The effects of demographic stochasticity on the long-term behaviour of endemic infectious diseases have been considered for long as a necessary addition to an underlying deterministic theory. The latter would explain the regular behaviour of recurrent epidemics and the former the superimposed noise of observed incidence patterns. Recently, a stochastic theory based on a mechanism of resonance with internal noise has shifted the role of stochasticity closer to the centre stage, by showing that the major dynamic patterns found in the incidence data can be explained as resonant fluctuations, whose behaviour is largely independent of the amplitude of seasonal forcing, and by contrast very sensitive to the basic epidemiological parameters. Here we elaborate on that approach, by adding an ingredient which is missing in standard epidemic models, the 'mixing network' through which infection may propagate. We find that spatial correlations have a major effect on the enhancement of the amplitude and the coherence of the resonant stochastic fluctuations, providing the ordered patterns of recurrent epidemics, whose period may differ significantly from that of the small oscillations around the deterministic equilibrium. We also show that the inclusion of a more realistic, timecorrelated recovery profile instead of exponentially distributed infectious periods may, even in the random-mixing limit, contribute to the same effect.

Abstract:We consider a simple model consisting of particles with four bonding sites ("patches"), two of type A and two of type B, on the square lattice, and investigate its global phase behavior by simulations and theory. We set the interaction between B patches to zero and calculate the phase diagram as the ratio between the AB and the AA interactions, epsilon(AB)*, varies. In line with previous work, on three-dimensional offlattice models, we show that the liquid-vapor phase diagram exhibits a re-entrant or "pinched" shape for the same range of epsilon(AB)*, suggesting that the ratio of the energy scales -and the corresponding empty fluid regime -is independent of the dimensionality of the system and of the lattice structure. In addition, the model exhibits an order-disorder transition that is ferromagnetic in the re-entrant regime. The use of low-dimensional lattice models allows the simulation of sufficiently large systems to establish the nature of the liquid-vapor critical points and to describe the structure of the liquid phase in the empty fluid regime, where the size of the "voids" increases as the temperature decreases. We have found that the liquid-vapor critical point is in the 2D Ising universality class, with a scaling region that decreases rapidly as the temperature decreases. The results of simulations and theoretical analysis suggest that the line of order-disorder transitions intersects the condensation line at a multi-critical point at zero temperature and density, for patchy particle models with a re-entrant, empty fluid, regime. (C)

In this paper, the affine connection approach [D. Baalss and S. Hess, Phys. Rev. Lett. 57, 86 (1986)] will be defined in terms of a local transformation. Accordingly, the macroscopic anisotropy of the nematic medium will be conceived as resulting from a local transformation where, at each point of the sample, the spherical molecules of an idealized hypothetic isotropic liquid have their shape changed to the ellipsoidal form of the nematic liquid crystals molecules. When such local character is imposed to this transformation, the patterns determined by the director configuration of the nematic medium acquire an intrinsic curvature whose correct treatment requires the replacement of the techniques and methods of the usual calculus by those of the differential geometry of nonflat surfaces. Such an approach will be used in the calculus of the nematic elastic constants. As a result, the dependence of the elastic constants on the scalar order parameter, on the eccentricity of the nematic molecules, and on the interaction between them will be determined and compared with the experimental data of the 4-methoxybenzylidene-4-n-butylaniline.

A comparative study of the temperature dependence of the elastic constants of the nematic liquid crystals known as PAA (p-azoxyanisole), MBBA 4'-methoxybenzylidene-4-n-butylaniline, and 5CB (4-n-pentyl-4'-cyanobiphenyl) will be made in this work. After a regularization of their values, and with use of a unique temperature scale, the experimental data of each of these parameters will be displayed along the lines of corresponding states that are not restricted to the neighborhoods of the nematic-isotropic phase transition point, as it would be the case in a usual corresponding states law, but encompass the entire nematic phase.

In this work a set of viscosity data selected from the nematic liquid crystals literature is compared with the currently accepted microscopic (molecular) theories for the nematic viscosity. It is shown that the kinetic theory of Doi [N. Kuzuu and M. Doi, J. Phys. Soc. of Jpn. 52, 3486 (1983)] and the affine transformation theory of Hess [D. Baalss and S. Hess, Phys. Rev. Lett. 57, 86 (1986)] equally predict that Miesowicz's coefficients of a given sample are not independent but, as it has been believed for many years [H. Kneppe, F. Scheneider, and N. K. Sharma, Ber. Bunsenges Phys. Chem. 85, 784 (1981)], they are connected by a linear relationship. Such conjecture gains a strong positive support when it is applied to a set of experimental data that we have collected. However, when these data are used to obtain the values of the parameters used to build these theories, it is found that the values assumed by them are in flagrant disagreement with the physical interpretation that they are supposed to have.