Rehabilitation Engineering in Parkinson's disease

Impairment of postural control is a common consequence of Parkinson's disease (PD) that becomes more and more critical with the progression of the disease, in spite of the available medications. Postural instability is one of the most disabling features of PD and induces difficulties with postural transitions, initiation of movements, gait disorders, inability to live independently at home, and is the major cause of falls. Falls are frequent (with over 38% falling each year) and may induce adverse consequences like soft tissue injuries, hip fractures, and immobility due to fear of falling. As the disease progresses, both postural instability and fear of falling worsen, which leads patients with PD to become increasingly immobilized. The main aims of this dissertation are to: 1) detect and assess, in a quantitative way, impairments of postural control in PD subjects, investigate the central mechanisms that control such motor performance, and how these mechanism are affected by levodopa; 2) develop and validate a protocol, using wearable inertial sensors, to measure postural sway and postural transitions prior to step initiation; 3) find quantitative measures sensitive to impairments of postural control in early stages of PD and quantitative biomarkers of disease progression; and 4) test the feasibility and effects of a recently-developed audio-biofeedback system in maintaining balance in subjects with PD. In the first set of studies, we showed how PD reduces functional limits of stability as well as the magnitude and velocity of postural preparation during voluntary, forward and backward leaning while standing. Levodopa improves the limits of stability but not the postural strategies used to achieve the leaning. Further, we found a strong relationship between backward voluntary limits of stability and size of automatic postural response to backward perturbations in control subjects and in PD subjects ON medication. Such relation might suggest that the central nervous system presets postural response parameters based on perceived maximum limits and this presetting is absent in PD patients OFF medication but restored with levodopa replacement. Furthermore, we investigated how the size of preparatory postural adjustments (APAs) prior to step initiation depend on initial stance width. We found that patients with PD did not scale up the size of their APA with stance width as much as control subjects so they had much more difficulty initiating a step from a wide stance than from a narrow stance. This results supports the hypothesis that subjects with PD maintain a narrow stance as a compensation for their inability to sufficiently increase the size of their lateral APA to allow speedy step initiation in wide stance. In the second set of studies, we demonstrated that it is possible to use wearable accelerometers to quantify postural performance during quiet stance and step initiation balance tasks in healthy subjects. We used a model to predict center of pressure displacements associated with accelerations at the upper and lower back and thigh. This approach allows the measurement of balance control without the use of a force platform outside the laboratory environment. We used wearable accelerometers on a population of early, untreated PD patients, and found that postural control in stance and postural preparation prior to a step are impaired early in the disease when the typical balance and gait intiation symptoms are not yet clearly manifested. These novel results suggest that technological measures of postural control can be more sensitive than clinical measures. Furthermore, we assessed spontaneous sway and step initiation longitudinally across 1 year in patients with early, untreated PD. We found that changes in trunk sway, and especially movement smoothness, measured as Jerk, could be used as an objective measure of PD and its progression. In the third set of studies, we studied the feasibility of adapting an existing audio-biofeedback device to improve balance control in patients with PD. Preliminary results showed that PD subjects found the system easy-to-use and helpful, and they were able to correctly follow the audio information when available. Audiobiofeedback improved the properties of trunk sway during quiet stance. Our results have many implications for i) the understanding the central mechanisms that control postural motor performance, and how these mechanisms are affected by levodopa; ii) the design of innovative protocols for measuring and remote monitoring of motor performance in the elderly or subjects with PD; and iii) the development of technologies for improving balance, mobility, and consequently quality of life in patients with balance disorders, such as PD patients with augmented biofeedback paradigms.

