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© Springer Nature Switzerland AG 2019. Conformal Geometric Algebra (CGA) provides a unified representation of both geometric primitives and conformal transformations, and as such holds great promise in the field of computer graphics [1–3]. In this paper we implement a simple ray tracer in CGA with a Blinn-Phong lighting model and use it to examine ray intersections with surfaces generated from interpolating between objects [7]. An analytical method for finding the normal line to these interpolated surfaces is described. The expression is closely related to the concept of surface principal curvature from differential geometry and provides a novel way of describing the curvature of evolving surfaces.

Ground curvature caused by underground mining is one of the most obvious deformation quantities in buildings. To study the influence of surface curvature on buildings and predict the movement and deformation of buildings caused by ground curvature, a prediction model of the influence function on mining subsidence was used to establish the relationship between surface curvature and wall deformation. The prediction model of wall deformation was then established and the surface curvature was obtained from mining subsidence prediction software. Five prediction lines were set up in the wall from bottom to top and the predicted deformation of each line was used to calculate the crack positions in the wall. Thus, the crack prediction model was obtained. The model was verified by a case study from a coalmine in Shanxi, China. The results show that when the ground curvature is positive, the crack in the wall is shaped like a "V"; when the ground curvature is negative, the crack is shaped like a "∧". The conclusion provides the basis for a damage evaluation method for buildings in coalmine areas.

Bu çalışma dört bölümden oluşmuştur. Birinci bölüm, giriş için ayrıldı. İkinci bölümde üçüncü ve son bölüm için gerekli temel tanım, teorem ve kavramlardan bahsedilmiştir. Üçüncü bölümde bir eğri boyunca çatı hareketlerin Darboux matrisleriyle yüksek mertebeden eğrilik matrisleri arasında bazı bağıntılar verilmiştir. İlk olarak E^n deki Frenet-Serret hareketinin Darboux matrislerinin bileşenleri tanımlanmıştır ve böylece bazı sonuçlar elde edilmiştir. Ayrıca E^n deki eğri-hiperyüzey çifti için doğal çatı alan hareketini sunuyoruz ve buradan bu hareketin Darboux matrisi ile bu çiftin eğrilik matrisi arasında bazı bağıntılar elde edilmiştir. Son bölümde ise, Cayley formülündeki bir eğri-hiperyüzey çiftinin eğrilik matrisini kullanarak bir şemsiye matris elde edilmiştir. Ayrıca şemsiye hareketinin Darboux matrisi ile eğrilik matrisi arasında bir ilişki verilip aynı zamanda bu şemsiye matrisini kullanarak bir infinitezimal şemsiye matris elde edilmiştir. This thesis consists of four chapters. The first chapter is devoted to the introduction. In the second section, we are given some relations between the Darboux matrices of the frame motions along a curve and the matrices of higher curvatures of the curve. First we describe entries of the Darboux matrix of the Serret-Frenet motion in E^n and hence we obtain some results. Furthermore we introduce motion of the natural frame field for the pair curve-hypersurface in E^n and so we obtain some relations between the Darboux matrix of this motion and the curvature matrix for this pair. In the third section, using the curvature matrix of a curve-hypersurface pair in the Cayley formula we obtain an umbrella matrix. Furthermore we give a relation between the Darboux matrix ofthe umbrella motion and the curvature matrix. In addition, using this umbrella matrix we also obtain an infinitesimal umbrella matrix. 63

Matrix nanotopography plays an important role in regulating cell behaviors by providing spatial as well as mechanical cues for cells to sense. It has been proposed that nanoscale topography is possible to modulate the tensions which direct the formation of cytoskeleton and the organization of the membrane receptor within the cell, which in turn regulate intracellular mechanical and biochemical signaling. With current studies on this topic being performed mainly in 2D platforms, the question on how nanotopography can influence cell bahaviors in 3D environments has yet to be addressed. In this paper, we explored this question by placing cells in 3D hollow spherical polydimethylsiloxane scaffolds. After culturing rat embryonic fibroblast cells in two kinds of scaffold, one with smooth surface and the other with numerous nano-spikes, we observed that cells in the smooth scaffold have more anchoring sites and more focal adhesions than in the etched scaffold. Moreover, we found the presence of correlation between cortical actin, the important component for supporting cell attachment, and local cell geometry. MOE (Min. of Education, S’pore)

Vascular morphology characterization is useful for disease diagnosis, risk stratification, treatment planning, and prediction of treatment durability. To quantify the dynamic surface geometry of tubular-shaped anatomic structures, we propose a simple, rigorous Lagrangian cylindrical coordinate system to monitor well-defined surface points. Specifically, the proposed system enables quantification of surface curvature and cross-sectional eccentricity. Using idealized software phantom examples, we validate the method's ability to accurately quantify longitudinal and circumferential surface curvature, as well as eccentricity and orientation of eccentricity. We then apply the method to several medical imaging data sets of human vascular structures to exemplify the utility of this coordinate system for analyzing morphology and dynamic geometric changes in blood vessels throughout the body. Graphical abstract Pointwise longitudinal curvature of a thoracic aortic endograft surface for systole and diastole, with their absolute difference.

This paper presents a novel method for surface curvature estimation. By using the k-nearest neighbors algorithm, an 8 neighbors ring is selected from point cloud for each point. Surface normal vector is estimated by neighbors coordinates. Local surfaces are classified using the point of interest and its 8 neighbors ring coordinates. In this paper surface curvature is calculated based on normal vector and neighbors ring coordinate. Surface curvature calculated using the novel method is called umbrella curvature. To evaluate how this method performs, the curvature of a sample surface was estimated by the umbrella curvature and surface variance method. The results show that the umbrella curvature performs well and is superior in terms of accuracy. However the method in computation is more expensive than variance method.

