7,626 research outputs found
Classical Bianchi type I cosmology in K-essence theory
We use one of the simplest forms of the K-essence theory and we apply it to
the classical anisotropic Bianchi type I cosmological model, with a barotropic
perfect fluid modeling the usual matter content and with cosmological constant.
The classical solutions for any but the stiff fluid and without cosmological
constant are found in closed form, using a time transformation. We also present
the solution whith cosmological constant and some particular values of the
barotropic parameter. We present the possible isotropization of the
cosmological model, using the ratio between the anisotropic parameters and the
volume of the universe and show that this tend to a constant or to zero for
different cases. We include also a qualitative analysis of the analog of the
Friedmann equation.Comment: 15 pages with one figure, accepted in Advances in High Energy Physic
Optimal system size for complex dynamics in random neural networks near criticality
In this Letter, we consider a model of dynamical agents coupled through a
random connectivity matrix, as introduced in [Sompolinsky et. al, 1988] in the
context of random neural networks. It is known that increasing the disorder
parameter induces a phase transition leading to chaotic dynamics. We observe
and investigate here a novel phenomenon in the subcritical regime : the
probability of observing complex dynamics is maximal for an intermediate system
size when the disorder is close enough to criticality. We give a more general
explanation of this type of system size resonance in the framework of extreme
values theory for eigenvalues of random matrices.Comment: 11 pages, 2 figure
The inhomogeneous Suslov problem
We consider the Suslov problem of nonholonomic rigid body motion with
inhomogeneous constraints. We show that if the direction along which the Suslov
constraint is enforced is perpendicular to a principal axis of inertia of the
body, then the reduced equations are integrable and, in the generic case,
possess a smooth invariant measure. Interestingly, in this generic case, the
first integral that permits integration is transcendental and the density of
the invariant measure depends on the angular velocities. We also study the
Painlev\'e property of the solutions.Comment: 10 pages, 5 figure
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