Graph theory, irreducibility, and structural analysis of differential-algebraic equation systems

The $\Sigma$-method for structural analysis of a differential-algebraic equation (DAE) system produces offset vectors from which the sparsity pattern of a system Jacobian is derived. This pattern implies a block-triangular form (BTF) of the DAE that can be exploited to speed up numerical solution. The paper compares this fine BTF with the usually coarser BTF derived from the sparsity pattern of the \sigmx. It defines a Fine-Block Graph with weighted edges, which gives insight into the relation between coarse and fine blocks, and the permitted ordering of blocks to achieve BTF. It also illuminates the structure of the set of normalised offset vectors of the DAE, e.g.\ this set is finite if and only if there is just one coarse block

How AD Can Help Solve Differential-Algebraic Equations

A characteristic feature of differential-algebraic equations is that one needs to find derivatives of some of their equations with respect to time, as part of so called index reduction or regularisation, to prepare them for numerical solution. This is often done with the help of a computer algebra system. We show in two significant cases that it can be done efficiently by pure algorithmic differentiation. The first is the Dummy Derivatives method, here we give a mainly theoretical description, with tutorial examples. The second is the solution of a mechanical system directly from its Lagrangian formulation. Here we outline the theory and show several non-trivial examples of using the "Lagrangian facility" of the Nedialkov-Pryce initial-value solver DAETS, namely: a spring-mass-multipendulum system, a prescribed-trajectory control problem, and long-time integration of a model of the outer planets of the solar system, taken from the DETEST testing package for ODE solvers

Classical and vector sturm—liouville problems: recent advances in singular-point analysis and shooting-type algorithms

AbstractSignificant advances have been made in the last year or two in algorithms and theory for Sturm—Liouville problems (SLPs). For the classical regular or singular SLP −(p(x)u′)′ + q(x)u = λw(x)u, a < x < b, we outline the algorithmic approaches of the recent library codes and what they can now routinely achieve.For a library code, automatic treatment of singular problems is a must. New results are presented which clarify the effect of various numerical methods of handling a singular endpoint.For the vector generalization −(P(x)u′)′+Q(x)u = λW(x)u where now u is a vector function of x, and P, Q, W are matrices, and for the corresponding higher-order vector self-adjoint problem, we outline the equally impressive advances in algorithms and theory

Factors affecting environmental attitudes and volunteering in England and Wales

This paper investigates the demographic, social, political and religious factors that affect people’s attitudes to the environment and their involvement in environmental volunteering in England and Wales, using data from four waves of the Home Office Citizenship Survey between 2003 and 2009. Approximately 14,000 people were included in each wave of the survey, with around 85%-90% of people having a positive attitude to the environment, while 7%-8% were involved in volunteering. The data were analysed using logistic regression models. Covariates included sex, ethnicity, age, income, education, religion and region. We found that positive attitude and volunteering increased up to the age of 65 before decreasing sharply. People on middling incomes between £20k and £60k were the most likely to have positive environmental attitude and activity. We found no evidence of behavioural change—the results on both environmental attitudes and volunteering remained stable across all four waves of the survey

Quantification of neurodegeneration by measurement of brain-specific proteins

Quantification of neurodegeneration in animal models is typically assessed by time-consuming and observer-dependent immunocytochemistry. This study aimed to investigate if newly developed ELISA techniques could provide an observer-independent, cost-effective and time-saving tool for this purpose. Neurofilament heavy chain (NfH(SM135)), astrocytic glial fibrillary acidic protein (GFAP), S100B and ferritin, markers of axonal loss, gliosis, astrocyte activation and microglial activation, respectively, were quantified in the spinal cord homogenates of mice with chronic relapsing experimental allergic encephalomyelitis (CREAE, n=8) and controls (n=7). Levels of GFAP were found to be threefold elevated in CREAE (13 ng/mg protein) when compared to control animals (4.5 ng/mg protein, p<0.001). The inverse was observed for NfH(SM135) (21 ng/mg protein vs. 63 ng/mg protein, p<0.001), ferritin (542 ng/mg protein vs. 858 ng/mg protein, p<0.001) and S100B (786 ng/mg protein vs. 2080 ng/mg protein, N.S.). These findings were confirmed by immunocytochemistry, which demonstrated intense staining for GFAP and decreased staining for NfH(SM135) in CREAE compared to control animals. These findings indicate that axonal loss and gliosis can be estimated biochemically using the newly developed ELISA assays for NfH(SM135) and GFAP. These assays may facilitate the quantification of pathological features involved in neurodegeneration

Plasmonic nanoparticle enhanced photocurrent in GaN/InGaN/GaN quantum well solar cells

We demonstrate enhanced external quantum efficiency and current-voltage characteristics due to scattering by 100 nm silver nanoparticles in a single 2.5 nm thick InGaN quantum well photovoltaic device. Nanoparticle arrays were fabricated on the surface of the device using an anodic alumina template masking process. The Ag nanoparticles increase light scattering, light trapping, and carrier collection in the III-N semiconductor layers leading to enhancement of the external quantum efficiency by up to 54%. Additionally, the short-circuit current in cells with 200 nm p-GaN emitter regions is increased by 6% under AM 1.5 illumination. AFORS-Het simulation software results were used to predict cell performance and optimize emitter layer thickness

Structural analysis based dummy derivative selection for differential algebraic equations

The signature matrix structural analysis method developed by Pryce provides more structural information than the commonly used Pantelides method and applies to differential-algebraic equations (DAEs) of arbitrary order. It is useful to consider how existing methods using the Pantelides algorithm can benefit from such structural analysis. The dummy derivative method is a technique commonly used to solve DAEs that can benefit from such exploitation of underlying DAE structures and information found in the Signature Matrix method. This paper gives a technique to find structurally necessary dummy derivatives and how to use different block triangular forms effectively when performing the dummy derivative method and then provides a brief complexity analysis of the proposed approach. We finish by outlining an approach that can simplify the task of dummy pivoting