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

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

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

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

Development of a programme to facilitate interprofessional simulation-based training for final year undergraduate healthcare students

Original report can be found at: http://www.health.heacademy.ac.uk/publications/miniproject/alinier260109.pdfIntroduction: Students have few opportunities to practise alongside students from other disciplines. Simulation offers an ideal context to provide them with concrete experience in a safe and controlled environment. This project was about the development of a programme to facilitate interprofessional scenario-based simulation training for final year undergraduate healthcare students and explored whether simulation improved trainees’ knowledge of other healthcare discipline’s roles and skills. Methods: A multidisciplinary academic project team was created and trained for the development and facilitation of this project. The team worked on the development of appropriate multiprofessional scenarios and a strategy to recruit the final year students on a volunteer basis to the project. By the end of the project 95 students were involved in small groups to one of fifteen 3-hour interprofessional simulation sessions. Staff role played the relatives, doctor on call, and patient when it was more appropriate than using a patient simulator (Laerdal SimMan/SimBaby) in the simulated community setting and paediatric or adult emergency department. Each session had 3 to 4 of the following disciplines represented (Adult/Children/Learning Disability Nursing, Paramedic, Radiography, Physiotherapy) and each student observed and took part in one long and relevant high-fidelity scenario. Half the students were randomly selected to fill in a 40-item questionnaire testing their knowledge of other disciplines before the simulation (control group) and the others after (experimental group). Students were assessed on the questions relating to the disciplines represented in their session. Results: By the end of the project 95 questionnaires were collected of which 45 were control group students (Questionnaire before simulation) and 50 experimental group students (Questionnaire after simulation). Both groups were comparable in terms of gender, discipline and age representation. Participants were: Adult nurses (n=46), Children’s nurses (n=4), Learning Disability nurses (n=7), Nurses, Paramedics (n=8), Radiographers (n=20), Physiotherapists (n=8). 15 sessions were run with an average of around 7 participants and at least 3 disciplines represented. The knowledge test results about the disciplines represented was significantly different between the control and experimental groups (Control 73.80%, 95% CI 70.95-76.65; and Experimental 78.81%, 95% CI 75.76-81.87, p=0.02). In addition, there were sometimes reliable differences between the groups in their view of multidisciplinary training; confidence about working as part of a multidisciplinary team was 3.33 (SD=0.80, Control) and 3.79 (SD=0.90, Experimental), p=0.011; their anticipation that working as part of a multidisciplinary team would make them feel anxious was 2.67 (SD=1.17, Control) and 2.25 (SD=1.04, Experimental), p=0.073; their perception of their knowledge of what other healthcare professionals can or cannot do was 3.00 (SD=0.91, Control) and 3.35 (SD=0.93, Experimental), p=0.066; their view that learning with other healthcare students before qualification will improve their relationship after qualification was 3.93 (SD=1.14, Control) and 4.33 (SD=0.81, Experimental), p=0.055; their opinion about interprofessional learning helping them to become better team workers before qualification was 3.96 (SD=1.24, Control) and 4.42 (SD=0.77, Experimental), p=0.036. Conclusions: Although the difference is relatively small (~5%), the results demonstrate that students gained confidence and knowledge about the skills and role of other disciplines involved in their session. Through simulation, the positivism of students about different aspects of learning or working with other healthcare disciplines has significantly improved. Students gained knowledge of other disciplines simply by being given the opportunity to take part in a multiprofessional scenario and observe another one. The results of the test and their reported perception about multidisciplinary team working suggest that they are better prepared to enter the healthcare workforce. Discussions during the debriefings highlighted the fact that multidisciplinary training is important. The main challenges identified have been the voluntary student attendance and timetabling issues forcing us to run the session late in the day due to the number of disciplines involved in each session and their different placement rota. The aim is now to timetable formally this session within their curriculum. Introducing simulation in the undergraduate curriculum should facilitate its implementation as Continuing Professional Development once these students become qualified healthcare professionals