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Unstable modes of the Q1-P0 element
No full textIn this paper the unstable eigenmodes of
Q1-P0 velocity/pressure finite element
approximation for incompressible flow problems are characterised.
It is shown that
the inf-sup stability constant is in two dimensions
and in three dimensions. The basic tool in the
analysis is the method of modified equations which is
applied to finite difference representations of the
underlying finite element equations. The asymptotic estimates
are confirmed and supplemented by numerical experiments
The finite Language for Computable Metric Spaces
No full textIn this paper we propose a model-theoretic characterisation of computable metric spaces and computability over them in a finite language
Lie powers and pseudo-idempotents
No full textWe give a new factorisation of the classical Dynkin operator,
an element of the integral group ring of the symmetric group that
facilitates projections of tensor powers onto Lie powers.
As an application we show that the iterated Lie power is
a module direct summand of the Lie power whenever the
characteristic of the ground field does not divide . An explicit
projection of the latter onto the former is exhibited in this case
HydraMP: Exploiting shared memory parallelism in HYDRA with OpenMP
Get PDFMulticore CPUs are now found in desktops, servers and supercomputers but many existing parallel performance analysis tools were designed for the single-core distributed-memory world. We investigate the practicality of taking an existing tool, namely the HYDRA response time analyser, and parallelising it with OpenMP to produce a multithreaded implementation suitable for execution on multicore shared-memory machines. We discuss the amount of software engineering work required and show that only a small number of lines of code need to be added to achieve dramatic speed-ups over the serial version. We also compare the run-times of our OpenMP-parallelised version with existing MPI-parallelised code on the same hardware
The Continuing Influence of Fiedler's Work on Companion Matrices
Get PDFThis is a reconstruction in article-like form
of a talk given at the
``Minisymposium in Honor of Miroslav Fiedler''
at the 17th ILAS Conference,
held at TU Braunschweig, Germany, on Thurs 25 Aug 2011
MODELLING AND DYNAMIC STABILISATION OF A COMPLIANT HUMANOID ROBOT, CoMan
No full textThis dissertation presents the results of a series of studies on dynamic stabilisation of CoMan, which is actuated by series elastic actuators. The main goal of this dissertation is to dynamically stabilise the humanoid robot on the floor by the simplest multivariate feedback control for the purpose of walking. The multivariable scheme is chosen to take into account the joints' interactions, as well as providing a systematic way of designing the feedback system to improve the bandwidth and tracking performance of CoMan's existing PID control. A detailed model is derived which includes all the motors and joints state variables and their multibody interactions which are often ignored in the previous studies on bipedal robots in the literature. The derived dynamic model is then used to design multivariable optimal control feedback and observers with a mathematical proof for the relative stability and robustness of the closed loop system in face of model uncertainties and disturbances. In addition, two decentralized optimal feedback design algorithms are presented that explicitly take the compliant dynamics and the multibody interactions into account while providing the mathematical proof for the stability of the overall system. The purpose of the proposed decentralized control methods is to provide a systematic model based PD-PID design to replace the existing PID controllers which are derived by a trial and error process. Moreover, the challenging constrained and compliant motion of the robot in double support is studied where a novel constrained feedback design is proposed which directly takes the compliance dynamics, interactions and the constraints into account to provide a closed loop feedback tracking system that drives the robot inside the constrained subspace. This method of control is particularly interesting since most control methods applied to closed kinematic chains (such as the double support phase) are over complicated for implementation purposes or have an ad-hoc approach to controller design.
In terms of walking trajectory generation, an extension to the ZMP walking trajectory generation is proposed to utilise the CoMan's upper body to tackle the non-minimum phase behaviour that is faced in trajectory generation. Simple inverted pendulum models of walking are then used to study the maximum feasible walking speed and step size where parameters of CoMan are used to provide numerical upper-bounds on the step size and walking speed. Use of straight knee and toe push-off during walking is shown to be beneficial for taking larger step lengths and hence achieving faster walking speeds.
Subsequently, the designed tracking systems are then applied to a dynamic walking simulator which is developed during this PhD project to accurately model the compliant walking behaviour of the CoMan. A walking gait is simulated and visualized to show the effectiveness of the developed walking simulator.
