3D numerical modelling of acoustic horns using the method of fundamental solutions

In the present work, a three-dimensional (3D) formulation based on the method of fundamental solutions (MFS) is applied to the study of acoustic horns. The implemented model follows and extends previous works that only considered two-dimensional and axisymmetric horn configurations. The more realistic case of 3D acoustic horns with symmetry regarding two orthogonal planes is addressed. The use of the domain decomposition technique with two interconnected sub-regions along a continuity boundary is proposed, allowing for the computation of the sound pressure generated by an acoustic horn installed on a rigid screen. In order to reduce the model discretization requirements for these cases, Green’s functions derived with the image source methodology are adopted, automatically accounting for the presence of symmetry conditions. A strategy for the calculation of an optimal position of the virtual sources used by the MFS to define the solution is also used, leading to improved reliability and flexibility of the proposed method. The responses obtained by the developed model are compared to reference solutions, computed by well-established models based on the boundary element method. Additionally, numerically calculated acoustic parameters, such as directivity and beamwidth, are compared with those evaluated experimentally.

An iterative method for solving nonsymmetric linear systems with dynamic estimation of parameters /

Vita.

Above | Below | Between

Thesis (Master's)--University of Washington, 2016-06

A Kinetic Vlasov Model for Plasma Simulation Using Discontinuous Galerkin Method on Many-Core Architectures

Thesis (Ph.D.)--University of Washington, 2016-03

Variable Step Maximum Power Point Tracking for Photovoltaic Modules with Embedded Temperature Sensing

Thesis (Master's)--University of Washington, 2016-06

Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method

We present an analysis of the free vibration of plates with internal discontinuities due to central cut-outs. A numerical formulation for a basic L-shaped element which is divided into appropriate sub-domains that are dependent upon the location of the cut-out is used as the basic building element. Trial functions formed to satisfy certain boundary conditions are employed to define the transverse deflection of each sub-domain. Mathematical treatments in terms of the continuities in displacement, slope, moment, and higher derivatives between the adjacent sub-domains are enforced at the interconnecting edges. The energy functional results, from the proper assembly of the coupled strain and kinetic energy contributions of each sub-domain, are minimized via the Ritz procedure to extract the vibration frequencies and. mode shapes of the plates. The procedures are demonstrated by considering plates with central cut-outs that are subjected to two types of boundary conditions. (C) 2003 Elsevier Ltd. All rights reserved.

Transparent boundary conditions for wave propagation on unbounded domains

The numerical solution of the time dependent wave equation in an unbounded domain generally leads to a truncation of this domain, which requires the introduction of an artificial boundary with associated boundary conditions. Such nonreflecting conditions ensure the equivalence between the solution of the original problem in the unbounded region and the solution inside the artificial boundary. We consider the acoustic wave equation and derive exact transparent boundary conditions that are local in time and can be directly used in explicit methods. These conditions annihilate wave harmonics up to a given order on a spherical artificial boundary, and we show how to combine the derived boundary condition with a finite difference method. The analysis is complemented by a numerical example in two spatial dimensions that illustrates the usefulness and accuracy of transparent boundary conditions.

Evaluation of the BEASY program using linear and piecewise linear approaches for the boundary conditions

The boundary element method (BEM) was used to study galvanic corrosion using linear and logarithmic boundary conditions. The linear boundary condition was implemented by using the linear approach and the piecewise linear approach. The logarithmic boundary condition was implemented by the piecewise linear approach. The calculated potential and current density distribution were compared with the prior analytical results. For the linear boundary condition, the BEASY program using the linear approach and the piecewise linear approach gave accurate predictions of the potential and the galvanic current density distributions for varied electrolyte conditions, various film thicknesses, various electrolyte conductivities and various area ratio of anode/cathode. The 50-point piecewise linear method could be used with both linear and logarithmic polarization curves.

Unlocking pathology archives for molecular genetic studies: a reliable method to generate probes for chromogenic and fluorescent in situ hybridization

Chromogenic (CISH) and fluorescent ( FISH) in situ hybridization have emerged as reliable techniques to identify amplifications and chromosomal translocations. CISH provides a spatial distribution of gene copy number changes in tumour tissue and allows a direct correlation between copy number changes and the morphological features of neoplastic cells. However, the limited number of commercially available gene probes has hindered the use of this technique. We have devised a protocol to generate probes for CISH that can be applied to formalin-fixed, paraffin-embedded tissue sections (FFPETS). Bacterial artificial chromosomes ( BACs) containing fragments of human DNA which map to specific genomic regions of interest are amplified with phi 29 polymerase and random primer labelled with biotin. The genomic location of these can be readily confirmed by BAC end pair sequencing and FISH mapping on normal lymphocyte metaphase spreads. To demonstrate the reliability of the probes generated with this protocol, four strategies were employed: (i) probes mapping to cyclin D1 (CCND1) were generated and their performance was compared with that of a commercially available probe for the same gene in a series of 10 FFPETS of breast cancer samples of which five harboured CCND1 amplification; (ii) probes targeting cyclin-dependent kinase 4 were used to validate an amplification identified by microarray-based comparative genomic hybridization (aCGH) in a pleomorphic adenoma; (iii) probes targeting fibroblast growth factor receptor 1 and CCND1 were used to validate amplifications mapping to these regions, as defined by aCGH, in an invasive lobular breast carcinoma with FISH and CISH; and (iv) gene-specific probes for ETV6 and NTRK3 were used to demonstrate the presence of t(12; 15)(p12; q25) translocation in a case of breast secretory carcinoma with dual colour FISH. In summary, this protocol enables the generation of probes mapping to any gene of interest that can be applied to FFPETS, allowing correlation of morphological features with gene copy number.

