Geant4 Monte Carlo simulations for the LPCTrap setup

The LPCTrap setup at GANIL is fully operational since 2006. The first breakthrough was the detection of 100000 coincidences between the $ \beta$ particles and the recoil ions from the decay of ⁶He⁺ produced by the SPIRAL source. After preparation, the decaying nuclei are confined in a transparent Paul trap which is surrounded by a $ \beta$ -telescope made of a double-sided silicon strip detector followed by a scintillator, and by a micro-channel plate position-sensitive detector to record in coincidence the $ \beta$ particles and the recoil ions. Simulations of this system are needed in order to study possible systematic effects and extract with high accuracy the $ \beta$ - $ \nu$ angular-correlation coefficient. A code based on Geant4 is well suited for this purpose. In this contribution the results from the simulations compared with those from the experiment will be presented and discussed.     

Structural and electronic properties of PtPd and PtNi nanoalloys

The lowest-energy structures of binary (PtPd)_n, (PtNi)_m, (PtNi₃)_s, and (Pt₃Ni)_s nanoclusters, with n=2–28, m=2–20, and s=4–6, modeled by the many-body Gupta potential, were obtained by using a genetic-symbiotic algorithm. These structures were further relaxed within the density functional theory framework in order to obtain the most stable structures for each composition. Segregation is confirmed in all the (PtPd)_n clusters, where the Pt atoms occupy the cluster core and the Pd atoms are situated on the cluster surface. In contrast, for the (PtNi)_m nanoalloys, the Ni atoms are mainly found in the cluster core and the Pt atoms are segregated to the cluster surface. Likewise, for the (PtNi₃)_s nanoalloys, Ni atoms mainly compose the cluster core but there is no clear segregation of the Pt atoms to the surface. Furthermore, for the (Pt₃Ni)_s bimetallic clusters the Pt atoms concentrate in the cluster core and the Ni atoms are segregated to the surface. On the other hand, it has been experimentally found that the Pt_0.75Ni_0.25 supported nanoparticles present a higher catalytic activity for the selective oxidation of CO in the presence of hydrogen than the Pt_0.5Ni_0.5 and Pt_0.25Ni_0.75 nanoparticles. In order to understand this tendency in the catalytic activity, we also performed density functional calculations of the molecular CO adsorption on bimetallic Pt-Ni nanoclusters with the mentioned compositions.     

Molecular relaxation effects in hydrogen chloride photoacoustic detection

A photoacoustic (PA) sensor has been developed to monitor hydrogen chloride at sub-ppm level in the 1740-nm region. The system was designed to control the process in the novel low-water-peak optical fiber manufacturing process. Relaxation effects in hydrogen chloride PA detection in oxygen–helium and nitrogen–helium gas mixtures are presented, showing that the generation of the PA signal is strongly affected by the ratio of these substances. In addition, the role of water vapor in the PA signal is investigated.     

Yang-Mills Detour Complexes and Conformal Geometry

Working over a pseudo-Riemannian manifold, for each vector bundle with connection we construct a sequence of three differential operators which is a complex (termed a Yang-Mills detour complex) if and only if the connection satisfies the full Yang-Mills equations. A special case is a complex controlling the deformation theory of Yang-Mills connections. In the case of Riemannian signature the complex is elliptic. If the connection respects a metric on the bundle then the complex is formally self-adjoint. In dimension 4 the complex is conformally invariant and generalises, to the full Yang-Mills setting, the composition of (two operator) Yang-Mills complexes for (anti-)self-dual Yang-Mills connections. Via a prolonged system and tractor connection a diagram of differential operators is constructed which, when commutative, generates differential complexes of natural operators from the Yang-Mills detour complex. In dimension 4 this construction is conformally invariant and is used to yield two new sequences of conformal operators which are complexes if and only if the Bach tensor vanishes everywhere. In Riemannian signature these complexes are elliptic. In one case the first operator is the twistor operator and in the other sequence it is the operator for Einstein scales. The sequences are detour sequences associated to certain Bernstein-Gelfand-Gelfand sequences.     

Determination of the three-dimensional orientation of single molecules

A simple method for real-time determination of the full three-dimensional orientation of the emission dipole of single molecules is presented. Introduction of a pi phase step in the back focal plane of the collector lens breaks the inherent symmetry, allowing the longitudinal dipole component to be measured. Experimental tolerances and the consequence of a nonzero bandwidth emission spectrum are also discussed. The scheme also allows for the longitudinal component of an electric field to be found experimentally.     

Understanding the enhanced synchronization of delay-coupled networks with fluctuating topology

We study the dynamics of networks with coupling delay, from which the connectivity changes over time. The synchronization properties are shown to depend on the interplay of three time scales: the internal time scale of the dynamics, the coupling delay along the network links and time scale at which the topology changes. Concentrating on a linearized model, we develop an analytical theory for the stability of a synchronized solution. In two limit cases, the system can be reduced to an “effective” topology: in the fast switching approximation, when the network fluctuations are much faster than the internal time scale and the coupling delay, the effective network topology is the arithmetic mean over the different topologies. In the slow network limit, when the network fluctuation time scale is equal to the coupling delay, the effective adjacency matrix is the geometric mean over the adjacency matrices of the different topologies. In the intermediate regime, the system shows a sensitive dependence on the ratio of time scales, and on the specific topologies, reproduced as well by numerical simulations. Our results are shown to describe the synchronization properties of fluctuating networks of delay-coupled chaotic maps.     

Wide binaries as a critical test of classical gravity

Modified gravity scenarios where a change of regime appears at acceleration scales a<a ₀ have been proposed. Since for 1M _⊙ systems the acceleration drops below a ₀ at scales of around 7000 AU, a statistical survey of wide binaries with relative velocities and separations reaching 10⁴ AU and beyond should prove useful to the above debate. We apply the proposed test to the best currently available data. Results show a constant upper limit to the relative velocities in wide binaries which is independent of separation for over three orders of magnitude, in analogy with galactic flat rotation curves in the same a<a ₀ acceleration regime. Our results are suggestive of a breakdown of Kepler’s third law beyond a≈a ₀ scales, in accordance with generic predictions of modified gravity theories designed not to require any dark matter at galactic scales and beyond.     

On Nodal Sets for Dirac and Laplace Operators

We prove that the nodal set (zero set) of a solution of a generalized Dirac equation on a Riemannian manifold has codimension 2 at least. If the underlying manifold is a surface, then the nodal set is discrete. We obtain a quick proof of the fact that the nodal set of an eigenfunction for the Laplace-Beltrami operator on a Riemannian manifold consists of a smooth hypersurface and a singular set of lower dimension. We also see that the nodal set of a Δ-harmonic differential form on a closed manifold has codimension 2 at least; a fact which is not true if the manifold is not closed. Examples show that all bounds are optimal. Received: 28 October 1996 / Accepted: 3 March 1997     

Higher-Order Simple Lie Algebras

It is shown that the non-trivial cocycles on simple Lie algebras may be used to introduce antisymmetric multibrackets which lead to higher-order Lie algebras, the definition of which is given. Their generalised Jacobi identities turn out to be satisfied by the antisymmetric tensors (or higher-order “structure constants”) which characterise the Lie algebra cocycles. This analysis allows us to present a classification of the higher-order simple Lie algebras as well as a constructive procedure for them. Our results are synthesised by the introduction of a single, complete BRST operator associated with each simple algebra. Received: 3 June 1996 / Accepted: 8 November 1996