Although much is known about the embryo during implantation, the architecture of the uterine environment in which the early embryo develops is not well understood. We employed confocal imaging in combination with 3D analysis to identify and quantify dynamic changes to the luminal structure of murine uterus in preparation for implantation. When applied to mouse mutants with known implantation defects, this method detected striking peri-implantation abnormalities in uterine morphology that cannot be visualized by histology. We revealed 3D organization of uterine glands and found that they undergo a stereotypical reorientation concurrent with implantation. Furthermore, we extended this technique to generate a 3D rendering of the cycling human endometrium. Analyzing the uterine and embryo structure in 3D for different genetic mutants and pathological conditions will help uncover novel molecular pathways and global structural changes contributing to successful implantation of an embryo.

Local solid shape applies to the surface curvature of small surface patches—essentially regions of approximately constant curvatures—of volumetric objects that are smooth volumetric regions in Euclidean 3-space. This should be distinguished from local shape in pictorial space. The difference is categorical. Although local solid shape has naturally been explored in haptics, results in vision are not forthcoming. We describe a simple experiment in which observers judge shape quality and magnitude of cinematographic presentations. Without prior training, observers readily use continuous shape index and Casorati curvature scales with reasonable resolution. ispartof: i-Perception vol:6 issue:5 pages:1-17 ispartof: location:United States status: published

Unsteady mixed convection flow over a rotating vertical slender cylinder under the combined effects of buoyancy force and thermal diffusion with injection/suction has been studied where the slender cylinder is inline with the flow. The effect of surface curvature is also taken into account, especially for the applications such as wire and fiber drawing, where accurate predictions are desired. The governing boundary layer equations along with the boundary conditions are first converted into dimensionless form by a non-similar transformation, and then resulting system of coupled nonlinear partial differential equations is solved by an implicit finite difference scheme in combination with the quasi-linearization technique. The effects of various parameters on velocity and temperature profiles and on skin friction coefficients and heat transfer rate at the wall are reported in the present study. � 2007 Elsevier Ltd. All rights reserved.

The time-independent nonhomogeneous diffusion equation is solved for the equilibrium distribution of wound-induced growth factor over a hemispherical surface. The growth factor is produced at the inner edge of a circular wound and stimulates healing in regions where the concentration exceeds a certain threshold value. An implicit analytic criterion is derived for complete healing of the wound.

Bu çalışmada R^n deki eğriler ve yüzeylerin sabit oranlı olma durumları incelenmiştir. Bu tez dört bölümden oluşmaktadır. Birinci bölüm giriş bölümüdür. İkinci bölümde çalışmanın ilerideki bölümlerinde kullanılan temel tanım ve kavramlar verilmiştir. Üçüncü bölümde R^n deki eğriler ele alınmıştır. Bu bölümde sabit oranlı eğriler ile ilgili temel sonuçlar elde edilmiştir. Dördüncü bölümde R^n deki yüzeyler ele alınmıştır. Bu bölümde sabit oranlı yüzeyler ile ilgili bazı sonuçlar elde edilmiştir. In this thesis, a characterizations of constant curvature ratio surfaces in R^n with the help of coefficients of the first and second fundamental form are given. This thesis consist of four chapters. Firs chapter is introduction. In the second chapter it is given some basic definitions and theorems which will be use in the other chapters. In the third chapter constant curvature ratio curves in n-dimensional Euclidean space R^n are considered. In the fourth chapter constant curvature ratio surfaces in n-dimensional Euclidean space are considered. Some of the original results were obtained.

We have developed an analytical technique for single molecule force spectroscopy (SMFS) data that avoids filtering prior to analysis and performs pattern recognition to identify distinct SMFS events. The technique characterizes the signal similarity between all curves in a data set and generates a hierarchical clustering tree, from which clusters can be identified, aligned, and examined to identify key patterns. This procedure was applied to alpha-lactalbumin (aLA) on polystyrene substrates with flat and nanoscale curvature, and bacteriorhodopsin (bR) adsorbed on mica substrates. Cluster patterns identified for the aLA data sets were associated with different higher-order protein-protein interactions. Changes in the frequency of the patterns showed an increase in the monomeric signal from flat to curved substrates. Analysis of the bR data showed a high level of multiple protein SMFS events and allowed for the identification of a set of characteristic three-peak unfolding events.

Bu tez çalışması, yedi bölümden oluşmuştur.Birinci bölüm tezin giriş bölümüdür. Bu bölümde, eğrilik teorisi ve robot uç-işlevci hareketinde kullanılması ile ilgili literatür bilgisi ve bu tezde yapılanlar hakkında kısaca bilgi verilir.İkinci bölümde, Minkowski uzayının temel kavramları verilir.Üçüncü bölümde, Minkowski uzayında spacelike ve timelike aykırı regle yüzeylerin eğrilik teorileri detaylı bir şekilde incelenir. Regle yüzeylerin ve bunların merkez normal yüzeylerinin çatıları bulunur. Bu çatılar arasındaki ilişkiler veriler. Regle yüzeyler ve merkez normal yüzeylerinin eğrilik fonksiyonları elde edilir.Dördüncü bölümde, Minkowski uzayında yegâne açılabilir regle yüzeyler olan silindir, koni ve teğet yüzeylerin eğrilik teorileri incelenir. Bu yüzeylerin eğrilik teorilerinin aykırı regle yüzeylerin eğrilik teorisinden farklılıkları ortaya koyulur.Beşinci bölümde, üçüncü bölümde ele alınan spacelike ve timelike aykırı regle yüzeylerin eğrilik teorileri yardımıyla robot uç-işlevci hareketi incelenir. Robot uç-işlevci hareketinin lineer ve açısal özellikleri, regle yüzeylerin diferansiyel özelliklerinden belirlenir.Altıncı bölümde, dual uzay ve dual Lorentziyen uzay ile ilgili temel kavramlar verilir.Yedinci bölümde, üçüncü bölümde ele alınan regle yüzeylere dual Lorentziyen uzayında karşılık gelen dual küresel eğriler bulunur. Robot uç-işlevci hareketinin diferansiyel özellikleri dual küresel eğrilerin eğrilik teorisi yardımıyla incelenir. This thesis consists of seven sections.First section is introduction. In this section, literature review about curvature theory and its using in robot end-effector motion and Some information about this thesis is given.In section two, preliminaries of Minkowski space is given.In section three, the curvature theories of spacelike and timelike ruled surfaces in Minkowski space are examined in detail. Frames of ruled surfaces and their central normal surfaces is found. Relations between these frames are given. Curvature functions of the ruled surfaces and their central normal surfaces are obtained.In section four, the curvature theory of cylinder, cone and tangent surface that are developable surfaces in Minkowski space, are examined. Differences between the curvature theory of these developable surfaces and the curvature theory of general ruled surfaces are showed.In section five, motion of robot end-effector is examined using the curvature theories of spacelike and timelike ruled surfaces which are considered in section three. Linear and angular properties of the motion of robot end-effector are determined by using the differential properties of ruled surfaces.In section six, preliminaries of dual space and dual Lorentzian space are given.In section seven, dual spherical curves in dual Lorentzian space corresponding the ruled surfaces that are considered in section three, are obtained. The differential properties of the motion of robot end-effector is investigated by using the curvature theory of the dual spherical curves. 132

