Winding patterns for biplanar MRI shim coils with rectangular and circular target-field regions

A method is presented for calculating the winding patterns required to design independent zonal and tesseral biplanar shim coils for magnetic resonance imaging. Streamline, target-field, Fourier integral and Fourier series methods are utilized. For both Fourier-based methods, the desired target field is specified on the surface of the conducting plates. For the Fourier series method it is possible to specify the target field at additional depths interior to the two conducting plates. The conducting plates are confined symmetrically in the xy plane with dimensions 2a x 2b, and are separated by 2d in the z direction. The specification of the target field is symmetric for the Fourier integral method, but can be over some asymmetric portion pa < x < qa and sb < y < tb of the coil dimensions (-1 < p < q < 1 and -1 < s < t < 1) for the Fourier series method. Arbitrary functions are used in the outer sections to ensure continuity of the magnetic field across the entire coil face. For the Fourier series case, the entire field is periodically extended as double half-range sine or cosine series. The resultant Fourier coefficients are substituted into the Fourier series and integral expressions for the internal and external magnetic fields, and stream functions on both the conducting surfaces. A contour plot of the stream function directly gives the required coil winding patterns. Spherical harmonic analysis of field calculations from a ZX shim coil indicates that example designs and theory are well matched.

A Lanczos-powered implementation of the Faber polynomial quantum time propagator for reaction probabilities

Complementing our recent work on subspace wavepacket propagation [Chem. Phys. Lett. 336 (2001) 149], we introduce a Lanczos-based implementation of the Faber polynomial quantum long-time propagator. The original version [J. Chem. Phys. 101 (1994) 10493] implicitly handles non-Hermitian Hamiltonians, that is, those perturbed by imaginary absorbing potentials to handle unwanted reflection effects. However, like many wavepacket propagation schemes, it encounters a bottleneck associated with dense matrix-vector multiplications. Our implementation seeks to reduce the quantity of such costly operations without sacrificing numerical accuracy. For some benchmark scattering problems, our approach compares favourably with the original. (C) 2004 Elsevier B.V. All rights reserved.

Recent developments in the quantum dynamical characterization of unimolecular resonances

We give a selective review of quantum mechanical methods for calculating and characterizing resonances in small molecular systems, with an emphasis on recent progress in Chebyshev and Lanczos iterative methods. Two archetypal molecular systems are discussed: isolated resonances in HCO, which exhibit regular mode and state specificity, and overlapping resonances in strongly bound HO2, which exhibit irregular and chaotic behavior. Recent progresses for non-zero total angular momentum J calculations of resonances including parallel computing models are also included and future directions in this field are discussed.

Simulation of galvanic corrosion of magnesium coupled to a steel fastener in NaCl solution

The galvanic corrosion of magnesium alloy AZ91D coupled to a steel fastener was studied using a boundary element method (BEM) model and experimental measurements. The BEM model used the measured polarization curves as boundary conditions. The experimental program involved measuring the total corrosion rate as a function of distance from the interface of the magnesium in the form of a sheet containing a mild steel circular insert (5 to 30 mm in diameter). The measured total corrosion rate was interpreted as due to galvanic corrosion plus self corrosion. For a typical case, the self corrosion was estimated typically to be similar to 230 mm/y for an area surrounding the interface and to a distance of about I cm from the interface. Scanning Kelvin Probe Force Microscopy (SKPFM) revealed microgalvanic cells with potential differences of approximately 100 mV across the AZ91D surface. These microgalvanic cells may influence the relative contributions of galvanic and self corrosion to the total corrosion of AZ91D.

Influence of geometry on galvanic corrosion of AZ91D coupled to steel

The influence of geometric factors on the galvanic current density distribution for AZ91D coupled to steel was investigated using experimental measurements and a BEM model. The geometric factors were area ratio of anode/cathode, insulation distance between anode and cathode, depth of solution film covering the galvanic couple and the manner of interaction caused by two independent interacting galvanic couples. The galvanic current density distribution calculated from the BEM model was in good agreement with the experimental measurements. The galvanic current density distribution caused by the interaction of two independent galvanic couples can be reasonably predicted as the linear addition of the galvanic current density caused by each individual galvanic couple. (c) 2005 Elsevier Ltd. All rights reserved.