Vibration as a method for muscular stimulation

Human reactions to vibration have been extensively investigated in the past. Vibration, as well as whole-body vibration (WBV), has been commonly considered as an occupational hazard for its detrimental effects on human condition and comfort. Although long term exposure to vibrations may produce undesirable side-effects, a great part of the literature is dedicated to the positive effects of WBV when used as method for muscular stimulation and as an exercise intervention. Whole body vibration training (WBVT) aims to mechanically activate muscles by eliciting neuromuscular activity (muscle reflexes) via the use of vibrations delivered to the whole body. The most mentioned mechanism to explain the neuromuscular outcomes of vibration is the elicited neuromuscular activation. Local tendon vibrations induce activity of the muscle spindle Ia fibers, mediated by monosynaptic and polysynaptic pathways: a reflex muscle contraction known as the Tonic Vibration Reflex (TVR) arises in response to such vibratory stimulus. In WBVT mechanical vibrations, in a range from 10 to 80 Hz and peak to peak displacements from 1 to 10 mm, are usually transmitted to the patient body by the use of oscillating platforms. Vibrations are then transferred from the platform to a specific muscle group through the subject body. To customize WBV treatments, surface electromyography (SEMG) signals are often used to reveal the best stimulation frequency for each subject. Use of SEMG concise parameters, such as root mean square values of the recordings, is also a common practice; frequently a preliminary session can take place in order to discover the more appropriate stimulation frequency. Soft tissues act as wobbling masses vibrating in a damped manner in response to mechanical excitation; Muscle Tuning hypothesis suggest that neuromuscular system works to damp the soft tissue oscillation that occurs in response to vibrations; muscles alters their activity to dampen the vibrations, preventing any resonance phenomenon. Muscle response to vibration is however a complex phenomenon as it depends on different parameters, like muscle-tension, muscle or segment-stiffness, amplitude and frequency of the mechanical vibration. Additionally, while in the TVR study the applied vibratory stimulus and the muscle conditions are completely characterised (a known vibration source is applied directly to a stretched/shortened muscle or tendon), in WBV study only the stimulus applied to a distal part of the body is known. Moreover, mechanical response changes in relation to the posture. The transmissibility of vibratory stimulus along the body segment strongly depends on the position held by the subject. The aim of this work was the investigation on the effects that the use of vibrations, in particular the effects of whole body vibrations, may have on muscular activity. A new approach to discover the more appropriate stimulus frequency, by the use of accelerometers, was also explored. Different subjects, not affected by any known neurological or musculoskeletal disorders, were voluntarily involved in the study and gave their informed, written consent to participate. The device used to deliver vibration to the subjects was a vibrating platform. Vibrations impressed by the platform were exclusively vertical; platform displacement was sinusoidal with an intensity (peak-to-peak displacement) set to 1.2 mm and with a frequency ranging from 10 to 80 Hz. All the subjects familiarized with the device and the proper positioning. Two different posture were explored in this study: position 1 - hack squat; position 2 - subject standing on toes with heels raised. SEMG signals from the Rectus Femoris (RF), Vastus Lateralis (VL) and Vastus medialis (VM) were recorded. SEMG signals were amplified using a multi-channel, isolated biomedical signal amplifier The gain was set to 1000 V/V and a band pass filter (-3dB frequency 10 - 500 Hz) was applied; no notch filters were used to suppress line interference. Tiny and lightweight (less than 10 g) three-axial MEMS accelerometers (Freescale semiconductors) were used to measure accelerations of onto patient’s skin, at EMG electrodes level. Accelerations signals provided information related to individuals’ RF, Biceps Femoris (BF) and Gastrocnemius Lateralis (GL) muscle belly oscillation; they were pre-processed in order to exclude influence of gravity. As demonstrated by our results, vibrations generate peculiar, not negligible motion artifact on skin electrodes. Artifact amplitude is generally unpredictable; it appeared in all the quadriceps muscles analysed, but in different amounts. Artifact harmonics extend throughout the EMG spectrum, making classic high-pass filters ineffective; however, their contribution was easy to filter out from the raw EMG signal with a series of sharp notch filters centred at the vibration frequency and its superior harmonics (1.5 Hz wide). However, use of these simple filters prevents the revelation of EMG power potential variation in the mentioned filtered bands. Moreover our experience suggests that the possibility of reducing motion artefact, by using particular electrodes and by accurately preparing the subject’s skin, is not easily viable; even though some small improvements were obtained, it was not possible to substantially decrease the artifact. Anyway, getting rid of those artifacts lead to some true EMG signal loss. Nevertheless, our preliminary results suggest that the use of notch filters at vibration frequency and its harmonics is suitable for motion artifacts filtering. In RF SEMG recordings during vibratory stimulation only a little EMG power increment should be contained in the mentioned filtered bands due to synchronous electromyographic activity of the muscle. Moreover, it is better to remove the artifact that, in our experience, was found to be more than 40% of the total signal power. In summary, many variables have to be taken into account: in addition to amplitude, frequency and duration of vibration treatment, other fundamental variables were found to be subject anatomy, individual physiological condition and subject’s positioning on the platform. Studies on WBV treatments that include surface EMG analysis to asses muscular activity during vibratory stimulation should take into account the presence of motion artifacts. Appropriate filtering of artifacts, to reveal the actual effect on muscle contraction elicited by vibration stimulus, is mandatory. However as a result of our preliminary study, a simple multi-band notch filtering may help to reduce randomness of the results. Muscle tuning hypothesis seemed to be confirmed. Our results suggested that the effects of WBV are linked to the actual muscle motion (displacement). The greater was the muscle belly displacement the higher was found the muscle activity. The maximum muscle activity has been found in correspondence with the local mechanical resonance, suggesting a more effective stimulation at the specific system resonance frequency. Holding the hypothesis that muscle activation is proportional to muscle displacement, treatment optimization could be obtained by simply monitoring local acceleration (resonance). However, our study revealed some short term effects of vibratory stimulus; prolonged studies should be assembled in order to consider the long term effectiveness of these results. Since local stimulus depends on the kinematic chain involved, WBV muscle stimulation has to take into account the transmissibility of the stimulus along the body segment in order to ensure that vibratory stimulation effectively reaches the target muscle. Combination of local resonance and muscle response should also be further investigated to prevent hazards to individuals undergoing WBV treatments.

Modellazione multibody di veicoli ferroviari: sviluppo ed implementazione di modelli innovativi per l'analisi del contatto ruota - rotaia

