Alkali and Alkaline Earth Metal Compounds: Core-Valence Basis Sets and Importance of Subvalence Correlation

Core-valence basis sets for the alkali and alkaline earth metals Li, Be, Na, Mg, K, and Ca are proposed. The basis sets are validated by calculating spectroscopic constants of a variety of diatomic molecules involving these elements. Neglect of $(3s,3p)$ correlation in K and Ca compounds will lead to erratic results at best, and chemically nonsensical ones if chalcogens or halogens are present. The addition of low-exponent $p$ functions to the K and Ca basis sets is essential for smooth convergence of molecular properties. Inclusion of inner-shell correlation is important for accurate spectroscopic constants and binding energies of all the compounds. In basis set extrapolation/convergence calculations, the explicit inclusion of alkali and alkaline earth metal subvalence correlation at all steps is essential for K and Ca, strongly recommended for Na, and optional for Li and Mg, while in Be compounds, an additive treatment in a separate `core correlation' step is probably sufficient. Consideration of $(1s)$ inner-shell correlation energy in first-row elements requires inclusion of $(2s,2p)$ `deep core' correlation energy in K and Ca for consistency. The latter requires special CCV$n$Z `deep core correlation' basis sets. For compounds involving Ca bound to electronegative elements, additional $d$ functions in the basis set are strongly recommended. For optimal basis set convergence in such cases, we suggest the sequence CV(D+3d)Z, CV(T+2d)Z, CV(Q+$d$)Z, and CV5Z on calcium.Comment: Molecular Physics, in press (W. G. Richards issue); supplementary material (basis sets in G98 and MOLPRO formats) available at http://theochem.weizmann.ac.il/web/papers/group12.htm

Stability of cluster solutions in a cooperative consumer chain model

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ Springer-Verlag Berlin Heidelberg 2012.We study a cooperative consumer chain model which consists of one producer and two consumers. It is an extension of the Schnakenberg model suggested in Gierer and Meinhardt [Kybernetik (Berlin), 12:30-39, 1972] and Schnakenberg (J Theor Biol, 81:389-400, 1979) for which there is only one producer and one consumer. In this consumer chain model there is a middle component which plays a hybrid role: it acts both as consumer and as producer. It is assumed that the producer diffuses much faster than the first consumer and the first consumer much faster than the second consumer. The system also serves as a model for a sequence of irreversible autocatalytic reactions in a container which is in contact with a well-stirred reservoir. In the small diffusion limit we construct cluster solutions in an interval which have the following properties: The spatial profile of the third component is a spike. The profile for the middle component is that of two partial spikes connected by a thin transition layer. The first component in leading order is given by a Green's function. In this profile multiple scales are involved: The spikes for the middle component are on the small scale, the spike for the third on the very small scale, the width of the transition layer for the middle component is between the small and the very small scale. The first component acts on the large scale. To the best of our knowledge, this type of spiky pattern has never before been studied rigorously. It is shown that, if the feedrates are small enough, there exist two such patterns which differ by their amplitudes.We also study the stability properties of these cluster solutions. We use a rigorous analysis to investigate the linearized operator around cluster solutions which is based on nonlocal eigenvalue problems and rigorous asymptotic analysis. The following result is established: If the time-relaxation constants are small enough, one cluster solution is stable and the other one is unstable. The instability arises through large eigenvalues of order O(1). Further, there are small eigenvalues of order o(1) which do not cause any instabilities. Our approach requires some new ideas: (i) The analysis of the large eigenvalues of order O(1) leads to a novel system of nonlocal eigenvalue problems with inhomogeneous Robin boundary conditions whose stability properties have been investigated rigorously. (ii) The analysis of the small eigenvalues of order o(1) needs a careful study of the interaction of two small length scales and is based on a suitable inner/outer expansion with rigorous error analysis. It is found that the order of these small eigenvalues is given by the smallest diffusion constant ε22.RGC of Hong Kon

Existence and Stability of a Spike in the Central Component for a Consumer Chain Model

