Der Grenzwert kleiner Deformationen in Anwesenheit eines gegebenen Risses wird in drei verschiedenen kontinuumsmechanischen Modellen betrachtet. Erstens wird für rein statische Elastizität mit finiter Spannung im Grenzwert kleiner Belastung bewiesen, dass die Nebenbedingung globaler Injektivität im Sinne der Gamma-Konvergenz eine lokale Nichtdurchdringungsbedingung auf dem Riss ergibt. Zweitens wird Deformationsplastizität mit finiten Spannungen und multiplikativer Zerlegung des Spannungstensors behandelt und die Gamma-Konvergenz zu linearisierter Deformationsplastizität mit Rissbedingungen gezeigt. Drittens wird die ratenunabhängige Evolution der Elastoplastizität betrachtet mit einer allgemeineren Klasse globaler Injektivitätsbedingungen für den finiten Fall. Hierbei wird einerseits die evolutionäre Gamma-Konvergenz unter Vernachlässigung der Nebenbedinung gezeigt, andererseits eine Vermutung aufgestellt, unter deren Voraussetzung die evolutionäre Gamma-Konvergenz auch mit Rissbedingungen gilt. / The small-deformation limit in presence of a given crack is considered in three distinct continuummechanical models. First, a purely static finite-strain elasticity model is considered in the limit of small loading, where the constraint of global injectivity is shown to converge in the sense of Gamma-convergence to a local constraint of non-interpenetration along the crack. Second, finitestrain deformation plasticity based on the multiplicative decomposition of the strain tensor is shown to Gamma-converge to linearized deformation elastoplasticity with crack conditions. Third, the rate-independent evolution of elastoplasticity is considered with a generalized class of global injectivity constraints for the finite-strain model. On the one hand, neglecting the constraints the evolutionary Gamma-converge to linearized elastoplasticity is proven. On the other hand, a conjecture is made, subject to which the evolutionary Gamma-convergence with constraints still holds.

Diese Dissertation umfasst drei Aufsätze zu Mindestlöhnen, zum Arbeitsangebot sowie zu öffentlichen Finanzen. Der Fokus liegt auf den Entwicklungen in Deutschland innerhalb der letzten zwei Jahrzehnte. Der erste Aufsatz untersucht Beschäftigungseffekte des Mindestlohns in einem Modell der Sucharbeitslosigkeit. Das Modell bildet Heterogenität auf Arbeitnehmer- und Arbeitgeberseite ab und schränkt die Richtung der Beschäftigungseffekte ein. Es erlaubt eine unterschiedliche Frequenz der Stellensuche von Beschäftigten und Arbeitslosen und modelliert die Rekrutierungsintensität der Unternehmen. Die Ergebnisse zeigen, dass die Arbeitslosigkeit eine nicht-monotone Funktion des Mindestlohns ist. Die Auswirkungen von verschiedenen Mindestlöhnen unterscheiden sich stark nach Arbeitsmarktsegmenten. Der zweite Aufsatz befasst sich mit Trends im Arbeitsangebotsverhalten in Deutschland. Dazu werden diskrete Wahlmodelle des Arbeitsangebots für die Jahre von 1998 bis 2018 geschätzt. Die implizierten Arbeitsangebotselastizitäten haben in den letzten zwei Jahrzehnten zugenommen, insbesondere für Paare und für alleinstehende Männer. Eine Zerlegungsanalyse zeigt, dass Veränderungen in der Demografie nur eine geringe Rolle bei der Verschiebung der Eigen- und Kreuzlohnelastizitäten von Männern spielen, da der größte Teil der Veränderungen durch Präferenzen oder Arbeitsmarktrestriktionen bedingt ist. Bei Frauen hingegen spielen demografische Veränderungen eine größere Rolle für den Anstieg der Elastizitäten. Der dritte Aufsatz befasst sich mit den deutschen Staatsfinanzen sowie mit Reformen aufgrund der Finanzkrise 2008/2009. Der Aufsatz stellt die makroökonomische Situation und die Entwicklung der Krise in Deutschland dar und beleuchtet die Bedeutung für die öffentlichen Finanzen. In dem Aufsatz werden zudem die Verteilungswirkungen der Reformen im Steuer- und Transfersystem mithilfe von Mikrosimulationen untersucht. / This dissertation consists of three essays on the minimum wage, labour supply, and public finances. The selected essays focus on the German experience and