Maximum principle, mean value operators and quasi boundedness in non-euclidean settings

This work deals with some classes of linear second order partial differential operators with non-negative characteristic form and underlying non- Euclidean structures. These structures are determined by families of locally Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot- Carath´eodory type. The Carnot-Carath´eodory metric related to a family {Xj}j=1,...,m is the control distance obtained by minimizing the time needed to go from two points along piecewise trajectories of vector fields. We are mainly interested in the causes in which a Sobolev-type inequality holds with respect to the X-gradient, and/or the X-control distance is Doubling with respect to the Lebesgue measure in RN. This study is divided into three parts (each corresponding to a chapter), and the subject of each one is a class of operators that includes the class of the subsequent one. In the first chapter, after recalling “X-ellipticity” and related concepts introduced by Kogoj and Lanconelli in [KL00], we show a Maximum Principle for linear second order differential operators for which we only assume a Sobolev-type inequality together with a lower terms summability. Adding some crucial hypotheses on measure and on vector fields (Doubling property and Poincar´e inequality), we will be able to obtain some Liouville-type results. This chapter is based on the paper [GL03] by Guti´errez and Lanconelli. In the second chapter we treat some ultraparabolic equations on Lie groups. In this case RN is the support of a Lie group, and moreover we require that vector fields satisfy left invariance. After recalling some results of Cinti [Cin07] about this class of operators and associated potential theory, we prove a scalar convexity for mean-value operators of L-subharmonic functions, where L is our differential operator. In the third chapter we prove a necessary and sufficient condition of regularity, for boundary points, for Dirichlet problem on an open subset of RN related to sub-Laplacian. On a Carnot group we give the essential background for this type of operator, and introduce the notion of “quasi-boundedness”. Then we show the strict relationship between this notion, the fundamental solution of the given operator, and the regularity of the boundary points.

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.

Studio e messa a punto del modello maximum-slope per l'analisi dei parametri perfusionali da sequenza di immagini tomografiche

Miglioramento delle prestazioni del modello mono-compartimentale del maximum slope dovuto all'introduzione di sistemi per l'eliminazione degli outliers.

A Design Method for Flexure-Based Compliant Mechanisms on the Basis of Stiffness and Stress Characteristics

Geometric nonlinearities of flexure hinges introduced by large deflections often complicate the analysis of compliant mechanisms containing such members, and therefore, Pseudo-Rigid-Body Models (PRBMs) have been well proposed and developed by Howell [1994] to analyze the characteristics of slender beams under large deflection. These models, however, fail to approximate the characteristics for the deep beams (short beams) or the other flexure hinges. Lobontiu's work [2001] contributed to the diverse flexure hinge analysis building on the assumptions of small deflection, which also limits the application range of these flexure hinges and cannot analyze the stiffness and stress characteristics of these flexure hinges for large deflection. Therefore, the objective of this thesis is to analyze flexure hinges considering both the effects of large-deflection and shear force, which guides the design of flexure-based compliant mechanisms. The main work conducted in the thesis is outlined as follows. 1. Three popular types of flexure hinges: (circular flexure hinges, elliptical flexure hinges and corner-filleted flexure hinges) are chosen for analysis at first. 2. Commercial software (Comsol) based Finite Element Analysis (FEA) method is then used for correcting the errors produced by the equations proposed by Lobontiu when the chosen flexure hinges suffer from large deformation. 3. Three sets of generic design equations for the three types of flexure hinges are further proposed on the basis of stiffness and stress characteristics from the FEA results. 4. A flexure-based four-bar compliant mechanism is finally studied and modeled using the proposed generic design equations. The load-displacement relationships are verified by a numerical example. The results show that a maximum error about the relationship between moment and rotation deformation is less than 3.4% for a flexure hinge, and it is lower than 5% for the four-bar compliant mechanism compared with the FEA results.

Non linear response of planar asymmetric systems

The seismic behaviour of one-storey asymmetric structures has been studied since 1970s by a number of researches studies which identified the coupled nature of the translational-to-torsional response of those class of systems leading to severe displacement magnifications at the perimeter frames and therefore to significant increase of local peak seismic demand to the structural elements with respect to those of equivalent not-eccentric systems (Kan and Chopra 1987). These studies identified the fundamental parameters (such as the fundamental period TL normalized eccentricity e and the torsional-to-lateral frequency ratio Ωϑ) governing the torsional behavior of in-plan asymmetric structures and trends of behavior. It has been clearly recognized that asymmetric structures characterized by Ωϑ >1, referred to as torsionally-stiff systems, behave quite different form structures with Ωϑ <1, referred to as torsionally-flexible systems. Previous research works by some of the authors proposed a simple closed-form estimation of the maximum torsional response of one-storey elastic systems (Trombetti et al. 2005 and Palermo et al. 2010) leading to the so called “Alpha-method” for the evaluation of the displacement magnification factors at the corner sides. The present paper provides an upgrade of the “Alpha Method” removing the assumption of linear elastic response of the system. The main objective is to evaluate how the excursion of the structural elements in the inelastic field (due to the reaching of yield strength) affects the displacement demand of one-storey in-plan asymmetric structures. The system proposed by Chopra and Goel in 2007, which is claimed to be able to capture the main features of the non-linear response of in-plan asymmetric system, is used to perform a large parametric analysis varying all the fundamental parameters of the system, including the inelastic demand by varying the force reduction factor from 2 to 5. Magnification factors for different force reduction factor are proposed and comparisons with the results obtained from linear analysis are provided.

