Nonlinear dynamics of cilia and flagella

Cilia and flagella are hairlike extensions of eukaryotic cells which generate oscillatory beat patterns that can propel micro-organisms and create fluid flows near cellular surfaces. The evolutionary highly conserved core of cilia and flagella consists of a cylindrical arrangement of nine microtubule doublets, called the axoneme. The axoneme is an actively bending structure whose motility results from the action of dynein motor proteins cross-linking microtubule doublets and generating stresses that induce bending deformations. The periodic beat patterns are the result of a mechanical feedback that leads to self-organized bending waves along the axoneme. Using a theoretical framework to describe planar beating motion, we derive a nonlinear wave equation that describes the fundamental Fourier mode of the axonemal beat. We study the role of nonlinearities and investigate how the amplitude of oscillations increases in the vicinity of an oscillatory instability. We furthermore present numerical solutions of the nonlinear wave equation for different boundary conditions. We find that the nonlinear waves are well approximated by the linearly unstable modes for amplitudes of beat patterns similar to those observed experimentally.

Mild wear in dry and lubricated sliding systems

A vertical pin on horizontal disc machine has been used to conduct a series of experiments in air under dry and lubricating sliding conditions. For dry sliding low load and speed combinations were chosen to correspond to the mild wear region below the Welsh T1 transition. Lubricated tests were conducted under flooded conditions using Esso Technical White Oil alone and with a 0.1% stearic acid additive, for load and speed ranges that produced substantial amounts of asperity contact and thus a boundary lubricated regime of wear. The test material in all cases was AISI 52100 steel, for unlubricated sliding subjected to loads from 5 to 50 N and a range of speeds from 10-3 to 1.0 ms-1, and for lubricated sliding loads of 50 to 123 N and for speeds of 10-2 to 1.0 ms-1. Unlubricated wear debris was found to be a mixture of -Fe_2O_3 and -Fe. Unlubricated wear was found to occur via a thin film logarithmic oxide growth followed by agglomeration into thicker oxide plateaux 2 to 10 m in thickness. Lubricated wear occurred via thick film diffusion controlled oxide growth producing homogeneous oxide plateaux 0.1 to 0.2 m in thickness. X-ray photoelectron spectroscopy identified the presence of a surface film on pins worn in White Oil with stearic acid, which is thought to be iron stearate. A model has been developed for unlubricated wear based upon the postulated growth of thin film oxides by a logarithmic rate law. The importance of sliding geometry and environment to the dominant wear mechanism has been illustrated.

Generic experiments at the sump model "Zittauer Strömungswanne" (ZSW) for the behaviour of mineral wool in the sump and the reactor core

The investigation of insulation debris transport, sedimentation, penetration into the reactor core and head loss build up becomes important to reactor safety research for PWR and BWR, when considering the long-term behaviour of emergency core cooling systems during loss of coolant accidents. Research projects are being performed in cooperation between the University of Applied Sciences Zittau/Görlitz and the Helmholtz-Zentrum Dresden-Rossendorf. The projects include experimental investigations of different processes and phenomena of insulation debris in coolant flow and the development of CFD models. Generic complex experiments serve for building up a data base for the validation of models for single effects and their coupling in CFD codes. This paper includes the description of the experimental facility for complex generic experiments (ZSW), an overview about experimental boundary conditions and results for upstream and down-stream phenomena as well as for the long-time behaviour due to corrosive processes. © Carl Hanser Verlag, München.

