A detailed view of the Gaussian–Lorentzian sum and product functions and their comparison with the Voigt function

The Gaussian–Lorentzian sum (GLS) and product (GLP) functions remain important in X-ray photoelectron spectroscopy (XPS) peak fitting. Here, we present a detailed view of these functions, comparing them with each other and with the Voigt function (the “LA(m)” function). First, we show the GLS, GLP, and LA(m) functions as a function of their mixing parameters, m, which reveals differences between them. We then illustrate the use of these functions to fit a series of spectra acquired at different pass energies (resolutions). Next, we show the underlying Gaussian and Lorentzian components of a series of GLS and GLP functions as a function of m, which confirms that the GLS is a simple linear combination of Gaussian and Lorentzian functions. However, one of the two functions used to make the GLP can be very wide, that is, at its extremes, one of these functions has infinite width. We then discuss a plot of the areas of the GLS, GLP, and LA(m) functions as a function of m, which reveals the expected, linear increase in area of the GLS, but nonlinear changes in the areas of the other two functions. Finally, to better understand them, we fit these functions to each other. These results indicate that the GLS and GLP better match the LA(m) function at lower and higher values of the mixing parameter, respectively.     

Impact of Intermolecular Non-Covalent Interactions in a CuI8PdII1 Discrete Assembly: Conformers’ Geometries and Stimuli-Sensitive Luminescence Properties

A new highly solid-state luminescent phase of a previously reported weakly luminescent Cu^I₈Pd^II₁ dicationic assembly is reported revealing the high geometrical versatility of this moiety that importantly alters its luminescent properties. This very minor new species B_c is based on a different conformer scaffold than the one encountered in the previously reported B_o form and, essentially differs from B_o by displaying shorter Cu^I-Cu^I intermetallic distances. DFT calculations allow concluding that the predominance in the solid-state of the weakly luminescent and less stable B_o phase is due to the extra stability induced by a larger number of intermolecular non-covalent π-CH interactions in its crystalline packing and not by the intrinsic stability of the Cu^I₈Pd^II₁ dicationic moiety. Calculations also revealed that a more stable conformation B_calc is expected in vacuum, which bears a different distribution of Cu^I-Cu^I intermetallic distances than the dications in B_o and B_c phases. Taking into account that the geometrical alterations are associated to drastic changes of luminescence properties, this confer to the Cu^I₈Pd^II₁ assembly high potentiality as stimuli-sensitive luminescent materials. Indeed, by applying mechanical or thermal stress to samples of B_o phase, new phases B_g and B_m , respectively, were obtained. Alterations of the solid-state photophysical properties of these new species compared to those recorded for B_o are reported together with a combined experimental and computed study of the structures/properties relationships observed in these phases.     

Soliton interactions and Yang–Baxter maps for the complex coupled short-pulse equation

The complex coupled short-pulse equation (ccSPE) describes the propagation of ultrashort optical pulses in nonlinear birefringent fibers. The system admits a variety of vector soliton solutions: fundamental solitons, fundamental breathers, composite breathers (generic or nongeneric), as well as so-called self-symmetric composite solitons. In this work, we use the dressing method and the Darboux matrices corresponding to the various types of solitons to investigate soliton interactions in the focusing ccSPE. The study combines refactorization problems on generators of certain rational loop groups, and long-time asymptotics of these generators, as well as the main refactorization theorem for the dressing factors that leads to the Yang–Baxter property for the refactorization map and the vector soliton interactions. Among the results obtained in this paper, we derive explicit formulas for the polarization shift of fundamental solitons that are the analog of the well-known formulas for the interaction of vector solitons in the Manakov system. Our study also reveals that upon interacting with a fundamental breather, a fundamental soliton becomes a fundamental breather and, conversely, that the interaction of two fundamental breathers generically yields two fundamental breathers with a polarization shifts, but may also result into a fundamental soliton and a fundamental breather. Explicit formulas for the coefficients that characterize the fundamental breathers, as well as for their polarization vectors are obtained. The interactions of other types of solitons are also derived and discussed in detail and illustrated with plots. New Yang–Baxter maps are obtained in the process.     

