Optimal shapes of compact strings

Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest packing fraction; only recently has it been proved that the answer for infinite systems is a face-centred-cubic lattice. This simply stated problem has had a profound impact in many areas, ranging from the crystallization and melting of atomic systems, to optimal packing of objects and subdivision of space. Here we study an analogous problem--that of determining the optimal shapes of closely packed compact strings. This problem is a mathematical idealization of situations commonly encountered in biology, chemistry and physics, involving the optimal structure of folded polymeric chains. We find that, in cases where boundary effects are not dominant, helices with a particular pitch-radius ratio are selected. Interestingly, the same geometry is observed in helices in naturally-occurring proteins.Comment: 8 pages, 3 composite ps figure

The liquid-glass-jamming transition in disordered ionic nanoemulsions

In quenched disordered out-of-equilibrium many-body colloidal systems, there are important distinctions between the glass transition, which is related to the onset of nonergodicity and loss of low-frequency relaxations caused by crowding, and the jamming transition, which is related to the dramatic increase in elasticity of the system caused by the deformation of constituent objects. For softer repulsive interaction potentials, these two transitions become increasingly smeared together, so measuring a clear distinction between where the glass ends and where jamming begins becomes very difficult or even impossible. Here, we investigate droplet dynamics in concentrated silicone oil-in-water nanoemulsions using light scattering. For zero or low NaCl electrolyte concentrations, interfacial repulsions are soft and longer in range, this transition sets in at lower concentrations, and the glass and the jamming regimes are smeared. However, at higher electrolyte concentrations the interactions are stiffer, and the characteristics of the glass-jamming transition resemble more closely the situation of disordered elastic spheres having sharp interfaces, so the glass and jamming regimes can be distinguished more clearly

Entry Mode Degree of Control, Firm Performance and Host Country Institutional Development: A Meta-Analysis

Among studies on performance outcomes of entry mode choices disagreement fueled by ambiguous research findings is apparent as regards whether the best per- formers are those firms that enter foreign countries with high or low entry mode degree of control. To solve this dilemma and test new hypotheses, the relationship between entry mode degree of control and firm performance is examined by meta- analyzing 133 studies (740,114 observations) covering entry mode choices from 1980 to 2010. We find that (a) overall high-control entry modes lead to higher per- formance, and (b) adopting high-control entry modes is particularly important for firms entering developing countries

Simulation and approximate formulae for the radial distribution functions of highly asymmetric hard sphere mixtures

The Henderson and Chan (HC) formulae for the contact values of the radial distribution functions (RDFs) of a highly asymmetric hard sphere mixture are reconsidered in light of a recent formula of Roth, Evans and Dietrich for the RDF of a pair of exceedingly large spheres at zero concentration in a solvent of small hard spheres. Two modifications of the HC formulae using this result give a large sphere-large sphere contact value that is considerably smaller than that of the original formulation. These new HC results are compared with the molecular dynamics simulations of Lue and Woodcock, for a diameter ratio of 1:10, supplemented by a few new results that are reported here. The new HC formulae are in much better agreement with the MD results than is the popular Boublik - Mansoori - Carnahan - Starling - Leland formula. Also, some simulation results for the RDFs as functions of separation are reported. © 2005 Taylor & Francis Group Ltd.link_to_subscribed_fulltex

Thermodynamics of gas-liquid criticality: Rigidity symmetry on gibbs density surface

The thermodynamic state function rigidity, defined simply as (dp/d rho)(T), where p is the pressure, rho is the density and T is the temperature, is the work required to reversibly increase the density of a fluid. Along any isotherm, rigidity (omega) decreases with density for a gas phase and increases with density for a liquid. Thermodynamics, therefore, can define a distinction between gas and liquid. For any one-phase system, rigidity is everywhere positive, in any two-phase region omega = 0. For temperatures above critical coexistence, the rigidity has a constant value in the mesophase that separates the percolation loci, which bound the limits of existence of liquid and gas phases in the supercritical region. The law of rectilinear diameters extends in the supercritical region as a defining line of the colloid-like inversion between gas-in-liquid and liquid-in-gas. Every equilibrium state of gas phase has a corresponding isothermal state on the liquid phase with the same rigidity. We illustrate this symmetry between gas and liquid empirically using literature rho(p, T) equations-of-state for some real fluids, notably carbon dioxide, water and steam, and argon. At the molecular level, the symmetry can be explained by a correspondence between statistical properties of available holes in a liquid and sites of molecular clusters in the gas with equivalent number density fluctuations for complementary states of gas and liquid