Transducer diffraction theory and development of an ultrasonic tomogram

The work described in this thesis is the development of an ultrasonic tomogram to provide outlines of cross-sections of the ulna in vivo. This instrument, used in conjunction with X-ray densitometry previously developed in this department, would provide actual bone mineral density to a high resolution. It was hoped that the accuracy of the plot obtained from the tomogram would exceed that of existing ultrasonic techniques by about five times. Repeat measurements with these instruments to follow bone mineral changes would involve very low X-ray doses. A theoretical study has been made of acoustic diffraction, using a geometrical transform applicable to the integration of three different Green's functions, for axisymmetric systems. This has involved the derivation of one of these in a form amenable to computation. It is considered that this function fits the boundary conditions occurring in medical ultrasonography more closely than those used previously. A three dimensional plot of the pressure field using this function has been made for a ring transducer, in addition to that for disc transducers using all three functions. It has been shown how the theory may be extended to investigate the nature and magnitude of the particle velocity, at any point in the field, for the three functions mentioned. From this study. a concept of diffraction fronts has been developed, which has made it possible to determine energy flow also in a diffracting system. Intensity has been displayed in a manner similar to that used for pressure. Plots have been made of diffraction fronts and energy flow direction lines.

A critical assessment of the finite element method for calculating electric and magnetic fields

The present dissertation is concerned with the determination of the magnetic field distribution in ma[.rnetic electron lenses by means of the finite element method. In the differential form of this method a Poisson type equation is solved by numerical methods over a finite boundary. Previous methods of adapting this procedure to the requirements of digital computers have restricted its use to computers of extremely large core size. It is shown that by reformulating the boundary conditions, a considerable reduction in core store can be achieved for a given accuracy of field distribution. The magnetic field distribution of a lens may also be calculated by the integral form of the finite element rnethod. This eliminates boundary problems mentioned but introduces other difficulties. After a careful analysis of both methods it has proved possible to combine the advantages of both in a .new approach to the problem which may be called the 'differential-integral' finite element method. The application of this method to the determination of the magnetic field distribution of some new types of magnetic lenses is described. In the course of the work considerable re-programming of standard programs was necessary in order to reduce the core store requirements to a minimum.

Finite element analysis of the statics of and vibrations in axisymmetric shells

The finite element process is now used almost routinely as a tool of engineering analysis. From early days, a significant effort has been devoted to developing simple, cost effective elements which adequately fulfill accuracy requirements. In this thesis we describe the development and application of one of the simplest elements available for the statics and dynamics of axisymmetric shells . A semi analytic truncated cone stiffness element has been formulated and implemented in a computer code: it has two nodes with five degrees of freedom at each node, circumferential variations in displacement field are described in terms of trigonometric series, transverse shear is accommodated by means of a penalty function and rotary inertia is allowed for. The element has been tested in a variety of applications in the statics and dynamics of axisymmetric shells subjected to a variety of boundary conditions. Good results have been obtained for thin and thick shell cases .

Development and deployment of an autonomous micro-drilling system for cochleostomy

This thesis describes the design and development of an autonomous micro-drilling system capable of accurately controlling the penetration of complaint tissues and its application to the drilling of the cochleostomy; a key stage in the cochlea implant procedure. The drilling of the cochleostomy is a precision micro-surgical task in which the control of the burr penetration through the outer bone tissue of the cochlea is vital to prevent damage to the structures within and requires a high degree of skill to perform successfully. The micro-drilling system demonstrates that the penetration of the cochlea can be achieved consistently and accurately. Breakthrough can be detected and controlled to within 20µm of the distal surface and the hole completed without perforation of the underlying endosteal membrane, leaving the membranous cochlea intact. This device is the first autonomous surgical tool successfully deployed in the operating theatre. The system is unique due to the way in which it uses real-time data from the cutting tool to derive the state of the tool-tissue interaction. Being a smart tool it uses this state information to actively control the way in which the drilling process progresses. This sensor guided strategy enables the tool to self-reference to the deforming tissue and navigate without the need for pre-operative scan data. It is this capability that enables the system to operate in circumstances where the tissue properties and boundary conditions are unknown, without the need to restrain the patient.

Loss fluctuations and temporal correlations in network queues

We consider data losses in a single node of a packet- switched Internet-like network. We employ two distinct models, one with discrete and the other with continuous one-dimensional random walks, representing the state of a queue in a router. Both models have a built-in critical behavior with a sharp transition from exponentially small to finite losses. It turns out that the finite capacity of a buffer and the packet-dropping procedure give rise to specific boundary conditions which lead to strong loss rate fluctuations at the critical point even in the absence of such fluctuations in the data arrival process.

