Technique to eliminate computational instability in multibody simulations employing the Lagrange multiplier

A programming technique to eliminate computational instability in multibody simulations that use the Lagrange multiplier is presented. The computational instability occurs when the attached bodies drift apart and violate the constraints. The programming technique uses the constraint equation, instead of integration, to determine the coordinates that are not independent. Although the equations of motion are unchanged, a complete derivation of the incorporation of the Lagrange multiplier into the equation of motion for two bodies is presented. A listing of a digital computer program which uses the programming technique to eliminate computational instability is also presented. The computer program simulates a solid rocket booster and parachute connected by a frictionless swivel

Responses by the Secretary of State for Education to the Education Select Committee

Michael Gove, the Secretary of State for Education, appeared before the Education Select Committee on 18 December 2013, to answer questions from Committee members related to various aspects of education policy, including careers guidance. It was the first time his views on careers guidance have been expressed in the public domain. This analysis of his comments is based on the uncorrected transcript2, which the Secretary of State will have an opportunity to correct. The transcript is therefore not yet an approved formal record of the proceedings

On the classification of quantum W-algebras

In this paper we consider the structure of general quantum W-algebras. We introduce the notions of deformability, positive-definiteness, and reductivity of a W-algebra. We show that one can associate a reductive finite Lie algebra to each reductive W-algebra. The finite Lie algebra is also endowed with a preferred $sl(2)$ subalgebra, which gives the conformal weights of the W-algebra. We extend this to cover W-algebras containing both bosonic and fermionic fields, and illustrate our ideas with the Poisson bracket algebras of generalised Drinfeld-Sokolov Hamiltonian systems. We then discuss the possibilities of classifying deformable W-algebras which fall outside this class in the context of automorphisms of Lie algebras. In conclusion we list the cases in which the W-algebra has no weight one fields, and further, those in which it has only one weight two field.Comment: 28 page

Careers work with young people: collapse or transition? An analysis of current developments in careers education and guidance for young people in England

This paper analyses the current information available (in July 2011) about the changes that are taking place in careers work following recent government policy initiatives and public-sector austerity measures. In particular, it examines the local developments that have emerged in relation to a national policy context in which: • Existing careers work is being radically reconfigured. • The new National Careers Service (NCS) will principally serve adults (apart from its telephone/web-based services, which will cover young people too). • Securing careers guidance for young people has been made the responsibility of schools. • The requirement for schools to provide careers education has been removed. • There has been very limited transition planning at national level: this has led to considerable local confusion. • In particular, there is continuing confusion about the future relationship of remaining face-to-face Connexions services to the NCS, and about the branding of such services. Implications for Connexions services, Local Authorities, schools, new market players and the careers profession are identified

Recent developments on the roles of employers and of careers professionals: a pivotal phase in determining future careers provision for young people.

This policy commentary reviews key statements and reports issued in February and the beginning of March 2014, including; Statements by Lord Nash (Parliamentary Under-Secretary for Schools) on the Government’s intentions with regard to the forthcoming revised Statutory Guidance for Schools; A speech by Nick Clegg (Deputy Prime Minister) in which he commented on careers guidance in schools; A progress report issued by the National Careers Council; and A Briefing Note issued by the Careers Sector Stakeholders Alliance.Careers Englan

Teachers and Careers: The role of school teachers in delivering career and employability learning

Teach Firs

One-point functions in finite volume/temperature: a case study

We consider finite volume (or equivalently, finite temperature) expectation values of local operators in integrable quantum field theories using a combination of numerical and analytical approaches. It is shown that the truncated conformal space approach, when supplemented with a recently proposed renormalization group, can be sufficiently extended to the low-energy regime that it can be matched with high precision by the low-temperature expansion proposed by Leclair and Mussardo. Besides verifying the consistency of the two descriptions, their combination leads to an evaluation of expectation values which is valid to a very high precision for all volume/temperature scales. As a side result of the investigation, we also discuss some unexpected singularities in the framework recently proposed by Pozsgay and Tak\'acs for the description of matrix elements of local operators in finite volume, and show that while some of these singularities are resolved by the inclusion of the class of exponential finite size corrections known as \mu-terms, these latter corrections themselves lead to the appearance of new singularities. We point out that a fully consistent description of finite volume matrix elements is expected to be free of singularities, and therefore a more complete and systematic understanding of exponential finite size corrections is necessary.Comment: v1: 29 pages, 10 eps figures. v2: 34 pages. A detailed comparison of the theoretically predicted and numerically computed cutoff dependence is added; notations explained in more details and some explanatory remarks are added; typos correcte

Enhancing choice? The role of technology in the career support market

This report explores the role that technology has played in the development of the career support market. This market is conceived broadly to include all possible resources that individuals might draw upon to support them in their career development. A key element is the role that is played by public-sector career services and by careers professionals; though these resources are supplemented by services paid for in a wide range of ways and delivered by a range of professionals and non-professionals.UKCE

A pitfall of piecewise-polytropic equation of state inference

The only messenger radiation in the Universe which one can use to statistically probe the Equation of State (EOS) of cold dense matter is that originating from the near-field vicinities of compact stars. Constraining gravitational masses and equatorial radii of rotating compact stars is a major goal for current and future telescope missions, with a primary purpose of constraining the EOS. From a Bayesian perspective it is necessary to carefully discuss prior definition; in this context a complicating issue is that in practice there exist pathologies in the general relativistic mapping between spaces of local (interior source matter) and global (exterior spacetime) parameters. In a companion paper, these issues were raised on a theoretical basis. In this study we reproduce a probability transformation procedure from the literature in order to map a joint posterior distribution of Schwarzschild gravitational masses and radii into a joint posterior distribution of EOS parameters. We demonstrate computationally that EOS parameter inferences are sensitive to the choice to define a prior on a joint space of these masses and radii, instead of on a joint space interior source matter parameters. We focus on the piecewise-polytropic EOS model, which is currently standard in the field of astrophysical dense matter study. We discuss the implications of this issue for the field.Comment: 16 pages, 9 figures. Accepted for publication in MNRA