Control problems for the wave and telegrapher's equations on metric graphs

Dissertation (Ph.D.) University of Alaska Fairbanks, 2022The dissertation focuses on control problems for the wave and telegrapher's equations on metric graphs. In the first part, an algorithm is constructed to solve the exact control problems on finite intervals. The algorithm is implemented numerically to solve the exact control problems on finite intervals. Moreover, we developed numerical algorithms for the solution of control problems on metric graphs based on the recent boundary controllability results of wave equations on metric graphs. We presented numerical solutions to shape control problems on quantum graphs. Specifically, we presented the results of numerical experiments involving a three-star graph. Our second part deals with the forward and control problems for the telegrapher's equations on metric graphs. We consider the forward problem on general graphs and develop an algorithm that solves equations with variable resistance, conductance, constant inductance, and constant capacitance. An algorithm is developed to solve the voltage and current control problems on a finite interval for constant inductance and capacitance, and variable resistance and conductance. Numerical results are also presented for this case. Finally, we consider the control problems for the telegrapher's equations on metric graphs. The control problem is considered on tree graphs, i.e. graphs without cycles, with some restrictions on the coefficients. Specifically, we consider equations with constant coefficients that do not depend on the edge. We obtained the necessary and sufficient conditions of the exact controllability and indicate the minimal control time.Chapter 1: General introduction -- Chapter 2: Control problems for the wave equation on metric graphs -- Chapter 3: Forward problems for the telegrapher's equations on metric graphs -- Chapter 4: Control problems for the telegrapher's equations on metric graphs -- Chapter 5: Conclusions -- References

Numerical modelling of the deformation of elastic material by the TLM method

The transmission line matrix (TLM) method is a numerical tool for the solution of wave and diffusion type equations. The application of TLM to physical phenomena such as heat flow and electromagnetic wave propagation is well established. A previous attempt to apply TLM models to the area of elastic wave propagation and elastic deformation had limited success. The work of this thesis extends the application base of TLM to the area of elastic deformation modelling and validates the model for several two-dimensional situations. In doing this it has been necessary to develop new nodal structures which facilitate the scaling of differential coefficients and incorporation of cross derivatives. Nodal structures which allow the modelling of two and three-dimensional, and anisotropic, elastic deformation are described.The technique is demonstrated by applying the elastic deformation model to several elastic problems. These include two-dimensional isotropic models and models of anisotropic elastic deformation. Provision is also made for the application of various boundary conditions which include displacement, force and frictional boundaries

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

The Schur algorithm and its applications

Includes bibliographical references (p. 47-50).Research supported by the Air Force Office of Scientific Research AFOSR-82-0135A Research supported by the Exxon Education Foundation.Andrew E. Yagle and Bernard C. Levy

Continuous Order Identification of PHWR Models Under Step-back for the Design of Hyper-damped Power Tracking Controller with Enhanced Reactor Safety

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.In this paper, discrete time higher integer order linear transfer function models have been identified first for a 500 MWe Pressurized Heavy Water Reactor (PHWR) which has highly nonlinear dynamical nature. Linear discrete time models of the nonlinear nuclear reactor have been identified around eight different operating points (power reduction or step-back conditions) with least square estimator (LSE) and its four variants. From the synthetic frequency domain data of these identified discrete time models, fractional order (FO) models with sampled continuous order distribution are identified for the nuclear reactor. This enables design of continuous order Proportional-Integral-Derivative (PID) like compensators in the complex w-plane for global power tracking at a wide range of operating conditions. Modeling of the PHWR is attempted with various levels of discrete commensurate-orders and the achievable accuracies are also elucidated along with the hidden issues, regarding modeling and controller design. Credible simulation studies are presented to show the effectiveness of the proposed reactor modeling and power level controller design. The controller pushes the reactor poles in higher Riemann sheets and thus makes the closed loop system hyper-damped which ensures safer reactor operation at varying dc-gain while making the power tracking temporal response slightly sluggish; but ensuring greater safety margin.This work has been supported by Department of Science and Technology (DST), Govt. of India, under the PURSE programme

