Den kopparbindande egenskapen hos prionproteiner är sannolikt kopplad till proteinets funtion. Det mänskliga prionproteinet innehåller ett kopparbindande oktapeptidområde, där PHGGGWGQ-sekvensen upprepas fyra gånger i följd. Syftet med detta arbete är att undersöka strukturen och dynamiken i oktapeptidområdet genom att använda teoretiska metoder. Med kvantkemisk strukturoptimering genomfördes en detaljerad jämförelse av växelverkan mellan flera katjoner och det kopparbindande området. Enligt dessa beräkningar är rodium(III) en möjlig ersättare för koppar(II) i NMR-specktroskopiska koordinationsstudier. Alternativa solvatiseringsmodeller i molekyldynamiksimuleringar har också jämförts. Periodiska randvillkor är mest lämpade för användning i de system som undersöks i detta arbete. Molekyldynamiksimuleringar användes för att jämföra oktapeptidområdets struktur och dynamik med och utan kopparjoner. Växelverkan mellan aminosyrornas ringar påverkar starkt strukturen i detta område i frånvaro av kopparjoner. Fyra olika icke-bindande och bindande modeller har studerats, vilka skiljer i sin beskrivning av växelverkan mellan koppar och proteinet. Teoretiska EXAFS spektra beräknades från dem simulerade strukturerna. Spektra som genererats för den bindande modellen är nästan identiska med experimentiella resultat, vilket stöder användandet av den bindande modellen. Detta arbete visar att kopparjoner interagerar med histidin imidazolringens Nδ, deprotonerade amidkväven hos de därpå följande glycinerna samt karbonylsyret hos den andra glycinen. Simuleringarna kunde visa att kopparjonen inte stabilt binder några axiella vattenmolekyler i lösning, till skillnad från en kristallstruktur av koordinationsstrukturen. Indolringen hos tryptofan interagerar direkt med kopparjonen genom stabiliserande katjon-π växelverkan utan direkt medverkan av någon vattenmolekyl. Växelverkan mellan indolringen och kopparjonen var väldefinierad och observerades kunna ske på båda sidor av koordinationsplanet. Molekyldynamiksimuleringarna med kopparjoner och oktapeptidområdet visade hur närvaron av kopparjoner ledde till ett mer strukturerat oktapeptidområde. / The copper-binding ability of the prion protein is thought to be closely related to its function. The human prion protein contains a copper-binding octapeptide region, where the octapeptide PHGGGWGQ is repeated four times consecutively. This work focuses on investigation of the structure and the dynamics of the octapeptide region by means of theoretical methods. Quantum chemical structural optimization allowed a detailed comparison of the interaction of several cations at the copper coordination site. These calculations identified rhodium(III) as a potent substitute for copper(II) that could be used to study the coordination site with NMR-spectroscopic methods. Solvation models that could be used in molecular dynamics simulations as an alternative to periodic boundary conditions were evaluated. Periodic boundary conditions are the best method for modeling the aqueous bulk in the kind of systems that are studied in this work. Molecular dynamics simulations were used to compare the behavior of the octapeptide region in the absence and presence of copper ions. Interaction between nonpolar rings strongly influences the structure of the region in the absence of copper ions. Four different non-bonded and bonded models for describing the interaction between copper and the protein were evaluated. Theoretical EXAFS spectra were calculated from the simulated structures. The results obtained for the bonded model are nearly identical with experimental data, which validates the use of the bonded model. This work thus shows strong evidence for copper(II) ions interacting with the octapeptide region through the histidine imidazole Nδ, the deprotonated nitrogen atoms of the following two glycine residues and the carbonyl oxygen atom of the second glycine residue. Notably, the simulations show that the axial sites of the copper ion do not stably coordinate water molecules in solution, as opposed to the crystal structure reported for the coordination site. Instead, the tryptophan indole ring interacted directly with the copper ion through stabilizing cation-π interaction without water mediation. The interaction of the indole ring with the copper ion was well-defined and was observed to occur on both sides of the coordination plane. The investigations of the interaction between copper ions and the octapeptide region with molecular dynamics simulations show how the presence of copper ions results in a more structured octapeptide region. / QC 20100816

