Une nouvelle mise en oeuvre de la méthode IIM pour les équations de Navier-Stokes en présence d'une force singulière

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

La méthode IIM pour une membrane immergée dans un fluide incompressible

La méthode IIM (Immersed Interface Method) permet d'étendre certaines méthodes numériques à des problèmes présentant des discontinuités. Elle est utilisée ici pour étudier un fluide incompressible régi par les équations de Navier-Stokes, dans lequel est immergée une membrane exerçant une force singulière. Nous utilisons une méthode de projection dans une grille de différences finies de type MAC. Une dérivation très complète des conditions de saut dans le cas où la viscosité est continue est présentée en annexe. Deux exemples numériques sont présentés : l'un sans membrane, et l'un où la membrane est immobile. Le cas général d'une membrane mobile est aussi étudié en profondeur.

Une nouvelle méthode smoothed particle hydrodynamics : simulation des interfaces immergées et de la dynamique Brownienne des molécules avec des interactions hydrodynamiques

Dans cette thèse, nous présentons une nouvelle méthode smoothed particle hydrodynamics (SPH) pour la résolution des équations de Navier-Stokes incompressibles, même en présence des forces singulières. Les termes de sources singulières sont traités d'une manière similaire à celle que l'on retrouve dans la méthode Immersed Boundary (IB) de Peskin (2002) ou de la méthode régularisée de Stokeslets (Cortez, 2001). Dans notre schéma numérique, nous mettons en oeuvre une méthode de projection sans pression de second ordre inspirée de Kim et Moin (1985). Ce schéma évite complètement les difficultés qui peuvent être rencontrées avec la prescription des conditions aux frontières de Neumann sur la pression. Nous présentons deux variantes de cette approche: l'une, Lagrangienne, qui est communément utilisée et l'autre, Eulerienne, car nous considérons simplement que les particules SPH sont des points de quadrature où les propriétés du fluide sont calculées, donc, ces points peuvent être laissés fixes dans le temps. Notre méthode SPH est d'abord testée à la résolution du problème de Poiseuille bidimensionnel entre deux plaques infinies et nous effectuons une analyse détaillée de l'erreur des calculs. Pour ce problème, les résultats sont similaires autant lorsque les particules SPH sont libres de se déplacer que lorsqu'elles sont fixes. Nous traitons, par ailleurs, du problème de la dynamique d'une membrane immergée dans un fluide visqueux et incompressible avec notre méthode SPH. La membrane est représentée par une spline cubique le long de laquelle la tension présente dans la membrane est calculée et transmise au fluide environnant. Les équations de Navier-Stokes, avec une force singulière issue de la membrane sont ensuite résolues pour déterminer la vitesse du fluide dans lequel est immergée la membrane. La vitesse du fluide, ainsi obtenue, est interpolée sur l'interface, afin de déterminer son déplacement. Nous discutons des avantages à maintenir les particules SPH fixes au lieu de les laisser libres de se déplacer. Nous appliquons ensuite notre méthode SPH à la simulation des écoulements confinés des solutions de polymères non dilués avec une interaction hydrodynamique et des forces d'exclusion de volume. Le point de départ de l'algorithme est le système couplé des équations de Langevin pour les polymères et le solvant (CLEPS) (voir par exemple Oono et Freed (1981) et Öttinger et Rabin (1989)) décrivant, dans le cas présent, les dynamiques microscopiques d'une solution de polymère en écoulement avec une représentation bille-ressort des macromolécules. Des tests numériques de certains écoulements dans des canaux bidimensionnels révèlent que l'utilisation de la méthode de projection d'ordre deux couplée à des points de quadrature SPH fixes conduit à un ordre de convergence de la vitesse qui est de deux et à une convergence d'ordre sensiblement égale à deux pour la pression, pourvu que la solution soit suffisamment lisse. Dans le cas des calculs à grandes échelles pour les altères et pour les chaînes de bille-ressort, un choix approprié du nombre de particules SPH en fonction du nombre des billes N permet, en l'absence des forces d'exclusion de volume, de montrer que le coût de notre algorithme est d'ordre O(N). Enfin, nous amorçons des calculs tridimensionnels avec notre modèle SPH. Dans cette optique, nous résolvons le problème de l'écoulement de Poiseuille tridimensionnel entre deux plaques parallèles infinies et le problème de l'écoulement de Poiseuille dans une conduite rectangulaire infiniment longue. De plus, nous simulons en dimension trois des écoulements confinés entre deux plaques infinies des solutions de polymères non diluées avec une interaction hydrodynamique et des forces d'exclusion de volume.

