Vacancy at the Si(111) unreconstructed surface: Electron states and absence of the Jahn-Teller distortion

The electron states of a vacancy at the Si(111) surface are calculated by means of a tight-binding scheme. The results for a vacancy at the surface layer show one state of A_l symmetry below the surface dangling bond band, and another doubly degenerate state of E symmetry above it. The Fermi energy at an isolated vacancy remains fixed by the surface. This allows to derive two important consequences: i) The vacancy state is a neutral one as can be shown by integrating the local density of states up to the Fermi energy. ii) The electronic charge around the vacancy has got the whole surface point symmetry and therefore a Jahn-Teller effect is not induced.     

Re-entrant phase behavior for systems with competition between phase separation and self-assembly

In patchy particle systems where there is a competition between the self-assembly of finite clusters and liquid-vapor phase separation, re-entrant phase behavior can be observed, with the system passing from a monomeric vapor phase to a region of liquid-vapor phase coexistence and then to a vapor phase of clusters as the temperature is decreased at constant density. Here, we present a classical statistical mechanical approach to the determination of the complete phase diagram of such a system. We model the system as a van der Waals fluid, but one where the monomers can assemble into monodisperse clusters that have no attractive interactions with any of the other species. The resulting phase diagrams show a clear region of re-entrance. However, for the most physically reasonable parameter values of the model, this behavior is restricted to a certain range of density, with phase separation still persisting at high densities.     

A hybrid optimization technique coupling an evolutionary and a local search algorithm

Evolutionary algorithms are robust and powerful global optimization techniques for solving large-scale problems that have many local optima. However, they require high CPU times, and they are very poor in terms of convergence performance. On the other hand, local search algorithms can converge in a few iterations but lack a global perspective. The combination of global and local search procedures should offer the advantages of both optimization methods while offsetting their disadvantages. This paper proposes a new hybrid optimization technique that merges a genetic algorithm with a local search strategy based on the interior point method. The efficiency of this hybrid approach is demonstrated by solving a constrained multi-objective mathematical test-case.     

Orbits of rational n-sets of projective spaces under the action of the linear group

Let k=Fq be a finite field. We enumerate k-rational n-sets of (unordered) points in a projective space PN over k, and we compute the generating function for the numbers of PGLN+1(k)-orbits of these n-sets. For N=1,2 we obtain a formula for these numbers of orbits as a polynomial in q with integer coefficients.     

Enumeration in Convex Geometries and Associated Polytopal Subdivisions of Spheres

We construct CW spheres from the lattices that arise as the closed sets of a convex closure, the meet-distributive lattices. These spheres are nearly polytopal, in the sense that their barycentric subdivisions are simplicial polytopes. The complete information on the numbers of faces and chains of faces in these spheres can be obtained from the defining lattices in a manner analogous to the relation between arrangements of hyperplanes and their underlying geometric intersection lattices.     

Determination of initial rates for a general class of chemical reactions: A methodology

The initial rate of any general nth order (n not necessarily integer) chemical reaction can be accurately and easily computed from the slope of a chord joining two points on the progress curve. Expressions for calculating the intermediate concentration corresponding to this initial rate are provided. Examples of the technique applied to second- and third-order reactions as well as an example of a reaction with fractional order (n = 0.6) are given.     

Formation of individual protein channels in lipid bilayers suspended in nanopores

Free-standing lipid bilayers are formed in regularly arranged nanopores of 200, 400 and 800 nm in a 300 nm thin hydrophobic silicon nitride membrane separating two fluid compartments. The extraordinary stability of the lipid bilayers allows us to monitor channel formation of the model peptide melittin and α-hemolysin from Staphylococcus aureus using electrochemical impedance spectroscopy and chronoamperometry. We observed that melittin channel formation is voltage-dependent and transient, whereas transmembrane heptameric α-hemolysin channels in nano-BLMs persist for hours. The onset of α-hemolysin-mediated conduction depends on the applied protein concentration and strongly on the diameter of the nanopores. Heptameric channel formation from adsorbed α-hemolysin monomers needs more time in bilayers suspended in 200 nm pores compared to bilayers in pores of 400 and 800 nm diameters. Diffusion of sodium ions across α-hemolysin channels present in a sufficiently high number in the bilayers was quantitatively and specifically determined using ion selective electrodes. The results demonstrate that relatively small variations of nano-dimensions have a tremendous effect on observable dynamic biomolecular processes. Such nanopore chips are potentially useful as supports for stable lipid bilayers to establish functional assays of membrane proteins needed in basic research and drug discovery.     

Analysis of phase transitions by photothermal probe beam deflection

A recent photothermal technique has been used to study the smectic A-nematic and nematic-isotropic phase transitions in 4-n-octyl-4prime;-cyanobiphenyl and in binary mixtures of 4-n-octyl- and 4-n-octyloxy-4prime;-cyanobiphenyl. A numerical analysis shows that both amplitude and phase of the photothermal signal are sensitive to the change of certain thermal parameters for the sample.