In this thesis, we study the scattering problem of a vertically offset dielectric slab waveguide, using continuous radiation modes. The calculation of radiation modes of an arbitrarily layered waveguide has been thoroughly investigated in the literature. Most approaches were based on launching two incident waves: one from above and one from below, resulting in two transmitted waves and two reflected waves. Radiation modes were obtained by algebraic adjustments of each incident wave¡¦s amplitude and phase. These radiation modes formed standing waves in both the substrates and superstrates. This implies that walls are located an infinite distance far from the first and the last interfaces. In addition to physical conflicts of simultaneous existence of the incident wave and the walls, the derivation details are complicated and non-intuitive. In our thesis, with a given propagation constant for an arbitrarily layered dielectric waveguide, we propose an intuitive method to obtain two independent radiation mode solutions. We also construct a specific procedure to orthogonalize and normalize these two radiation modes. The second part of this thesis is focused on applying these radiation modes into a customized coupled transverse mode integral equation formulation (CTMIE), to the study of vertically offset slab waveguides. CTMIE requires two artificial boundaries placed in the substrate and superstrate. We choose to compute discretized radiation modes with the periodic boundary conditions. Under these circumstances, modes correspond to different spatial frequencies and thereby do not inter-couple. This means the matrix of the overlap integral between these two groups of modes (slightly vertically shifted) are block-diagonally dominated. The off-diagonal elements are two orders of magnitude smaller than the diagonal ones. As a result, when the two artificial boundaries are pushed towards infinity in the CTMIE formulation, we may obtain an exact inverse of the Greene¡¦s matrix without relying on numerical inversion.

No description available.

There is an increasing need for accurate models describing the electrical behaviour of individual biological cells exposed to electromagnetic fields. In this area of solving linear problem, the most frequently used technique for computing the EM field is the Finite-Difference Time-Domain (FDTD) method. When modelling objects that are small compared with the wavelength, for example biological cells at radio frequencies, the standard Finite-Difference Time-Domain (FDTD) method requires extremely small time-step sizes, which may lead to excessive computation times. The problem can be overcome by implementing a quasi-static approximate version of FDTD, based on transferring the working frequency to a higher frequency and scaling back to the frequency of interest after the field has been computed. An approach to modeling and analysis of biological cells, incorporating the Hodgkin and Huxley membrane model, is presented here. Since the external medium of the biological cell is lossy material, a modified Berenger absorbing boundary condition is used to truncate the computation grid. Linear assemblages of cells are investigated and then Floquet periodic boundary conditions are imposed to imitate the effect of periodic replication of the assemblages. Thus, the analysis of a large structure of cells is made more computationally efficient than the modeling of the entire structure. The total fields of the simulated structures are shown to give reasonable and stable results at 900MHz, 1800MHz and 2450MHz. This method will facilitate deeper investigation of the phenomena in the interaction between EM fields and biological systems. Moreover, the nonlinear response of biological cell exposed to a 0.9GHz signal was discussed on observing the second harmonic at 1.8GHz. In this, an electrical circuit model has been proposed to calibrate the performance of nonlinear RF energy conversion inside a high quality factor resonant cavity with known nonlinear device. Meanwhile, the first and second harmonic responses of the cavity due to the loading of the cavity with the lossy material will also be demonstrated. The results from proposed mathematical model, give good indication of the input power required to detect the weakly effects of the second harmonic signal prior to perform the measurement. Hence, this proposed mathematical model will assist to determine how sensitivity of the second harmonic signal can be detected by placing the required specific input power.