The wheel - rail contact analysis plays a fundamental role in the multibody modeling of railway vehicles. A good contact model must provide an accurate description of the global contact phenomena (contact forces and torques, number and position of the contact points) and of the local contact phenomena (position and shape of the contact patch, stresses and displacements). The model has also to assure high numerical efficiency (in order to be implemented directly online within multibody models) and a good compatibility with commercial multibody software (Simpack Rail, Adams Rail). The wheel - rail contact problem has been discussed by several authors and many models can be found in the literature. The contact models can be subdivided into two different categories: the global models and the local (or differential) models. Currently, as regards the global models, the main approaches to the problem are the so - called rigid contact formulation and the semi – elastic contact description. The rigid approach considers the wheel and the rail as rigid bodies. The contact is imposed by means of constraint equations and the contact points are detected during the dynamic simulation by solving the nonlinear algebraic differential equations associated to the constrained multibody system. Indentation between the bodies is not permitted and the normal contact forces are calculated through the Lagrange multipliers. Finally the Hertz’s and the Kalker’s theories allow to evaluate the shape of the contact patch and the tangential forces respectively. Also the semi - elastic approach considers the wheel and the rail as rigid bodies. However in this case no kinematic constraints are imposed and the indentation between the bodies is permitted. The contact points are detected by means of approximated procedures (based on look - up tables and simplifying hypotheses on the problem geometry). The normal contact forces are calculated as a function of the indentation while, as in the rigid approach, the Hertz’s and the Kalker’s theories allow to evaluate the shape of the contact patch and the tangential forces. Both the described multibody approaches are computationally very efficient but their generality and accuracy turn out to be often insufficient because the physical hypotheses behind these theories are too restrictive and, in many circumstances, unverified. In order to obtain a complete description of the contact phenomena, local (or differential) contact models are needed. In other words wheel and rail have to be considered elastic bodies governed by the Navier’s equations and the contact has to be described by suitable analytical contact conditions. The contact between elastic bodies has been widely studied in literature both in the general case and in the rolling case. Many procedures based on variational inequalities, FEM techniques and convex optimization have been developed. This kind of approach assures high generality and accuracy but still needs very large computational costs and memory consumption. Due to the high computational load and memory consumption, referring to the current state of the art, the integration between multibody and differential modeling is almost absent in literature especially in the railway field. However this integration is very important because only the differential modeling allows an accurate analysis of the contact problem (in terms of contact forces and torques, position and shape of the contact patch, stresses and displacements) while the multibody modeling is the standard in the study of the railway dynamics. In this thesis some innovative wheel – rail contact models developed during the Ph. D. activity will be described. Concerning the global models, two new models belonging to the semi – elastic approach will be presented; the models satisfy the following specifics: 1) the models have to be 3D and to consider all the six relative degrees of freedom between wheel and rail 2) the models have to consider generic railway tracks and generic wheel and rail profiles 3) the models have to assure a general and accurate handling of the multiple contact without simplifying hypotheses on the problem geometry; in particular the models have to evaluate the number and the position of the contact points and, for each point, the contact forces and torques 4) the models have to be implementable directly online within the multibody models without look - up tables 5) the models have to assure computation times comparable with those of commercial multibody software (Simpack Rail, Adams Rail) and compatible with RT and HIL applications 6) the models have to be compatible with commercial multibody software (Simpack Rail, Adams Rail). The most innovative aspect of the new global contact models regards the detection of the contact points. In particular both the models aim to reduce the algebraic problem dimension by means of suitable analytical techniques. This kind of reduction allows to obtain an high numerical efficiency that makes possible the online implementation of the new procedure and the achievement of performance comparable with those of commercial multibody software. At the same time the analytical approach assures high accuracy and generality. Concerning the local (or differential) contact models, one new model satisfying the following specifics will be presented: 1) the model has to be 3D and to consider all the six relative degrees of freedom between wheel and rail 2) the model has to consider generic railway tracks and generic wheel and rail profiles 3) the model has to assure a general and accurate handling of the multiple contact without simplifying hypotheses on the problem geometry; in particular the model has to able to calculate both the global contact variables (contact forces and torques) and the local contact variables (position and shape of the contact patch, stresses and displacements) 4) the model has to be implementable directly online within the multibody models 5) the model has to assure high numerical efficiency and a reduced memory consumption in order to achieve a good integration between multibody and differential modeling (the base for the local contact models) 6) the model has to be compatible with commercial multibody software (Simpack Rail, Adams Rail). In this case the most innovative aspects of the new local contact model regard the contact modeling (by means of suitable analytical conditions) and the implementation of the numerical algorithms needed to solve the discrete problem arising from the discretization of the original continuum problem. Moreover, during the development of the local model, the achievement of a good compromise between accuracy and efficiency turned out to be very important to obtain a good integration between multibody and differential modeling. At this point the contact models has been inserted within a 3D multibody model of a railway vehicle to obtain a complete model of the wagon. The railway vehicle chosen as benchmark is the Manchester Wagon the physical and geometrical characteristics of which are easily available in the literature. The model of the whole railway vehicle (multibody model and contact model) has been implemented in the Matlab/Simulink environment. The multibody model has been implemented in SimMechanics, a Matlab toolbox specifically designed for multibody dynamics, while, as regards the contact models, the CS – functions have been used; this particular Matlab architecture allows to efficiently connect the Matlab/Simulink and the C/C++ environment. The 3D multibody model of the same vehicle (this time equipped with a standard contact model based on the semi - elastic approach) has been then implemented also in Simpack Rail, a commercial multibody software for railway vehicles widely tested and validated. Finally numerical simulations of the vehicle dynamics have been carried out on many different railway tracks with the aim of evaluating the performances of the whole model. The comparison between the results obtained by the Matlab/ Simulink model and those obtained by the Simpack Rail model has allowed an accurate and reliable validation of the new contact models. In conclusion to this brief introduction to my Ph. D. thesis, we would like to thank Trenitalia and the Regione Toscana for the support provided during all the Ph. D. activity. Moreover we would also like to thank the INTEC GmbH, the society the develops the software Simpack Rail, with which we are currently working together to develop innovative toolboxes specifically designed for the wheel rail contact analysis.

Shear behavior of reinforced concrete slabs under concentrated load: an investigation through Sequentially Linear Analysis