Gewebsbildung ist ein wichtiger Prozess für die Entstehung und Aufrechterhaltung unserer Organe. Die verschiedenen Gewebe unseres Körpers werden kontinuierlich von Zellen aufgebaut, umgebaut und repariert, beispielsweise während Morphogenese, Wundheilung oder Knochenumbau. Obwohl diese biologischen Prozesse genetisch codiert sind, spielen auch die biochemische Zusammensetzung und die physikalischen Eigenschaften der Umgebung eine wichtige Rolle bei der Gewebebildung und ermöglichen den Zellen, ihre Aktivität den externen Anforderungen anzupassen. Beispielsweise werden Muskel- und Knochenaufbau durch sportliche Aktivitäten verstärkt. Andererseits können Fehler im Gleichgewicht des Knochenumbaus die mechanische Funktion des Organs beschädigen, etwa bei Osteoporose. Indem wir verstehen, wie Gewebewachstum gesteuert wird, können wir viele biologische Prozesse und damit verbundene Krankheiten besser erklären.Trotz des kontinuierlichen Umbaus bleiben die geometrischen Eigenschaften von Organen wie etwa Knochen grundsätzlich erhalten. Geometrie wurde deswegen als ein mögliches Signal für die Kontrolle der Gewebsbildung vorgeschlagen. Es wurde bereits gezeigt, dass dieser physikalische Parameter biologischen Mechanismen auf subzellulärer, zellulärer und mehrzelliger Ebene beeinflussen kann. Über die Rolle von Geometrie auf der Gewebeskala ist jedoch bis jetzt nur ein wenig bekannt. Diese Arbeit zielt daher darauf ab zu verstehen, wie die Geometrie eines Substrats die Bildung und Organisation von Knochengewebe beeinflusst.Osteoblasten wurden kultiviert, um Knochengewebe im dreidimensionalen Gerüsten aus Hydroxyapatit in-vitro wachsen zu lassen. Parallel dazu wurde die Hypothese „die Geometrie einer Oberfläche beeinflusst die lokale Gewebsbildung“ in ein Rechenmodell für krümmungsabhängiges Wachstum umgesetzt. Ein Vergleich der experimentellen und simulierten Wachstumsmuster zeigt nicht nur die Relevanz des geometrischen Modells für die quantitative Beschreibung des Gewebewachstums auf komplexen Oberflächen, sondern auch, dass durch Optimierung der Geometrie des Substrats eine schnellere Gewebebildung erzielt werden kann.Außerdem wurde mathematisch bewiesen, dass ein einfaches Anlagern linearer dehnbarer Elemente, die für längliche kontraktile Zellen stehen - das sogenannte Sehnenmodell - äquivalent zu krümmungsabhängigem Wachstum ist. Eine qualitative Analyse der Zellorganisation im Gewebe unterstützt die biologische Relevanz dieses geometrischen Modells. Eine Ausweitung der strukturellen Untersuchungen auf die extrazelluläre Matrix hat zusätzliche Erkenntnisse zu den Mechanismen geliefert, die an der Gewebestrukturierung und -organisation beteiligt sind. Beispielsweise wurde gezeigt, dass die mechanische Spannung, die durch die Zellen aufgebaut wird, essentiell für die Organisation der Fibronektin und Kollagenfasern und ganz allgemein für die mechanische Stabilität des Gewebes ist.Schließlich wurde ein Computermodell des Wachstums in Abhängigkeit von der mittleren Krümmung der dreidimensionalen Oberfläche vorgeschlagen, um das aktuelle experimentelle System besser zu beschreiben und um zukünftige Untersuchungen über den Einfluss der dritten Dimension zu motivieren.Ein besseres Verständnis, wie Geometrie an der Gewebsbildung beteiligt ist, ist nicht nur interessant für die biomedizinische Forschung, sondern ist auch eine wichtige Inspirationsquelle für Tissue Engineering., Tissue formation is a key process for the genesis and the maintenance of our organs. As in morphogenesis, wound healing and bone remodelling, the various tissues of our body are continuously modelled, remodelled and repaired by the cells. Even if these biological processes are encoded in genetics, the biochemical composition and the physical cues of the surroundings also play a major role in tissue formation and enable cells to adapt their activity in response to external stimuli. For example, muscle and bone formation is enhanced in individuals practicing physical activities. On the other hand, a failure in the balance of bone remodelling can impair the mechanical function of the organ like in osteoporosis. Understanding how tissue formation is controlled is thus determining to clarify many biological processes and their associated pathologies. The geometrical features of organs like bones are generally conserved despite a continuous remodelling. As geometry also sets the boundary conditions for the mechanical environment that cells respond to, geometry has been proposed as a potential cue controlling tissue formation. This physical parameter has been shown to influence biological mechanisms at the sub-cellular, cellular and multi-cellular levels, but only a little is known about the tissue scale. This thesis aims therefore at understanding how the geometry of a substrate influences the deposition and organisation of tissue. Osteoblasts were cultured to grow bone tissue in three-dimensional hydroxyapatite scaffolds in-vitro. In parallel, the hypothesis that geometry locally influences tissue deposition on a surface was implemented into a computational model of curvature-driven growth. Comparing the experimental and simulated growth patterns not only confirmed the relevance of the geometrical model to describe quantitatively tissue growth on complex surfaces, but also proved that faster tissue formation can be obtained by optimising the geometry of the substrate. Moreover, a simple construction assembling tensile elements that represent elongated contractile cells – the chord model – was demonstrated to be equivalent to the curvature-driven growth simulation. A qualitative analysis of cells organisation in the tissue supported the biological relevance of this geometrical model. Extending the structural investigations to the extracellular matrix further clarified the mechanisms involved in tissue patterning and organisation. For example, the tension built by the cells was shown to be essential for organising the fibronectin and collagens fibres and more generally for the mechanical stability of the tissue. Finally, a computational model of growth driven by the mean curvature of the three-dimensional surface was proposed to better describe the current experimental system and inspire future investigations to evaluate the effects of the third dimension. Understanding how geometry is involved in tissue formation will not only benefit to biomedical research but will also profit to tissue engineering., La formation de tissu est un processus clé de la genèse et la maintenance de nos organes. Pendant la morphogenèse, la cicatrisation et le remodelage osseux, les divers tissus de notre organisme sont continuellement modelés, remodelés et réparés par les cellules. Bien que ces processus biologiques soient encodés génétiquement, la composition biochimique et les propriétés physiques des milieux jouent aussi un rôle important dans la formation de tissu et permettent aux cellules d’adapter leur activité en réponse aux stimulations extérieures. Par exemple, la formation de muscle et d’os est accrue chez les personnes pratiquant une activité physique. D’autre part, un déséquilibre du remodelageosseux peut affecter la fonction mécanique de l’os, c’est le cas dans l’ostéoporose.Les caractéristiques géométriques d’organes comme l’os sont généralement conservées malgré un remodelage continuel. Comme la géométrie impose également les conditions aux limites de l’environnement mécanique auquel répondent les cellules, la géométrie a été proposée comme étant potentiellement impliquée dans le contrôle de la formation du tissu. Il a été montré que ce paramètre physique influence des mécanismes biologiques aux échelles subcellulaire, cellulaire et multicellulaire, mais très peu est connu à l’échelle tissulaire. Cette thèse a donc pour but de comprendre comment la géométrie d’un substrat influence la déposition et l’organisation des tissus.Des ostéoblastes ont été cultivés in-vitro pour produire du tissu osseux dans des structures tridimensionnelles en hydroxyapatite. L’hypothèse proposant que la géométrie influence localement la formation de tissu sur une surface a été transcrite dans un modèle numérique de croissance contrôlée par la courbure. La comparaison des motifs de croissance expérimentaux et simulés a non seulement confirmé la pertinence du modèle géométrique pour décrire la croissance du tissu de manière quantitative sur des surfaces complexes, mais a aussi montré qu’une croissance plus rapide du tissu peut être obtenue en optimisant la géométrie du substrat.Il a également été montré qu’un « modèle des cordes » consistant à assembler des éléments sous tension qui représentent les cellules contractiles, est équivalent à la simulation de croissance contrôlée par la courbure. Une analyse qualitative de l’organisation des cellules dans le tissu a conforté la pertinence de ce modèle géométrique. Etendre les études structurelles à la matrice extracellulaire a permis de clarifier les mécanismes impliqués dans l’organisation du tissu. Par exemple, la tension générée par les cellules s’est montrée indispensable à l’organisation des fibres de fibronectine et de collagènes, et de manière générale à la stabilité mécanique du tissu.Enfin, un modèle de croissance contrôlée par la courbure moyenne d’une surface en trois dimensions a été proposé pour décrire le système expérimental et inspirer de nouvelles études pour évaluer les effets de la troisième dimension.Comprendre comment la géométrie est impliquée dans la formation du tissu profitera à la fois à la recherche biomédicale et à l’ingénierie tissulaire.