This thesis describes the results of experimental work on polyelectrolyte gels and their interaction with oppositely charged surfactants, and presents two new algorithms applicable to the simulation of colloid and polymer systems. The model systems investigated were crosslinked poly(acrylate) (PA) and poly(styrene sulphonate) (PSS), and the surfactant was dodecyl trimethylammonium bromide (DoTAB). Pure gel materials were studied using dynamic light scattering. It was shown that the diffusion coefficient (D) increases with increasing degree of swelling and the concentration dependence is larger than predicted by scaling arguments. For gels at swelling equilibrium D increases with increasing degree of crosslinking. In subsequent studies on gel particles in DoTAB solution, Raman spectra were recorded at different positions in the gel. For both types of gels two distinct regions could be observed. For PA the surfactant is localised in the outer phase without any surfactant in the core, while for PSS the surfactant was distributed such that it had the same concentration relative to the polymer throughout the gel. In a second experiment, the kinetics for the deswelling of microscopic PSS particles in DoTAB solution was studied. It was found that the final volume varied linearly with the DoTAB concentration, and the rate of volume decrease could be fitted to a single exponential indicating stagnant layer diffusion to be the rate limiting process for the deswelling of the PSS particles. In the second part, I first describe an algorithm showing an efficient way to detect percolation in simulations, with periodic boundary conditions, using recursion. Spherical boundary conditions is an alternative to periodic boundary conditions for systems with long-range interactions. In the last part, the possibility to use the surface of a hypersphere in four dimensions for simulations of polymer systems is investigated, and algorithms for Monte Carlo and Brownian dynamics simulations are described.

In this research, a new technique for modeling periodic structures in the finite-difference time-domain (FDTD) method is developed, and the technique is applied to the study of structural color in insects. Various recent supplements to the FDTD method, such as a nearly-perfect plane-wave injector and convolutional perfectly matched layer boundary condition, are used. A method for implementing the FDTD method on a parallel, distributed-memory computer cluster is given. To model a periodic structure, a single periodic cell is terminated by periodic boundary conditions (PBCs). A new technique for incorporating PBCs into the FDTD method is presented. The simplest version of the technique is limited to two-dimensional, singly-periodic geometries. The accuracy is demonstrated by comparing to independent results calculated with a frequency-domain, mode-matching method. The periodic FDTD method is then extended to the more general case of three-dimensional, doubly-periodic problems. This extension requires additional steps and imposes new limitations. The computational cost and limitations of the method are presented. Certain species of butterflies exhibit structural color, which is caused by quasi-periodic structures on the scales covering the wings. Numerical experiments are performed to develop a technique for modeling quasi-periodic structures using the periodic FDTD method. The observed structural color of butterflies is then calculated from the electromagnetic data using colorimetric theory. Three types of butterflies are considered. The first type are from the Morpho genus. These are typically a brilliant, almost metallic, blue color. The second type is the Troides magellanus, which exhibits an interplay of structural and pigmentary color, but the structural color is only visible near grazing incidence. The final type is the Ancyluris meliboeus, which exhibits iridescence on the ventral side. For all cases, the effects of changing the dimensions of various structural elements are considered. Finally, some earlier work on the design of TEM horn antennas is presented. The TEM horn is a simple and popular antenna, but only limited design information is available in the literature. A parametric study was performed, and the results are given. A complete derivation of the characteristic impedance of the basic antenna is also presented.

De nombreux phénomènes physiques ne peuvent être compris qu'en s'intéressant à la structure électronique. Cette dernière peut être interprétée en termes de propriétés électromagnétiques, chacune de ces propriétés révélant diverses informations sur le système étudié. Il est donc important d'avoir des outils efficaces afin de calculer de telles propriétés. C'est dans ce contexte que cette thèse a été écrite, notre principal objectif ayant été de développer une méthode générale donnant accès à une vaste gamme de propriétés électromagnétiques. Dans la première partie de cette thèse, nous décrivons le socle théorique au sein duquel nous travaillons, en particulier la théorie de la fonctionnelle de la densité de courant dépendante du temps (TDCDFT), qui est une approche qui permet de décrire la réponse du système à un champ magnétique. La seconde partie est consacrée à la méthode que nous avons mise au point pour calculer diverses propriétés magnétiques en préservant l'invariance de jauge. Nous démontrons en particulier qu'en utilisant une simple règle de somme, il est possible de placer les courants diamagnétique et paramagnétique sur un pied d'égalité, évitant par là même les écueils habituels intrinsèques au calcul de propriétés magnétiques, comme la dépendance en l'origine de la jauge du vecteur potentiel. Nous illustrons notre méthode en l'appliquant notamment au calcul de la magnétisabilité et du dichroïsme circulaire, qui est une propriété possédant d'importantes applications pratiques, notamment en biologie. Dans la dernière partie, plus exploratoire, nous tentons d'étendre notre formalisme aux systèmes périodiques. Nous y discutons plusieurs stratégies afin de calculer l'aimantation dans des systèmes décrits par des conditions aux limites périodiques. / Various phenomena of matter can only be understood by probing its electronic structure. The latter can be interpreted in terms of electromagnetic properties, each property revealing a different piece of information. Having a reliable method to calculate such properties is thus of great importance. This thesis is to be regarded in this context. Our main goal was to develop a general method that gives access to a wide variety of electromagnetic properties. In the first part of this thesis, we describe the theoretical background with which we work, and in particular time-dependent current-density-functional theory (TDCDFT), which is a density-functional approach that can describe the response due to a magnetic field. The second part is dedicated to the method we developed in order to calculate various magnetic properties in a gauge-invariant manner. In particular, we show that by using a simple sum rule, we can put the diamagnetic and paramagnetic currents on equal footing. We thus avoid the usual problems that arise when calculating magnetic properties, such as the dependence on the gauge origin of the vector potential. We illustrate our method by applying it to the calculation of magnetizabilities and circular dichroism, which has important applications, notably in biology. In the last part, which is more explorative, we aim at extending our formalism to periodic systems. We discuss several strategies to calculate magnetization in systems described with periodic boundary conditions.