ABSTRACT (italiano) Con crescente attenzione riguardo al problema della sicurezza di ponti e viadotti esistenti nei Paesi Bassi, lo scopo della presente tesi è quello di studiare, mediante la modellazione con Elementi Finiti ed il continuo confronto con risultati sperimentali, la risposta in esercizio di elementi che compongono infrastrutture del genere, ovvero lastre in calcestruzzo armato sollecitate da carichi concentrati. Tali elementi sono caratterizzati da un comportamento ed una crisi per taglio, la cui modellazione è, da un punto di vista computazionale, una sfida piuttosto ardua, a causa del loro comportamento fragile combinato a vari effetti tridimensionali. La tesi è incentrata sull'utilizzo della Sequentially Linear Analysis (SLA), un metodo di soluzione agli Elementi Finiti alternativo rispetto ai classici approcci incrementali e iterativi. Il vantaggio della SLA è quello di evitare i ben noti problemi di convergenza tipici delle analisi non lineari, specificando direttamente l'incremento di danno sull'elemento finito, attraverso la riduzione di rigidezze e resistenze nel particolare elemento finito, invece dell'incremento di carico o di spostamento. Il confronto tra i risultati di due prove di laboratorio su lastre in calcestruzzo armato e quelli della SLA ha dimostrato in entrambi i casi la robustezza del metodo, in termini di accuratezza dei diagrammi carico-spostamento, di distribuzione di tensioni e deformazioni e di rappresentazione del quadro fessurativo e dei meccanismi di crisi per taglio. Diverse variazioni dei più importanti parametri del modello sono state eseguite, evidenziando la forte incidenza sulle soluzioni dell'energia di frattura e del modello scelto per la riduzione del modulo elastico trasversale. Infine è stato effettuato un paragone tra la SLA ed il metodo non lineare di Newton-Raphson, il quale mostra la maggiore affidabilità della SLA nella valutazione di carichi e spostamenti ultimi insieme ad una significativa riduzione dei tempi computazionali. ABSTRACT (english) With increasing attention to the assessment of safety in existing dutch bridges and viaducts, the aim of the present thesis is to study, through the Finite Element modeling method and the continuous comparison with experimental results, the real response of elements that compose these infrastructures, i.e. reinforced concrete slabs subjected to concentrated loads. These elements are characterized by shear behavior and crisis, whose modeling is, from a computational point of view, a hard challenge, due to their brittle behavior combined with various 3D effects. The thesis is focused on the use of Sequentially Linear Analysis (SLA), an alternative solution technique to classical non linear Finite Element analyses that are based on incremental and iterative approaches. The advantage of SLA is to avoid the well-known convergence problems of non linear analyses by directly specifying a damage increment, in terms of a reduction of stiffness and strength in the particular finite element, instead of a load or displacement increment. The comparison between the results of two laboratory tests on reinforced concrete slabs and those obtained by SLA has shown in both the cases the robustness of the method, in terms of accuracy of load-displacements diagrams, of the distribution of stress and strain and of the representation of the cracking pattern and of the shear failure mechanisms. Different variations of the most important parameters have been performed, pointing out the strong incidence on the solutions of the fracture energy and of the chosen shear retention model. At last a confrontation between SLA and the non linear Newton-Raphson method has been executed, showing the better reliability of the SLA in the evaluation of the ultimate loads and displacements, together with a significant reduction of computational times.

Optische Mikroskopie an kolloidalen Suspensionen unter Nichtgleichgewichtsbedingungen

Kolloidale Suspensionen eignen sich aufgrund der für sierelevanten Längeskalen hervorragend zur Beobachtung mittelsoptischer Mikroskopie. Die Verwendung speziellerKontrastierverfahren kann bestimmte Aspekte kolloidalerStrukturen besonders hervorheben und eine verbesserteAnalyse von Nichtgleichgewichtszuständen in kolloidalenSystemen ermöglichen. Mittels Phasen- und Interferenzkontrast konnte die Ursachedes Kleinwinkelstreumaximums in der Lichtstreuung an einerSuspension aus Mikronetzteilchen auf die unterschiedlichenStrukturfaktoren von Kristall und Korngrenze zurückgeführtwerden.Der Zusammenhang von Struktur und Farbe eingetrockneterMultilagen wurde in hochauflösender Durchlichtmikroskopiedemonstriert und zur Analyse der inneren Struktur derKristalldomänen inklusive von Versetzungen und Stapelfehlernbenutzt.Mit der Polarisationsmikroskopie konnte die Veränderung derPartikelzahldichte um ein Ionentauscherbruchstück auf einenSalzkonzentrationsgradienten zurückgeführt werden. Die Untersuchung kolloidaler Suspensionen in einem Scherfeldmittels Fourier-Mikroskopie lieferte im Bereich fluiderGleichgewichtsstrukturen den Nachweis scherinduzierterhexagonaler Strukturen. Die Ultramikroskopie mit erweiterterSchärfentiefe ermöglichte die direkte Beobachtung desGleitmechanismus von verscherten hexagonalen Lagen und dieKlassifizierung durch die entwickelte2D-Partikelkorrelation. Die Scherung induziert in fluidenStrukturen hexagonale Ordnung und zerstört bei großenScherraten existierende Ordnung. Es wird eineWandstabilisierung der hexagonalen Strukturen beobachtet. Mittels Bragg-Mikroskopie konnte unter Scherung dieHomogenität der Struktur innerhalb der Scherzelledokumentiert werden sowie nach Scherung die Entstehung derGleichgewichts bcc Phase.

Centrifuge modeling of earth-reinforced retaining walls

Object of this thesis has been centrifuge modelling of earth reinforced retaining walls with modular blocks facing in order to investigate on the influence of design parameters, such as length and vertical spacing of reinforcement, on the behaviour of the structure. In order to demonstrate, 11 models were tested, each one with different length of reinforcement or spacing. Each model was constructed and then placed in the centrifuge in order to artificially raise gravitational acceleration up to 35 g, reproducing the soil behaviour of a 5 metre high wall. Vertical and horizontal displacements were recorded by means of a special device which enabled tracking of deformations in the structure along its longitudinal cross section, essentially drawing its deformed shape. As expected, results confirmed reinforcement parameters to be the governing factor in the behaviour of earth reinforced structures since increase in length and spacing improved structural stability. However, the influence of the length was found out to be the leading parameter, reducing facial deformations up to five times, and the spacing playing an important role especially in unstable configurations. When failure occurred, failure surface was characterised by the same shape (circular) and depth, regardless of the reinforcement configuration. Furthermore, results confirmed the over-conservatism of codes, since models with reinforcement layers 0.4H long showed almost negligible deformations. Although the experiments performed were consistent and yielded replicable results, further numerical modelling may allow investigation on other issues, such as the influence of the reinforcement stiffness, facing stiffness and varying backfills.

