Understanding the nucleation mechanisms of Carbon Nanotubes in catalytic Chemical Vapor Deposition

The nucleation of carbon caps on small nickel clusters is studied using a tight binding model coupled to grand canonical Monte Carlo simulations. It takes place in a well defined carbon chemical potential range, when a critical concentration of surface carbon atoms is reached. The solubility of carbon in the outermost Ni layers, that depends on the initial, crystalline or disordered, state of the catalyst and on the thermodynamic conditions, is therefore a key quantity to control the nucleation

Time-dependent Fr\"ohlich transformation approach for two-atom entanglement generated by successive passage through a cavity

Time-dependent Fr\"ohlich transformations can be used to derive an effective Hamiltonian for a class of quantum systems with time-dependent perturbations. We use such a transformation for a system with time-dependent atom-photon coupling induced by the classical motion of two atoms in an inhomogeneous electromagnetic field. We calculate the entanglement between the two atoms resulting from their motion through a cavity as a function of their initial position difference and velocity.Comment: 7 pages, 3 figure

Robust variable selection in partially varying coefficient single-index model

By combining basis function approximations and smoothly clipped absolute deviation (SCAD) penalty, this paper proposes a robust variable selection procedure for a partially varying coefficient single-index model based on modal regression. The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components. With appropriate selection of the tuning parameters, we establish the theoretical properties of our procedure, including consistency in variable selection and the oracle property in estimation. Furthermore, we also discuss the bandwidth selection and propose a modified expectation-maximization (EM)-type algorithm for the proposed estimation procedure. The finite sample properties of the proposed estimators are illustrated by some simulation examples.The research of Zhu is partially supported by National Natural Science Foundation of China (NNSFC) under Grants 71171075, 71221001 and 71031004. The research of Yu is supported by NNSFC under Grant 11261048

Integration of twisted Dirac brackets

The correspondence between Poisson structures and symplectic groupoids, analogous to the one of Lie algebras and Lie groups, plays an important role in Poisson geometry; it offers, in particular, a unifying framework for the study of hamiltonian and Poisson actions. In this paper, we extend this correspondence to the context of Dirac structures twisted by a closed 3-form. More generally, given a Lie groupoid $G$ over a manifold $M$, we show that multiplicative 2-forms on $G$ relatively closed with respect to a closed 3-form $\phi$ on $M$ correspond to maps from the Lie algebroid of $G$ into the cotangent bundle $T^*M$ of $M$, satisfying an algebraic condition and a differential condition with respect to the $\phi$-twisted Courant bracket. This correspondence describes, as a special case, the global objects associated to twisted Dirac structures. As applications, we relate our results to equivariant cohomology and foliation theory, and we give a new description of quasi-hamiltonian spaces and group-valued momentum maps.Comment: 42 pages. Minor changes, typos corrected. Revised version to appear in Duke Math.

Robustness of predator-prey models for confinement regime transitions in fusion plasmas

Energy transport and confinement in tokamak fusion plasmas is usually determined by the coupled nonlinear interactions of small-scale drift turbulence and larger scale coherent nonlinear structures, such as zonal flows, together with free energy sources such as temperature gradients. Zero-dimensional models, designed to embody plausible physical narratives for these interactions, can help to identify the origin of enhanced energy confinement and of transitions between confinement regimes. A prime zero-dimensional paradigm is predator-prey or Lotka-Volterra. Here, we extend a successful three-variable (temperature gradient; microturbulence level; one class of coherent structure) model in this genre [M. A. Malkov and P. H. Diamond, Phys. Plasmas 16, 012504 (2009)], by adding a fourth variable representing a second class of coherent structure. This requires a fourth coupled nonlinear ordinary differential equation. We investigate the degree of invariance of the phenomenology generated by the model of Malkov and Diamond, given this additional physics. We study and compare the long-time behaviour of the three-equation and four-equation systems, their evolution towards the final state, and their attractive fixed points and limit cycles. We explore the sensitivity of paths to attractors. It is found that, for example, an attractive fixed point of the three-equation system can become a limit cycle of the four-equation system. Addressing these questions which we together refer to as “robustness” for convenience is particularly important for models which, as here, generate sharp transitions in the values of system variables which may replicate some key features of confinement transitions. Our results help to establish the robustness of the zero-dimensional model approach to capturing observed confinement phenomenology in tokamak fusion plasmas