The programming language python in earth system simulations

-scale vary from a planetary scale and million years for convection problems to 100km and 10 years for fault systems simulations. Various techniques are in use to deal with the time dependency (e.g. Crank-Nicholson), with the non-linearity (e.g. Newton-Raphson) and weakly coupled equations (e.g. non-linear Gauss-Seidel). Besides these high-level solution algorithms discretization methods (e.g. finite element method (FEM), boundary element method (BEM)) are used to deal with spatial derivatives. Typically, large-scale, three dimensional meshes are required to resolve geometrical complexity (e.g. in the case of fault systems) or features in the solution (e.g. in mantel convection simulations). The modelling environment escript allows the rapid implementation of new physics as required for the development of simulation codes in earth sciences. Its main object is to provide a programming language, where the user can define new models and rapidly develop high-level solution algorithms. The current implementation is linked with the finite element package finley as a PDE solver. However, the design is open and other discretization technologies such as finite differences and boundary element methods could be included. escript is implemented as an extension of the interactive programming environment python (see www.python.org). Key concepts introduced are Data objects, which are holding values on nodes or elements of the finite element mesh, and linearPDE objects, which are defining linear partial differential equations to be solved by the underlying discretization technology. In this paper we will show the basic concepts of escript and will show how escript is used to implement a simulation code for interacting fault systems. We will show some results of large-scale, parallel simulations on an SGI Altix system. Acknowledgements: Project work is supported by Australian Commonwealth Government through the Australian Computational Earth Systems Simulator Major National Research Facility, Queensland State Government Smart State Research Facility Fund, The University of Queensland and SGI.

Relaxation of alternating iterative algorithms for the Cauchy problem associated with the modified Helmholtz equation

We propose two algorithms involving the relaxation of either the given Dirichlet data or the prescribed Neumann data on the over-specified boundary, in the case of the alternating iterative algorithm of ` 12 ` 12 `$12 `&12 `#12 `^12 `_12 `%12 `~12 *Kozlov91 applied to Cauchy problems for the modified Helmholtz equation. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed methods.

On the numerical solution of a Cauchy problem in an elastostatic half-plane with a bounded inclusion

We propose an iterative procedure for the inverse problem of determining the displacement vector on the boundary of a bounded planar inclusion given the displacement and stress fields on an infinite (planar) line-segment. At each iteration step mixed boundary value problems in an elastostatic half-plane containing the bounded inclusion are solved. For efficient numerical implementation of the procedure these mixed problems are reduced to integral equations over the bounded inclusion. Well-posedness and numerical solution of these boundary integral equations are presented, and a proof of convergence of the procedure for the inverse problem to the original solution is given. Numerical investigations are presented both for the direct and inverse problems, and these results show in particular that the displacement vector on the boundary of the inclusion can be found in an accurate and stable way with small computational cost.

A procedure for determining a spacewise dependent heat source and the initial temperature

The inverse problem of determining a spacewise dependent heat source, together with the initial temperature for the parabolic heat equation, using the usual conditions of the direct problem and information from two supplementary temperature measurements at different instants of time is studied. These spacewise dependent temperature measurements ensure that this inverse problem has a unique solution, despite the solution being unstable, hence the problem is ill-posed. We propose an iterative algorithm for the stable reconstruction of both the initial data and the source based on a sequence of well-posed direct problems for the parabolic heat equation, which are solved at each iteration step using the boundary element method. The instability is overcome by stopping the iterations at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented for a typical benchmark test example, which has the input measured data perturbed by increasing amounts of random noise. The numerical results show that the proposed procedure gives accurate numerical approximations in relatively few iterations.