Moreover, the experimental results and challenges faced during the implementation of the designed tracking control systems are discussed where it is shown that the LQR feedback results in 50\% less control effort and tracking errors in comparison with CoMan's existing independent PID control. This advantage directly affects the feasible walking speed. In addition, a set of standard and repeatable tests for CoMan are designed to quantify and compare the performance of various control system designs. Finally, the conclusions and future directions are pointed out
The SuBliMinaL Toolbox: automating steps in the reconstruction of metabolic networks
Get PDFThe generation and use of metabolic network reconstructions has increased over recent years. The development of such reconstructions has typically involved a time-consuming, manual process. Recent work has shown that steps undertaken in reconstructing such metabolic networks are amenable to automation.
The SuBliMinaL Toolbox (http://www.mcisb.org/subliminal/) facilitates the reconstruction process by providing a number of independent modules to perform common tasks, such as generating draft reconstructions, determining metabolite protonation state, mass and charge balancing reactions, suggesting intracellular compartmentalisation, adding transport reactions and a biomass function, and formatting the reconstruction to be used in third-party analysis packages. The individual modules manipulate reconstructions encoded in Systems Biology Markup Language (SBML), and can be chained to generate a reconstruction pipeline, or used individually during a manual curation process.
This work describes the individual modules themselves, and a study in which the modules were used to develop a metabolic reconstruction of Saccharomyces cerevisiae from the existing data resources KEGG and MetaCyc. The automatically generated reconstruction is analysed for blocked reactions, and suggestions for future improvements to the toolbox are discussed
A Framework for Analyzing Nonlinear Eigenproblems and Parametrized Linear Systems
Get PDFAssociated with an matrix polynomial of degree , , are the eigenvalue problem and the linear system problem , where in the latter case is to be computed for many values of the parameter . Both problems can be solved by conversion to an equivalent problem or that is linear in the parameter or . This linearization process has received much attention in recent years for the eigenvalue problem, but it is less well understood for the linear system problem. We develop a framework in which more general versions of both problems can be analyzed, based on one-sided factorizations connecting a general nonlinear matrix function to a simpler function , typically a polynomial of degree 1 or 2. Our analysis relates the solutions of the original and lower degree problems and in the linear system case indicates how to choose the right-hand side and recover the solution from . For the eigenvalue problem this framework includes many special cases studied in the literature, including the vector spaces of pencils and recently introduced by Mackey, Mackey, Mehl, and Mehrmann and a class of rational problems. We use the framework to investigate the conditioning and stability of the parametrized linear system and thereby study the effect of scaling, both of the original polynomial and of the pencil . Our results identify situations in which scaling can potentially greatly improve the conditioning and stability and our numerical results show that dramatic improvements can be achieved in practice
A truncated ILU smoother for multigrid preconditioning of convection dominated flow problems
Get PDFMultigrid methods are known to be efficient preconditioners and solvers for linear systems obtained from discretizing second-order, scalar elliptic problems. Singular perturbations involving these problems (such as the convection-diffusion equation) introduce new properties into the discrete problem, and this typically leads to the deterioration in the effectiveness of multigrid methods using standard point smoothers when close to the perturbation limit. In this paper we propose a new smoothing strategy, based on incomplete factorisation of truncated matrices arizing in the multigrid hierarchy. The truncation procedure is based on the heuristics used to determine strong connections in the classical (Ruge-Stuben) algebraic multigrid method. We report results of tests of the new smoother both for geometric and for algebraic multigrid on benchmark problems in two and three spatial dimensions
On the Bott periodicity, J-homomorphisms, and
Get PDFThe Curtis conjecture predicts that the only spherical classes in are the Hopf invariant
one and the Kervaire invariant one elements. We consider Sullivan's decomposition
Q_0S^0 = J \times \cokerJ
where is the fibre of ( at the prime 2) and observe that the Curtis conjecture holds when
we restrict to . We then use the Bott periodicity and the -homomorphism H(Q_0S^0; Z/p)pp = 2H_*( \Omega^k_0J; Z/2)H_*(Q_0-k}; Z/2)JH_*(\Omega^k_0 \coker J; Z/2)J$-homomorphisms