28,167 research outputs found
Three dimensional Lifshitz black hole and the Korteweg-de Vries equation
We consider a solution of three dimensional New Massive Gravity with a
negative cosmological constant and use the AdS/CTF correspondence to inquire
about the equivalent two dimensional model at the boundary. We conclude that
there should be a close relation with the Korteweg-de Vries equation.Comment: 4 page
Discrete time piecewise affine models of genetic regulatory networks
We introduce simple models of genetic regulatory networks and we proceed to
the mathematical analysis of their dynamics. The models are discrete time
dynamical systems generated by piecewise affine contracting mappings whose
variables represent gene expression levels. When compared to other models of
regulatory networks, these models have an additional parameter which is
identified as quantifying interaction delays. In spite of their simplicity,
their dynamics presents a rich variety of behaviours. This phenomenology is not
limited to piecewise affine model but extends to smooth nonlinear discrete time
models of regulatory networks. In a first step, our analysis concerns general
properties of networks on arbitrary graphs (characterisation of the attractor,
symbolic dynamics, Lyapunov stability, structural stability, symmetries, etc).
In a second step, focus is made on simple circuits for which the attractor and
its changes with parameters are described. In the negative circuit of 2 genes,
a thorough study is presented which concern stable (quasi-)periodic
oscillations governed by rotations on the unit circle -- with a rotation number
depending continuously and monotonically on threshold parameters. These regular
oscillations exist in negative circuits with arbitrary number of genes where
they are most likely to be observed in genetic systems with non-negligible
delay effects.Comment: 34 page
Effect of particle polydispersity on the irreversible adsorption of fine particles on patterned substrates
We performed extensive Monte Carlo simulations of the irreversible adsorption
of polydispersed disks inside the cells of a patterned substrate. The model
captures relevant features of the irreversible adsorption of spherical
colloidal particles on patterned substrates. The pattern consists of (equal)
square cells, where adsorption can take place, centered at the vertices of a
square lattice. Two independent, dimensionless parameters are required to
control the geometry of the pattern, namely, the cell size and cell-cell
distance, measured in terms of the average particle diameter. However, to
describe the phase diagram, two additional dimensionless parameters, the
minimum and maximum particle radii are also required. We find that the
transition between any two adjacent regions of the phase diagram solely depends
on the largest and smallest particle sizes, but not on the shape of the
distribution function of the radii. We consider size dispersions up-to 20% of
the average radius using a physically motivated truncated Gaussian-size
distribution, and focus on the regime where adsorbing particles do not interact
with those previously adsorbed on neighboring cells to characterize the jammed
state structure. The study generalizes previous exact relations on monodisperse
particles to account for size dispersion. Due to the presence of the pattern,
the coverage shows a non-monotonic dependence on the cell size. The pattern
also affects the radius of adsorbed particles, where one observes preferential
adsorption of smaller radii particularly at high polydispersity.Comment: 9 pages, 5 figure
On Useful Conformal Tranformations In General Relativity
Local conformal transformations are known as a useful tool in various
applications of the gravitational theory, especially in cosmology. We describe
some new aspects of these transformations, in particular using them for
derivation of Einstein equations for the cosmological and Schwarzschild
metrics. Furthermore, the conformal transformation is applied for the
dimensional reduction of the Gauss-Bonnet topological invariant in to the
spaces of lower dimensions.Comment: 17 pages, LaTeX. The paper is intended mainly for pedagogical
purposes and represents a collection of exercises concerning local conformal
transformations and dimensional reduction. To be published in "Gravitation
and Cosmology
- …