- and in the low-Tc case the power is large enough to allow the operation of such a device in applications.Comment: uuencoded, gzipped tar archive containing 11 pages of REVTeX text + 4 PostScript figures. To appear in Supercond. Sci. Techno

Experimental observation of second-harmonic generation and diffusion inside random media

We have experimentally measured the distribution of the second-harmonic intensity that is generated inside a highly-scattering slab of porous gallium phosphide. Two complementary techniques for determining the distribution are used. First, the spatial distribution of second-harmonic light intensity at the side of a cleaved slab has been recorded. Second, the total second-harmonic radiation at each side of the slab has been measured for several samples at various wavelengths. By combining these measurements with a diffusion model for second-harmonic generation that incorporates extrapolated boundary conditions, we present a consistent picture of the distribution of the second-harmonic intensity inside the slab. We find that the ratio $\ell_{2\omega}/L_c$ of the mean free path at the second-harmonic frequency to the coherence length, which was suggested by some earlier calculations, cannot describe the second-harmonic yield in our samples. For describing the total second-harmonic yield, our experiments show that the scattering parameter at the fundamental frequency \k_{1\omega}\ell_{1\omega} is the most relevant parameter in our type of samples.Comment: 10 pages, 7 figure

Resonant flux motion and I-V -characteristics in frustrated Josephson junctions

We describe the dynamics of fluxons moving in a frustrated Josephson junction with p, d, and f-wave symmetry and calculate the I-V characteristics. The behavior of fluxons is quite distinct in the long and short length junction limit. For long junctions the intrinsic flux is bound at the center and the moving integer fluxon or antifluxon interacts with it only when it approaches the junction's center. For small junctions the intrinsic flux can move as a bunched type fluxon introducing additional steps in the I-V characteristics. Possible realization in quantum computation is presented.Comment: 21 pages, 8 figure

Rough Sets Determined by Quasiorders

In this paper, the ordered set of rough sets determined by a quasiorder relation $R$ is investigated. We prove that this ordered set is a complete, completely distributive lattice. We show that on this lattice can be defined three different kinds of complementation operations, and we describe its completely join-irreducible elements. We also characterize the case in which this lattice is a Stone lattice. Our results generalize some results of J. Pomykala and J. A. Pomykala (1988) and M. Gehrke and E. Walker (1992) in case $R$ is an equivalence.Comment: 18 pages, major revisio

Decreased Interfacial Tension of Demixed Aqueous Polymer Solutions due to Charge

Electric charge at the water-water interface of demixed solutions of neutral polymer and polyelectrolyte decreases the already ultralow interfacial tension. This is demonstrated in experiments on aqueous mixtures of dextran (neutral) and nongelling fish gelatin (charged). Upon phase separation, electric charge and a potential difference develop spontaneously at the interface, decreasing the interfacial tension purely electrostatically in a way that can be accounted for quantitatively by Poisson-Boltzmann theory. Interfacial tension is a key property when it comes to manipulating the water-water interface, for instance to create novel water-in-water emulsions.Supramolecular & Biomaterials Chemistr

Hydrodynamic interactions in colloidal ferrofluids: A lattice Boltzmann study

We use lattice Boltzmann simulations, in conjunction with Ewald summation methods, to investigate the role of hydrodynamic interactions in colloidal suspensions of dipolar particles, such as ferrofluids. Our work addresses volume fractions $\phi$ of up to 0.20 and dimensionless dipolar interaction parameters $\lambda$ of up to 8. We compare quantitatively with Brownian dynamics simulations, in which many-body hydrodynamic interactions are absent. Monte Carlo data are also used to check the accuracy of static properties measured with the lattice Boltzmann technique. At equilibrium, hydrodynamic interactions slow down both the long-time and the short-time decays of the intermediate scattering function $S(q,t)$, for wavevectors close to the peak of the static structure factor $S(q)$, by a factor of roughly two. The long-time slowing is diminished at high interaction strengths whereas the short-time slowing (quantified via the hydrodynamic factor $H(q)$) is less affected by the dipolar interactions, despite their strong effect on the pair distribution function arising from cluster formation. Cluster formation is also studied in transient data following a quench from $\lambda = 0$; hydrodynamic interactions slow the formation rate, again by a factor of roughly two