Mixed Mode Fracture Behaviour of Piezoelectric Materials

Piezoelectrics present an interactive electromechanical behaviour that, especially in recent years, has generated much interest since it renders these materials adapt for use in a variety of electronic and industrial applications like sensors, actuators, transducers, smart structures. Both mechanical and electric loads are generally applied on these devices and can cause high concentrations of stress, particularly in proximity of defects or inhomogeneities, such as flaws, cavities or included particles. A thorough understanding of their fracture behaviour is crucial in order to improve their performances and avoid unexpected failures. Therefore, a considerable number of research works have addressed this topic in the last decades. Most of the theoretical studies on this subject find their analytical background in the complex variable formulation of plane anisotropic elasticity. This theoretical approach bases its main origins in the pioneering works of Muskelishvili and Lekhnitskii who obtained the solution of the elastic problem in terms of independent analytic functions of complex variables. In the present work, the expressions of stresses and elastic and electric displacements are obtained as functions of complex potentials through an analytical formulation which is the application to the piezoelectric static case of an approach introduced for orthotropic materials to solve elastodynamics problems. This method can be considered an alternative to other formalisms currently used, like the Stroh’s formalism. The equilibrium equations are reduced to a first order system involving a six-dimensional vector field. After that, a similarity transformation is induced to reach three independent Cauchy-Riemann systems, so justifying the introduction of the complex variable notation. Closed form expressions of near tip stress and displacement fields are therefore obtained. In the theoretical study of cracked piezoelectric bodies, the issue of assigning consistent electric boundary conditions on the crack faces is of central importance and has been addressed by many researchers. Three different boundary conditions are commonly accepted in literature: the permeable, the impermeable and the semipermeable (“exact”) crack model. This thesis takes into considerations all the three models, comparing the results obtained and analysing the effects of the boundary condition choice on the solution. The influence of load biaxiality and of the application of a remote electric field has been studied, pointing out that both can affect to a various extent the stress fields and the angle of initial crack extension, especially when non-singular terms are retained in the expressions of the electro-elastic solution. Furthermore, two different fracture criteria are applied to the piezoelectric case, and their outcomes are compared and discussed. The work is organized as follows: Chapter 1 briefly introduces the fundamental concepts of Fracture Mechanics. Chapter 2 describes plane elasticity formalisms for an anisotropic continuum (Eshelby-Read-Shockley and Stroh) and introduces for the simplified orthotropic case the alternative formalism we want to propose. Chapter 3 outlines the Linear Theory of Piezoelectricity, its basic relations and electro-elastic equations. Chapter 4 introduces the proposed method for obtaining the expressions of stresses and elastic and electric displacements, given as functions of complex potentials. The solution is obtained in close form and non-singular terms are retained as well. Chapter 5 presents several numerical applications aimed at estimating the effect of load biaxiality, electric field, considered permittivity of the crack. Through the application of fracture criteria the influence of the above listed conditions on the response of the system and in particular on the direction of crack branching is thoroughly discussed.

Untersuchungen zur Visuomotorik des Menschen

Motorische Bewegungen werden über die visuelle Rückmeldung auf ihre Genauigkeit kontrolliert und ggf. korrigiert. Über einen technischen Eingriff, wie beispielsweise einer Prismenbrille, kann man eine Differenz zwischen optisch wahrgenommener und haptisch erlebter Umwelt erzeugen, um die Fähigkeiten des visuomotorischen Systems zu testen. In dieser Arbeit wurde eine computergestützte Methode entwickelt, eine solche visuomotorische Differenz zu simulieren. Die Versuchspersonen führen eine ballistische Bewegung mit Arm und Hand aus in der Absicht, ein vorgegebenes Ziel zu treffen. Die Trefferpunkte werden durch einen Computer mit Hilfe eines Digitalisierungstablettes aufgenommen. Die visuelle Umwelt, welche den Versuchspersonen präsentiert wird, ist auf einem Monitor dargestellt. Das Monitorabbild – ein Kreuz auf weißem Hintergrund – betrachten die Testpersonen über einen Spiegel. Dieser ist in einem entsprechenden Winkel zwischen Monitor und Digitalisierungstablett angebracht, so dass das Zielbild auf dem Digitalisierungstablett projiziert wird. Die Testpersonen nehmen das Zielkreuz auf dem Digitalisierungstablett liegend wahr. Führt die Versuchsperson eine Zielbewegung aus, können die aufgenommenen Koordinaten als Punkte auf dem Monitor dargestellt werden und die Testperson erhält über diese Punktanzeige ein visuelles Feedback ihrer Bewegung. Der Arbeitsbereich des Digitalisierungstabletts kann über den Computer eingerichtet und so motorische Verschiebungen simuliert werden. Die verschiedenartigen Möglichkeiten dieses Aufbaus wurden zum Teil in Vorversuchen getestet um Fragestellungen, Methodik und technische Einrichtungen aufeinander abzustimmen. Den Hauptversuchen galt besonderes Interesse an der zeitlichen Verzögerung des visuellen Feedbacks sowie dem intermanuellen Transfer. Hierbei ergaben sich folgende Ergebnisse: ● Die Versuchspersonen adaptieren an eine räumlich verschobene Umwelt. Der Adaptationsverlauf lässt sich mit einer Exponentialfunktion mathematisch berechnen und darstellen. ● Dieser Verlauf ist unabhängig von der Art des visuellen Feedbacks. Die Beobachtung der Handbewegung während der Adaptation zeigt die gleiche Zielabfolge wie eine einfache Punktprojektion, die den Trefferort der Bewegung darstellt. ● Der exponentielle Verlauf der Adaptationsbewegung ist unabhängig von den getesteten zeitlichen Verzögerungen des visuellen Feedbacks. ● Die Ergebnisse des Folgeeffektes zeigen, dass bei zunehmender zeitlicher Verzögerung des visuellen Feedbacks während der Adaptationsphase, die Größe des Folgeeffektwertes geringer wird, d.h. die anhaltende Anpassungsleistung an eine visuomotorische Differenz sinkt. ● Die Folgeeffekte weisen individuelle Eigenheiten auf. Die Testpersonen adaptieren verschieden stark an eine simulierte Verschiebung. Ein Vergleich mit den visuomotorischen Herausforderungen im Vorleben der Versuchspersonen ließ vermuten, dass das visuomotorische System des Menschen trainierbar ist und sich - je nach Trainingszustand – unterschiedlich an wahrgenommene Differenzen anpasst. ● Der intermanuelle Transfer konnte unter verschiedenen Bedingungen nachgewiesen werden. ● Ein deutlich stärkerer Folgeeffekt kann beobachtet werden, wenn die wahrgenommene visuomotorische Differenz zwischen Ziel und Trefferpunkt in eine Gehirnhälfte projiziert wird und der Folgeeffekt mit der Hand erfolgt, welche von dieser Hirnhemisphäre gesteuert wird. Der intermanuelle Transfer wird demnach begünstigt, wenn die visuelle Projektion der Fehlerbeobachtung in die Gehirnhälfte erfolgt, die während der Adaptationsphase motorisch passiv ist.