Gewebsbildung ist ein wichtiger Prozess für die Entstehung und Aufrechterhaltung unserer Organe. Die verschiedenen Gewebe unseres Körpers werden kontinuierlich von Zellen aufgebaut, umgebaut und repariert, beispielsweise während Morphogenese, Wundheilung oder Knochenumbau. Obwohl diese biologischen Prozesse genetisch codiert sind, spielen auch die biochemische Zusammensetzung und die physikalischen Eigenschaften der Umgebung eine wichtige Rolle bei der Gewebebildung und ermöglichen den Zellen, ihre Aktivität den externen Anforderungen anzupassen. Beispielsweise werden Muskel- und Knochenaufbau durch sportliche Aktivitäten verstärkt. Andererseits können Fehler im Gleichgewicht des Knochenumbaus die mechanische Funktion des Organs beschädigen, etwa bei Osteoporose. Indem wir verstehen, wie Gewebewachstum gesteuert wird, können wir viele biologische Prozesse und damit verbundene Krankheiten besser erklären.Trotz des kontinuierlichen Umbaus bleiben die geometrischen Eigenschaften von Organen wie etwa Knochen grundsätzlich erhalten. Geometrie wurde deswegen als ein mögliches Signal für die Kontrolle der Gewebsbildung vorgeschlagen. Es wurde bereits gezeigt, dass dieser physikalische Parameter biologischen Mechanismen auf subzellulärer, zellulärer und mehrzelliger Ebene beeinflussen kann. Über die Rolle von Geometrie auf der Gewebeskala ist jedoch bis jetzt nur ein wenig bekannt. Diese Arbeit zielt daher darauf ab zu verstehen, wie die Geometrie eines Substrats die Bildung und Organisation von Knochengewebe beeinflusst.Osteoblasten wurden kultiviert, um Knochengewebe im dreidimensionalen Gerüsten aus Hydroxyapatit in-vitro wachsen zu lassen. Parallel dazu wurde die Hypothese „die Geometrie einer Oberfläche beeinflusst die lokale Gewebsbildung“ in ein Rechenmodell für krümmungsabhängiges Wachstum umgesetzt. Ein Vergleich der experimentellen und simulierten Wachstumsmuster zeigt nicht nur die Relevanz des geometrischen Modells für die quantitative Beschreibung des Gewebewachstums auf komplexen Oberflächen, sondern auch, dass durch Optimierung der Geometrie des Substrats eine schnellere Gewebebildung erzielt werden kann.Außerdem wurde mathematisch bewiesen, dass ein einfaches Anlagern linearer dehnbarer Elemente, die für längliche kontraktile Zellen stehen - das sogenannte Sehnenmodell - äquivalent zu krümmungsabhängigem Wachstum ist. Eine qualitative Analyse der Zellorganisation im Gewebe unterstützt die biologische Relevanz dieses geometrischen Modells. Eine Ausweitung der strukturellen Untersuchungen auf die extrazelluläre Matrix hat zusätzliche Erkenntnisse zu den Mechanismen geliefert, die an der Gewebestrukturierung und -organisation beteiligt sind. Beispielsweise wurde gezeigt, dass die mechanische Spannung, die durch die Zellen aufgebaut wird, essentiell für die Organisation der Fibronektin und Kollagenfasern und ganz allgemein für die mechanische Stabilität des Gewebes ist.Schließlich wurde ein Computermodell des Wachstums in Abhängigkeit von der mittleren Krümmung der dreidimensionalen Oberfläche vorgeschlagen, um das aktuelle experimentelle System besser zu beschreiben und um zukünftige Untersuchungen über den Einfluss der dritten Dimension zu motivieren.Ein besseres Verständnis, wie Geometrie an der Gewebsbildung beteiligt ist, ist nicht nur interessant für die biomedizinische Forschung, sondern ist auch eine wichtige Inspirationsquelle für Tissue Engineering., Tissue formation is a key process for the genesis and the maintenance of our organs. As in morphogenesis, wound healing and bone remodelling, the various tissues of our body are continuously modelled, remodelled and repaired by the cells. Even if these biological processes are encoded in genetics, the biochemical composition and the physical cues of the surroundings also play a major role in tissue formation and enable cells to adapt their activity in response to external stimuli. For example, muscle and bone formation is enhanced in individuals practicing physical activities. On the other hand, a failure in the balance of bone remodelling can impair the mechanical function of the organ like in osteoporosis. Understanding how tissue formation is controlled is thus determining to clarify many biological processes and their associated pathologies. The geometrical features of organs like bones are generally conserved despite a continuous remodelling. As geometry also sets the boundary conditions for the mechanical environment that cells respond to, geometry has been proposed as a potential cue controlling tissue formation. This physical parameter has been shown to influence biological mechanisms at the sub-cellular, cellular and multi-cellular levels, but only a little is known about the tissue scale. This thesis aims therefore at understanding how the geometry of