developments over the last two decades. The first essay is an analysis of unemployment effects of the German minimum wage in an empirical equilibrium job search model. The estimated model with worker and firm heterogeneity does not restrict the sign of employment effects a priori; it allows for different job offer arrival rates for the employed and the unemployed and lets firms optimally choose their recruiting intensity. Results show that unemployment is a non-monotonic function of the minimum wage level, and effects differ strongly by labour market segment. The second essay is on the topic of labour supply elasticities in Germany. In order to analyse recent trends in labour supply in Germany, a static discrete choice model of unitary household labour supply is estimated for each year 1998 to 2018. Findings are that own-wage labour supply elasticities implied by the models have increased over the last two decades, especially for couples, and for single males. A decomposition analysis shows that compositional changes in demographics play only a minor role in the shift in males' own- and cross-wage elasticities, since most of the changes in elasticities are driven by preferences or labour market restrictions. For females, changes in composition play a bigger role in the rise of elasticities. The third essay reviews German public finances through the financial crisis 2008/2009. The essay starts with a presentation of the macroeconomic situation and how the crisis unfolded in Germany, before focusing on the situation of the public finances. Finally, the distributional effects of policy responses to the financial crisis are analysed on the individual level using microsimulation.

The master‘s thesis focuses on testing the shotcrete prepared in laboratory conditions. The main observed properties are compresive strenght of shotcrete and modulus of elasticity. The aim is assessment of methods for measuring those parameters. The calibrating correlations for strenght characteristics of shotcrete are given by obtaining the results of used methods. The shotcrete composition, amount and type of accelerating additive as well as economic aspect of using shotcrete is also assessed.

Optimal control problems for finite-strain elasticity are considered. An inner pressure or an inner fiber tension is acting as a driving force. Such internal forces are typical, for instance, for the motion of heliotropic plants, and for muscle tissue. Non-standard objective functions relevant for elasticity problems are introduced. Optimality conditions are derived on a formal basis, and a limited-memory quasi-Newton algorithm for their solution is formulated in function space. Numerical experiments confirm the expected mesh-independent performance.

Myosin 1c (Myo1c) is a molecular motor involved in regulation of tension-gated ion channels, exocytosis, endocytosis, motility and other membrane-related events. Moreover, it acts as a dynamic linker between the cell membrane and cortical actin network, contributing to the maintenance of plasma membrane tension. In contrast, nuclear myosin 1 (NM1), an isoform of Myo1c, has been described only in the nucleus where it participates in various nuclear processes, including transcription or chromatin remodeling. However, although traditionally regarded as exclusively cytoplasmic or nuclear, all myosin 1c isoforms participate in nuclear functions and they are present in the cytoplasm as well. The main focus of this study was to characterize the functional significance of NM1 in the cytoplasm. We have found that NM1 localizes to plasma membrane and shows a uniform punctuated distribution with a high concentration at the cell periphery. Moreover, atomic force microscopy measurements of mouse NM1 KO fibroblasts revealed a significant increase in an overall plasma membrane elasticity in comparison to WT cells, indicating a disruption in the regulation of plasma membrane tension caused by the loss of NM1. Since a higher membrane elasticity and deformability is a characteristic marker of cancer cells,...

