Solitary waves in the Nonlinear Dirac Equation

In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associated explicit solutions in one dimension and numerically obtain their analogues in higher dimensions. The stability is subsequently discussed from a theoretical perspective and then complemented with numerical computations. Finally, the dynamics of the solutions is explored and compared to its non-relativistic analogue, which is the nonlinear Schr{\"o}dinger equation. A few special topics are also explored, including the discrete variant of the nonlinear Dirac equation and its solitary wave properties, as well as the PT-symmetric variant of the model

On a smoothed penalty-based algorithm for global optimization

This paper presents a coercive smoothed penalty framework for nonsmooth and nonconvex constrained global optimization problems. The properties of the smoothed penalty function are derived. Convergence to an ε -global minimizer is proved. At each iteration k, the framework requires the ε(k) -global minimizer of a subproblem, where ε(k)→ε . We show that the subproblem may be solved by well-known stochastic metaheuristics, as well as by the artificial fish swarm (AFS) algorithm. In the limit, the AFS algorithm convergence to an ε(k) -global minimum of the real-valued smoothed penalty function is guaranteed with probability one, using the limiting behavior of Markov chains. In this context, we show that the transition probability of the Markov chain produced by the AFS algorithm, when generating a population where the best fitness is in the ε(k)-neighborhood of the global minimum, is one when this property holds in the current population, and is strictly bounded from zero when the property does not hold. Preliminary numerical experiments show that the presented penalty algorithm based on the coercive smoothed penalty gives very competitive results when compared with other penalty-based methods.The authors would like to thank two anonymous referees for their valuable comments and suggestions to improve the paper. This work has been supported by COMPETE: POCI-01-0145-FEDER-007043 and FCT - Fundac¸ao para a Ci ˜ encia e Tecnologia within the projects UID/CEC/00319/2013 and ˆ UID/MAT/00013/2013.info:eu-repo/semantics/publishedVersio

Experimental study of a high intensity radio-frequency cooler

International audienceWithin the framework of the DESIR/SPIRAL-2 project, a radio-frequency quadrupole cooler named SHIRaC has been studied. SHIRaC is a key device of SPIRAL-2, designed to enhance the beam quality required by DESIR. The preliminary study and development of this device has been carried out at Laboratoire de Physique Corpusculaire de CAEN (LPC Caen), France. The goal of this paper is to present the experimental studies conducted on a SHIRaC prototype. The main peculiarity of this cooler is its efficient handling and cooling of ion beams with currents going up as high as 1  μA which has never before been achieved in any of the previous coolers. Much effort has been made lately into these studies for development of appropriate optics, vacuum and rf systems which allow cooling of beams of large emittance (∼80π  mm mrad) and high current. The dependencies of SHIRaC’s transmission and the cooled beam parameters in terms of geometrical transverse emittance and the longitudinal energy spread have also been discussed. Investigation of beam purity at optimum cooling condition has also been done. Results from the experiments indicate that an emittance reduction of less than 2.5π  mm mrad and a longitudinal energy spread reduction of less than 4 eV are obtained with more than 70% of ion transmission. The emittance is at expected values whereas the energy spread is not

Precise measurement of the angular correlation parameter aβν in the β decay of 35^{35}Ar with LPCTrap

Expérience GANIL/SPIRALInternational audienc