Determination of a spacewise dependent heat source

This paper investigates the inverse problem of determining a spacewise dependent heat source in the parabolic heat equation using the usual conditions of the direct problem and information from a supplementary temperature measurement at a given single instant of time. The spacewise dependent temperature measurement ensures that the inverse problem has a unique solution, but this solution is unstable, hence the problem is ill-posed. For this inverse problem, we propose an iterative algorithm based on a sequence of well-posed direct problems which are solved at each iteration step using the boundary element method (BEM). The instability is overcome by stopping the iterations at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented for various typical benchmark test examples which have the input measured data perturbed by increasing amounts of random noise.

A New Algorithm for Monte Carlo for American Options

2000 Mathematics Subject Classification: 91B28, 65C05.

Assessment of primary energy conversions of oscillating water columns. I. Hydrodynamic analysis

This is an investigation on the development of a numerical assessment method for the hydrodynamic performance of an oscillating water column (OWC) wave energy converter. In the research work, a systematic study has been carried out on how the hydrodynamic problem can be solved and represented reliably, focusing on the phenomena of the interactions of the wave-structure and the wave-internal water surface. These phenomena are extensively examined numerically to show how the hydrodynamic parameters can be reliably obtained and used for the OWC performance assessment. In studying the dynamic system, a two-body system is used for the OWC wave energy converter. The first body is the device itself, and the second body is an imaginary “piston,” which replaces part of the water at the internal water surface in the water column. One advantage of the two-body system for an OWC wave energy converter is its physical representations, and therefore, the relevant mathematical expressions and the numerical simulation can be straightforward. That is, the main hydrodynamic parameters can be assessed using the boundary element method of the potential flow in frequency domain, and the relevant parameters are transformed directly from frequency domain to time domain for the two-body system. However, as it is shown in the research, an appropriate representation of the “imaginary” piston is very important, especially when the relevant parameters have to be transformed from frequency-domain to time domain for a further analysis. The examples given in the research have shown that the correct parameters transformed from frequency domain to time domain can be a vital factor for a successful numerical simulation.

Comparison of different methods to detect genetic barriers in a small mammal population

Habitat fragmentation and the consequently the loss of connectivity between populations can reduce the individuals interchange and gene flow, increasing the chances of inbreeding, and the increase the risk of local extinction. Landscape genetics is providing more and better tools to identify genetic barriers.. To our knowledge, no comparison of methods in terms of consistency has been made with observed data and species with low dispersal ability. The aim of this study is to examine the consistency of the results of five methods to detect barriers to gene flow in a Mediterranean pine vole population Microtus duodecimcostatus: F-statistics estimations, Non-Bayesian clustering, Bayesian clustering, Boundary detection and Simple/Partial Mantel tests. All methods were consistent in detecting the stream as a non-genetic barrier. However, no consistency in results among the methods were found regarding the role of the highway as a genetic barrier. Fst, Bayesian clustering assignment test and Partial Mantel test identifyed the highway as a filter to individual interchange. The Mantel tests were the most sensitive method. Boundary detection method (Monmonier’s Algorithm) and Non-Bayesian approaches did not detect any genetic differentiation of the pine vole due to the highway. Based on our findings we recommend that the genetic barrier detection in low dispersal ability populations should be analyzed with multiple methods such as Mantel tests, Bayesian clustering approaches because they show more sensibility in those scenarios and with boundary detection methods by having the aim of detect drastic changes in a variable of interest between the closest individuals. Although simulation studies highlight the weaknesses and the strengths of each method and the factors that promote some results, tests with real data are needed to increase the effectiveness of genetic barrier detection.

Ku metodzie integralnej w teologii fundamentalnej. Sposoby konstruowania interdyscyplinarnych działań w poszukiwaniu locorum theologicorum. Zastosowanie i weryfikacja na przykładzie życia i twórczości Simone Weil