Monte-Carlo-Simulationen zum Phasenverhalten binärer Polymerbürsten

Diese Arbeit beschäftigt sich mit Strukturbildung im schlechten Lösungsmittel bei ein- und zweikomponentigen Polymerbürsten, bei denen Polymerketten durch Pfropfung am Substrat verankert sind. Solche Systeme zeigen laterale Strukturbildungen, aus denen sich interessante Anwendungen ergeben. Die Bewegung der Polymere erfolgt durch Monte Carlo-Simulationen im Kontinuum, die auf CBMC-Algorithmen sowie lokalen Monomerverschiebungen basieren. Eine neu entwickelte Variante des CBMC-Algorithmus erlaubt die Bewegung innerer Kettenteile, da der bisherige Algorithmus die Monomere in Nähe des Pfropfmonomers nicht gut relaxiert. Zur Untersuchung des Phasenverhaltens werden mehrere Analysemethoden entwickelt und angepasst: Dazu gehören die Minkowski-Maße zur Strukturuntersuchung binären Bürsten und die Pfropfkorrelationen zur Untersuchung des Einflusses von Pfropfmustern. Bei einkomponentigen Bürsten tritt die Strukturbildung nur beim schwach gepfropften System auf, dichte Pfropfungen führen zu geschlossenen Bürsten ohne laterale Struktur. Für den graduellen Übergang zwischen geschlossener und aufgerissener Bürste wird ein Temperaturbereich bestimmt, in dem der Übergang stattfindet. Der Einfluss des Pfropfmusters (Störung der Ausbildung einer langreichweitigen Ordnung) auf die Bürstenkonfiguration wird mit den Pfropfkorrelationen ausgewertet. Bei unregelmäßiger Pfropfung sind die gebildeten Strukturen größer als bei regelmäßiger Pfropfung und auch stabiler gegen höhere Temperaturen. Bei binären Systemen bilden sich Strukturen auch bei dichter Pfropfung aus. Zu den Parametern Temperatur, Pfropfdichte und Pfropfmuster kommt die Zusammensetzung der beiden Komponenten hinzu. So sind weitere Strukturen möglich, bei gleicher Häufigkeit der beiden Komponenten bilden sich streifenförmige, lamellare Muster, bei ungleicher Häufigkeit formt die Minoritätskomponente Cluster, die in der Majoritätskomponente eingebettet sind. Selbst bei gleichmäßig gepfropften Systemen bildet sich keine langreichweitige Ordnung aus. Auch bei binären Bürsten hat das Pfropfmuster großen Einfluss auf die Strukturbildung. Unregelmäßige Pfropfmuster führen schon bei höheren Temperaturen zur Trennung der Komponenten, die gebildeten Strukturen sind aber ungleichmäßiger und etwas größer als bei gleichmäßig gepfropften Systemen. Im Gegensatz zur self consistent field-Theorie berücksichtigen die Simulationen Fluktuationen in der Pfropfung und zeigen daher bessere Übereinstimmungen mit dem Experiment.

Magma injections and destabilization of basaltic volcanoes: a numerical study. Application to La Reunion (Indian ocean, France) and Stromboli (Tyrrhenian sea, Italy)

Most basaltic volcanoes are affected by recurrent lateral instabilities during their evolution. Numerous factors have been shown to be involved in the process of flank destabilization occurring over long periods of time or by instantaneous failures. However, the role of these factors on the mechanical behaviour and stability of volcanic edifices is poorly-constrained as lateral failure usually results from the combined effects of several parameters. Our study focuses on the morphological and structural comparison of two end-member basaltic systems, La Reunion (Indian ocean, France) and Stromboli (southern Tyrrhenian sea, Italy). We showed that despite major differences on their volumes and geodynamic settings, both systems present some similarities as they are characterized by an intense intrusive activity along well-developed rift zones and recurrent phenomena of flank collapse during their evolution. Among the factors of instability, the examples of la Reunion and Stromboli evidence the major contribution of intrusive complexes to volcano growth and destruction as attested by field observations and the monitoring of these active volcanoes. Classical models consider the relationship between vertical intrusions of magma and flank movements along a preexisting sliding surface. A set of published and new field data from Piton des Neiges volcano (La Reunion) allowed us to recognize the role of subhorizontal intrusions in the process of flank instability and to characterize the geometry of both subvertical and subhorizontal intrusions within basaltic edifices. This study compares the results of numerical modelling of the displacements associated with high-angle and low-angle intrusions within basaltic volcanoes. We use a Mixed Boundary Element Method to investigate the mechanical response of an edifice to the injection of magmatic intrusions in different stress fields. Our results indicate that the anisotropy of the stress field favours the slip along the intrusions due to cointrusive shear stress, generating flank-scale displacements of the edifice, especially in the case of subhorizontal intrusions, capable of triggering large-scale flank collapses on basaltic volcanoes. Applications of our theoretical results to real cases of flank displacements on basaltic volcanoes (such as the 2007 eruptive crisis at La Reunion and Stromboli) revealed that the previous model of subvertical intrusions-related collapse is a likely mechanism affecting small-scale steeply-sloping basaltic volcanoes like Stromboli. Furthermore, our field study combined to modelling results confirms the importance of shallow-dipping intrusions in the morpho-structural evolution of large gently-sloping basaltic volcanoes like Piton de la Fournaise, Etna and Kilauea, with particular regards to flank instability, which can cause catastrophic tsunamis.