Analysis of transient eddy currents in MRI using a cylindrical FDTD method

Most magnetic resonance imaging (MRI) spatial encoding techniques employ low-frequency pulsed magnetic field gradients that undesirably induce multiexponentially decaying eddy currents in nearby conducting structures of the MRI system. The eddy currents degrade the switching performance of the gradient system, distort the MRI image, and introduce thermal loads in the cryostat vessel and superconducting MRI components. Heating of superconducting magnets due to induced eddy currents is particularly problematic as it offsets the superconducting operating point, which can cause a system quench. A numerical characterization of transient eddy current effects is vital for their compensation/control and further advancement of the MRI technology as a whole. However, transient eddy current calculations are particularly computationally intensive. In large-scale problems, such as gradient switching in MRI, conventional finite-element method (FEM)-based routines impose very large computational loads during generation/solving of the system equations. Therefore, other computational alternatives need to be explored. This paper outlines a three-dimensional finite-difference time-domain (FDTD) method in cylindrical coordinates for the modeling of low-frequency transient eddy currents in MRI, as an extension to the recently proposed time-harmonic scheme. The weakly coupled Maxwell's equations are adapted to the low-frequency regime by downscaling the speed of light constant, which permits the use of larger FDTD time steps while maintaining the validity of the Courant-Friedrich-Levy stability condition. The principal hypothesis of this work is that the modified FDTD routine can be employed to analyze pulsed-gradient-induced, transient eddy currents in superconducting MRI system models. The hypothesis is supported through a verification of the numerical scheme on a canonical problem and by analyzing undesired temporal eddy current effects such as the B-0-shift caused by actively shielded symmetric/asymmetric transverse x-gradient head and unshielded z-gradient whole-body coils operating in proximity to a superconducting MRI magnet.

A new relaxation method for roll forming problems

Finite element analysis (FEA) of nonlinear problems in solid mechanics is a time consuming process, but it can deal rigorously with the problems of both geometric, contact and material nonlinearity that occur in roll forming. The simulation time limits the application of nonlinear FEA to these problems in industrial practice, so that most applications of nonlinear FEA are in theoretical studies and engineering consulting or troubleshooting. Instead, quick methods based on a global assumption of the deformed shape have been used by the roll-forming industry. These approaches are of limited accuracy. This paper proposes a new form-finding method - a relaxation method to solve the nonlinear problem of predicting the deformed shape due to plastic deformation in roll forming. This method involves applying a small perturbation to each discrete node in order to update the local displacement field, while minimizing plastic work. This is iteratively applied to update the positions of all nodes. As the method assumes a local displacement field, the strain and stress components at each node are calculated explicitly. Continued perturbation of nodes leads to optimisation of the displacement field. Another important feature of this paper is a new approach to consideration of strain history. For a stable and continuous process such as rolling and roll forming, the strain history of a point is represented spatially by the states at a row of nodes leading in the direction of rolling to the current one. Therefore the increment of the strain components and the work-increment of a point can be found without moving the object forward. Using this method we can find the solution for rolling or roll forming in just one step. This method is expected to be faster than commercial finite element packages by eliminating repeated solution of large sets of simultaneous equations and the need to update boundary conditions that represent the rolls.

A structural method for the design of fault tolerant distributed control systems

Distributed digital control systems provide alternatives to conventional, centralised digital control systems. Typically, a modern distributed control system will comprise a multi-processor or network of processors, a communications network, an associated set of sensors and actuators, and the systems and applications software. This thesis addresses the problem of how to design robust decentralised control systems, such as those used to control event-driven, real-time processes in time-critical environments. Emphasis is placed on studying the dynamical behaviour of a system and identifying ways of partitioning the system so that it may be controlled in a distributed manner. A structural partitioning technique is adopted which makes use of natural physical sub-processes in the system, which are then mapped into the software processes to control the system. However, communications are required between the processes because of the disjoint nature of the distributed (i.e. partitioned) state of the physical system. The structural partitioning technique, and recent developments in the theory of potential controllability and observability of a system, are the basis for the design of controllers. In particular, the method is used to derive a decentralised estimate of the state vector for a continuous-time system. The work is also extended to derive a distributed estimate for a discrete-time system. Emphasis is also given to the role of communications in the distributed control of processes and to the partitioning technique necessary to design distributed and decentralised systems with resilient structures. A method is presented for the systematic identification of necessary communications for distributed control. It is also shwon that the structural partitions can be used directly in the design of software fault tolerant concurrent controllers. In particular, the structural partition can be used to identify the boundary of the conversation which can be used to protect a specific part of the system. In addition, for certain classes of system, the partitions can be used to identify processes which may be dynamically reconfigured in the event of a fault. These methods should be of use in the design of robust distributed systems.

