17,575 research outputs found
No phase transition for Gaussian fields with bounded spins
Let a<b, \Omega=[a,b]^{\Z^d} and H be the (formal) Hamiltonian defined on
\Omega by
H(\eta) = \frac12 \sum_{x,y\in\Z^d} J(x-y) (\eta(x)-\eta(y))^2 where
J:\Z^d\to\R is any summable non-negative symmetric function (J(x)\ge 0 for all
x\in\Z^d, \sum_x J(x)<\infty and J(x)=J(-x)). We prove that there is a unique
Gibbs measure on \Omega associated to H. The result is a consequence of the
fact that the corresponding Gibbs sampler is attractive and has a unique
invariant measure.Comment: 7 page
Hall-MHD small-scale dynamos
Much of the progress in our understanding of dynamo mechanisms has been made
within the theoretical framework of magnetohydrodynamics (MHD). However, for
sufficiently diffuse media, the Hall effect eventually becomes non-negligible.
We present results from three dimensional simulations of the Hall-MHD equations
subjected to random non-helical forcing. We study the role of the Hall effect
in the dynamo efficiency for different values of the Hall parameter, using a
pseudospectral code to achieve exponentially fast convergence. We also study
energy transfer rates among spatial scales to determine the relative importance
of the various nonlinear effects in the dynamo process and in the energy
cascade. The Hall effect produces a reduction of the direct energy cascade at
scales larger than the Hall scale, and therefore leads to smaller energy
dissipation rates. Finally, we present results stemming from simulations at
large magnetic Prandtl numbers, which is the relevant regime in hot and diffuse
media such a the interstellar medium.Comment: 11 pages and 11 figure
Competition interfaces and second class particles
The one-dimensional nearest-neighbor totally asymmetric simple exclusion
process can be constructed in the same space as a last-passage percolation
model in Z^2. We show that the trajectory of a second class particle in the
exclusion process can be linearly mapped into the competition interface between
two growing clusters in the last-passage percolation model. Using technology
built up for geodesics in percolation, we show that the competition interface
converges almost surely to an asymptotic random direction. As a consequence we
get a new proof for the strong law of large numbers for the second class
particle in the rarefaction fan and describe the distribution of the asymptotic
angle of the competition interface.Comment: Published at http://dx.doi.org/10.1214/009117905000000080 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Stability Conditions for Coupled Autonomous Vehicles Formations
In this paper, we give necessary conditions for stability of coupled
autonomous vehicles in R. We focus on linear arrays with decentralized
vehicles, where each vehicle interacts with only a few of its neighbors. We
obtain explicit expressions for necessary conditions for stability in the cases
that a system consists of a periodic arrangement of two or three different
types of vehicles, i.e. configurations as follows: ...2-1-2-1 or
...3-2-1-3-2-1. Previous literature indicated that the (necessary) condition
for stability in the case of a single vehicle type (...1-1-1) held that the
first moment of certain coefficients of the interactions between vehicles has
to be zero. Here, we show that that does not generalize. Instead, the
(necessary) condition in the cases considered is that the first moment plus a
nonlinear correction term must be zero
Lyapunov-type Inequalities for Partial Differential Equations
In this work we present a Lyapunov inequality for linear and quasilinear
elliptic differential operators in dimensional domains . We also
consider singular and degenerate elliptic problems with coefficients
involving the Laplace operator with zero Dirichlet boundary condition.
As an application of the inequalities obtained, we derive lower bounds for
the first eigenvalue of the Laplacian, and compare them with the usual ones
in the literature
Upgrading investment regulations in second pillar pension systems : a proposal for Colombia
The passivity of the demand for pension products is one of the striking features of mandatory pension systems. Consequently, the provision of multiple investment alternatives to households (multifund schemes) does not ensure that contributions are invested efficiently. In addition, despite the theoretical findings that short term return maximization is not conductive to long-term return maximization, the regulatory framework of pension fund management companies puts excessive emphasis on short-term maximization. Therefore, it is not obvious that typical regulatory framework of pension funds is conductive to optimal pensions. By establishing a set of default options on investment portfolios, this paper proposes a mechanism to align the incentives of the pension fund management companies with the long-term objectives of the contributors. The paper provides a methodology, which is subsequently applied to Colombia.Debt Markets,Emerging Markets,Financial Literacy,Mutual Funds,Investment and Investment Climate
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