a substrate influences the deposition and organisation of tissue. Osteoblasts were cultured to grow bone tissue in three-dimensional hydroxyapatite scaffolds in-vitro. In parallel, the hypothesis that geometry locally influences tissue deposition on a surface was implemented into a computational model of curvature-driven growth. Comparing the experimental and simulated growth patterns not only confirmed the relevance of the geometrical model to describe quantitatively tissue growth on complex surfaces, but also proved that faster tissue formation can be obtained by optimising the geometry of the substrate. Moreover, a simple construction assembling tensile elements that represent elongated contractile cells – the chord model – was demonstrated to be equivalent to the curvature-driven growth simulation. A qualitative analysis of cells organisation in the tissue supported the biological relevance of this geometrical model. Extending the structural investigations to the extracellular matrix further clarified the mechanisms involved in tissue patterning and organisation. For example, the tension built by the cells was shown to be essential for organising the fibronectin and collagens fibres and more generally for the mechanical stability of the tissue. Finally, a computational model of growth driven by the mean curvature of the three-dimensional surface was proposed to better describe the current experimental system and inspire future investigations to evaluate the effects of the third dimension. Understanding how geometry is involved in tissue formation will not only benefit to biomedical research but will also profit to tissue engineering., La formation de tissu est un processus clé de la genèse et la maintenance de nos organes. Pendant la morphogenèse, la cicatrisation et le remodelage osseux, les divers tissus de notre organisme sont continuellement modelés, remodelés et réparés par les cellules. Bien que ces processus biologiques soient encodés génétiquement, la composition biochimique et les propriétés physiques des milieux jouent aussi un rôle important dans la formation de tissu et permettent aux cellules d’adapter leur activité en réponse aux stimulations extérieures. Par exemple, la formation de muscle et d’os est accrue chez les personnes pratiquant une activité physique. D’autre part, un déséquilibre du remodelageosseux peut affecter la fonction mécanique de l’os, c’est le cas dans l’ostéoporose.Les caractéristiques géométriques d’organes comme l’os sont généralement conservées malgré un remodelage continuel. Comme la géométrie impose également les conditions aux limites de l’environnement mécanique auquel répondent les cellules, la géométrie a été proposée comme étant potentiellement impliquée dans le contrôle de la formation du tissu. Il a été montré que ce paramètre physique influence des mécanismes biologiques aux échelles subcellulaire, cellulaire et multicellulaire, mais très peu est connu à l’échelle tissulaire. Cette thèse a donc pour but de comprendre comment la géométrie d’un substrat influence la déposition et l’organisation des tissus.Des ostéoblastes ont été cultivés in-vitro pour produire du tissu osseux dans des structures tridimensionnelles en hydroxyapatite. L’hypothèse proposant que la géométrie influence localement la formation de tissu sur une surface a été transcrite dans un modèle numérique de croissance contrôlée par la courbure. La comparaison des motifs de croissance expérimentaux et simulés a non seulement confirmé la pertinence du modèle géométrique pour décrire la croissance du tissu de manière quantitative sur des surfaces complexes, mais a aussi montré qu’une croissance plus rapide du tissu peut être obtenue en optimisant la géométrie du substrat.Il a également été montré qu’un « modèle des cordes » consistant à assembler des éléments sous tension qui représentent les cellules contractiles, est équivalent à la simulation de croissance contrôlée par la courbure. Une analyse qualitative de l’organisation des cellules dans le tissu a conforté la pertinence de ce modèle géométrique. Etendre les études structurelles à la matrice extracellulaire a permis de clarifier les mécanismes impliqués dans l’organisation du tissu. Par exemple, la tension générée par les cellules s’est montrée indispensable à l’organisation des fibres de fibronectine et de collagènes, et de manière générale à la stabilité mécanique du tissu.Enfin, un modèle de croissance contrôlée par la courbure moyenne d’une surface en trois dimensions a été proposé pour décrire le système expérimental et inspirer de nouvelles études pour évaluer les effets de la troisième dimension.Comprendre comment la géométrie est impliquée dans la formation du tissu profitera à la fois à la recherche biomédicale et à l’ingénierie tissulaire.