Studies on the dynamics and rheology of dilute suspensions of Brownian particles in simple shear flow under the action of an external force

We present a novel approach to computing the orientation moments and rheological properties of a dilute suspension of spheroids in a simple shear flow at arbitrary Peclct number based on a generalised Langevin equation method. This method differs from the diffusion equation method which is commonly used to model similar systems in that the actual equations of motion for the orientations of the individual particles are used in the computations, instead of a solution of the diffusion equation of the system. It also differs from the method of 'Brownian dynamics simulations' in that the equations used for the simulations are deterministic differential equations even in the presence of noise, and not stochastic differential equations as in Brownian dynamics simulations. One advantage of the present approach over the Fokker-Planck equation formalism is that it employs a common strategy that can be applied across a wide range of shear and diffusion parameters. Also, since deterministic differential equations are easier to simulate than stochastic differential equations, the Langevin equation method presented in this work is more efficient and less computationally intensive than Brownian dynamics simulations.We derive the Langevin equations governing the orientations of the particles in the suspension and evolve a procedure for obtaining the equation of motion for any orientation moment. A computational technique is described for simulating the orientation moments dynamically from a set of time-averaged Langevin equations, which can be used to obtain the moments when the governing equations are harder to solve analytically. The results obtained using this method are in good agreement with those available in the literature.The above computational method is also used to investigate the effect of rotational Brownian motion on the rheology of the suspension under the action of an external force field. The force field is assumed to be either constant or periodic. In the case of con- I stant external fields earlier results in the literature are reproduced, while for the case of periodic forcing certain parametric regimes corresponding to weak Brownian diffusion are identified where the rheological parameters evolve chaotically and settle onto a low dimensional attractor. The response of the system to variations in the magnitude and orientation of the force field and strength of diffusion is also analyzed through numerical experiments. It is also demonstrated that the aperiodic behaviour exhibited by the system could not have been picked up by the diffusion equation approach as presently used in the literature.The main contributions of this work include the preparation of the basic framework for applying the Langevin method to standard flow problems, quantification of rotary Brownian effects by using the new method, the paired-moment scheme for computing the moments and its use in solving an otherwise intractable problem especially in the limit of small Brownian motion where the problem becomes singular, and a demonstration of how systems governed by a Fokker-Planck equation can be explored for possible chaotic behaviour.

SPATIAL UNDERSTANDING OF MATRIX INVERSION FOR INVERSE FORCE ESTIMATION

A basic approach to study a NVH problem is to break down the system in three basic elements – source, path and receiver. While the receiver (response) and the transfer path can be measured, it is difficult to measure the source (forces) acting on the system. It becomes necessary to predict these forces to know how they influence the responses. This requires inverting the transfer path. Singular Value Decomposition (SVD) method is used to decompose the transfer path matrix into its principle components which is required for the inversion. The usual approach to force prediction requires rejecting the small singular values obtained during SVD by setting a threshold, as these small values dominate the inverse matrix. This assumption of the threshold may be subjected to rejecting important singular values severely affecting force prediction. The new approach discussed in this report looks at the column space of the transfer path matrix which is the basis for the predicted response. The response participation is an indication of how the small singular values influence the force participation. The ability to accurately reconstruct the response vector is important to establish a confidence in force vector prediction. The goal of this report is to suggest a solution that is mathematically feasible, physically meaningful, and numerically more efficient through examples. This understanding adds new insight to the effects of current code and how to apply algorithms and understanding to new codes.

Relationship Between Orofacial Function, Dentofacial Morphology, And Bite Force In Young Subjects.

The aim was to evaluate the relationship between orofacial function, dentofacial morphology, and bite force in young subjects. Three hundred and sixteen subjects were divided according to dentition stage (early, intermediate, and late mixed and permanent dentition). Orofacial function was screened using the Nordic Orofacial Test-Screening (NOT-S). Orthodontic treatment need, bite force, lateral and frontal craniofacial dimensions and presence of sleep bruxism were also assessed. The results were submitted to descriptive statistics, normality and correlation tests, analysis of variance, and multiple linear regression to test the relationship between NOT-S scores and the studied independent variables. The variance of NOT-S scores between groups was not significant. The evaluation of the variables that significantly contributed to NOT-S scores variation showed that age and presence of bruxism related to higher NOT-S total scores, while the increase in overbite measurement and presence of closed lip posture related to lower scores. Bite force did not show a significant relationship with scores of orofacial dysfunction. No significant correlations between craniofacial dimensions and NOT-S scores were observed. Age and sleep bruxism were related to higher NOT-S scores, while the increase in overbite measurement and closed lip posture contributed to lower scores of orofacial dysfunction.

Bipolar Tribocharging Signal During Friction Force Fluctuations At Metal-insulator Interfaces.

