An algebra of Stein operators

We build upon recent advances on the distributional aspect of Stein's method to propose a novel and flexible technique for computing Stein operators for random variables that can be written as products of independent random variables. We show that our results are valid for a wide class of distributions including normal, beta, variance-gamma, generalized gamma and many more. Our operators are $k$th degree differential operators with polynomial coefficients; they are straightforward to obtain even when the target density bears no explicit handle. As an application, we derive a new formula for the density of the product of $k$ independent symmetric variance-gamma distributed random variables.Comment: 20 page

Neutral low-dimensional assemblies of a Mn(III) schiff base complex and octacyanotungstate(V) : synthesis, characterization, and magnetic properties

International audienceTwo novel low-dimensional molecular magnetic materials were prepared by the self-assembly of 3d- and 5d-metal complexes. These are the first neutral heterobimetallic cyanobridged compounds involving one anisotropic Mn(III) Schiff base complex and one octacyanotungstate(V) per molecular unit. A slow diffusion of the constituents’ solutions leads to the formation of the 0D crystalline complex 1, due to coordination of a water molecule to the Mn center, which prevents polymer formation. A rapid mixing of reagents results in the precipitation of the microcrystalline powder of complex 2, which based on the totality of experimental data, possesses a 1D polymeric structure. The magnetic studies have shown that antiferromagnetic exchange interactions prevail in 1 (J/kB = −13.1(7) K, D = −3.0(1.3) K, zJ' = −0.16(20) K and gav = 2.00(1)); while the presence of the significant intramolecular Mn(III)–W(V) ferromagnetic coupling through cyanide bridge is characteristic for 2 (J/kB = 46.1(5) K, gMn = 2.11(3), fixed gW = 2.0). Due to the weak interchain interactions, zJ′/kB = −0.8(2) K, and compound 2 is a metamagnet with the Néel temperature of 9.5 K undergoing a spin-flip transition at 2 kOe. The slow magnetization dynamics of 2 were investigated at a DC field of 0 and 2 kOe, giving the values of τ0 32(15) and 36(15) ps, respectively, well within the range typical for single-chain magnets (SCMs). The respective ∆τ/kB values were 48.4(1.2) and 44.9(1.0) K

A fast, low-memory, and stable algorithm for implementing multicomponent transport in direct numerical simulations

Implementing multicomponent diffusion models in reacting-flow simulations is computationally expensive due to the challenges involved in calculating diffusion coefficients. Instead, mixture-averaged diffusion treatments are typically used to avoid these costs. However, to our knowledge, the accuracy and appropriateness of the mixture-averaged diffusion models has not been verified for three-dimensional turbulent premixed flames. In this study we propose a fast,efficient, low-memory algorithm and use that to evaluate the role of multicomponent mass diffusion in reacting-flow simulations. Direct numerical simulation of these flames is performed by implementing the Stefan-Maxwell equations in NGA. A semi-implicit algorithm decreases the computational expense of inverting the full multicomponent ordinary diffusion array while maintaining accuracy and fidelity. We first verify the method by performing one-dimensional simulations of premixed hydrogen flames and compare with matching cases in Cantera. We demonstrate the algorithm to be stable, and its performance scales approximately with the number of species squared. Then, as an initial study of multicomponent diffusion, we simulate premixed, three-dimensional turbulent hydrogen flames, neglecting secondary Soret and Dufour effects. Simulation conditions are carefully selected to match previously published results and ensure valid comparison. Our results show that using the mixture-averaged diffusion assumption leads to a 15% under-prediction of the normalized turbulent flame speed for a premixed hydrogen-air flame. This difference in the turbulent flame speed motivates further study into using the mixture-averaged diffusion assumption for DNS of moderate-to-high Karlovitz number flames.Comment: 36 pages, 14 figure

Gaussian solitary waves and compactons in Fermi-Pasta-Ulam lattices with Hertzian potentials

We consider a class of fully-nonlinear Fermi-Pasta-Ulam (FPU) lattices, consisting of a chain of particles coupled by fractional power nonlinearities of order $\alpha >1$. This class of systems incorporates a classical Hertzian model describing acoustic wave propagation in chains of touching beads in the absence of precompression. We analyze the propagation of localized waves when $\alpha$ is close to unity. Solutions varying slowly in space and time are searched with an appropriate scaling, and two asymptotic models of the chain of particles are derived consistently. The first one is a logarithmic KdV equation, and possesses linearly orbitally stable Gaussian solitary wave solutions. The second model consists of a generalized KdV equation with H\"older-continuous fractional power nonlinearity and admits compacton solutions, i.e. solitary waves with compact support. When $\alpha \rightarrow 1^+$, we numerically establish the asymptotically Gaussian shape of exact FPU solitary waves with near-sonic speed, and analytically check the pointwise convergence of compactons towards the limiting Gaussian profile

Decomposing the site frequency spectrum: the impact of tree topology on neutrality tests

We investigate the dependence of the site frequency spectrum (SFS) on the topological structure of genealogical trees. We show that basic population genetic statistics - for instance estimators of $\theta$ or neutrality tests such as Tajima's $D$ - can be decomposed into components of waiting times between coalescent events and of tree topology. Our results clarify the relative impact of the two components on these statistics. We provide a rigorous interpretation of positive or negative values of an important class of neutrality tests in terms of the underlying tree shape. In particular, we show that values of Tajima's $D$ and Fay and Wu's $H$ depend in a direct way on a peculiar measure of tree balance which is mostly determined by the root balance of the tree. We present a new test for selection in the same class as Fay and Wu's $H$ and discuss its interpretation and power. Finally, we determine the trees corresponding to extreme expected values of these neutrality tests and present formulae for these extreme values as a function of sample size and number of segregating sites.Comment: 23 pages, 8 figure

Annealing studies and electrical properties of SnS-based solar cells

Thin films of SnS (tin sulphide) were thermally evaporated onto glass and CdS/ITO (cadmium sulphide/indium tin oxide) coated glass substrates and then annealed in vacuum with the aim of optimising them for use in photovoltaic solar cell device structures. The chemical and physical properties of the layers were determined using scanning electron microscopy, energy dispersive x-ray analysis, x-ray diffraction, and transmittance versus wavelength measurements. “Superstrate configuration” devices were also made using indium tin oxide as the transparent conductive oxide, thermally evaporated cadmium sulphide as the buffer layer and evaporated copper/indium as the back contact material. Capacitance-voltage data are given for the fabricated devices. Capacitance- voltage, spectral response and I-V data are given for the fabricated devices

3D printing of gas jet nozzles for laser-plasma accelerators

Recent results on laser wakefield acceleration in tailored plasma channels have underlined the importance of controlling the density profile of the gas target. In particular it was reported that appropriate density tailoring can result in improved injection, acceleration and collimation of laser-accelerated electron beams. To achieve such profiles innovative target designs are required. For this purpose we have reviewed the usage of additive layer manufacturing, commonly known as 3D printing, in order to produce gas jet nozzles. Notably we have compared the performance of two industry standard techniques, namely selective laser sintering (SLS) and stereolithography (SLA). Furthermore we have used the common fused deposition modeling (FDM) to reproduce basic gas jet designs and used SLA and SLS for more sophisticated nozzle designs. The nozzles are characterized interferometrically and used for electron acceleration experiments with the Salle Jaune terawatt laser at Laboratoire d'Optique Appliqu\'ee