Distributed systems are everywhere. From large datacenters to mobile devices, an ever richer assortment of applications and services relies on distributed systems, infrastructure, and protocols. Despite their ubiquity, testing and debugging distributed systems remains notoriously hard. Moreover, aside from inherent design challenges posed by partial failure, concurrency, or asynchrony, there remain significant challenges in the implementation of distributed systems. These programming challenges stem from the increasing complexity of the concurrent activities and reactive behaviors in a distributed system on the one hand, and the need to effectively leverage the parallelism offered by modern multi-core hardware, on the other hand. This thesis contributes Kompics, a programming model designed to alleviate some of these challenges. Kompics is a component model and programming framework for building distributed systems by composing message-passing concurrent components. Systems built with Kompics leverage multi-core machines out of the box, and they can be dynamically reconfigured to support hot software upgrades. A simulation framework enables deterministic execution replay for debugging, testing, and reproducible behavior evaluation for large-scale Kompics distributed systems. The same system code is used for both simulation and production deployment, greatly simplifying the system development, testing, and debugging cycle. We highlight the architectural patterns and abstractions facilitated by Kompics through a case study of a non-trivial distributed key-value storage system. CATS is a scalable, fault-tolerant, elastic, and self-managing key-value store which trades off service availability for guarantees of atomic data consistency and tolerance to network partitions. We present the composition architecture for the numerous protocols employed by the CATS system, as well as our methodology for testing the correctness of key CATS algorithms using the Kompics simulation framework. Results from a comprehensive performance evaluation attest that CATS achieves its claimed properties and delivers a level of performance competitive with similar systems which provide only weaker consistency guarantees. More importantly, this testifies that Kompics admits efficient system implementations. Its use as a teaching framework as well as its use for rapid prototyping, development, and evaluation of a myriad of scalable distributed systems, both within and outside our research group, confirm the practicality of Kompics. / Kompics / CATS / REST

O timo é um órgão linfoide primário, localizado em região mediastinal, cuja importância funcional é a diferenciação e maturação de todas as subpopulações de linfócitos T provenientes da medula óssea assim como a seleção de células autorreativas. Sua hipoplasia ou aplasia resultam em síndromes de imunodeficiência. Embora de vital importância, o estudo clínico de sua função não é rotineiro na prática clínica, o que pode ser atribuído a sua dificuldade de avaliação em razão de sua localização, necessidade de uso de métodos de imagem não inócuos ao paciente (tomografia computadorizada (TC), PET-SCAN) e complexidade das análises em sangue periférico de subpopulações de células T por citometria de fluxo e, mais recentemente, medição de T cell receptor excision circles (TRECs), por PCR. Um possível método da avaliação do timo sem radiação ionizante ou dor ao paciente seria a elastografia de timo por ultrassom e seu uso na prática clínica poderia substituir a TC, como ocorre na avaliação de lesões hepáticas ou mamárias. Objetivo - Este estudo se propõe a 1. Implantar este método na avaliação da função tímica, 2. Estabelecer valores de referência de TRECs na faixa etária estudada, 3. Investigar se há correlação entre os dois parâmetros. Métodos - Foram incluídas sessenta e quatro crianças de 0-5 anos em acompanhamento no ambulatório de cirurgia infantil sem doença sistêmica ou infecção aguda, e que iriam coletar amostra de sangue para exames pré-operatórios. Quarenta e oito destas coletaram amostra de sangue para avaliação de TRECs, vinte e nove realizaram elastografia num mesmo momento, porém apenas 13 destas apresentaram resultado confiável. A média da idade foi de 36 ± 16meses, predomínio do grupo foi masculino (75%), nascidos a termo (72%) e a principal intervenção cirúrgica foi do tipo urológica de pequeno porte. A elastografia mostrou média de 1,21 ± 0,24m/s, sem diferença significativa quando comparada ano a ano. Observamos uma média de TRECs de 195,6 ± 120,5 cópias/µL, mostrando valores significativamente mais altos quando comparados a adolescentes hígidos da base de dados do laboratório. Os valores de TRECs observados mostram uma ampla variabilidade na faixa etária estudada, sem diferença significativa quando separados por idade ano a ano. Não se encontrou correlação significativa entre a dureza do timo analisada à elastografia e valores de TRECs em sangue periférico. Concluímos que a elastografia é um método que possibilita a avaliação das dimensões