Methods for Clearance Influence Analysis in Planar and Spatial Mechanisms

This doctoral dissertation presents a new method to asses the influence of clearancein the kinematic pairs on the configuration of planar and spatial mechanisms. The subject has been widely investigated in both past and present scientific literature, and is approached in different ways: a static/kinetostatic way, which looks for the clearance take-up due to the external loads on the mechanism; a probabilistic way, which expresses clearance-due displacements using probability density functions; a dynamic way, which evaluates dynamic effects like the actual forces in the pairs caused by impacts, or the consequent vibrations. This dissertation presents a new method to approach the problem of clearance. The problem is studied from a purely kinematic perspective. With reference to a given mechanism configuration, the pose (position and orientation) error of the mechanism link of interest is expressed as a vector function of the degrees of freedom introduced in each pair by clearance: the presence of clearance in a kinematic pair, in facts, causes the actual pair to have more degrees of freedom than the theoretical clearance-free one. The clearance-due degrees of freedom are bounded by the pair geometry. A proper modelling of clearance-affected pairs allows expressing such bounding through analytical functions. It is then possible to study the problem as a maximization problem, where a continuous function (the pose error of the link of interest) subject to some constraints (the analytical functions bounding clearance- due degrees of freedom) has to be maximize. Revolute, prismatic, cylindrical, and spherical clearance-affected pairs have been analytically modelled; with reference to mechanisms involving such pairs, the solution to the maximization problem has been obtained in a closed form.

Strategie di personalizzazione della terapia di resincronizzazione cardiaca

Solo il 60% dei candidati alla resincronizzazione cardiaca risponde in termini di rimodellamento ventricolare inverso che è il più forte predittore di riduzione della mortalità e delle ospedalizzazioni. Due cause possibili della mancata risposta sono la programmazione del dispositivo e i limiti dell’ approccio transvenoso. Nel corso degli anni di dottorato ho effettuato tre studi per ridurre il numero di non responder. Il primo studio valuta il ritardo interventricolare. Al fine di ottimizzare le risorse e fornire un reale beneficio per il paziente ho ricercato la presenza di predittori di ritardo interventricolare diverso dal simultaneo, impostato nella programmazione di base. L'unico predittore è risultato essere l’ intervallo QRS> 160 ms, quindi ho proposto una flow chart per ottimizzare solo i pazienti che avranno nella programmazione ottimale un intervallo interventricolare non simultaneo. Il secondo lavoro valuta la fissazione attiva del ventricolo sinistro con stent. I dislocamenti, la soglia alta di stimolazione del miocardio e la stimolazione del nervo frenico sono tre problematiche che limitano la stimolazione biventricolare. Abbiamo analizzato più di 200 angiografie per vedere le condizioni anatomiche predisponenti la dislocazione del catetere. Prospetticamente abbiamo deciso di utilizzare uno stent per fissare attivamente il catetere ventricolare sinistro in tutti i pazienti che presentavano le caratteristiche anatomiche favorenti la dislocazione. Non ci sono più state dislocazioni, c’è stata una migliore risposta in termini di rimodellamento ventricolare inverso e non ci sono state modifiche dei parametri elettrici del catetere. Il terzo lavoro ha valutato sicurezza ed efficacia della stimolazione endoventricolare sinistra. Abbiamo impiantato 26 pazienti giudicati non responder alla terapia di resincronizzazione cardiaca. La procedura è risultata sicura, il rischio di complicanze è simile alla stimolazione biventricolare classica, ed efficace nell’arrestare la disfunzione ventricolare sinistra e / o migliorare gli effetti clinici in un follow-up medio.

Störungstheoretische Behandlung relativistischer Korrekturen zu Gleichgewichtsstrukturen im Rahmen der Coupled-Cluster-Theorie

