Global trajectory optimisation: can we prune the solution space when considering deep space manoeuvres?

This document contains a report on the work done under the ESA/Ariadna study 06/4101 on the global optimization of space trajectories with multiple gravity assist (GA) and deep space manoeuvres (DSM). The study was performed by a joint team of scientists from the University of Reading and the University of Glasgow.

Distributed space-time block coding for 3 and 4 relay nodes: Imperfect synchronisation and a solution

Most research on distributed space time block coding (STBC) has so far focused on the case of 2 relay nodes and assumed that the relay nodes are perfectly synchronised at the symbol level. By applying STBC to 3-or 4-relay node systems, this paper shows that imperfect synchronisation causes significant performance degradation to the conventional detector. To this end, we propose a new STBC detection solution based on the principle of parallel interference cancellation (PIC). The PIC detector is moderate in computational complexity but is very effective in suppressing the impact of imperfect synchronisation.

Consistent Dirichlet Boundary Conditions for Numerical Solution of Moving Boundary Problems

We consider the imposition of Dirichlet boundary conditions in the finite element modelling of moving boundary problems in one and two dimensions for which the total mass is prescribed. A modification of the standard linear finite element test space allows the boundary conditions to be imposed strongly whilst simultaneously conserving a discrete mass. The validity of the technique is assessed for a specific moving mesh finite element method, although the approach is more general. Numerical comparisons are carried out for mass-conserving solutions of the porous medium equation with Dirichlet boundary conditions and for a moving boundary problem with a source term and time-varying mass.

Synthesis, structure and solution chemistry of a family of dinuclear hydrazonato-vanadium(V) complexes with [OV(mu-O)VO](4+) core

Dinuclear trioxidic [{VOL}(2)mu-O] (1-4) complexes were synthesized from the reaction of [(VO)-O-IV(acac)(2)] with an equimolar amount of H2L [H2L is the general abbreviation of hydrazone ligands (H2L1-4) derived from the condensation of benzoyl hydrazine with either 2-hydroxyacetophenone or its para substituted derivatives] in acetone or CH2Cl2 or acetonitrile. These V2O3L2 complexes were also obtained from the reaction of VOSO4 with H2L in the presence of two equivalents sodium acetate in aqueous-methanolic (50% V/V) medium and also from the decomposition of [(VO)-O-IV(L)(bipy/phen)] complexes in CH2Cl2 Solution. Black monoclinic crystals of 2 and 4 with C2/c space group were obtained from the reaction of [(VO)-O-IV(acac)(2)], respectively, with H2L2 and H2L4 in acetone in which the respective ligands are bonded meridionally to vanadium in their fully deprotonated enol forms. The V-O bond lengths follow the order: V-O(oxo) < V-O(oxo-bridged) < V-O(phenolate) < V-O(enolate). Complexes (1-4) are diamagnetic exhibiting LMCT transition band near 380 nm in CH2Cl2 solution and they are electroactive displaying a quasi-reversible reduction peak in the 0.14-0.30 V versus SCE region. The and the reduction peak potential (E-p(c)) values show linear relationships with the Hammett constant (sigma) of the substituents in the hydrazone ligands. These dinuclear complexes are converted to the corresponding mononuclear cis dioxo complexes K(H2O)(+)[(VO2)-O-V(L)](-) (5-8) and mixed-ligand [(VO)-O-V(L)(hq)] complexes on reaction, respectively, with two equivalents KOH in methanol and two equivalents 8-hydroxyquinoline (Hhq) in CHCl3. Ascorbic acid reduces the dioxovanadium(V) complexes reversibly under aerobic condition. (C) 2008 Elsevier Ltd. All rights reserved.

A moving-mesh finite element method and its application to the numerical solution of phase-change problems

A distributed Lagrangian moving-mesh finite element method is applied to problems involving changes of phase. The algorithm uses a distributed conservation principle to determine nodal mesh velocities, which are then used to move the nodes. The nodal values are obtained from an ALE (Arbitrary Lagrangian-Eulerian) equation, which represents a generalization of the original algorithm presented in Applied Numerical Mathematics, 54:450--469 (2005). Having described the details of the generalized algorithm it is validated on two test cases from the original paper and is then applied to one-phase and, for the first time, two-phase Stefan problems in one and two space dimensions, paying particular attention to the implementation of the interface boundary conditions. Results are presented to demonstrate the accuracy and the effectiveness of the method, including comparisons against analytical solutions where available.

Robust control system design for generalized state-space systems

Robustness in multi-variable control system design requires that the solution to the design problem be insensitive to perturbations in the system data. In this paper we discuss measures of robustness for generalized state-space, or descriptor, systems and describe algorithmic techniques for optimizing robustness for various applications.

Sparse space-time boundary element methods for the heat equation

The goal of this work is the efficient solution of the heat equation with Dirichlet or Neumann boundary conditions using the Boundary Elements Method (BEM). Efficiently solving the heat equation is useful, as it is a simple model problem for other types of parabolic problems. In complicated spatial domains as often found in engineering, BEM can be beneficial since only the boundary of the domain has to be discretised. This makes BEM easier than domain methods such as finite elements and finite differences, conventionally combined with time-stepping schemes to solve this problem. The contribution of this work is to further decrease the complexity of solving the heat equation, leading both to speed gains (in CPU time) as well as requiring smaller amounts of memory to solve the same problem. To do this we will combine the complexity gains of boundary reduction by integral equation formulations with a discretisation using wavelet bases. This reduces the total work to O(h