Niniejsza praca powstała z rozpoznanej potrzeby projektowania nowych ujęć poznawczych w teologii obejmujących, w tym samym stopniu, odniesienia do dziedzin teologicznych, jak i innych nauk. Podjęto próbę skonstruowania procedur badawczych, które mogą stać się punktem wyjścia ku stworzeniu pełnej metody integralnej w teologii fundamentalnej. Stąd tytuł pracy Ku metodzie integralnej w teologii fundamentalnej. Budowanie nowych zasad aktywności badawczej związane jest zawsze z etapem konstrukcyjnym i etapem weryfikacyjnym przygotowanych narzędzi, co zostało wyartykułowane w podtytułach: Sposoby konstruowania interdyscyplinarnych działań w poszukiwaniu »locorum theologicorum«. Zastosowanie i weryfikacja na przykładzie życia i twórczości Simone Weil. Tym samym praca jest dwuczęściowa. Celem pierwszej części jest przedstawienie, w jaki sposób konstruować poszukiwania nowych locorum theologicorum. Druga część pracy ma charakter weryfikacyjny. Opracowane narzędzia badawcze zostały zastosowane do odpowiedzi na pytanie: Na ile życie i twórczość francuskiej myślicielki, Simone Weil, może stać się źródłem dla tworzonych współcześnie opinii teologicznych? W przedstawianej pracy powiązano, dość ściśle, konstruowanie integralnego ujęcia badawczego z poszukiwaniem nowych czy reinterpretacją już rozeznanych miejsc teologicznych. Główny cel pracy związany jest z opisywaniem działań, które uprawdopodobniają otrzymanie nowych treści. Przyjęty sposób działania to wyjaśnianie, nie mające statusu pełnej prawdziwości logicznej; jednak jest ono procedurą, która pozwala w pewnym stopniu obiektywizować subiektywne dane płynące z otaczającej nas rzeczywistości. Pozwoliło to na kompetentne poruszanie się w przestrzeni zdań uznanych za prawdziwe zarówno w ramach teologii, jak i innych nauk. Dlatego w tej pracy skupiono się na przedstawieniu procedur poszukiwań, weryfikacji i możliwego zastosowania w badaniach naukowych współczesnych miejsc teologicznych. Ważniejszy jest sposób otrzymywania określonych wyników, a wynik tychże działań doceniony jest dopiero na etapie weryfikacyjnym skonstruowanych narzędzi badawczych. W części pierwszej pracy skupiono się na tworzeniu ogólnych zasad myślenia w ramach teologii fundamentalnej. Konstruowanie narzędzi badawczych rozpoczęto od rozeznania i przedstawienia najgłębszych fundamentów, korzeni zastosowanych procedur poprzez opis zasad opracowywania i przygotowywania działań operacyjnych. Określenie tych zasad związane jest z wprowadzeniem nowego sposobu ujmowania problematyki badawczej poprzez tak zwane myślenie modelowe. Pozwala ono na włączenie w proces uzasadniania otrzymanych wyników, oprócz dowodzenia i tłumaczenia, również tak zwanego wyjaśniania, poprzez zataczanie coraz wyższych kręgów po metodycznej spirali, której osią jest odniesienie do Bożego Objawienia odczytanego we wspólnocie Kościoła. Dzięki temu otrzymano śmiałą hipotezę, w której uwzględniono w tym samym stopniu Objawienie Boga, jak i adresata tegoż, z jego pełnym osadzeniem w rzeczywistościach ziemskich. Holistyczne, w ramach tworzonego modelu, ujmowanie problematyki pozwoliło również na ukazywanie ciągle nowych aspektów tworzonej metody integralnej. Opracowane zostały zasady konstruowania modelu ujmowania rzeczywistości Objawienia w aspekcie przedmiotowym. Jako podstawę działań przyjęto istniejącą już w teologii fundamentalnej metodę historiozbawczą. Przechodząc do systematycznej prezentacji, jako odniesienia graniczne tworzonego modelu «przestrzeni eklezjalnej» wprowadzono ujęcia teologiczne św. Ireneusza z Lyonu i św. Justyna Męczennika. Konstruując narzędzia pozwalające na ujęcia podmiotowe treści przeżyć odbiorcy Objawienia jako odniesienia graniczne wprowadzono koncepcje Umberto Eco, Geralda O’Collinsa i Paula Ricoeura. Pozwalają one na modelowe ujęcie ludzkich przeżyć jako «dzieła otwartego». W etapie czwartym podjęto próbę ustalenia zasad wzajemnego przenikania się ujęć przedmiotowych i podmiotowych problematyki badawczej, by stworzyć ujęcie integralne w opracowywaniu treści teologicznych. Powstały model «wzajemnych oddziaływań» okazał się przydatnym narzędziem w ocenie teologicznego potencjału interdyscyplinarnych oddziaływań pomiędzy teologią fundamentalną a treściami innych nauk. Pozwolił on doprecyzować warunki możliwości przyjęcia jakiejś ludzkiej aktywności jako locus theologicus z zachowaniem odpowiedniej relacji do Objawienia odczytanego we wspólnocie Kościoła z możliwym do osiągnięcia stopniem obiektywizacji. W cześć drugiej pracy realizuje się konieczną w naukach weryfikację opracowanych narzędzi badawczych i uwiarygodnienia działań operacyjnych poprzez zastosowanie do analizy konkretnego przypadku, którym jest życie i twórczość Simone Weil. Praca w tej części również została podzielona na etapy według aspektowego ujęcia umożliwiającego różne punkty widzenia tego samego przedmiotu badawczego. Ponieważ opracowane modele teoretyczne tworzą ramy dla nowej twórczości badacza, kolejne etapy weryfikacyjne są dalszym ciągiem budowania sposobów ujęcia ukonkretnionej tematyki. Życie i twórczość Simone Weil zostały przedstawione w czterech perspektywach badawczych. Pierwsza z nich jest ujęciem z punktu widzenia relacji «dzieło – autor dzieła», kolejna wprowadza dodatkowe odniesienia związane z relacją «dzieło – odbiorca dzieła». Trzeci aspekt skupia się na możliwych do odczytania z twórczości Simone Weil, treściach teologicznych na bazie relacji «dzieło – badacz dzieła». Najpłodniejszym badawczo okazało się odniesienie «dzieła», któremu na imię Simone Weil ku wymiarowi eschatologicznemu chrześcijaństwa. Opracowana metoda i przedstawione warunki weryfikacyjne ustalające kryteria w uznaniu jej przemyśleń i koncepcji jako locus theologicus ukazały się jako niezwykle przydatne.

