Inertial and dimensional effects on the instability of a thin film

We consider here the effects of inertia on the instability of a flat liquid film under the effects of capillary and intermolecular forces (van der Waals interaction). Firstly, we perform the linear stability analysis within the long wave approximation, which shows that the inclusion of inertia does not produce new regions of instability other than the one previously known from the usual lubrication case. The wavelength, $\lambda_m$, corresponding to he maximum growth, $\omega_m$, and the critical (marginal) wavelength do not change at all. The most affected feature of the instability under an increase of the Laplace number is the noticeable decrease of the growth rates of the unstable modes. In order to put in evidence the effects of the bidimensional aspects of the flow (neglected in the long wave approximation), we also calculate the dispersion relation of the instability from the linearized version of the complete Navier-Stokes (N-S) equation. Unlike the long wave approximation, the bidimensional model shows that $\lambda_m$ can vary significantly with inertia when the aspect ratio of the film is not sufficiently small. We also perform numerical simulations of the nonlinear N-S equations and analyze to which extent the linear predictions can be applied depending on both the amount of inertia involved and the aspect ratio of the film

A model for cross-cultural reciprocal interactions through mass media

We investigate the problem of cross-cultural interactions through mass media in a model where two populations of social agents, each with its own internal dynamics, get information about each other through reciprocal global interactions. As the agent dynamics, we employ Axelrod's model for social influence. The global interaction fields correspond to the statistical mode of the states of the agents and represent mass media messages on the cultural trend originating in each population. Several phases are found in the collective behavior of either population depending on parameter values: two homogeneous phases, one having the state of the global field acting on that population, and the other consisting of a state different from that reached by the applied global field; and a disordered phase. In addition, the system displays nontrivial effects: (i) the emergence of a largest minority group of appreciable size sharing a state different from that of the applied global field; (ii) the appearance of localized ordered states for some values of parameters when the entire system is observed, consisting of one population in a homogeneous state and the other in a disordered state. This last situation can be considered as a social analogue to a chimera state arising in globally coupled populations of oscillators.Comment: 8 pages and 7 figure

On algebraic classification of quasi-exactly solvable matrix models

We suggest a generalization of the Lie algebraic approach for constructing quasi-exactly solvable one-dimensional Schroedinger equations which is due to Shifman and Turbiner in order to include into consideration matrix models. This generalization is based on representations of Lie algebras by first-order matrix differential operators. We have classified inequivalent representations of the Lie algebras of the dimension up to three by first-order matrix differential operators in one variable. Next we describe invariant finite-dimensional subspaces of the representation spaces of the one-, two-dimensional Lie algebras and of the algebra sl(2,R). These results enable constructing multi-parameter families of first- and second-order quasi-exactly solvable models. In particular, we have obtained two classes of quasi-exactly solvable matrix Schroedinger equations.Comment: LaTeX-file, 16 pages, submitted to J.Phys.A: Math.Ge

Suspensions Thermal Noise in the LIGO Gravitational Wave Detector

We present a calculation of the maximum sensitivity achievable by the LIGO Gravitational wave detector in construction, due to limiting thermal noise of its suspensions. We present a method to calculate thermal noise that allows the prediction of the suspension thermal noise in all its 6 degrees of freedom, from the energy dissipation due to the elasticity of the suspension wires. We show how this approach encompasses and explains previous ways to approximate the thermal noise limit in gravitational waver detectors. We show how this approach can be extended to more complicated suspensions to be used in future LIGO detectors.Comment: 28 pages, 13 figure

Noise suppression due to long-range Coulomb interaction: Crossover between diffusive and ballistic transport regimes

We present a Monte Carlo analysis of shot-noise suppression due to long-range Coulomb interaction in semiconductor samples under a crossover between diffusive and ballistic transport regimes. By varying the mean time between collisions we find that the strong suppression observed under the ballistic regime persists under quasi-ballistic conditions, before being washed out when a complete diffusive regime is reached.Comment: RevTex, 3 pages, 4 figures, minor correction