Transient simulation of complex electronic circuits and systems operating at ultra high frequencies

The electronics industry worldwide faces increasingly difficult challenges in a bid to produce ultra-fast, reliable and inexpensive electronic devices. Electronic manufacturers rely on the Electronic Design Automation (EDA) industry to produce consistent Computer A id e d Design (CAD) simulation tools that w ill enable the design of new high-performance integrated circuits (IC), the key component of a modem electronic device. However, the continuing trend towards increasing operational frequencies and shrinking device sizes raises the question of the capability of existing circuit simulators to accurately and efficiently estimate circuit behaviour. The principle objective of this thesis is to advance the state-of-art in the transient simulation of complex electronic circuits and systems operating at ultra high frequencies. Given a set of excitations and initial conditions, the research problem involves the determination of the transient response o f a high-frequency complex electronic system consisting of linear (interconnects) and non-linear (discrete elements) parts with greatly improved efficien cy compared to existing methods and with the potential for very high accuracy in a way that permits an effective trade-off between accuracy and computational complexity. High-frequency interconnect effects are a major cause of the signal degradation encountered b y a signal propagating through linear interconnect networks in the modem IC. Therefore, the development of an interconnect model that can accurately and efficiently take into account frequency-dependent parameters of modem non-uniform interconnect is of paramount importance for state-of-art circuit simulators. Analytical models and models based on a set of tabulated data are investigated in this thesis. Two novel, h igh ly accurate and efficient interconnect simulation techniques are developed. These techniques combine model order reduction methods with either an analytical resonant model or an interconnect model generated from frequency-dependent sparameters derived from measurements or rigorous full-wave simulation. The latter part o f the thesis is concerned with envelope simulation. The complex mixture of profoundly different analog/digital parts in a modern IC gives rise to multitime signals, where a fast changing signal arising from the digital section is modulated by a slower-changing envelope signal related to the analog part. A transient analysis of such a circuit is in general very time-consuming. Therefore, specialised methods that take into account the multi-time nature o f the signal are required. To address this issue, a novel envelope simulation technique is developed. This technique combines a wavelet-based collocation method with a multi-time approach to result in a novel simulation technique that enables the desired trade-off between the required accuracy and computational efficiency in a simple and intuitive way. Furthermore, this new technique has the potential to greatly reduce the overall design cycle

Time-dependent simplified spherical harmonics formulations for a nuclear reactor system

[EN] The steady-state simplified spherical harmonics equations (SPNequations) are a higher order approximation to the neutron transport equations than the neutron diffusion equation that also have reasonable computational demands. This work extends these results for the analysis of transients by comparing of two formulations of time-dependent SPN equations considering different treatments for the time derivatives of the field moments. The first is the full system of equations and the second is a diffusive approximation of these equations that neglects the time derivatives of the odd moments. The spatial discretization of these methodologies is made by using a high order finite element method. For the time discretization, a semi-implicit Euler method is used. Numerical results show that the diffusive formulation for the time-dependent simplified spherical harmonics equations does not present a relevant loss of accuracy while being more computationally efficient than the full systemThis work has been partially supported by Spanish Ministerio de Economia y Competitividad under projects ENE2017-89029-P and MTM2017-85669-P. Furthermore, this work has been financed by the Generalitat Valenciana under the project PROMETEO/2018/035Carreño, A.; Vidal-Ferràndiz, A.; Ginestar Peiro, D.; Verdú Martín, GJ. (2021). Time-dependent simplified spherical harmonics formulations for a nuclear reactor system. Nuclear Engineering and Technology. 53(12):3861-3878. https://doi.org/10.1016/j.net.2021.06.010S38613878531

TLM models of deformation and their application to vitreous china ware during firing

During firing, the deformation of ceramic articles under their own weight may be problematic particularly in the sanitary ware industry where articles are large. A model has been developed that predicts the viscoelastic deformation of a range of vitreous china testpieces during the firing process. The model constitutes a novel application of the transmission line modelling technique to viscoelastic deformation. The applicability of the model to the sanitary ware industry is addressed