Induced Damping on Vibrating Circular Plates Submerged in still Fluid

When a structure vibrates immersed in a fluid it is known that the dynamic properties of the system are modified. The surrounding fluid will, in general, contribute to the inertia, the rigidity and the damping coefficient of the coupled fluid-structure system. For light structures, like spacecraft antennas, even when the fluid is air the contribution to the dynamic properties can be important. For not so light structures the ratio of the equivalent fluid/structure mass and rigidity can be very small and the fluid contribution could be neglected. For the ratio of equivalent fluid/structure damping both terms are of the same order and therefore the fluid contribution must be studied. The working life of the spacecraft structure would be on space and so without any surrounding fluid. The response of a spacecraft structure on its operational life would be attenuated by the structural damping alone but when the structure is dynamically tested on the earth the dynamic modal test is performed with the fluid surrounding it. The results thus are contaminated by the effects of the fluid. If the damping added by the fluid is of the same order as the structural damping the response of the structure in space can be quite different to the response predicted on earth. It is therefore desirable to have a method able to determine the amount of damping induced by the fluid and that should be subtracted of the total damping measured on the modal vibration test. In this work, a method for the determination of the effect of the surrounding fluid on the dynamic characteristics of a circular plate has been developed. The plate is assumed to vibrate harmonically with the vacuum modes and the generalized forces matrix due to the fluid is thus computed. For a compressible fluid this matrix is formed by complex numbers including terms of inertia, rigidity and damping. The matrix due to the fluid loading is determined by a boundary element method (BEM). The BEM used is of circular rings on the plate surface so the number of elements to obtain an accurate result is very low. The natural frequencies of the system are computed by an iteration procedure one by one and also the damping fluid contribution. Comparisons of the present method with various experimental data and other theories show the efficiency and accuracy of the method for any support condition of the plate.