e função do timo em crianças a partir de 2 anos de idade, entretanto estudos adicionais são necessários para que se possa recomendar a larga implantação deste método com essa finalidade / The thymus is a primary lymphoid gland responsible for the maturation of T cells as well as the immunological central tolerance. It has been a neglected organ by physicians, despite its relevance in early immunity. Thymic function can be indirectly measured by Computerized Tomography imaging and PET SCAN, T cell subpopulation flow cytometry. More recently, in the beginning of this century, a direct measurement represented by TRECs (T cell receptors excision circles) was developed. Classical thymic imaging has used ionized radiation, which poses a major risk for the pediatric patient and new techniques are needed. Objectives and methods - In this work, we tested the use of elastography ultrasound for the evaluation of the thymus in a group of < 5-year- old healthy children. In parallel, we measured TRECs in peripheral blood and compared the values obtained from both methods. We have reached sixty-four children at the pediatric surgery outpatients ambulatory, scheduled for minor surgeries. A sample of blood was taken during pre operatory and then patients were sent to the imaging service for elastography. Of all, sixty-four had undertaken TRECs and seventeen, elastography. The median age was 36 ±16 months and we had 75% of boys for surgical correction of urologic minor defects. The elastography results showed a median of 1.2 ± 0.24 m/s in all ages, the same stiffness as the liver, as shown in other works. Our median TREC/µL value was 195.6 ± 120.5 copies/µL showing a trend of reduction in older ages, and with statistical significance when compared with healthy teenagers\' values from the lab database. We concluded that elastography may be a good diagnostic tool for thymus evaluation, and additional works are needed for its recommendation in clinical practice. Our TRECs values showed a large variability, as also demonstrated in previous works, and a trend of reduction over age. We could not observe any significant correlation between elastography and TRECs values

Objetivo Avaliar os efeitos do tabagismo sobre o sistema cardiovascular, através de metodologia não invasiva, analisando as alterações hemodinâmicas clínicas e propriedades elásticas arteriais, após exposição ao fumo. Métodos Estudo realizado em 45 voluntários sendo 18 (F) e 27 (M), fumantes T (n = 25, idade 40 ± 9 anos) e não fumantes NT (n = 20, idade 39 ± 9 anos), que foram submetidos a determinação do monóxido de carbono (CO) e avaliação das propriedades elásticas arteriais por ultrassonografia e teste de função endotelial (hiperemia reativa - HR) antes (B1) e após (B2) a exposição por 20 minutos a um cigarro ou à degustação de uma bala. Resultados Os grupos NT e T mostraram-se homogêneos. A concentração de CO no grupo T era maior do que no grupo NT em condições basais. A concentração de CO no grupo NT não variou antes e após à exposição proposta (bala) mas no grupo T aumentou de maneira significante após o cigarro. A pressão arterial sistólica (PAS) foi igual no B1 nos dois grupos, mas significativamente maior no B2 para o Gr T. A pressão arterial diastólica (PAD) no B1 e B2 não mostrou variação estatísticamente significante nos dois grupos. A freqüência cardíaca (FC) apresentou comportamento estatisticamente diferente nos dois grupos (NT apresentou redução e T apresentou aumento). Em relação às propriedades elásticas arteriais e resposta do fluxo regional: a complacência e a distensibilidade já se mostraram diferentes (p < 0,001) no período basal sendo maior no grupo NT comparado ao grupo T; mas após a HR 1 e 2, o grupo T mostrou elevação estatísticamente significante destas duas propriedades, sendo que o grupo NT não mostrou tais achados. O diâmetro máximo da artéria braquial mostrou-se aumentado em relação ao basal tanto após HR1 como após HR2 apenas no grupo T. O índice de fluxo total (IFT) não era diferente nos dois grupos no B1 e B2, mas após HR 1 e 2 ambos mostraram aumentos significantes (p < 0,001). Houve correlação positiva entre variáveis CO com PAD e FC no grupo T. No grupo NT não houve correlação do CO com PAS, PAD ou FC. Conclusão O tabagismo altera as propriedades elásticas das artérias e tem papel na hemodinâmica com provável participação do monóxido de carbono. / Objective to evaluate the effects of cigarette smoking on cardiovascular system, with non-invasive methodology, analysing hemodynamic disturbs and arterial elastic properties after being exposed to tobacco. METHODS This study was realized in 45 volunteers, 18 female and 27 male smokers T (n=25, age 40 ± 9 years) and non-smokers NT (n=20, age 39 ± 9 years), who were submitted to the determination of carbon monoxide (CO) to the evaluation of the arterial elastic properties by ultrassonography and test endotelial function (reactive hyperemia - HR) before (B1) and after (B2) the exposition for 20 minutes to a cigarette or a candy. RESULTS Both NT and T