On the Inverse Scattering Method for Integrable PDEs on a Star Graph

We present a framework to solve the open problem of formulating the inverse scattering method (ISM) for an integrable PDE on a star-graph. The idea is to map the problem on the graph to a matrix initial-boundary value (IBV) problem and then to extend the unified method of Fokas to such a matrix IBV problem. The nonlinear Schrödinger equation is chosen to illustrate the method. The framework unifies all previously known examples which are recovered as particular cases. The case of general Robin conditions at the vertex is discussed: the notion of linearizable initial-boundary conditions is introduced. For such conditions, the method is shown to be as efficient as the ISM on the full-line.     

Hypersurfaces in hyperbolic space with support function

Based on [19], we develop a global correspondence between immersed hypersurfaces ?:Mⁿ→Hⁿ⁺¹$?:{\mathrm{M}}^n\to {\mathbb{H}}^{n+1}$ satisfying an exterior horosphere condition, also called here horospherically concave hypersurfaces, and complete conformal metrics e^2ρ_gSn$e^{2\rho }{g}_{{\mathbb{S}}^n}$ on domains Ω in the boundary Sⁿ${\mathbb{S}}^n$ at infinity of Hⁿ⁺¹${\mathbb{H}}^{n+1}$, where ρ   is the horospherical support function, _∂∞?(Mⁿ)=∂Ω${\partial }_{\infty }?({\mathrm{M}}^n)=\partial \mathrm{\Omega }$, and Ω is the image of the Gauss map G:Mⁿ→Sⁿ$G:{\mathrm{M}}^n\to {\mathbb{S}}^n$. To do so we first establish results on when the Gauss map G:Mⁿ→Sⁿ$G:{\mathrm{M}}^n\to {\mathbb{S}}^n$ is injective. We also discuss when an immersed horospherically concave hypersurface can be unfolded along the normal flow into an embedded one. These results allow us to establish general Alexandrov reflection principles for elliptic problems of both immersed hypersurfaces in Hⁿ⁺¹${\mathbb{H}}^{n+1}$ and conformal metrics on domains in Sⁿ${\mathbb{S}}^n$. Consequently, we are able to obtain, for instance, a strong Bernstein theorem for a complete, immersed, horospherically concave hypersurface in Hⁿ⁺¹${\mathbb{H}}^{n+1}$ of constant mean curvature.     

Towards large eddy simulation of isothermal two-phase flows: Governing equations and a priori tests

This article reports on the potential of application of LES in the calculation of turbulent two-phase flows, in the case where each phase is resolved and interfaces remain much larger than the mesh size. In comparison with single-phase flow, successful application of LES to resolve two-phase flow problems should account for the complex interaction between turbulence and interfaces. Non-linear transfers of turbulent energy across the interface have to be accurately modeled. The derivation of the complete filtered two-phase flow governing equations has been formulated to deal with turbulence at the interface in a comprehensive and practical way. Explicit filtering of 2D direct numerical simulations has been employed to evaluate the order of magnitude of the new subgrid contributions. A parametric study on the academic test case of two counter-rotative vortices and a more complex test case of phase inversion in a closed box have been utilized to perform an order of magnitude analysis of different transport mechanisms. Important features of turbulent energy transfer across the interface have been discussed. Analyses of the numerical results have been conducted to derive conclusions on the relative importance of the different subgrid scale contributions, and modeling issues and solutions are provided.     

H2 evolution and molecular electrocatalysts: determination of overpotentials and effect of homoconjugation

In an effort to standardize the determination of overpotential values for H(2)-evolving catalysts in non-aqueous solvents and allow a reliable comparison of catalysts prepared and assayed by different groups, we propose to adopt the half-wave potential as reference potential. We provide a simple method for measuring it from usual stationary cyclic voltammograms, and we derive the formulas to which the measured potential should be compared, taking into account the effect of homoconjugation. We also revisit tabulated values of the standard reduction potential of protons in nonaqueous solvents, E(H+/H(2))°.