Friction and triboelectrification of materials show a strong correlation during sliding contacts. Friction force fluctuations are always accompanied by two tribocharging events at metal-insulator [e.g., polytetrafluoroethylene (PTFE)] interfaces: injection of charged species from the metal into PTFE followed by the flow of charges from PTFE to the metal surface. Adhesion maps that were obtained by atomic force microscopy (AFM) show that the region of contact increases the pull-off force from 10 to 150 nN, reflecting on a resilient electrostatic adhesion between PTFE and the metallic surface. The reported results suggest that friction and triboelectrification have a common origin that must be associated with the occurrence of strong electrostatic interactions at the interface.

Da busca pela natureza aos ambientes artificiais : reflexões sobre a escalada esportiva

Universidade Estadual de Campinas . Faculdade de Educação Física

Retention force of T-bar clasps for titanium and cobalt-chromium removable partial dentures

The objective of this study was to evaluate the retention force of T-bar clasps made from commercially pure titanium (CP Ti) and cobalt-chromium (Co-Cr) alloy by the insertion/removal test simulating 5 years use. Thirty-six frameworks were cast from CP Ti (n=18) and Co-Cr alloy (n=18) with identical prefabricated patterns on refractory casts from a distal extension mandibular hemi-arch segment. The castings were made on a vacuum-pressure machine, under vacuum and argon atmosphere. Each group was subdivided in three, corresponding to 0.25 mm, 0.50 mm and 0.75 mm undercuts, respectively. No polishing procedures were performed to ensure uniformity. The specimens were subjected to an insertion/removal test and data was analyzed statistically to compare CP Ti and Co-Cr alloy in the same undercut (Student's t-test for independent samples) and each material in different undercuts (one-way ANOVA) (p=0.05). Comparisons between materials revealed significant differences (p=0.017) only for the 0.50-mm undercut. No significant differences (p>0.05) were found when comparing the same material for the undercuts. It may be concluded that for different undercuts, both Co-Cr alloy and CP Ti had no significant differences for T-bar clasps; CP Ti showed the lowest retention force values when compared to Co-Cr alloy in each undercut, but with significant difference only for the 0.50-mm undercut; and both materials maintained the retentive capacity during the simulation test.

Bite force in temporomandibular dysfunction (TMD) and healthy complete denture wearers

The signs and symptoms of temporomandibular dysfunction (TMD) may contribute to reduce bite force and muscular activity. The aims of this study were to compare bite force in complete denture wearers with TMD (TMD group) and without TMD (healthy group).The TMD group consisted of 9 individuals, who had worn a maxillary and a mandibular complete removable denture for more than 10 years. The healthy group consisted of 9 participants who wore dentures and had satisfactory interocclusal and maxillomandibular relationship. Helkimo Index was used to analyze the dysfunction level. Maximum bite force was measured using a digital dynamometer with capacity of 100 kgf and adapted to oral conditions.The TMD group presented smaller mean bite force values than the healthy group, though without statistical significance (p>0.05). This outcome suggests that the TMD signs and symptoms and the structural conditions of the dentures did not affect the maximal bite force of complete denture wearers.

Do synergies improve accuracy? A study of speed-accuracy trade-offs during finger force production

We explored possible effects of negative covariation among finger forces in multifinger accurate force production tasks on the classical Fitts's speed-accuracy trade-off. Healthy subjects performed cyclic force changes between pairs of targets ""as quickly and accurately as possible."" Tasks with two force amplitudes and six ratics of force amplitude to target size were performed by each of the four fingers of the right hand and four finger combinations. There was a close to linear relation between movement time and the log-transformed ratio of target amplitude to target size across all finger combinations. There was a close to linear relation between standard deviation of force amplitude and movement time. There were no differences between the performance of either of the two ""radial"" fingers (index and middle) and the multifinger tasks. The ""ulnar"" fingers (little and ring) showed higher indices of variability and longer movement times as compared with both ""radial"" fingers and multifinger combinations. We conclude that potential effects of the negative covariation and also of the task-sharing across a set of fingers are counterbalanced by an increase in individual finger force variability in multifinger tasks as compared with single-finger tasks. The results speak in favor of a feed-forward model of multifinger synergies. They corroborate a hypothesis that multifinger synergies are created not to improve overall accuracy, but to allow the system larger flexibility, for example to deal with unexpected perturbations and concomitant tasks.