groups were similar.The CO concentration in the T group was higher than in the NT group on basal conditions. The CO concentration in the NT group have not changed before and after the proposed exposition (candy) but in the T group it was significant in creased after the cigarette exposition.The systolic blood pressure (PAS) was similar on B1 for both groups, but it was significantly higher on B2 for the T group. The diastolic blood pressure (PAD) on B1 and B2 didn´t exposition significant statistical variation on both groups. The cardiac frequency (FC) presented a different result for both groups with statistical significance ( NT had decrease and T had improved). Regarding the arterial elastic properties and the regional flux response: the complacence and the distensibility were different (p < 0,001) in the basal period and they were higher in the NT group compared to the T group. After HR 1 and 2, the T group showed a significant statistical increase of those two properties and the NT group didn´t show those results. The righest diameter of the brachial artery was increased in relation to the basal diameter after HR1 as well as after HR2 only in the T group. The total flux index (IFT) were not different in both groups in B1 and B2, but after HR1 and 2 both showed significant increase (p < 0,001). There was a positive correlation between the CO variations in relation to PAD and FC in the T group. In the NT group there was a no correlation of CO with PAS, PAD or FC. CONCLUSION Cigarette smoking changes the arterial elastic properties and it has a role in the hemodynamic with possible participation of the carbon monoxide

O timo é um órgão linfoide primário, localizado em região mediastinal, cuja importância funcional é a diferenciação e maturação de todas as subpopulações de linfócitos T provenientes da medula óssea assim como a seleção de células autorreativas. Sua hipoplasia ou aplasia resultam em síndromes de imunodeficiência. Embora de vital importância, o estudo clínico de sua função não é rotineiro na prática clínica, o que pode ser atribuído a sua dificuldade de avaliação em razão de sua localização, necessidade de uso de métodos de imagem não inócuos ao paciente (tomografia computadorizada (TC), PET-SCAN) e complexidade das análises em sangue periférico de subpopulações de células T por citometria de fluxo e, mais recentemente, medição de T cell receptor excision circles (TRECs), por PCR. Um possível método da avaliação do timo sem radiação ionizante ou dor ao paciente seria a elastografia de timo por ultrassom e seu uso na prática clínica poderia substituir a TC, como ocorre na avaliação de lesões hepáticas ou mamárias. Objetivo - Este estudo se propõe a 1. Implantar este método na avaliação da função tímica, 2. Estabelecer valores de referência de TRECs na faixa etária estudada, 3. Investigar se há correlação entre os dois parâmetros. Métodos - Foram incluídas sessenta e quatro crianças de 0-5 anos em acompanhamento no ambulatório de cirurgia infantil sem doença sistêmica ou infecção aguda, e que iriam coletar amostra de sangue para exames pré-operatórios. Quarenta e oito destas coletaram amostra de sangue para avaliação de TRECs, vinte e nove realizaram elastografia num mesmo momento, porém apenas 13 destas apresentaram resultado confiável. A média da idade foi de 36 ± 16meses, predomínio do grupo foi masculino (75%), nascidos a termo (72%) e a principal intervenção cirúrgica foi do tipo urológica de pequeno porte. A elastografia mostrou média de 1,21 ± 0,24m/s, sem diferença significativa quando comparada ano a ano. Observamos uma média de TRECs de 195,6 ± 120,5 cópias/µL, mostrando valores significativamente mais altos quando comparados a adolescentes hígidos da base de dados do laboratório. Os valores de TRECs observados mostram uma ampla variabilidade na faixa etária estudada, sem diferença significativa quando separados por idade ano a ano. Não se encontrou correlação significativa entre a dureza do timo analisada à elastografia e valores de TRECs em sangue periférico. Concluímos que a elastografia é um método que possibilita a avaliação das dimensões e função do timo em crianças a partir de 2 anos de idade, entretanto estudos adicionais são necessários para que se possa recomendar a larga implantação deste método com essa finalidade / The thymus is a primary lymphoid gland responsible for the maturation of T cells as well as the immunological central tolerance. It has been a neglected organ by physicians, despite its relevance in early immunity. Thymic function can be indirectly measured by Computerized Tomography imaging and PET SCAN, T cell subpopulation flow cytometry. More recently, in the beginning of this century, a direct measurement represented by TRECs (T cell receptors excision circles) was developed. Classical thymic imaging has used ionized radiation, which poses a major risk for the pediatric patient and new techniques are needed. Objectives and methods - In this work, we tested the use of elastography ultrasound for the evaluation of the thymus in