Transient temperature rise in a mouse due to low-frequency regional hyperthermia

A refined nonlinear heat transfer model of a mouse has been developed to simulate the transient temperature rise in a neoplastic tumour and neighbouring tissue during regional hyperthermia using a 150 kHz inductive coil. In this study, we incorporate various bio-energetic enhancements to the heat transfer equation and numerical validations based on experimental findings for the mouse, in terms of nonlinear metabolic heat production, homeothermy, blood perfusion parameters, thermoregulation, psychological and physiological effects. The discretized bio-heat transfer equation has been validated with the commercial software FEMLAB on a canonical multi-sphere object before applying the scheme to the inhomogeneous mouse voxel phantom. The time-dependent numerical results of regional hyperthermia of mouse thigh have been compared with the available experimental temperature results with only a few small disparities. During the first 20 min of local unfocused heating, the temperature in the tumour and the surrounding tissue increased by around 7.5 degrees C. The objective of this preliminary study was to develop a validated electrothermal numerical scheme for inductive hyperthermia of a small mammal with the intention of expanding the model into a complete numerical solution involving ferromagnetic nanoparticles for targeted heating of tumours at low frequencies. In addition, the numerical scheme herein could assist in optimizing and tailoring of focused electromagnetic fields for hyperthermia.

Mathematical methods in power system stability studies

In this thesis various mathematical methods of studying the transient and dynamic stabiIity of practical power systems are presented. Certain long established methods are reviewed and refinements of some proposed. New methods are presented which remove some of the difficulties encountered in applying the powerful stability theories based on the concepts of Liapunov. Chapter 1 is concerned with numerical solution of the transient stability problem. Following a review and comparison of synchronous machine models the superiority of a particular model from the point of view of combined computing time and accuracy is demonstrated. A digital computer program incorporating all the synchronous machine models discussed, and an induction machine model, is described and results of a practical multi-machine transient stability study are presented. Chapter 2 reviews certain concepts and theorems due to Liapunov. In Chapter 3 transient stability regions of single, two and multi~machine systems are investigated through the use of energy type Liapunov functions. The treatment removes several mathematical difficulties encountered in earlier applications of the method. In Chapter 4 a simple criterion for the steady state stability of a multi-machine system is developed and compared with established criteria and a state space approach. In Chapters 5, 6 and 7 dynamic stability and small signal dynamic response are studied through a state space representation of the system. In Chapter 5 the state space equations are derived for single machine systems. An example is provided in which the dynamic stability limit curves are plotted for various synchronous machine representations. In Chapter 6 the state space approach is extended to multi~machine systems. To draw conclusions concerning dynamic stability or dynamic response the system eigenvalues must be properly interpreted, and a discussion concerning correct interpretation is included. Chapter 7 presents a discussion of the optimisation of power system small sjgnal performance through the use of Liapunov functions.

Theoretical studies of the mid-latitude ionosphere

Following a brief description of the atmosphere and ionosphere in Chapter I we describe how the equations of continuity and momentum for 0+, H+, He+, 0++ are derived from the formulations of St-Maurice and Schunk(1977) and Quegan et al.(1981) in Chapter II. In Chapter III we investigate the nature of the downward flow of protons in a collapsing post-sunset ionosphere. We derive an analytical form for the limiting temperature, we also note the importance of the polarization field term and concluded that the flow will remain subsonic for realistic conditions. The time-dependent behaviour of He+ under sunspot minimum conditions is investigated in Chapter IV. This is achieved by numerical solution of the 0+, H+ and,He+ continuity and momentum equations, treating He+ as a minor ion with 0+ , H+ as major ions. We found that He+ flows upwards during the day-time and downwards during the nighttime. He+ flux tube content reached a maximum on the 8th day of the integration period and started to decreasing. This is due to the large amount of H+ present at the late stages of the integration period which makes He+ unable to diffuse through the H+ layer away from the loss region. In Chapter V we investigate the behaviour of 0++ using sunspot maximum parameters. Although our results support the findings of Geis and Young (1981) that the large amounts of 0++ at the equator are caused mainly by thermal diffusion, the model used by Geis and Young overemphesizes the effect of thermal diffusion. The importance of 0++ - 0+ collision frequency is also noted. In Chapter VI we extend the work of Chapter IV, presenting a comparative study of H and He at sunspot minimum and sunspot maximum.In this last Chapter all three ions, O+ ,H+ and He+ , are treated theoretically as major ions and we concentrate mainly on light ion contents and fluxes. The results of this Chapter indicate that by assuming He+ as a minor ion we under-estimate He+ and over-estimate. H+. Some interesting features concerning the day to day behaviour of the light ion fluxes arise. In particular the day-time H+ fluxes decrease from day to day in contrast to the work of Murphy et al.(1976). In appendix.A we derive some analytical forms for the optical depth so that the models can include a realistic description of photoionization.