Developments and extensions of Roth's method of double Fourier series with applications to the solution of electromagnetic field problems

The first part of the thesis compares Roth's method with other methods, in particular the method of separation of variables and the finite cosine transform method, for solving certain elliptic partial differential equations arising in practice. In particular we consider the solution of steady state problems associated with insulated conductors in rectangular slots. Roth's method has two main disadvantages namely the slow rate of con­vergence of the double Fourier series and the restrictive form of the allowable boundary conditions. A combined Roth-separation of variables method is derived to remove the restrictions on the form of the boundary conditions and various Chebyshev approximations are used to try to improve the rate of convergence of the series. All the techniques are then applied to the Neumann problem arising from balanced rectangular windings in a transformer window. Roth's method is then extended to deal with problems other than those resulting from static fields. First we consider a rectangular insulated conductor in a rectangular slot when the current is varying sinusoidally with time. An approximate method is also developed and compared with the exact method.The approximation is then used to consider the problem of an insulated conductor in a slot facing an air gap. We also consider the exact method applied to the determination of the eddy-current loss produced in an isolated rectangular conductor by a transverse magnetic field varying sinusoidally with time. The results obtained using Roth's method are critically compared with those obtained by other authors using different methods. The final part of the thesis investigates further the application of Chebyshdev methods to the solution of elliptic partial differential equations; an area where Chebyshev approximations have rarely been used. A poisson equation with a polynomial term is treated first followed by a slot problem in cylindrical geometry.

Approximating differentiable relationships between delay embedded dynamical systems with radical basis functions

This thesis is about the study of relationships between experimental dynamical systems. The basic approach is to fit radial basis function maps between time delay embeddings of manifolds. We have shown that under certain conditions these maps are generically diffeomorphisms, and can be analysed to determine whether or not the manifolds in question are diffeomorphically related to each other. If not, a study of the distribution of errors may provide information about the lack of equivalence between the two. The method has applications wherever two or more sensors are used to measure a single system, or where a single sensor can respond on more than one time scale: their respective time series can be tested to determine whether or not they are coupled, and to what degree. One application which we have explored is the determination of a minimum embedding dimension for dynamical system reconstruction. In this special case the diffeomorphism in question is closely related to the predictor for the time series itself. Linear transformations of delay embedded manifolds can also be shown to have nonlinear inverses under the right conditions, and we have used radial basis functions to approximate these inverse maps in a variety of contexts. This method is particularly useful when the linear transformation corresponds to the delay embedding of a finite impulse response filtered time series. One application of fitting an inverse to this linear map is the detection of periodic orbits in chaotic attractors, using suitably tuned filters. This method has also been used to separate signals with known bandwidths from deterministic noise, by tuning a filter to stop the signal and then recovering the chaos with the nonlinear inverse. The method may have applications to the cancellation of noise generated by mechanical or electrical systems. In the course of this research a sophisticated piece of software has been developed. The program allows the construction of a hierarchy of delay embeddings from scalar and multi-valued time series. The embedded objects can be analysed graphically, and radial basis function maps can be fitted between them asynchronously, in parallel, on a multi-processor machine. In addition to a graphical user interface, the program can be driven by a batch mode command language, incorporating the concept of parallel and sequential instruction groups and enabling complex sequences of experiments to be performed in parallel in a resource-efficient manner.

Informal boundary-spanning links and networks in successful technological innovation

The sources of ideas embodied within successful technological innovation has been a subject of interest in many studies since the 1950s. This research suggests that sources external to the innovating organisation account for between one and two-thirds of the inputs important to the innovation process. In addition, studies have long highlighted the important role played by the personal boundary-spanning relationships of engineers and scientists as a channel for the transference of such inputs. However, research concerning the role and nature of personal boundary-spanning links in the innovation process have either been primarily structurally orientated, seeking to map out the informal networks of scientists and engineers, or more typically, anecdotal. The objective of this research was to reveal and build upon our knowledge of the role, nature and importance of informal exchange activity in the innovation process. In order to achieve this, an empirical study was undertaken to determine the informal sources, channels and mechanisms employed in the development of thirty five award-winning innovations. Through the adoption of the network perspective, the multiple sources and pluralistic patterns of collaboration and communication in the innovation process were systematically explored. This approach provided a framework that allowed for the detailed study of both the individual dyadic links and morphology of the innovation action-sets in which these dyads were embedded. The research found, for example, that the mobilisation of boundary-spanning links and networks was an important or critical factor in nineteen (54%) of the development projects. Of these, informal boundary-spanning exchange activity was considered to be important or critical in eight (23%).