a group of < 5-year- old healthy children. In parallel, we measured TRECs in peripheral blood and compared the values obtained from both methods. We have reached sixty-four children at the pediatric surgery outpatients ambulatory, scheduled for minor surgeries. A sample of blood was taken during pre operatory and then patients were sent to the imaging service for elastography. Of all, sixty-four had undertaken TRECs and seventeen, elastography. The median age was 36 ±16 months and we had 75% of boys for surgical correction of urologic minor defects. The elastography results showed a median of 1.2 ± 0.24 m/s in all ages, the same stiffness as the liver, as shown in other works. Our median TREC/µL value was 195.6 ± 120.5 copies/µL showing a trend of reduction in older ages, and with statistical significance when compared with healthy teenagers\' values from the lab database. We concluded that elastography may be a good diagnostic tool for thymus evaluation, and additional works are needed for its recommendation in clinical practice. Our TRECs values showed a large variability, as also demonstrated in previous works, and a trend of reduction over age. We could not observe any significant correlation between elastography and TRECs values

Pour les roches saturées, la comparaison entre les mesures ultrasoniques (1 MHz) au laboratoire et les mesures sismiques (100 Hz) ou de diagraphie (10 kHz) sur le terrain n’est pas directe à cause de la dispersion des vitesses des ondes. Les mécanismes impliqués dans la dépendance en fréquence sont les écoulements de fluides à différentes échelles provoqués par le passage de l’onde. La dispersion et l’atténuation des modules élastiques de roches carbonatées ont été étudiées expérimentalement. Les calcaires étudiés sont : un Lavoux, un Indiana intact et craqué thermiquement, un calcaire Urgonien de Provence (Rustrel), et un coquina pré-sel du Congo. Les mesures ont été faites sur une large gamme de fréquence, en combinant les techniques d’oscillations forcées (10-3 to 102 Hz) et ultrasoniques (1 MHz) dans une presse triaxiale, pour différentes pressions effectives. Le forçage peut être hydrostatique pour mesurer un module d’incompressibilité, ou axial pour mesurer le module de Young et le coefficient de Poisson. Pour étudier l’effet de la viscosité, les mesures ont été faites en condition sèche, puis saturée en glycérine et en eau. Le drainage global et le mécanisme d’écoulement crack-pore ont été caractérisés, en termes d’amplitude de dispersion, d’atténuation viscoélastique, et de fréquence de coupure. Pour nos échantillons, la théorie de Biot-Gassmann s’est montrée valide pour les fréquences sismiques (10-100 Hz) sauf pour l’Indiana craqué thermiquement. La dispersion liée à des écoulements crackspores a été observée pour tous les échantillons sauf le Lavoux. Les fréquences de coupures de ceux-ci sont toutes dans la gamme des fréquences des diagraphies (10 kHz) pour des conditions de saturation en eau. Un modèle simple, combinant poroélasticité et milieux effectifs, a été développé pour prédire la dispersion des modules sur toute la gamme de fréquence, et s’est montré généralement en accord avec les résultats expérimentaux. / For fluid-saturated rocks, comparing ultrasonic measurements (1 MHz) in the laboratory and seismic (100 Hz) or logging (10 kHz) measurements in the field is not straightforward due to dispersion of the bodywave velocities. The frequency-dependent mechanisms involved are wave-induced fluid flows that occur at different scales. The dispersion and the attenuation of the elastic moduli of four fluid-saturated carbonate rocks have been studied experimentally. The selected limestones were a Lavoux, an intact and thermally cracked Indiana, a Urgonian limestone from Provence (Rustrel), and a presalt coquina from offshore Congo. Measurements were done over a large frequency range, by the combination of forced oscillations (10-3 to 102 Hz) and ultrasonic measurements (1 MHz) in a triaxial cell, at various effective pressures. The forced oscillations were either hydrostatic to deduce the bulk modulus, or axial to deduce Young’s modulus and Poisson’s ratio. The measurements were done in dry-, glycerinand water-saturated conditions to investigate the effect of viscosity. For all our samples, the global drainage and the squirt-flow mechanisms were characterized experimentally, in terms of amplitude of dispersion, amount of viscoelastic attenuation, and cut-off frequencies. Biot- Gassmann’s theory was found to be valid at seismic frequencies (10-100 Hz) for all the samples except the thermally cracked Indiana. Squirt-flow transitions were observed for all the samples, except the Lavoux. The cut-off frequencies were all in the range of logging frequencies (10 kHz), for watersaturated conditions. A simple model, combining poroelasticity and the noninteraction approximation effective medium, was developed to predict the dispersion of the moduli over the whole frequency range, and was generally in agreement with the experimental results.