Bifurcation contrasts between plane Poiseuille flow and plane Magnetohydrodynamic flow

The stability characteristics of an incompressible viscous pressure-driven flow of an electrically conducting fluid between two parallel boundaries in the presence of a transverse magnetic field are compared and contrasted with those of Plane Poiseuille flow (PPF). Assuming that the outer regions adjacent to the fluid layer are perfectly electrically insulating, the appropriate boundary conditions are applied. The eigenvalue problems are then solved numerically to obtain the critical Reynolds number Rec and the critical wave number ac in the limit of small Hartmann number (M) range to produce the curves of marginal stability. The non-linear two-dimensional travelling waves that bifurcate by way of a Hopf bifurcation from the neutral curves are approximated by a truncated Fourier series in the streamwise direction. Two and three dimensional secondary disturbances are applied to both the constant pressure and constant flux equilibrium solutions using Floquet theory as this is believed to be the generic mechanism of instability in shear flows. The change in shape of the undisturbed velocity profile caused by the magnetic field is found to be the dominant factor. Consequently the critical Reynolds number is found to increase rapidly with increasing M so the transverse magnetic field has a powerful stabilising effect on this type of flow.

Effect of aspect ratio on thermal convection in open and closed systems

Internally heated fluids are found across the nuclear fuel cycle. In certain situations the motion of the fluid is driven by the decay heat (i.e. corium melt pools in severe accidents, the shutdown of liquid metal reactors, molten salt and the passive control of light water reactors) as well as normal operation (i.e. intermediate waste storage and generation IV reactor designs). This can in the long-term affect reactor vessel integrity or lead to localized hot spots and accumulation of solid wastes that may prompt local increases in activity. Two approaches to the modeling of internally heated convection are presented here. These are based on numerical analysis using codes developed in-house and simulations using widely available computational fluid dynamics solvers. Open and closed fluid layers at around the transition between conduction and convection of various aspect ratios are considered. We determine optimum domain aspect ratio (1:7:7 up to 1:24:24 for open systems and 5:5:1, 1:10:10 and 1:20:20 for closed systems), mesh resolutions and turbulence models required to accurately and efficiently capture the convection structures that evolve when perturbing the conductive state of the fluid layer. Note that the open and closed fluid layers we study here are bounded by a conducting surface over an insulating surface. Conclusions will be drawn on the influence of the periodic boundary conditions on the flow patterns observed. We have also examined the stability of the nonlinear solutions that we found with the aim of identifying the bifurcation sequence of these solutions en route to turbulence.

Quasi-separation of the biharmonic partial differential equation

In this paper, we consider analytical and numerical solutions to the Dirichlet boundary-value problem for the biharmonic partial differential equation on a disc of finite radius in the plane. The physical interpretation of these solutions is that of the harmonic oscillations of a thin, clamped plate. For the linear, fourth-order, biharmonic partial differential equation in the plane, it is well known that the solution method of separation in polar coordinates is not possible, in general. However, in this paper, for circular domains in the plane, it is shown that a method, here called quasi-separation of variables, does lead to solutions of the partial differential equation. These solutions are products of solutions of two ordinary linear differential equations: a fourth-order radial equation and a second-order angular differential equation. To be expected, without complete separation of the polar variables, there is some restriction on the range of these solutions in comparison with the corresponding separated solutions of the second-order harmonic differential equation in the plane. Notwithstanding these restrictions, the quasi-separation method leads to solutions of the Dirichlet boundary-value problem on a disc with centre at the origin, with boundary conditions determined by the solution and its inward drawn normal taking the value 0 on the edge of the disc. One significant feature for these biharmonic boundary-value problems, in general, follows from the form of the biharmonic differential expression when represented in polar coordinates. In this form, the differential expression has a singularity at the origin, in the radial variable. This singularity translates to a singularity at the origin of the fourth-order radial separated equation; this singularity necessitates the application of a third boundary condition in order to determine a self-adjoint solution to the Dirichlet boundary-value problem. The penultimate section of the paper reports on numerical solutions to the Dirichlet boundary-value problem; these results are also presented graphically. Two specific cases are studied in detail and numerical values of the eigenvalues are compared with the results obtained in earlier studies.

