Extended order parameter and conjugate field for the dynamic phase transition in a Ginzburg-Landau mean-field model in an oscillating field.

We present numerical evidence for an extended order parameter and conjugate field for the dynamic phase transition in a Ginzburg-Landau mean-field model driven by an oscillating field. The order parameter, previously taken to be the time-averaged magnetization, comprises the deviations of the Fourier components of the magnetization from their values at the critical period. The conjugate field, previously taken to be the time-averaged magnetic field, comprises the even Fourier components of the field. The scaling exponents ß and δ associated with the extended order parameter and conjugate field are shown numerically to be consistent with their values in the equilibrium mean-field model.

Random phenotypic variation of yeast (Saccharomyces cerevisiae) single-gene knockouts fits a double pareto-lognormal distribution.

BACKGROUND: Distributed robustness is thought to influence the buffering of random phenotypic variation through the scale-free topology of gene regulatory, metabolic, and protein-protein interaction networks. If this hypothesis is true, then the phenotypic response to the perturbation of particular nodes in such a network should be proportional to the number of links those nodes make with neighboring nodes. This suggests a probability distribution approximating an inverse power-law of random phenotypic variation. Zero phenotypic variation, however, is impossible, because random molecular and cellular processes are essential to normal development. Consequently, a more realistic distribution should have a y-intercept close to zero in the lower tail, a mode greater than zero, and a long (fat) upper tail. The double Pareto-lognormal (DPLN) distribution is an ideal candidate distribution. It consists of a mixture of a lognormal body and upper and lower power-law tails. OBJECTIVE AND METHODS: If our assumptions are true, the DPLN distribution should provide a better fit to random phenotypic variation in a large series of single-gene knockout lines than other skewed or symmetrical distributions. We fit a large published data set of single-gene knockout lines in Saccharomyces cerevisiae to seven different probability distributions: DPLN, right Pareto-lognormal (RPLN), left Pareto-lognormal (LPLN), normal, lognormal, exponential, and Pareto. The best model was judged by the Akaike Information Criterion (AIC). RESULTS: Phenotypic variation among gene knockouts in S. cerevisiae fits a double Pareto-lognormal (DPLN) distribution better than any of the alternative distributions, including the right Pareto-lognormal and lognormal distributions. CONCLUSIONS AND SIGNIFICANCE: A DPLN distribution is consistent with the hypothesis that developmental stability is mediated, in part, by distributed robustness, the resilience of gene regulatory, metabolic, and protein-protein interaction networks. Alternatively, multiplicative cell growth, and the mixing of lognormal distributions having different variances, may generate a DPLN distribution.

Computational model for the formation of uniform silver spheres by aggregation of nanosize precursors.

We present results of computational modeling of the formation of uniform spherical silver particles prepared by rapid mixing of ascorbic acid and silver-amine complex solutions in the absence of a dispersing agent. Using an accelerated integration scheme to speed up the calculation of particle size distributions in the latter stages, we find that the recently reported experimental results-some of which are summarized here-can be modeled effectively by the two-stage formation mechanism used previously to model the preparation of uniform gold spheres. We treat both the equilibrium concentration of silver atoms and the surface tension of silver precursor nanocrystals as free parameters, and find that the experimental reaction time scale is fit by a narrow region of this two-parameter space. The kinetic parameter required to quantitatively match the final particle size is found to be very close to that used previously in modeling the formation of gold particles, suggesting that similar kinetics governs the aggregation process and providing evidence that the two-stage model of burst nucleation of nanocrystalline precursors followed by their aggregation to form the final colloids can be applied to systems both with and without dispersing agents. The model also reproduced semiquantitatively the effects of solvent viscosity and temperature on the particle preparation.

Model of nanocrystal formation in solution by burst nucleation and diffusional growth.

The phenomenon of burst nucleation in solution, in which a period of apparent chemical inactivity is followed by a sudden and explosive growth of nucleated particles from a solute species, has been given a widely accepted qualitative explanation by LaMer and co-workers. Here, we present a model with the assumptions of instantaneous re-thermalization below the critical nucleus size and irreversible diffusive growth above the critical size, which for the first time formulates LaMer's explanation of burst nucleation in a manner allowing quantitative calculations. The behavior of the model at large times, t, is derived with the result that the average cluster size, as measured by the number of atoms, grows approximately t, while the width of the cluster distribution grows approximately (sq root)1. We develop an effective numerical scheme to integrate the equations of the model and compare the asymptotic expressions to results from numerical simulation. Finally, we discuss the physical effects which cause real nucleation processes in solution to deviate from the behavior of the model.

Simulation of hysteresis in magnetic nanoparticles with Nosé thermostating.

The magnetic hysteresis of a two-dimensional lattice of rotors with four-way anisotropy interaction and a Heisenberg exchange interaction is studied. The Hamiltonian dynamics of the lattice is thermostated using the Nosé thermostat, resulting in a system that approaches thermal equilibrium and which under certain conditions can remain in metastable states. Using physically realistic values for the interactions in a nanoparticle of monolayer thickness, we locate the Curie temperature of our lattice by determining the peak of the heat capacity curve. We then compare the coercive field of our two-dimensional lattice below this Curie temperature to the coercive field of an elliptical cobalt nanoparticle measured in experiment. We find an order of magnitude agreement between our lattice model and the experimental results, even though the value of the anisotropy used is more appropriate for a monolayer film than for the nanoparticle.