Effect of strong opinions on the dynamics of the majority-vote model

We study how the presence of individuals with strong opinions affects a square lattice majority-vote model with noise. In a square lattice network we perform Monte-Carlo simulations and replace regular actors σ with strong actors μ in a random distribution. We find that the value of the critical noise parameter q c is a decreasing function of the concentration r of strong actors in the social interaction network. We calculate the critical exponents β/ν, γ/ν, and 1/ν and find that the presence of strong actors does not change the Ising universality class of the isotropic majority-vote model.The authors acknowledge financial support from UPE (PFA2016, PIAEXT2016) and the funding agencies FACEPE (APQ-0565-1.05/14), CAPES and CNPq. The Boston University Center for Polymer Studies is supported by NSF Grants PHY-1505000, CMMI-1125290, and CHE-1213217, by DTRA Grant HDTRA1-14-1-0017, and by DOE Contract DE-AC07-05Id14517. (UPE (PFA, PIAEXT); APQ-0565-1.05/14 - FACEPE; CAPES; CNPq; PHY-1505000 - NSF; CMMI-1125290 - NSF; CHE-1213217 - NSF; HDTRA1-14-1-0017 - DTRA; DE-AC07-05Id14517 - DOE)Published versio

Büchwald-Hartwig reaction applied to synthesis of new luminescent liquid crystal triarylamines derived from isoxazoles

© 2015 Taylor & Francis Group, LLC. The present work describes the synthesis and characterization of novel series of triarylamines isoxazoles (TAA) addressed to the organic photovoltaic materials. Diarylisoxazoles were synthesized by sequential [3+2] 1,3-dipolar cycloaddition reaction between arylnitrile oxides and selected arylalkenes followed by MnO2-oxidation. Isoxazoles were coupled to diarylamines by Büchwald-Hartwig reaction to afford desired compounds 6a-k. Some TAA display liquid-crystalline behaviour and UV-Vis absorption and fluorescence emission were analysed for all samples of TAA 6a-k

Stability Analysis of a Hybrid Cellular Automaton Model of Cell Colony Growth

Cell colonies of bacteria, tumour cells and fungi, under nutrient limited growth conditions, exhibit complex branched growth patterns. In order to investigate this phenomenon we present a simple hybrid cellular automaton model of cell colony growth. In the model the growth of the colony is limited by a nutrient that is consumed by the cells and which inhibits cell division if it falls below a certain threshold. Using this model we have investigated how the nutrient consumption rate of the cells affects the growth dynamics of the colony. We found that for low consumption rates the colony takes on a Eden-like morphology, while for higher consumption rates the morphology of the colony is branched with a fractal geometry. These findings are in agreement with previous results, but the simplicity of the model presented here allows for a linear stability analysis of the system. By observing that the local growth of the colony is proportional to the flux of the nutrient we derive an approximate dispersion relation for the growth of the colony interface. This dispersion relation shows that the stability of the growth depends on how far the nutrient penetrates into the colony. For low nutrient consumption rates the penetration distance is large, which stabilises the growth, while for high consumption rates the penetration distance is small, which leads to unstable branched growth. When the penetration distance vanishes the dispersion relation is reduced to the one describing Laplacian growth without ultra-violet regularisation. The dispersion relation was verified by measuring how the average branch width depends on the consumption rate of the cells and shows good agreement between theory and simulations.Comment: 8 pages, 6 figure

Exact results of the limited penetrable horizontal visibility graph associated to random time series and its application

The limited penetrable horizontal visibility algorithm is a new time analysis tool and is a further development of the horizontal visibility algorithm. We present some exact results on the topological properties of the limited penetrable horizontal visibility graph associated with random series. We show that the random series maps on a limited penetrable horizontal visibility graph with exponential degree distribution $P(k)\sim exp[-\lambda (k-2\rho-2)], \lambda = ln[(2\rho+3)/(2\rho+2)],\rho=0,1,2,...,k=2\rho+2,2\rho+3,...$, independent of the probability distribution from which the series was generated. We deduce the exact expressions of the mean degree and the clustering coefficient and demonstrate the long distance visibility property. Numerical simulations confirm the accuracy of our theoretical results. We then examine several deterministic chaotic series (a logistic map, the H$\acute{e}$non map, the Lorentz system, and an energy price chaotic system) and a real crude oil price series to test our results. The empirical results show that the limited penetrable horizontal visibility algorithm is direct, has a low computational cost when discriminating chaos from uncorrelated randomness, and is able to measure the global evolution characteristics of the real time series.Comment: 23 pages, 12 figure

Stochastic Solution of a KPP-Type Nonlinear Fractional Differential Equation

Mathematics Subject Classification: 26A33, 76M35, 82B31A stochastic solution is constructed for a fractional generalization of the KPP (Kolmogorov, Petrovskii, Piskunov) equation. The solution uses a fractional generalization of the branching exponential process and propagation processes which are spectral integrals of Levy processes