Characterizations of non-normalized discrete probability distributions and their application in statistics

From the distributional characterizations that lie at the heart of Stein’s method we derive explicit formulae for the mass functions of discrete probability laws that identify those distributions. These identities are applied to develop tools for the solution of statistical problems. Our characterizations, and hence the applications built on them, do not require any knowledge about normalization constants of the probability laws. To demonstrate that our statistical methods are sound, we provide comparative simulation studies for the testing of fit to the Poisson distribution and for parameter estimation of the negative binomial family when both parameters are unknown. We also consider the problem of parameter estimation for discrete exponential-polynomial models which generally are non-normalized

Carrier-envelope phase control over pathway interference in strong-field dissociation of H2+_2^+

The dissociation of an H$_2^+$ molecular-ion beam by linearly polarized, carrier-envelope-phase-tagged 5 fs pulses at 4$\times10^{14}$W/cm$^2$ with a central wavelength of 730 nm was studied using a coincidence 3D momentum imaging technique. Carrier-envelope-phase-dependent asymmetries in the emission direction of H$^+$ fragments relative to the laser polarization were observed. These asymmetries are caused by interference of odd and even photon number pathways, where net-zero photon and 1-photon interference predominantly contributes at H$^+$+H kinetic energy releases of 0.2 -- 0.45 eV, and net-2-photon and 1-photon interference contributes at 1.65 -- 1.9 eV. These measurements of the benchmark H$_2^+$ molecule offer the distinct advantage that they can be quantitatively compared with \textit{ab initio} theory to confirm our understanding of strong-field coherent control via the carrier-envelope phase

Sintered alumina with low dielectric loss

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Fragmentation of CD+ induced by intense ultrashort laser pulses

Citation: Graham, L., Zohrabi, M., Gaire, B., Ablikim, U., Jochim, B., Berry, B., . . . Ben-Itzhak, I. (2015). Fragmentation of CD+ induced by intense ultrashort laser pulses. Physical Review A, 91(2), 11. doi:10.1103/PhysRevA.91.023414The fragmentation of CD[superscript +] in intense ultrashort laser pulses was investigated using a coincidence three-dimensional momentum imaging technique improved by employing both transverse and longitudinal electric fields. This allowed clear separation of all fragmentation channels and the determination of the kinetic energy release down to nearly zero, for a molecule with significant mass asymmetry. The most probable dissociation pathways for the two lowest dissociation limits, C[superscript +]+D and C+D[superscript +], were identified for both 22-fs, 798-nm and 50-fs, 392-nm pulses. Curiously, the charge asymmetric dissociation of CD[superscript 2+] was not observed for 392-nm photons, even though it was clearly visible for the fundamental 798 nm at the same peak intensity

A computational framework for polyconvex large strain elasticity for geometrically exact beam theory

In this paper, a new computational framework is presented for the analysis of nonlinear beam finite elements subjected to large strains. Specifically, the methodology recently introduced in Bonet et al. (Comput Methods Appl Mech Eng 283:1061–1094, 2015) in the context of three dimensional polyconvex elasticity is extended to the geometrically exact beam model of Simo (Comput Methods Appl Mech Eng 49:55–70, 1985), the starting point of so many other finite element beam type formulations. This new variational framework can be viewed as a continuum degenerate formulation which, moreover, is enhanced by three key novelties. First, in order to facilitate the implementation of the sophisticated polyconvex constitutive laws particularly associated with beams undergoing large strains, a novel tensor cross product algebra by Bonet et al. (Comput Methods Appl Mech Eng 283:1061–1094, 2015) is adopted, leading to an elegant and physically meaningful representation of an otherwise complex computational framework. Second, the paper shows how the novel algebra facilitates the re-expression of any invariant of the deformation gradient, its cofactor and its determinant in terms of the classical beam strain measures. The latter being very useful whenever a classical beam implementation is preferred. This is particularised for the case of a Mooney–Rivlin model although the technique can be straightforwardly generalised to other more complex isotropic and anisotropic polyconvex models. Third, the connection between the two most accepted restrictions for the definition of constitutive models in three dimensional elasticity and beams is shown, bridging the gap between the continuum and its degenerate beam description. This is carried out via a novel insightful representation of the tangent operator

Observation of strong final-state effects in pi+ production in pp collisions at 400 MeV

Differential cross sections of the reactions $pp \to d\pi^+$ and $pp \to pn\pi^+$ have been measured at $T_p = 400$ MeV by detecting the charged ejectiles in the angular range $4^0 \leq \Theta_{Lab} \leq 21^\circ$. The deduced total cross sections agree well with those published previously for neighbouring energies. The invariant mass spectra are observed to be strongly affected by $\Delta$ production and $NN$ final-state interaction. The data are well described by Monte Carlo simulations including both these effects. The ratio of $pp \to pn\pi^+$ and $pp \to d\pi^+$ cross sections also compares favourably to a recent theoretical prediction which suggests a dominance of $np$-production in the relative $^3S_1$-state.Comment: 17 pages, 5 figure

Topological Order in the Projected Entangled-Pair States Formalism: Transfer Operator and Boundary Hamiltonians

We study the structure of topological phases and their boundaries in the projected entangled-pair states (PEPS) formalism. We show how topological order in a system can be identified from the structure of the PEPS transfer operator and subsequently use these findings to analyze the structure of the boundary Hamiltonian, acting on the bond variables, which reflects the entanglement properties of the system. We find that in a topological phase, the boundary Hamiltonian consists of two parts: A universal nonlocal part which encodes the nature of the topological phase and a nonuniversal part which is local and inherits the symmetries of the topological model, which helps to infer the structure of the boundary Hamiltonian and thus possibly of the physical edge modes