Gravity in the Randall-Sundrum Brane World

We discuss the weak gravitational field created by isolated matter sources in the Randall-Sundrum brane-world. In the case of two branes of opposite tension, linearized Brans-Dicke (BD) gravity is recovered on either wall, with different BD parameters. On the wall with positive tension the BD parameter is larger than 3000 provided that the separation between walls is larger than 4 times the AdS radius. For the wall of negative tension, the BD parameter is always negative but greater than -3/2. In either case, shadow matter from the other wall gravitates upon us. For equal Newtonian mass, light deflection from shadow matter is 25 % weaker than from ordinary matter. Hence, the effective mass of a clustered object containing shadow dark matter would be underestimated if naively measured through its lensing effect. For the case of a single wall of positive tension, Einstein gravity is recovered on the wall to leading order, and if the source is stationary the field stays localized near the wall. We calculate the leading Kaluza-Klein corrections to the linearized gravitational field of a non-relativistic spherical object and find that the metric is different from the Schwarzschild solution at large distances. We believe that our linearized solution corresponds to the field far from the horizon after gravitational collapse of matter on the brane.Comment: 8 pages, 1 figure. Replaced with revised version to be published in Phys. Rev. Lett. Some comments adde

Canards from Chua's circuit

The aim of this work is to extend Beno\^it's theorem for the generic existence of "canards" solutions in singularly perturbed dynamical systems of dimension three with one fast variable to those of dimension four. Then, it is established that this result can be found according to the Flow Curvature Method. Applications to Chua's cubic model of dimension three and four enable to state the existence of "canards" solutions in such systems.Comment: arXiv admin note: text overlap with arXiv:1408.489

Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields

In the present study we consider planar piecewise linear vector fields with two zones separated by the straight line $x=0$. Our goal is to study the existence of simultaneous crossing and sliding limit cycles for such a class of vector fields. First, we provide a canonical form for these systems assuming that each linear system has center, a real one for $y<0$ and a virtual one for $y>0$, and such that the real center is a global center. Then, working with a first order piecewise linear perturbation we obtain piecewise linear differential systems with three crossing limit cycles. Second, we see that a sliding cycle can be detected after a second order piecewise linear perturbation. Finally, imposing the existence of a sliding limit cycle we prove that only one adittional crossing limit cycle can appear. Furthermore, we also characterize the stability of the higher amplitude limit cycle and of the infinity. The main techniques used in our proofs are the Melnikov method, the Extended Chebyshev systems with positive accuracy, and the Bendixson transformation.Comment: 24 pages, 7 figure

Reviews

Índex de l'Obra ressenyada: Alexandre JAUME I ROSSELLO, Complete works of Alexandre Jaume Rosselló. Palma: Lleonard Muntaner, 201

Melnikov analysis in nonsmooth differential systems with nonlinear switching manifold

We study the family of piecewise linear differential systems in the plane with two pieces separated by a cubic curve. Our main result is that 7 is a lower bound for the Hilbert number of this family. In order to get our main result, we develop the Melnikov functions for a class of nonsmooth differential systems, which generalizes, up to order 2, some previous results in the literature. Whereas the first order Melnikov function for the nonsmooth case remains the same as for the smooth one (i.e. the first order averaged function) the second order Melnikov function for the nonsmooth case is different from the smooth one (i.e. the second order averaged function). We show that, in this case, a new term depending on the jump of discontinuity and on the geometry of the switching manifold is added to the second order averaged function

Millennia of legal content criteria of lies and truths: wisdom or common-sense folly?

Long before experimental psychology, religious writers, orators, and playwrights described examples of lie detection based on the verbal content of statements. Legal scholars collected evidence from individual cases and systematized them as “rules of evidence”. Some of these resemble content cues used in contemporary research, while others point to working hypotheses worth exploring. To examine their potential validity, we re-analyzed data from a quasi-experimental study of 95 perjury cases. The outcomes support the fruitfulness of this approach. Travelling back in time searching for testable ideas about content cues to truth and deception may be worthwhile

El Derecho penal frente al terrorismo : cuestiones y perspectivas

Lliçó inaugural del curs 2005-2006

Address: The New York City Experience: Lessons For A National Future

In this address, former Mayor of New York Ed Koch discussed the successful efforts of his administration to create New York’s Campaign Finance Reform Act, a voluntary program imposing lower spending limits and detailed public disclosure requirements on candidates for the five New York City offices who chose to seek public financing. Speaking from the unique position as the first candidate to ever be fined under the Act, Mr. Koch illustrated the importance of the nonpartisan board created under the Act. He then recounted briefly the history of the program and discussed some of the specifics of the original Campaign Finance Reform Act and subsequent amendments. Mr. Koch then turned to the issue of soft money and federal reform, discussing the House’s Shays-Meehan bill and the Senate’s McCain-Feingold bill and articulating a belief that current regulations of soft money contribution limits could work, if amended to provide adjustments for inflation. Next, Mr. Koch advocated for public financing in elections and equal limits on corporate and labor union contributions. Finally, Mr. Koch listed specific reforms generally, and to New York City’s program specifically that he believed were necessary even if by amendment, such as eliminating the use of private wealth, application of contribution limits and disclosure requirements to all candidates (instead of just those seeking public financing) and restrictions on the campaign season’s time period. This transcript was taken at From the Ground Up: Local Lessons for National Reform, a national conference on campaign finance reform held on November 9, 1998, sponsored by the New York City Campaign Finance Board and the Association of the Bar of the City of New York