Tooth Movement Activates the Central Amygdala and the Lateral Hypothalamus by the Magnitude of the Force Applied

Objective: To determine if the magnitude of the force used to induce incisor tooth movement promotes distinct activation in cells in the central amygdala (CEA) and lateral hypothalamus (LH) of rats. Also, the effect of morphine on Fos immunoreactivity (Fos-IR) was investigated in these nuclei. Materials and Methods: Adult male rats were anesthetized and divided into six groups: only anesthetized (control), without orthodontic appliance (OA), OA but without force, OA activated with 30g or 70g, OA with 70g in animals pretreated with morphine (2 mg/kg, intraperitoneal). Three hours after the onset of the experiment the rats were reanesthetized and perfused with 4% paraformaldehyde. The brains were removed and fixed, and sections containing CEA and LH were processed for Fos protein immunohistochemistry. Results: The results show that in the control group, the intramuscular injection of a ketamine/xylazine mixture did not induce Fos-IR cells in the CEA or in the LH. Again, the without force group showed a little Fos-IR. However, in the 70g group the Fos-IR was the biggest observed (P < .05, Tukey) in the CEA and LH compared with the other groups. In the 30g group, the Fos-IR did not differ from the control group, the without OA group, and the without force group. Furthermore, pretreatment with morphine in the 70g group reduced Fos-IR in these regions. Conclusions: Tooth movement promotes Fos-IR in the CEA and LH according to the magnitude of the force applied. (Angle Orthod. 2010;80:111-115.)

Relationship Between Surface Topography and Energy Density Distribution of Er,Cr:YSGG Beam on Irradiated Dentin: An Atomic Force Microscopy Study

Objective: The aim of this study was to assess by atomic force microscopy (AFM) the effect of Er,Cr:YSGG laser application on the surface microtopography of radicular dentin. Background: Lasers have been used for various purposes in dentistry, where they are clinically effective when used in an appropriate manner. The Er, Cr: YSGG laser can be used for caries prevention when settings are below the ablation threshold. Materials and Methods: Four specimens of bovine dentin were irradiated using an Er, Cr:YSGG laser (lambda = 2.78 mu m), at a repetition rate of 20 Hz, with a 750-mu m-diameter sapphire tip and energy density of 2.8 J/cm(2) (12.5 mJ/pulse). After irradiation, surface topography was analyzed by AFM using a Si probe in tapping mode. Quantitative and qualitative information concerning the arithmetic average roughness (Ra) and power spectral density analyses were obtained from central, intermediate, and peripheral areas of laser pulses and compared with data from nonirradiated samples. Results: Dentin Ra for different areas were as follows: central, 261.26 (+/- 21.65) nm; intermediate, 83.48 (+/- 6.34) nm; peripheral, 45.8 (+/- 13.47) nm; and nonirradiated, 35.18 (+/- 2.9) nm. The central region of laser pulses presented higher ablation of intertubular dentin, with about 340-760 nm height, while intermediate, peripheral, and nonirradiated regions presented no difference in height of peritubular and interperitubular dentin. Conclusion: According to these results, we can assume that even when used at a low-energy density parameter, Er, Cr: YSGG laser can significantly alter the microtopography of radicular dentin, which is an important characteristic to be considered when laser is used for clinical applications.

Novel method for measuring nanofriction by atomic force microscope

The authors describe a novel approach to the measurement of nanofriction, and demonstrate the application of the method by measurement of the coefficient of friction for diamondlike carbon (DLC) on DLC, Si on DLC, and Si on Si surfaces. The technique employs an atomic force microscope in a mode in which the tip moves only in the z (vertical) direction and the sample surface is sloped. As the tip moves vertically on the sloped surface, lateral tip slipping occurs, allowing the cantilever vertical deflection and the frictional (lateral) force to be monitored as a function of tip vertical deflection. The advantage of the approach is that cantilever calibration to obtain its spring constants is not necessary. Using this method, the authors have measured friction coefficients, for load range 0 < L M 6 mu N, of 0.047 +/- 0.002 for Si on Si, 0.0173 +/- 0.0009 for Si on DLC, and 0.0080 +/- 0.0005 for DLC on DLC. For load range 9 < L < 13 mu N, the DLC on DLC coefficient of friction increased to 0.051 +/- 0.003. (C) 2008 American Vacuum Society.

The force, power, and energy of the 100 meter sprint

At the 2008 Summer Olympics in Beijing, Usain Bolt broke the world record for the 100 m sprint. Just one year later, at the 2009 World Championships in Athletics in Berlin he broke it again. A few months after Beijing, Eriksen [Am. J. Phys. 77, 224-228 (2009)] studied Bolt's performance and predicted that Bolt could have run about one-tenth of a second faster, which was confirmed in Berlin. In this paper we extend the analysis of Eriksen to model Bolt's velocity time dependence for the Beijing 2008 and Berlin 2009 records. We deduce the maximum force, the maximum power, and the total mechanical energy produced by Bolt in both races. Surprisingly, we conclude that all of these values were smaller in 2009 than in 2008.