An alternating potential based approach for a Cauchy problem for the Laplace equation in a planar domain with a cut

We consider a Cauchy problem for the Laplace equation in a bounded region containing a cut, where the region is formed by removing a sufficiently smooth arc (the cut) from a bounded simply connected domain D. The aim is to reconstruct the solution on the cut from the values of the solution and its normal derivative on the boundary of the domain D. We propose an alternating iterative method which involves solving direct mixed problems for the Laplace operator in the same region. These mixed problems have either a Dirichlet or a Neumann boundary condition imposed on the cut and are solved by a potential approach. Each of these mixed problems is reduced to a system of integral equations of the first kind with logarithmic and hypersingular kernels and at most a square root singularity in the densities at the endpoints of the cut. The full discretization of the direct problems is realized by a trigonometric quadrature method which has super-algebraic convergence. The numerical examples presented illustrate the feasibility of the proposed method.

An empirical examination of the strategic decision-making process:the relationship between context, process, and outcomes

Despite concerted academic interest in the strategic decision-making process (SDMP) since the 1980s, a coherent body of theory capable of guiding practice has not materialised. This is because many prior studies focus only on a single process characteristic, often rationality or comprehensiveness, and have paid insufficient attention to context. To further develop theory, research is required which examines: (i) the influence of context from multiple theoretical perspectives (e.g. upper echelons, environmental determinism); (ii) different process characteristics from both synoptic formal (e.g. rationality) and political incremental (e.g. politics) perspectives, and; (iii) the effects of context and process characteristics on a range of SDMP outcomes. Using data from 30 interviews and 357 questionnaires, this thesis addresses several opportunities for theory development by testing an integrative model which incorporates: (i) five SDMP characteristics representing both synoptic formal (procedural rationality, comprehensiveness, and behavioural integration) and political incremental (intuition, and political behaviour) perspectives; (ii) four SDMP outcome variables—strategic decision (SD) quality, implementation success, commitment, and SD speed, and; (iii) contextual variables from the four theoretical perspectives—upper echelons, SD-specific characteristics, environmental determinism, and firm characteristics. The present study makes several substantial and original contributions to knowledge. First, it provides empirical evidence of the contextual boundary conditions under which intuition and political behaviour positively influence SDMP outcomes. Second, it establishes the predominance of the upper echelons perspective; with TMT variables explaining significantly more variance in SDMP characteristics than SD specific characteristics, the external environment, and firm characteristics. A newly developed measure of top management team expertise also demonstrates highly significant direct and indirect effects on the SDMP. Finally, it is evident that SDMP characteristics and contextual variables influence a number of SDMP outcomes, not just overall SD quality, but also implementation success, commitment, and SD speed.

Population lensing vs thermal lensing in Yb:YAG rods and disks

The induced lenses in the Yb:YAG rods and disks end-pumped by a Gaussian beam were analyzed both analytically and numerically. The thermally assisted mechanisms of the lens formation were considered to include: the conventional volume thermal index changes ("dn/dT"), the bulging of end faces, the photoelastic effect, and the bending (for a disk). The heat conduction equations (with an axial heat flux for a disk and a radial heat flux for a rod), and quasi-static thermoelastic equations (in the plane-stress approximation with free boundary conditions) were solved to find the thermal lens power. The population rate equation with saturation (by amplified spontaneous emission or an external wave) was examined to find the electronic lens power in the active elements.

Determining the temperature from incomplete boundary data

An iterative procedure for determining temperature fields from Cauchy data given on a part of the boundary is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the heat operator and its adjoint. A convergence proof of this method in a weighted L2-space is included, as well as a stopping criteria for the case of noisy data. Moreover, a solvability result in a weighted Sobolev space for a parabolic initial boundary value problem of second order with mixed boundary conditions is presented. Regularity of the solution is proved. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)