Metoda koneÄnch prvk implementovan v programu COMSOL Multiphysics je vyu­vna k analze tzv. free-standing kmitoÄtovÄ selektivn­ch povrch ve 3D. Tyto modely jsou nslednÄ doplnÄny o periodick© okrajov© podm­nky. Dle jsou free-standing povrchy doplnÄny o vrstvy dielektrika a je zkoumn jejich vliv na modul Äinitele odrazu. V analytick© Ästi jsou vyhodnoceny vlivy poÄtu element diskretizaÄn­ m­ky na pesnost vsledku a d©lku vpoÄt. Vsledky jsou srovnvny vzhledem k vsledkm uvedenm v literatue [5]. V zvÄreÄn© Ästi prce je vysvÄtlen postup pi generovn­ m-file pro obd©ln­kov element a pouit­ globln­ho optimalizaÄn­ho algoritmu PSO, kter automaticky upravuje rozmÄry vodiv©ho motivu tak, aby bylo dosaeno prbÄhu modulu Äinitele odrazu podle poadovan©ho prbÄhu.

yes / There is an increasing need for accurate models describing the electrical behaviour of individual biological cells exposed to electromagnetic fields. In this area of solving linear problem, the most frequently used technique for computing the EM field is the Finite-Difference Time-Domain (FDTD) method. When modelling objects that are small compared with the wavelength, for example biological cells at radio frequencies, the standard Finite-Difference Time-Domain (FDTD) method requires extremely small time-step sizes, which may lead to excessive computation times. The problem can be overcome by implementing a quasi-static approximate version of FDTD, based on transferring the working frequency to a higher frequency and scaling back to the frequency of interest after the field has been computed. An approach to modeling and analysis of biological cells, incorporating the Hodgkin and Huxley membrane model, is presented here. Since the external medium of the biological cell is lossy material, a modified Berenger absorbing boundary condition is used to truncate the computation grid. Linear assemblages of cells are investigated and then Floquet periodic boundary conditions are imposed to imitate the effect of periodic replication of the assemblages. Thus, the analysis of a large structure of cells is made more computationally efficient than the modeling of the entire structure. The total fields of the simulated structures are shown to give reasonable and stable results at 900MHz, 1800MHz and 2450MHz. This method will facilitate deeper investigation of the phenomena in the interaction between EM fields and biological systems. Moreover, the nonlinear response of biological cell exposed to a 0.9GHz signal was discussed on observing the second harmonic at 1.8GHz. In this, an electrical circuit model has been proposed to calibrate the performance of nonlinear RF energy conversion inside a high quality factor resonant cavity with known nonlinear device. Meanwhile, the first and second harmonic responses of the cavity due to the loading of the cavity with the lossy material will also be demonstrated. The results from proposed mathematical model, give good indication of the input power required to detect the weakly effects of the second harmonic signal prior to perform the measurement. Hence, this proposed mathematical model will assist to determine how sensitivity of the second harmonic signal can be detected by placing the required specific input power.