We report on the ability of human observers to discriminate local second-order shape of quadratic stereo-defined surfaces. Local second-order shape can be specified by two parameters: the curvedness (a scale-dependent quantity describing overall curvature of a shape) and the shape index (a scale-independent quantity describing the shape's appearance). We measured shape index discrimination thresholds of shapes subject to attitude and curvedness transformations. Results show that neither slant nor curvedness manipulations affect or bias observers' judgements of surface shape. Furthermore, ideal detector simulations show that observers do not perform optimally: they do not exploit all available information.

This paper presents a comprehensive computational work on the hydrodynamic, thermal, and mass transfer characteristics of a circular cylinder, subjected to confined flow at the cylinder Reynolds number of Re(d) = 40. As the two-dimensional, steady and incompressible momentum and energy equations are solved using ANSYS-CFX (version II.0), the moisture distributions are computed by a new alternating direction implicit method based software. The significant results, highlighting the influence of blockage (beta = 0.200-0.800) on the flow and heat transfer mechanism and clarifying the combined roles of beta and moisture diffusivity (D = 1 X 10(-8)-1 X 10(-5) m(2)/s) on the mass transfer behavior, are obtained for practical applications. It is shown that the blockage augments the friction coefficients (C(f)) and Nusselt numbers (Nu) on the complete cylinder surface, where the average Nu are evaluated as Nu(ave) = 3.66, 4.05, 4.97, and 6.51 for beta = 0.200, 0.333, 0.571, and 0.800. Moreover, the blockage shifts separation (theta(s)) and maximum C(f) locations (theta(Cf-max)) downstream to the positions of theta(s) = 54.10, 50.20, 41.98, and 37.30 deg and theta(Cf-max) = 51.5, 53.4, 74.9, and 85.4 deg. The highest blockage of beta = 0.800 encourages the downstream backward velocity values, which as a consequence disturbs the boundary layer and weakens the fluid-solid contact. The center and average moisture contents differ significantly at the beginning Of drying process, but in the last 5% of the drying period they vary only by 1.6%. Additionally, higher blockage augments mass transfer coefficients (h(m)) on the overall cylinder surface; however, the growing rate of back face mass transfer coefficients (h(m-bf)) is dominant to that of the front face values (h(m-ff)), with the interpreting ratios of (h) over bar (m-bf)/(h) over bar (m)= 0.50 and 0.57 and h (h) over bar (m-ff)/(h) over bar (m) = 1.50 and 1.43 for beta = 0.200 and 0.800.

Uzaklık haritaları ile ifade edilen üç boyutlu (3B) yüzeylerin, ortalama (H) veGaussian (K) eğrilik analizleri kullanılarak özniteliklerinin çıkartılması, nesnealgılamadan tanımaya kadar olan birçok bilgisayar görüntü işleme algoritması içinönemli bir teknik olarak görülmektedir. Ortalama ve Gaussian eğrilik analizleribilgisayarlar üzerinde yazılım tabanlı olarak geliştirilmiş ve uygulanmıştır. Buçalışmada, FPGA üzerinde gerçek zamanlı çalışan sayısal eğrilik işlemcisitasarlanmıştır. Hız bakımından yazılım tabanlı uygulamalara alternatif olarak,çoklu ölçekler üzerinde H ve K analizlerine göre yüzey sınıflandırması yapabilen,iki adet farklı sayısal eğrilik işlemcisi geliştirilmiştir. Bu iki işlemci farklı türevhesaplama yaklaşımları kullanmaktadır. İşlemciler içerisinde, analizler içingerekli olan gerçek zamanlı karekök hesaplama devresi tasarlanmıştır. Bu devre,giriş sayılarının olasılıklarını göz önünde tutarak, hatanın en az olması için gereklibölgelerde RAM kullanan yada doğrusal tahmin yapan bir yapıdır. Analiz edilenyüzeyler sabit noktalı sayı temsilleri ile ifade edilmektedir. İşlemciler MatLabüzerinde tasarlanmış ve test edilmiş, VHDL donanım dili ile iki farklı FPGAüzerinde çalıştırılmıştır. Donanım, simülasyon ve yazılım sonuçları birbirleri ilekıyaslanmıştır. Ayrıca hız sonuçları ve güç tüketimleri de verilmiştir. Three dimensional (3D) surface feature extractions based on mean (H) andGaussian (K) curvature analysis of range maps, also known as depth maps, is animportant tool for machine vision applications such as object detection,registration and recognition. Mean and Gaussian curvature calculation algorithmshave already been implemented and examined as software. In this thesis,hardware based digital curvature processors are designed. Two types of real timesurface feature extraction and classification hardware are developed whichperform mean and Gaussian curvature analysis at different scale levels. Thetechniques use different gradient approximations. A fast square root algorithmusing both LUT (look up table) and linear fitting technique is developed tocalculate H and K values of the surface described by the 3D Range Map formedby fixed point numbers. The proposed methods are simulated in MatLab softwareand implemented on different FPGAs using VHDL hardware language.Calculation times, outputs and power analysis of these techniques are compared toCPU based 64 bit float data type calculations. 122

