Simplification and analysis of a model of social interaction in voting

A recently proposed model of social interaction in voting is investigated by simplifyingit down into a version that is more analytically tractable and which allows a mathematicalanalysis to be performed. This analysis clarifies the interplay of the different elementspresent in the system – social influence, heterogeneity and noise – and leads to a betterunderstanding of its properties. The origin of a regime of bistability is identified. Theinsight gained in this way gives further intuition into the behaviour of the originalmodel.     

Analogy between the Lorenz strange attractor and a bistable stochastic oscillator

The relation between the aperiodic solution of the Lorenz model and that of a stochastic anharmonic oscillator is explored. The stochastic oscillator is constructed by replacing (t) in the Lorenz model by a stochastic variable(t) of specified statistics. The resulting system is of course not isomorphic to the Lorenz model, but does share with it a number of statistical properties. Thus, within the confines of these measures the two systems are physically very similar.     

Extension of statistical replacement to systems with time-correlated fluctuations

Nonlinear systems with correlated stochastic parameters are approximated by simpler systems. This method is an extension of an earlier version of statistical replacement and statistical linearization. The extended method is applicable to systems with correlated fluctuations. We show how this general method reduces to the earlier methods in special cases.     

Modular invariance for interacting bosonic strings at finite temperature

We study the finite temperature string path integral introduced by Polchinski [1]. It is shown that on an arbitrary genus world sheet all windings of the fields around the compact time direction can be rotated into a single cycle. The modular invariance of this result is demonstrated.     

The measurement of solid–liquid interfacial energy in colloidal suspensions using grain boundary grooves

Interfacial energy is a fundamental physiochemical property of any multi-phase system. Among the most direct approaches for determining solid–liquid interfacial energy is a technique based on measuring the shape of grain boundary grooves in specimens subjected to a linear temperature gradient. This technique was adapted to crystallizing colloids in a gravitational field. Such colloids exhibit a freezing–melting phase transition and are important not only as self-assembling precursors to photonic crystals, but also as physical models of atomic and molecular systems. The grain boundary groove technique was tested using suspensions of sterically stabilized poly(methyl methacrylate) spheres, which have been shown to closely approximate the hard sphere potential. Whereas isotropic models did not fit grain boundary groove data well, the capillary vector model, which is suitable for both isotropic and anisotropic surface energies, produced γ₁₁₀?=?0.58?±?0.05 k _B T/σ². This value of interfacial energy is in agreement with many of the published values for hard spheres, supporting the validity of our grain boundary groove technique adaptations to colloidal systems in a gravitational field. Finally, kinks observed in groove profiles suggest a minimum anisotropy parameter of ε?=?0.029 for hard spheres.     

A beaker without walls: formation of deeply supercooled binary liquid solutions of alcohols from nanoscale amorphous solid films

Layered nanoscale amorphous solid films of methanol and ethanol undergo complete intermixing prior to the onset of measurable desorption at 120 K. This intermixing precedes and inhibits crystallization. Subsequent desorption of the film is described quantitatively by a kinetic model describing evaporation from a continuously mixed ideal binary liquid solution. This occurs at temperatures below the melting point of the binary mixture, indicating ideal behavior for the supercooled liquid solution. This approach provides a new method for preparing and examining deeply supercooled solutions.     

TEM Imaging of Mass-selected Polymer Molecules

Polyethylene glycol (PEG) molecules with masses below 1300amu are electrosprayed (ES) from solution, mobility-selected at high resolution in a differential mobility analyzer (DMA), collected on a grid and imaged by transmission electron microscopy (ES–DMA–TEM). The DMA resolves individual n-mers, and selects only one out of the many present in the original sample. Ion identity is established from parallel mass spectra (ES-MS). The images reveal spherical particles 1.46nm in diameter, in good agreement with the known ion mass and bulk density. The DMA-selection technique opens new paths for the study of very small particles.     

A numerical study of a rotationally degenerate hyperbolic system. Part I. The Riemann problem

We study numerically the Riemann problem for a 2 x 2 system of conservation laws with a cubic flux function, a particular case of the class of models introduced by Keyfitz and Kranzer. The system is not strictly hyperbolic, and the classical Lax theory for hyperbolic systems is not directly applicable. Correspondingly, some numerical schemes which are accurate for strictly hyperbolic systems are not well behaved for this example. When they do work, different schemes yield markedly different results for certain data. We explain this effect by observing that, near these data, viscous regularization is non-uniform as the viscosity tends to zero. This fact does not contradict the well-posedness of the hyperbolic model; it does imply that precise control of the viscosity introduced into a computational method is crucial for generating the correct numerical solutions. We examine all of these issues and comment on their implications for similar systems which arise in continuum mechanics.