Quantenchemische Untersuchungen von Atomen und Molekülen haben in den letzten Jahren durch die systematische Erweiterung der Methoden und Computerresourcen zunehmend für die Interpretation und Vorhersage experimenteller Ergebnisse an Bedeutung gewonnen. Relativistische Effekte in der Chemie werden zum Beispiel für die gelbe Farbe von Gold und den flüssigen Aggregatzustand von Quecksilber verantwortlich gemacht und müssen daher in quantenchemischen Rechnungen berücksichtigt werden. Relativistische Effekte sind bei leichten Elementen oft so klein, daß sie in vielen quantenchemischen Betrachtungen vernachlässigt werden. Dennoch sind es gerade diese Beiträge, die verbleibende Abweichungen von noch so genauen nichtrelativistischen Rechnungen von ebenso genauen experimentellen Ergebnissen ausmachen können. Relativistische Effekte können auf viele Arten in quantenchemischen Rechnungen berücksichtigt werden. Eine Möglichkeit ist die Störungstheorie. Ein derartiger Ansatz ist die Mass-velocity-Darwin-Näherung, ein anderer die Direkte Störungstheorie. Hier entspricht die relativistische Energiekorrektur erster Ordnung der ersten Ableitung der Energie nach einem relativistischen Störparameter. Für eine Bestimmung der Gleichgewichtsstruktur eines Moleküls müssen die Kräfte auf die Atomkerne bestimmt werden. Diese entsprechen einer ersten Ableitung der Gesamtenergie nach den Kernkoordinaten. Eine Einbeziehung der relativistischen Effekte auf diese Kräfte erfordert daher die gemischte zweite Ableitung der Energie nach dem relativistischen Störparameter und den Kernkoordinaten. Diese relativistischen Korrekturen wurden in dem quantenchemischen Programmpaket ACES2 implementiert. Ein Resultat dieser Arbeit ist, daß nun erstmalig eine Implementierung analytischer Gradienten für die Berechnung relativistischer Korrekturen zu Strukturparametern mit Hilfe der relativistischen Störungstheorie für den Coupled-Cluster-Ansatz bereit steht. Die Coupled-Cluster-Theorie eignet sich besonders gut für die hochgenaue Vorhersage von molekularen Eigenschaften, wie der Gleichgewichtsstruktur. Im Rahmen dieser Arbeit wurde die Basissatzabhängigkeit der relativistischen Beiträge zu Energien, Strukturparametern und harmonischen Schwingungsfrequenzen im Detail untersucht. Für die hier untersuchten Moleküle sind die relativistischen Effekte und Effekte aufgrund der Elektronenkorrelation nicht additiv, so verkürzt die Berücksichtigung relativistischer Effekte bei Hartree-Fock-Rechnungen die Bindung in den Hydrogenhalogeniden, während die Einbeziehung der Elektronenkorrelation durch CCSD(T)-Rechnungen zu einer verlängerten Bindung im Fluorwasserstoff und weniger stark ausgeprägten Korrekturen im Chlor- und Bromwasserstoff führt. Für die anderen hier untersuchten mehratomigen Moleküle findet sich kein einheitlicher Trend; dies unterstreicht die Notwendigkeit expliziter Rechnungen. Damit steht ein leistungsfähiges und vielseitiges Werkzeug für die Berechnung relativistischer Korrekturen auf verschiedenste molekulare Eigenschaften zur Verfügung, das mit modernen, systematisch verbesserbaren quantenchemischen Methoden verknüpft ist. Hiermit ist es möglich, hochgenaue Rechnungen zur Vorhersage und Interpretation von Experimenten durchzuführen.

Crystal phases and glassy dynamics in monodisperse hard ellipsoids

We have performed Monte Carlo and molecular dynamics simulations of suspensions of monodisperse, hard ellipsoids of revolution. Hard-particle models play a key role in statistical mechanics. They are conceptually and computationally simple, and they offer insight into systems in which particle shape is important, including atomic, molecular, colloidal, and granular systems. In the high density phase diagram of prolate hard ellipsoids we have found a new crystal, which is more stable than the stretched FCC structure proposed previously . The new phase, SM2, has a simple monoclinic unit cell containing a basis of two ellipsoids with unequal orientations. The angle of inclination is very soft for length-to-width (aspect) ratio l/w=3, while the other angles are not. A symmetric state of the unit cell exists, related to the densest-known packings of ellipsoids; it is not always the stable one. Our results remove the stretched FCC structure for aspect ratio l/w=3 from the phase diagram of hard, uni-axial ellipsoids. We provide evidence that this holds between aspect ratios 3 and 6, and possibly beyond. Finally, ellipsoids in SM2 at l/w=1.55 exhibit end-over-end flipping, warranting studies of the cross-over to where this dynamics is not possible. Secondly, we studied the dynamics of nearly spherical ellipsoids. In equilibrium, they show a first-order transition from an isotropic phase to a rotator phase, where positions are crystalline but orientations are free. When over-compressing the isotropic phase into the rotator regime, we observed super-Arrhenius slowing down of diffusion and relaxation, and signatures of the cage effect. These features of glassy dynamics are sufficiently strong that asymptotic scaling laws of the Mode-Coupling Theory of the glass transition (MCT) could be tested, and were found to apply. We found strong coupling of positional and orientational degrees of freedom, leading to a common value for the MCT glass-transition volume fraction. Flipping modes were not slowed down significantly. We demonstrated that the results are independent of simulation method, as predicted by MCT. Further, we determined that even intra-cage motion is cooperative. We confirmed the presence of dynamical heterogeneities associated with the cage effect. The transit between cages was seen to occur on short time scales, compared to the time spent in cages; but the transit was shown not to involve displacements distinguishable in character from intra-cage motion. The presence of glassy dynamics was predicted by molecular MCT (MMCT). However, as MMCT disregards crystallization, a test by simulation was required. Glassy dynamics is unusual in monodisperse systems. Crystallization typically intervenes unless polydispersity, network-forming bonds or other asymmetries are introduced. We argue that particle anisometry acts as a sufficient source of disorder to prevent crystallization. This sheds new light on the question of which ingredients are required for glass formation.

Valutazione della risposta sismica di edifici mediante modelli anelastici equivalenti

Nella presente tesi è proposta una metodologia per lo studio e la valutazione del comportamento sismico di edifici a telaio. Il metodo prevede la realizzazione di analisi non-lineari su modelli equivalenti MDOF tipo stick, in accordo alla classificazione data nel report FEMA 440. Gli step per l’applicazione del metodo sono descritti nella tesi. Per la validazione della metodologia si sono utilizzati confronti con analisi time-history condotte su modelli tridimensionali dettagliati delle strutture studiate (detailed model). I parametri ingegneristici considerati nel confronto, nell’ottica di utilizzare il metodo proposto in un approccio del tipo Displacement-Based Design sono lo spostamento globale in sommità, gli spostamenti di interpiano, le forze di piano e la forza totale alla base. I risultati delle analisi condotte sui modelli stick equivalenti, mostrano una buona corrispondenza, ottima in certi casi, con quelli delle analisi condotte sui modelli tridimensionali dettagliati. Le time-history realizzate sugli stick model permettono però, un consistente risparmio in termini di onere computazionale e di tempo per il post-processing dei risultati ottenuti.