We study a three-component consumer chain model which is based on Schnakenberg type kinetics. In this model there is one consumer feeding on the producer and a second consumer feeding on the first consumer. This means that the first consumer (central component) plays a hybrid role: it acts both as consumer and producer. The model is an extension of the Schnakenberg model suggested in \cite{gm,schn1} for which there is only one producer and one consumer. It is assumed that both the producer and second consumer diffuse much faster than the central component. We construct single spike solutions on an interval for which the profile of the first consumer is that of a spike. The profiles of the producer and the second consumer only vary on a much larger spatial scale due to faster diffusion of these components. It is shown that there exist two different single spike solutions if the feed rates are small enough: a large-amplitude and a small-amplitude spike. We study the stability properties of these solutions in terms of the system parameters. We use a rigorous analysis for the linearized operator around single spike solutions based on nonlocal eigenvalue problems. The following result is established: If the time-relaxation constants for both producer and second consumer vanish, the large-amplitude spike solution is stable and the small-amplitude spike solution is unstable. We also derive results on the stability of solutions when these two time-relaxation constants are small. We show a new effect: if the time-relaxation constant of the second consumer is very small, the large-amplitude spike solution becomes unstable. To the best of our knowledge this phenomenon has not been observed before for the stability of spike patterns. It seems that this behavior is not possible for two-component reaction-diffusion systems but that at least three components are required. Our main motivation to study this system is mathematical since the novel interaction of a spike in the central component with two other components results in new types of conditions for the existence and stability of a spike. This model is realistic if several assumptions are made: (i) cooperation of consumers is prevalent in the system, (ii) the producer and the second consumer diffuse much faster than the first consumer, and (iii) there is practically an unlimited pool of producer. The first assumption has been proven to be correct in many types of consumer groups or populations, the second assumption occurs if the central component has a much smaller mobility than the other two, the third assumption is realistic if the consumers do not feel the impact of the limited amount of producer due to its large quantity. This chain model plays a role in population biology, where consumer and producer are often called predator and prey. This system can also be used as a model for a sequence of irreversible autocatalytic reactions in a container which is in contact with a well-stirred reservoir

Flow-distributed spikes for Schnakenberg kinetics

This is the post-print version of the final published paper. The final publication is available at link.springer.com by following the link below. Copyright @ 2011 Springer-Verlag.We study a system of reaction–diffusion–convection equations which combine a reaction–diffusion system with Schnakenberg kinetics and the convective flow equations. It serves as a simple model for flow-distributed pattern formation. We show how the choice of boundary conditions and the size of the flow influence the positions of the emerging spiky patterns and give conditions when they are shifted to the right or to the left. Further, we analyze the shape and prove the stability of the spikes. This paper is the first providing a rigorous analysis of spiky patterns for reaction-diffusion systems coupled with convective flow. The importance of these results for biological applications, in particular the formation of left–right asymmetry in the mouse, is indicated.RGC of Hong Kon

Identifying factors likely to influence compliance with diagnostic imaging guideline recommendations for spine disorders among chiropractors in North America: a focus group study using the Theoretical Domains Framework