Among the many active materials in use today, piezoelectric composite patches have enabled notable advances in emerging technologies such as disturbance sensing, control of flexible structures, and energy harvesting. The macro fiber composite (MFC), in particular, is well known for its outstanding performance. Multiscale models are typically required for smart-structure design with MFCs. This is due to the need for predicting the macroscopic response (such as tip deflection under a transverse load or applied voltage) while accounting for the fact that the MFC has microscale details. Current multiscale models of the MFC exclusively focus on predicting the macroscopic response with homogenized material properties. There are a limited number of homogenized properties available from physical experiments and various aspects of existing homogenization techniques for the MFC are shown here to be inadequate. Thus, new homogenized models of the MFC are proposed to improve smart-structure predictions and therefore improve device design. It is notable that current multiscale modeling efforts for MFCs are incomplete since, after homogenization, the local fields such as stresses and electric fields have not been recovered. Existing methods for obtaining local fields are not applicable since the electrodes of the MFC are embedded among passive layers. Therefore, another objective of this work was to find the local fields of the MFC without having the computational burden of fully modeling the microscopic features of the MFC over a macroscale area. This should enable smart-structure designs with improved reliability because failure studies of MFCs will be enabled. Large-scale 3D finite element (FE) models that included microscale features were constructed throughout this work to verify the multiscale methodologies. Note that after creating a free account on cdmhub.org, many files used to create the results in this work can be downloaded from https://cdmhub.org/projects/ernestocamarena.<br><br>First, the Mechanics of Structure Genome (MSG) was extended to provide a rigorous analytical homogenization method. The MFC was idealized to consist of a stack of homogeneous layers where some of the layers were homogenized with existing rules of mixtures. For the analytical model, the electrical behavior caused by the interdigitated electrodes (IDEs) was approximated with uniform poling and uniform electrodes. All other assumptions on the field variables were avoided; thus an exact solution for a stack of homogeneous layers was found with MSG. In doing so, it was proved that in any such multi-layered composite, the in-plane strains and the transverse stresses are equal in each layer and the in-plane electric fields and transverse electric displacement are constant between the electrodes. Using this knowledge, a hybrid rule of mixtures was developed to homogenize the entire MFC layup so as to obtain the complete set of effective device properties. Since various assumptions were avoided and since the property set is now complete, it is expected that greater energy equivalence between reality and the homogenized model has been made possible. The derivation clarified what the electrical behavior of a homogenized solid with internal electrodes should be—an issue that has not been well understood. The behavior was verified by large-scale FE models of an isolated MFC patch.<br> <br>Increased geometrical fidelity for homogenization was achieved with an FE-based RVE analysis that accounted for finite-thickness effects. The presented theory also rectifies numerous issues in the literature with the use of the periodic boundary conditions. The procedure was first developed without regard to the internal electrodes (ie a homogenization of the active layer). At this level, the boundary conditions were shown to satisfy a piezoelectric macrohomogeneity condition. The methodology was then applied to the full MFC layup, and modifications were implemented so that both types of MFC electrodes would be accounted for. The IDE case considered nonuniform poling and electric fields, but fully poled material was assumed. The inherent challenges associated with these nonuniformities are explored, and a solution is proposed. Based on the homogenization boundary conditions, a dehomogenization procedure was proposed that enables the recovery of local fields. The RVE analysis results for the effective properties revealed that the homogenization procedure yields an unsymmetric constitutive relation; which suggests that the MFC cannot be homogenized as rigorously as expected. Nonetheless, the obtained properties were verified to yield favorable results when compared to a large-scale 3D FE model.<br> <br>As a final test of the obtained effective properties, large-scale 3D FE models of MFCs acting in a static unimorph configuration were considered. The most critical case to test was the smallest MFC available. Since none of the homogenized models account for the passive MFC regions that surround the piezoelectric fiber array, some of the test models were constructed with and without the passive regions. Studying the deflection of the host substrate revealed that ignoring the passive area in smaller MFCs can overpredict the response by up to 20%. Satisfactory agreement between the homogenized models and a direct numerical simulation were obtained with a larger MFC (about a 5% difference for the tip deflection). Furthermore, the uniform polarization assumption (in the analytical model) for the IDE case was found to be inadequate. Lastly, the recovery of the local fields was found to need improvement.<br><br><br>