An integral equation method for a mixed initial boundary value problem for unsteady Stokes system in a doubly-connected domain

We present a novel numerical method for a mixed initial boundary value problem for the unsteady Stokes system in a planar doubly-connected domain. Using a Laguerre transformation the unsteady problem is reduced to a system of boundary value problems for the Stokes resolvent equations. Employing a modied potential approach we obtain a system of boundary integral equations with various singularities and we use a trigonometric quadrature method for their numerical solution. Numerical examples are presented showing that accurate approximations can be obtained with low computational cost.

On an indirect integral equation approach for stationary heat transfer in semi-infinite layered domains in R3 with cavities

Regions containing internal boundaries such as composite materials arise in many applications.We consider a situation of a layered domain in IR3 containing a nite number of bounded cavities. The model is stationary heat transfer given by the Laplace equation with piecewise constant conductivity. The heat ux (a Neumann condition) is imposed on the bottom of the layered region and various boundary conditions are imposed on the cavities. The usual transmission (interface) conditions are satised at the interface layer, that is continuity of the solution and its normal derivative. To eciently calculate the stationary temperature eld in the semi-innite region, we employ a Green's matrix technique and reduce the problem to boundary integral equations (weakly singular) over the bounded surfaces of the cavities. For the numerical solution of these integral equations, we use Wienert's approach [20]. Assuming that each cavity is homeomorphic with the unit sphere, a fully discrete projection method with super-algebraic convergence order is proposed. A proof of an error estimate for the approximation is given as well. Numerical examples are presented that further highlights the eciency and accuracy of the proposed method.

Recovering boundary data in planar heat conduction using boundary integral equation method

We consider a Cauchy problem for the heat equation, where the temperature field is to be reconstructed from the temperature and heat flux given on a part of the boundary of the solution domain. We employ a Landweber type method proposed in [2], where a sequence of mixed well-posed problems are solved at each iteration step to obtain a stable approximation to the original Cauchy problem. We develop an efficient boundary integral equation method for the numerical solution of these mixed problems, based on the method of Rothe. Numerical examples are presented both with exact and noisy data, showing the efficiency and stability of the proposed procedure and approximations.

An iterative method for the reconstruction of a stationary flow

In this article, an iterative algorithm based on the Landweber-Fridman method in combination with the boundary element method is developed for solving a Cauchy problem in linear hydrostatics Stokes flow of a slow viscous fluid. This is an iteration scheme where mixed well-posed problems for the stationary generalized Stokes system and its adjoint are solved in an alternating way. A convergence proof of this procedure is included and an efficient stopping criterion is employed. The numerical results confirm that the iterative method produces a convergent and stable numerical solution. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007

Breakup of a multisoliton state of the linearly damped nonlinear Schrödinger equation

We address the breakup (splitting) of multisoliton solutions of the nonlinear Schrödinger equation (NLSE), occurring due to linear loss. Two different approaches are used for the study of the splitting process. The first one is based on the direct numerical solution of the linearly damped NLSE and the subsequent analysis of the eigenvalue drift for the associated Zakharov-Shabat spectral problem. The second one involves the multisoliton adiabatic perturbation theory applied for studying the evolution of the solution parameters, with the linear loss taken as a small perturbation. We demonstrate that in the case of strong nonadiabatic loss the evolution of the Zakharov-Shabat eigenvalues can be quite nontrivial. We also demonstrate that the multisoliton breakup can be correctly described within the framework of the adiabatic perturbation theory and can take place even due to small linear loss. Eventually we elucidate the occurrence of the splitting and its dependence on the phase mismatch between the solitons forming a two-soliton bound state. © 2007 The American Physical Society.