Contributo sperimentale alla ridefinizione della diffusione in parete della camera di prova della galleria del vento Dallara

Joseph Nicolas Cugnot built the first primitive car in 1769 and approximately one hundred year later the first automotive race took place. Thanks to this, for the first time the aerodynamics principles began to be applied to cars. The aerodynamic study of a car is important to improve the performance on the road, or on the track. It purposely enhances the stability in the turns and increases the maximum velocity. However, it is also useful, decrease the fuel consumption, in order to reduce the pollution. Given that cars are a very complex body, the aerodynamic study cannot be conducted following an analytical method, but it is possible, in general, to choose between two different approaches: the numerical or the experimental one. The results of numerical studies depend on the computers’ potential and on the method use to implement the mathematical model. Today, the best way to perform an aerodynamic study is still experimental, which means that in the first phase of the design process the study is performed in a wind tunnel and in later phases directly on track. The automotive wind tunnels are singular mainly due to the test chamber, which typically contains a ground simulation system. The test chamber can have different types of walls: open walls, closed walls, adaptive walls or slotted walls. The best solution is to use the slotted walls because they minimize the interference between the walls and the streamlines, the interaction between the flow and the environment, and also to contain the overall costs. Furthermore, is necessary minimize the boundary layer at the walls, without accelerating the flow, in order to provide the maximum section of homogeneous flow. This thesis aims at redefining the divergent angle of the Dallara Automobili S.P.A. wind tunnel’s walls, in order to improve the overall homogeneity. To perform this study it was necessary to acquire the pressure data of the boundary layer, than it was created the profile of the boundary layer velocity and, to minimize the experimental errors, it was calculated the displacement thickness. The results obtained shows, even if the instrument used to the experiment was not the best one, that the boundary layer thickness could be minor in case of a low diffusion angle. So it is convenient to perform another experiment with a most sensitive instrument to verified what is the better wall configuration.

Studio di fattibilità per l'applicazione dei "positive displacement motors" in ambienti HT-HP

Questo studio concerne uno studio di fattibilità per l'applicazione dei "positive displacement motors" in ambienti ambienti fortemente critici, soggetti ad alta pressione e alta temperatura. Tali motori sono utilizzati nell'industria Oil & Gas per la perforazione di pozzi petroliferi. L’analisi è stata portata a termine attraverso definizione dell’intervallo di temperatura per cui le performance degli strumenti in commercio presenta il maggior numero di failures, compreso tra i 175°C e i 225°C , e per il quale si vuole riuscire a limitare i rischi connessi e le criticità associate, garantendo così il raggiungimento dei target con un maggior grado di affidabilità e disponibilità del PDM utilizzato. Analizzando le sollecitazioni agenti sul motore durante le fasi di utilizzo, è stato possibile rilevare le principali cause di rottura e malfunzionamento che, nella maggior parte dei casi, possono essere attribuite al rigonfiamento e alla degradazione del materiale elastomerico che costituisce lo statore della power section. Investigando in merito alle differenze e alle proprietà di resistenza di numerosi materiali elastomerici a diversi range di temperatura, sono stati evidenziati dei margini di ottimizzazione in particolare relativi alla potenziale riduzione e totale sostituzione della superficie elastomerica con materiale metallico. Ciò ha fatto si che fosse necessario un approfondimento sulle caratteristiche degli acciai e delle leghe metalliche, in termini di resistenza a corrosione, costo del materiale, resistenza meccanica e della capacità di mantenere elevate proprietà meccaniche con l’aumento della temperatura, al fine di individuare i migliori “candidati” per sostituire interamente il materiale elastomerico dello statore in materiale metallico e risolvere così il problema dell’applicazione dei PDM in ambienti HT-HP.

Immunomodulatory therapy to achieve maximum efficacy: doses, monitoring, compliance, and self-infusion at home

The Oxford Programme for Immunomodulatory Immunoglobulin Therapy has been operating since 1992 at Oxford Radcliffe Hospitals in the UK. Initially, this program was set up for patients with multifocal motor neuropathy or chronic inflammatory demyelinating poly-neuropathy to receive reduced doses of intravenous immunoglobulin (IVIG) in clinic on a regular basis (usually every 3 weeks). The program then rapidly expanded to include self-infusion at home, which monitoring showed to be safe and effective. It has been since extended to the treatment of other autoimmune diseases in which IVIG has been shown to be efficacious.

Maximum flight velocity of blood drops in analysing blood traces

When analysing blood spatters, traces often occur which regarding the collision angle, cannot be allocated to any supposed centre of origin. Drops following highly curved (ballistic) trajectories usually form these types of traces. The reconstruction of such trajectories requires knowledge of the mass, the diameter (of which approximations are known) and the velocity of the blood drops. This article provides an upper range of the velocity in relation to the diameter of the blood drops based on physical laws. This is very helpful in analysing ballistic trajectories.