Precision measurements in nuclear {\beta}-decay with LPCTrap

The experimental achievements and the current program with the LPCTrap device installed at the LIRAT beam line of the SPIRAL1-GANIL facility are presented. The device is dedicated to the study of the weak interaction at low energy by means of precise measurements of the {\beta}-{\nu} angular correlation parameter. Technical aspects as well as the main results are reviewed. The future program with new available beams is briefly discussed.Comment: Annalen der Physik (2013

On quasi-local charges and Newman--Penrose type quantities in Yang--Mills theories

We generalize the notion of quasi-local charges, introduced by P. Tod for Yang--Mills fields with unitary groups, to non-Abelian gauge theories with arbitrary gauge group, and calculate its small sphere and large sphere limits both at spatial and null infinity. We show that for semisimple gauge groups no reasonable definition yield conserved total charges and Newman--Penrose (NP) type quantities at null infinity in generic, radiative configurations. The conditions of their conservation, both in terms of the field configurations and the structure of the gauge group, are clarified. We also calculate the NP quantities for stationary, asymptotic solutions of the field equations with vanishing magnetic charges, and illustrate these by explicit solutions with various gauge groups.Comment: 22 pages, typos corrected, appearing in Classical and Quantum Gravit

On the existence and the number of limit cycles in evolutionary games

In this paper it is shown that an extended evolutionary system proposed by Hofbauer and Sigmund (1998) may be transformed into a Kukles system. Then a Dulac-Cherkas function related to the Kukles system is derived, which allows us to determine the number of limit cycles or its non-existence.limit cycles, evolutionary game theory, Kukles system, Dulac-Cherkas function

Simultaneous Bifurcation of Limit Cycles and Critical Periods

Altres ajuts: Acord transformatiu CRUE-CSICThe present work introduces the problem of simultaneous bifurcation of limit cycles and critical periods for a system of polynomial differential equations in the plane. The simultaneity concept is defined, as well as the idea of bi-weakness in the return map and the period function. Together with the classical methods, we present an approach which uses the Lie bracket to address the simultaneity in some cases. This approach is used to find the bi-weakness of cubic and quartic Liénard systems, the general quadratic family, and the linear plus cubic homogeneous family. We finish with an illustrative example by solving the problem of simultaneous bifurcation of limit cycles and critical periods for the cubic Liénard family