Background: The Theoretical Domains Framework (TDF) was developed to investigate determinants of specific clinical behaviors and inform the design of interventions to change professional behavior. This framework was used to explore the beliefs of chiropractors in an American Provider Network and two Canadian provinces about their adherence to evidence-based recommendations for spine radiography for uncomplicated back pain. The primary objective of the study was to identify chiropractors’ beliefs about managing uncomplicated back pain without xrays and to explore barriers and facilitators to implementing evidence-based recommendations on lumbar spine xrays. A secondary objective was to compare chiropractors in the United States and Canada on their beliefs regarding the use of spine x-rays. Methods: Six focus groups exploring beliefs about managing back pain without x-rays were conducted with a purposive sample. The interview guide was based upon the TDF. Focus groups were digitally recorded, transcribed verbatim, and analyzed by two independent assessors using thematic content analysis based on the TDF. Results: Five domains were identified as likely relevant. Key beliefs within these domains included the following: conflicting comments about the potential consequences of not ordering x-rays (risk of missing a pathology, avoiding adverse treatment effects, risks of litigation, determining the treatment plan, and using x-ray-driven techniques contrasted with perceived benefits of minimizing patient radiation exposure and reducing costs; beliefs about consequences); beliefs regarding professional autonomy, professional credibility, lack of standardization, and agreement with guidelines widely varied (social/professional role & identity); the influence of formal training, colleagues, and patients also appeared to be important factors (social influences); conflicting comments regarding levels of confidence and comfort in managing patients without x-rays (belief about capabilities); and guideline awareness and agreements (knowledge). Conclusions: Chiropractors’ use of diagnostic imaging appears to be influenced by a number of factors. Five key domains may be important considering the presence of conflicting beliefs, evidence of strong beliefs likely to impact the behavior of interest, and high frequency of beliefs. The results will inform the development of a theorybased survey to help identify potential targets for behavioral-change strategies

A Comprehensive Case Study of Macrosegregation in a Steel Ingot

This is the author accepted manuscript. The final version is available from Springer via http://dx.doi.org/10.1007/s11663-015-0386-yA case study is presented that examines the macrosegregation and grain structure present in a 12-tonne steel ingot, which was cast for experimental purposes. Details of the casting procedure were well documented and the resulting ingot was characterized using a number of techniques that measured chemical segregation, shrinkage, and porosity. The formation of the porosity and segregation patterns is discussed in reference to the particular grain structure observed in the ingot. It is hoped that this case study can be used as a tool for the validation of future macromodels.This work was undertaken as part of a Project sponsored by Rolls-Royce Power Nuclear plc in collaboration with Sheffield Forgemasters International

Railway bridge structural health monitoring and fault detection: state-of-the-art methods and future challenges

Railway importance in the transportation industry is increasing continuously, due to the growing demand of both passenger travel and transportation of goods. However, more than 35% of the 300,000 railway bridges across Europe are over 100-years old, and their reliability directly impacts the reliability of the railway network. This increased demand may lead to higher risk associated with their unexpected failures, resulting safety hazards to passengers and increased whole life cycle cost of the asset. Consequently, one of the most important aspects of evaluation of the reliability of the overall railway transport system is bridge structural health monitoring, which can monitor the health state of the bridge by allowing an early detection of failures. Therefore, a fast, safe and cost-effective recovery of the optimal health state of the bridge, where the levels of element degradation or failure are maintained efficiently, can be achieved. In this article, after an introduction to the desired features of structural health monitoring, a review of the most commonly adopted bridge fault detection methods is presented. Mainly, the analysis focuses on model-based finite element updating strategies, non-model-based (data-driven) fault detection methods, such as artificial neural network, and Bayesian belief network–based structural health monitoring methods. A comparative study, which aims to discuss and compare the performance of the reviewed types of structural health monitoring methods, is then presented by analysing a short-span steel structure of a railway bridge. Opportunities and future challenges of the fault detection methods of railway bridges are highlighted

Recommendations for diagnosis and treatment of methemoglobinemia

Methemoglobinemia is a rare disorder associated with oxidization of divalent ferro-iron of hemoglobin (Hb) to ferri-iron of methemoglobin (MetHb). Methemoglobinemia can result from either inherited or acquired processes. Acquired forms are the most common, mainly due to the exposure to substances that cause oxidation of the Hb both directly or indirectly. Inherited forms are due either to autosomal recessive variants in the CYB5R3 gene or to autosomal dominant variants in the globin genes, collectively known as HbM disease. Our recommendations are based on a systematic literature search. A series of questions regarding the key signs and symptoms, the methods for diagnosis, the clinical management in neonatal/childhood/adulthood period, and the therapeutic approach of methemoglobinemia were formulated and the relative recommendations were produced. An agreement was obtained using a Delphi-like approach and the experts panel reached a final consensus >75% of agreement for all the questions.Genetics of disease, diagnosis and treatmen