We present an approach to integrate a preprocessing step of the region of interest ROI localization into 3-D scanners laser or ste- reoscopic. The definite objective is to make the 3-D scanner intelligent enough to localize rapidly in the scene, during the preprocessing phase, the regions with high surface curvature, so that precise scanning will be done only in these regions instead of in the whole scene. In this way, the scanning time can be largely reduced, and the results contain only per- tinent data. To test its feasibility and efficiency, we simulated the prepro- cessing process under an active stereoscopic system composed of two cameras and a video projector. The ROI localization is done in an itera- tive way. First, the video projector projects a regular point pattern in the scene, and then the pattern is modified iteratively according to the local surface curvature of each reconstructed 3-D point. Finally, the last pat- tern is used to determine the ROI. Our experiments showed that with this approach, the system is capable to localize all types of objects, including small objects with small depth. © 2009 Society of Photo-Optical Instrumentation

Otitis media, which is an upper respiratory tract infection that affect the middle ear, is the second most common disease in childhood, outnumbered in prevalence only by the common cold. Diagnosis of middle ear inflammation is often performed in the primary healthcare where the normal procedure involves anamnesis and physical examination of the tympanic membranes (TM) of the patient, usually be means of otoscopy. The general aim of this thesis was to develop optical methods that enable quantification of TM characteristics associated with otitis media. Diffuse reflectance spectroscopy was applied to quantify TM erythema using previously suggested erythema detection algorithms. Healthy TM:s were significantly distinguished from TM:s with induced erythema (p < 0.01) and from TM:s in ears with mucous middle ear effusion (p < 0.05). A new technique for surface shape assessment based on an on-axis dual fibre array incorporated in an otoscope was developed and evaluated in ear models and on tympanic membranes from harvested temporal bones. The technique utilises the combined effects of source-detector fibre separation and fibre-to-sample distance on the detected light intensity. Optical phantoms, both polyacetal plastic solids and latex membranes, were utilised to demonstrate the ability of the surface shape assessment technique to differentiate between convex and concave surfaces – as a bulging tympanic membrane is typically associated with acute otitis media whereas a retracted eardrum is associated with otitis media with effusion. Monte Carlo simulations of the surface shape data were performed in order to validate the experimental results with a theoretical model that are consistent with light transport theory. Retracted and bulging tympanic membranes from harvested temporal bones could be separated with a single measurement, given that variations in measurement distance were accounted for and that measurement from normally positioned tympanic membranes were used for signal normalization. In conclusion, the studies implicate that for individual otitis diagnosis, the hyperaemic tympanic membrane was separated from the healthy by application of erythema indices using diffuse reflectance spectroscopy. Moreover, bulging and retracted positions of the tympanic membrane were separable by means of the source-detector intensity matrix. For further clinical studies it is reasonable to assume that data from both methods are needed for diagnosis.

This article is concerned with accelerating and decelerating flows over straight; concave and convex surfaces encompassing laminar and turbulent boundary layers. Flow and heat transfer experiments were carried in a blowing-type, low-speed wind tunnel and measurements indicated that the concave curvature and acceleration caused thinner boundary layers and augmented heat transfer rates, whereas the convex wall and deceleration resulted in the contrary. A new empirical equation. is derived to model the combined effects of boundary layer development, surface curvature and pressure gradient on surface heat transfer values, which coincides with the experimental data within a deviation range of +/- 3 %.

International audience; no abstract

The effect of bio-surfaces of contrasting curvature, on the kinetic parameters of ortho-nitrophenyl-β-D-galactopiranoside hydrolysis catalyzed by E. coli β-galactosidase, was investigated. The self-aggregating state and structure of the amphiphiles (Phosphatidylcholine, Lubrol-PX, Triton X-100, DocNa, SDS and CTAB) were inferred from their c.m.c. values and light-scattering measurements. Low curvature phosphatidylcholine or mixed phosphatidylcholine-detergent vesicles increased V max without affecting K M. High curvature micellar structures containing ionic detergents modulated negatively the enzyme activity (decreased or abolished V max and increased K M). Neither micelles containing non-ionic detergents nor the amphiphiles in a monomeric form, affected enzyme activity. CTAB at a concentration bellow its c.m.c but incorporated into a bilayer, became an activator (K M decreased respect to the control). Non-enzymatic interfacial hydrolysis of the substrate was discarded. Enzyme-membrane interaction and membrane elasticity, were evaluated using monomolecular layers at the air-water interface. Beyond particular molecular structures, topology affected the direction of the modulatory effects exerted by these amphiphiles on β-galactosidase activity. © 2002 Elsevier Science B.V. All rights reserved. Fil: Sanchez, Julieta Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Investigaciones Biológicas y Tecnológicas. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales. Instituto de Investigaciones Biológicas y Tecnológicas; Argentina Fil: Perillo, Maria Angelica. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Investigaciones Biológicas y Tecnológicas. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas, Físicas y Naturales. Instituto de Investigaciones Biológicas y Tecnológicas; Argentina

