37,068 research outputs found
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, , corresponding to he maximum
growth, , 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 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
Shot-noise anomalies in nondegenerate elastic diffusive conductors
We present a theoretical investigation of shot-noise properties in
nondegenerate elastic diffusive conductors. Both Monte Carlo simulations and
analytical approaches are used. Two new phenomena are found: (i) the display of
enhanced shot noise for given energy dependences of the scattering time, and
(ii) the recovery of full shot noise for asymptotic high applied bias. The
first phenomenon is associated with the onset of negative differential
conductivity in energy space that drives the system towards a dynamical
electrical instability in excellent agreement with analytical predictions. The
enhancement is found to be strongly amplified when the dimensionality in
momentum space is lowered from 3 to 2 dimensions. The second phenomenon is due
to the suppression of the effects of long range Coulomb correlations that takes
place when the transit time becomes the shortest time scale in the system, and
is common to both elastic and inelastic nondegenerate diffusive conductors.
These phenomena shed new light in the understanding of the anomalous behavior
of shot noise in mesoscopic conductors, which is a signature of correlations
among different current pulses.Comment: 9 pages, 6 figures. Final version to appear in Phys. Rev.
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
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