A variational conjugate gradient method for determining the fluid velocity of a slow viscous flow

The problem considered is that of determining the fluid velocity for linear hydrostatics Stokes flow of slow viscous fluids from measured velocity and fluid stress force on a part of the boundary of a bounded domain. A variational conjugate gradient iterative procedure is proposed based on solving a series of mixed well-posed boundary value problems for the Stokes operator and its adjoint. In order to stabilize the Cauchy problem, the iterations are ceased according to an optimal order discrepancy principle stopping criterion. Numerical results obtained using the boundary element method confirm that the procedure produces a convergent and stable numerical solution.

Dimensioning of Telecommunication Network Based on Quality of Services Demand and Detailed Behaviour of Users

The aim of this paper is to be determined the network capacity (number of necessary internal switching lines) based on detailed users’ behaviour and demanded quality of service parameters in an overall telecommunication system. We consider detailed conceptual and its corresponded analytical traffic model of telecommunication system with (virtual) circuit switching, in stationary state with generalized input flow, repeated calls, limited number of homogeneous terminals and losses due to abandoned and interrupted dialing, blocked and interrupted switching, not available intent terminal, blocked and abandoned ringing (absent called user) and abandoned conversation. We propose an analytical - numerical solution for finding the number of internal switching lines and values of the some basic traffic parameters as a function of telecommunication system state. These parameters are requisite for maintenance demand level of network quality of service (QoS). Dependencies, based on the numericalanalytical results are shown graphically. For proposed conceptual and its corresponding analytical model a network dimensioning task (NDT) is formulated, solvability of the NDT and the necessary conditions for analytical solution are researched as well. It is proposed a rule (algorithm) and computer program for calculation of the corresponded number of the internal switching lines, as well as corresponded values of traffic parameters, making the management of QoS easily.

Active Monitoring and Decision Making Problem

Active monitoring and problem of non-stable of sound signal parameters in the regime of piling up response signal of environment is under consideration. Math model of testing object by set of weak stationary dynamic actions is offered. The response of structures to the set of signals is under processing for getting important information about object condition in high frequency band. Making decision procedure by using researcher’s heuristic and aprioristic knowledge is discussed as well. As an example the result of numerical solution is given.

Time–Harmonic Behaviour of a Cracked Piezoelectric Solid by BIEM

ACM Computing Classification System (1998): J.2, G.1.9

Modeling of Cylindrical Couette Flow of Rarefied Gas Between Rotating Cylinders

Петър Господинов, Добри Данков, Владимир Русинов, Стефан Стефанов - Изследвано е цилиндрично течение на Кует за разреден газ между два въртящи се цилиндъра. Получени са профилите на налягането, скоростта и температурата по метода на прякото статистическо моделиране (DSMC) и чрез числено решаване на уравненията на Навие-Стокс за свиваем флуид. Резултатите сочат много добро съвпадение за малки числа на Кнудсен Kn = 0.02. Показано е, че при различни кинематични гранични условия, газът изостава или избързва спрямо скоростта на стената, или има поведение на твърдо еластично тяло. Получените резултати са важни при решаването на неравнинни, задачи от микрофлуидиката с отчитане на ефектите на кривината.

Comparative Analysis of the Opposite Rotating Cylinders Impact over Couette Flow for Rarefied Gas

Петър Господинов, Добри Данков, Владимир Русинов, Стефан Стефанов - Иследвано е цилиндрично течение на Кует на разреден газ в случая на въртене на два коаксиални цилиндъра с еднакви по големина скорости, но в различни посоки. Целта на изследването е да се установи влиянието на малки скорости на въртене върху макрохарактеристиките – ρ, V , . Числените резултати са получени чрез използване на DSMC и числено решение на уравненията на Навие-Стокс за относително малки (дозвукови) скорости на въртене. Установено е добро съвпадение на резултатите получени по двата метода за Kn = 0.02. Установено е, че съществува “стационарна” точка за плътността и скоростта. Получените резултати са важни при решаването на неравнини, задачи от микрофлуидиката с отчитане на ефектите на кривината. Ключови думи: Механика на флуидите, Кинетична теория, Разреден газ, DSMC

Parallel Algorithm for the Local Variations Method

Димитър С. Илиев, Станимир Д. Илиев - Актуално е изследването на поведението на течен менискус в околността на хетерогенна стена. До сега няма получено числено решение за формата на менискуса около стена, която е с хаотична хетерогенност. В настоящата статия е разработен алгоритъм за метода на локалните вариации, който може да се използва на многопроцесорни системи. С този метод е получен за първи път профила на равновесен течен менискус около вертикална стена с хаотична хетерогенност.