KONKAV, DÜZ VE KONVEKS YÜZEY SINIR TABAKALARINDA HIZ VE ISI TRANSFERİ KARAKTERİSTİKLERİNİN HIZLANAN VE YAVAŞLAYAN AKIŞLARDA İNCELENMESİ ÖZET Düz ve eğrisel yüzeyler üzerinde sınır tabaka oluşumu, akış ve ısı transferi karakteristikleri açısından, taşıt ve uçak aerodinamiği ve turbomakina araştırmaları için büyük öneme sahip olduğu için literatürde bu konu ile ilgili pek çok çalışma bulunmaktadır. Bu tezde akış yönündeki Reynolds sayısı (Rex) ve basmç gradyanlannm (k) hidrodinamik ve termik sınır tabakalar üzerindeki etkileri birlikte incelenmiştir. Deneysel çalışmalar düz ve eğrilik yarıçapları 1500 mm olan konkav ve konveks yüzeyler üzerinde -1.8xl0`6£k£1.8xl0'* basmç gradyan aralığında, 5, 10 ve 15 m/s ilk hızlarda ve laminer, geçiş ve türbülanslı akışlarda gerçekleştirilmiştir. Pozitif gradyanlar (hızlanan akış) düz ve konkav yüzey üzerinde Ree'nın azalmasına ve biçim faktörünün (H) artmasına neden olmaktadır. Diğer taraftan, negatif gradyanlar (yavaşlayan akış) konveks yüzey üzerinde H*nü arttırmakta; ve diğer iki yüzey üzerinde Ree'nı arttırmakta ve H*nü azaltmaktadır. Düz yüzey sınır tabakasında geçiş 4xl05 değerindeki Re^'nda başlar ve 1.8x1ü`6 pozitif gradyanında 6x1 05 değerine kadar uzamaktadır. Konkav yüzeyin, aynı Rex aralığında, türbülansa geçişi hızlandırdığı tespit edilirken, konveks eğrilik geçişi 7x1 05 değerindeki Rex'na kadar uzatmakta ve türbülansa geçişi ertelemektedir. Sıfir basınç gradyanı için, geçiş bölgesindeki düz yüzey ısı transfer değerleri konkav ve konveks yüzey değerlerinin akış yönünde sırasıyla %26-%55.5 ve %9-%19.5 aralığında altındadır. Düz ve konkav yüzey türbülanslı ısı transferi değerleri konveks yüzey değerlerinin sırasıyla %22.4-%22 ve %21.4-%28.2 üzerindedir. Konveks yüzey üzerinde, pozitif gradyanlann etkisinde, geçiş bölgesindeki ısı transferi artışı düz ve konkav yüzey artış oranlarının sırasıyla %2-%4.1 ve %2.2-%ll altodadır ki, bu durum konveks eğriliğin ısı transferini azaltmaya yönelik etkisi şeklinde yorumlanabilir. Bununla birlikte pozitif ve negatif gradyanlar, türbülanslı bölgede, konkav ve konveks yüzeyler üzerinde benzer ısı transferi değişimleri oluşturmuşlardır. ANAHTAR KELİMELER: Basmç Gradyanı, Hidrodinamik ve Termik Sınır Tabaka, Konkav-Konveks Yüzey Eğriliği. 11 INVESTIGATION OF VELOCITY AND HEAT TRANSFER CHARACTERISTICS IN ACCELERATING AND DECELARATING CONCAVE, FLAT AND CONVEX SURFACE BOUNDARY LAYERS ABSTRACT Boundary layer development on flat and curved surfaces, in terms of flow and heat transfer characteristics, is of great importance for vehicle and plane aerodynamics and turbomachinery so that there have been plenty of work in literature. Streamwise distance Reynolds number (Rex) and pressure gradient (k) effects on hydrodynamic and thermal boundary layers have been investigated simultaneously in this thesis. Experimental work is carried out on flat plate and concave and convex surfaces with 1500 mm in radius of curvature, in the pressure gradient range of-l.SxlO'^k^l.SxlO`6 and at initial velocities of 5, 10, and IS m/s in laminar, transitional and turbulent flows. Positive gradients (accelerating flow) causes Ree to decrease and shape factor (H) to increase in the flow direction on the flat plate and concave surface. On the other hand, negative gradients (decelerating flow) increase H on the convex surface; and on the other two surfaces increase Ree and decrease H. Transition in flat plate boundary layer starts at Re» of 4xl05 and extends to 6xl05 for the positive gradient 1.8x1ü`6. Concave surface, for the same Rex range, is determined to enhance transition, whereas convex curvature extends transition up to Rex of 7x10s and delays turbulent structure. For zero pressure gradient, flat plate heat transfer values, in the transition region, are below the concave and convex surface values by 26% to 55.5% and 9% to 19.5% in the flow direction respectively. Flat plate and concave surface turbulent heat transfer values are above the that of convex surface by 22.4%-22% and 21.4%-28.2% respectively. The amount of increase in heat transfer due to positive gradients on the convex surface in the transition region are below the flat plate and concave surface ratios by 2% to 4.1% and 2.2% to 11% respectively, that might be attributed to the reducing effect of convex surface on the heat transfer. However, positive and negative gradients caused similar heat transfer variations in the turbulent region on concave and convex surfaces. KEYWORDS: Pressure Gradient, Hydrodynamic and Thermal Boundary Layers, Concave-Convex Surface Curvature. 165