DSpace Community:
https://dspace.lboro.ac.uk/2134/89
2016-07-29T17:59:57ZBifurcation analysis of the behavior of partially wetting liquids on a rotating cylinder
https://dspace.lboro.ac.uk/2134/22134
Title: Bifurcation analysis of the behavior of partially wetting liquids on a rotating cylinder
Authors: Lin, Te-Sheng; Rogers, Steven; Tseluiko, Dmitri; Thiele, Uwe
Abstract: We discuss the behavior of partially wetting liquids on a rotating cylinder using a model
that takes into account the effects of gravity, viscosity, rotation, surface tension and wettability. Such a system can be considered as a prototype for many other systems where the interplay of spatial heterogeneity and a lateral driving force in the proximity of a first- or second-order phase transition results in intricate behavior. So does a partially wetting drop
on a rotating cylinder undergo a depinning transition as the rotation speed is increased, whereas for ideally wetting liquids the behavior only changes quantitatively. We analyze the bifurcations that occur when the rotation speed is increased for several values of the
equilibrium contact angle of the partially wetting liquids. This allows us to discuss how the entire bifurcation structure and the flow behavior it encodes changes with changing wettability. We employ various numerical continuation techniques that allow us to track stable/unstable steady and time-periodic film and drop thickness profiles. We support our findings by time-dependent numerical simulations and asymptotic analyses of steady and time-periodic profiles for large rotation numbers.
Description: This paper was accepted for publication in the journal Physics of Fluids and the definitive published version will be available at http://scitation.aip.org/content/aip/journal/pof22016-01-01T00:00:00ZThe use of differential equations in optimization
https://dspace.lboro.ac.uk/2134/22089
Title: The use of differential equations in optimization
Authors: Zghier, Abbas K.
Abstract: A new approach for unconstrained optimization of a function f(x)
has been investigated. The method is based on solving the differential
equation dx/dt = ± ∇f(x) which defines orthogonal trajectories in Rⁿ-space.
A number of numerical integration techniques have been used for solving
the above differential equation, the most powerful one which gives rise to
a very efficient optimization algorithm is the generalization of the
Trapezoidal rule. The interaction between the parameters which appear
as a result of using the numerical integration has been investigated.
In the above approach factorization of the positive definite matrix
(θG + λI), allowing some control over the diagonal elements of the matrix.
is presented.
A Liapunov function approach has been used in constructing a number
of different differential equations of the above form. It is well known
that if a Liapunov function which satisfies certain conditions can be
found for a given system of differential equations then the origin of
the system is stable. Pursuing this idea further we constructed a Liapunov
function and then the corresponding differential equation. Application
of this differential equation to the problem of finding a minimum of a
function f is shown to yield a vector that converges to a point where
∇f = 0.
The use of differential equations is also extended to the optimal
control problem. The technique is only applicable to unconstrained optimal
control problems. If a terminal condition and inequality constraints are
presented, the problem should be converted to unconstrained form, e.g. by
the use of penalty functions. The method tends to converge, even from a
poor approximation point to the minimum without using line searches.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.1981-01-01T00:00:00ZSafety system design optimisation
https://dspace.lboro.ac.uk/2134/22019
Title: Safety system design optimisation
Authors: Pattison, Rachel L.
Abstract: This thesis investigates the efficiency of a design optimisation scheme that is
appropriate for systems which require a high likelihood of functioning on demand.
Traditional approaches to the design of safety critical systems follow the preliminary
design, analysis, appraisal and redesign stages until what is regarded as an acceptable
design is achieved. For safety systems whose failure could result in loss of life it is
imperative that the best use of the available resources is made and a system which is
optimal, not just adequate, is produced.
The object of the design optimisation problem is to minimise system unavailability
through manipulation of the design variables, such that limitations placed on them by
constraints are not violated.
Commonly, with mathematical optimisation problem; there will be an explicit
objective function which defines how the characteristic to be minimised is related to
the variables. As regards the safety system problem, an explicit objective function
cannot be formulated, and as such, system performance is assessed using the fault tree
method. By the use of house events a single fault tree is constructed to represent the
failure causes of each potential design to overcome the time consuming task of
constructing a fault tree for each design investigated during the optimisation
procedure. Once the fault tree has been constructed for the design in question it is
converted to a BDD for analysis.
A genetic algorithm is first employed to perform the system optimisation, where the
practicality of this approach is demonstrated initially through application to a High-Integrity
Protection System (HIPS) and subsequently a more complex Firewater
Deluge System (FDS).
An alternative optimisation scheme achieves the final design specification by solving
a sequence of optimisation problems. Each of these problems are defined by
assuming some form of the objective function and specifying a sub-region of the
design space over which this function will be representative of the system
unavailability.
The thesis concludes with attention to various optimisation techniques, which possess
features able to address difficulties in the optimisation of safety critical systems.
Specifically, consideration is given to the use of a statistically designed experiment
and a logical search approach.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.2000-01-01T00:00:00ZOn conjugacy classes of the Klein simple group in Cremona group
https://dspace.lboro.ac.uk/2134/21966
Title: On conjugacy classes of the Klein simple group in Cremona group
Authors: Ahmadinezhad, Hamid
Abstract: We consider countably many three-dimensional PSL2((Formula presented.) 7)-del Pezzo surface fibrations over ℙ1. Conjecturally, they are all irrational except two families, one of which is the product of a del Pezzo surface with ℙ1. We show that the other model is PSL2((Formula presented.) 7)-equivariantly birational to ℙ2×ℙ1. Based on a result of Prokhorov, we show that they are non-conjugate as subgroups of the Cremona group Cr3(ℂ).
Description: This paper is embargoed until December 2016.2016-01-01T00:00:00Z