4,449 research outputs found
Flow in pipes with non-uniform curvature and torsion
No full textThis paper describes steady and unsteady flows in pipes with small, slowly varying curvature and torsion. Four new pipe shapes are studied, using Germano's extension of the Dean equations. Analytic and numerical solutions are obtained for flows driven by a steady pressure gradient. Oscillatory flows in pipes with non-uniform curvature are obtained by numerical methods. The effects of the non-uniformities in curvature and torsion are discussed, with particular reference to wall shear stress. </p
Characteristics of Conservation Laws for Difference Equations
No full textEach conservation law of a given partial differential equation is determined (up to equivalence) by a function known as the characteristic. This function is used to find conservation laws, to prove equivalence between conservation laws, and to prove the converse of Noether's Theorem. Transferring these results to difference equations is nontrivial, largely because difference operators are not derivations and do not obey the chain rule for derivatives. We show how these problems may be resolved and illustrate various uses of the characteristic. In particular, we establish the converse of Noether's Theorem for difference equations, we show (without taking a continuum limit) that the conservation laws in the infinite family generated by Rasin and Schiff are distinct, and we obtain all five-point conservation laws for the potential Lotka-Volterra equation
Comparative analysis of Mycobacterium tuberculosis pe and ppe genes reveals high sequence variation and an apparent absence of selective constraints.
No full textContains fulltext :
110619.pdf (Publisher’s version ) (Open Access)Mycobacterium tuberculosis complex (MTBC) genomes contain 2 large gene families termed pe and ppe. The function of pe/ppe proteins remains enigmatic but studies suggest that they are secreted or cell surface associated and are involved in bacterial virulence. Previous studies have also shown that some pe/ppe genes are polymorphic, a finding that suggests involvement in antigenic variation. Using comparative sequence analysis of 18 publicly available MTBC whole genome sequences, we have performed alignments of 33 pe (excluding pe_pgrs) and 66 ppe genes in order to detect the frequency and nature of genetic variation. This work has been supplemented by whole gene sequencing of 14 pe/ppe (including 5 pe_pgrs) genes in a cohort of 40 diverse and well defined clinical isolates covering all the main lineages of the M. tuberculosis phylogenetic tree. We show that nsSNP's in pe (excluding pgrs) and ppe genes are 3.0 and 3.3 times higher than in non-pe/ppe genes respectively and that numerous other mutation types are also present at a high frequency. It has previously been shown that non-pe/ppe M. tuberculosis genes display a remarkably low level of purifying selection. Here, we also show that compared to these genes those of the pe/ppe families show a further reduction of selection pressure that suggests neutral evolution. This is inconsistent with the positive selection pressure of "classical" antigenic variation. Finally, by analyzing such a large number of genes we were able to detect large differences in mutation type and frequency between both individual genes and gene sub-families. The high variation rates and absence of selective constraints provides valuable insights into potential pe/ppe function. Since pe/ppe proteins are highly antigenic and have been studied as potential vaccine components these results should also prove informative for aspects of M. tuberculosis vaccine design
Automorphisms of real Lie algebras of dimension five or less
No full textThe Lie algebra version of the Krull-Schmidt Theorem is formulated and proved. This leads to a method for constructing the automorphisms of a direct sum of Lie algebras from the automorphisms of its indecomposable components. For finite-dimensional Lie algebras, there is a well-known algorithm for finding such components, so the theorem considerably simplifies the problem of classifying the automorphism groups. We illustrate this by classifying the automorphisms of all indecomposable real Lie algebras of dimension five or less. Our results are presented very concisely, in tabular form
Multisymplectic formulation of fluid dynamics using the inverse map
No full text13.02.14 KB. Ok to add accepted version to spiral, embargo expired. RS policyWe construct multisymplectic formulations of fluid dynamics using the inverse of the Lagrangian path map. This inverse map, the ‘back-to-labels’ map, gives the initial Lagrangian label of the fluid particle that currently occupies each Eulerian position. Explicitly enforcing the condition that the fluid particles carry their labels with the flow in Hamilton's principle leads to our multisymplectic formulation. We use the multisymplectic one-form to obtain conservation laws for energy, momentum and an infinite set of conservation laws arising from the particle relabelling symmetry and leading to Kelvin's circulation theorem. We discuss how multisymplectic numerical integrators naturally arise in this approach
Introduction to symmetry methods in the solution of differential equations that occur in chemistry and chemical biology
No full text
Multi-symplectic formulation of near-local Hamiltonian balanced models
No full textWe transform near-local Hamiltonian balanced models (HBMs) describing nearly geostrophic fluid motion (with constant Coriolis parameter) into multi-symplectic (MS) systems. This allows us to determine conservation of Lagrangian momentum, energy and potential vorticity for Salmon's L1 dynamics; a similar approach works for other near-local balanced models (such as the -model). The MS approach also enables us to determine a class of systems that have a contact structure similar to that of the semigeostrophic model. The contact structure yields a contact transformation that makes the problem of front formation tractable. The new class includes the first local model with a variable Coriolis parameter that preserves all of the most useful geometric features of the semigeostrophic model
- …
