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1
Habermann, Karen. "Geometry of sub-Riemannian diffusion processes." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/271855.
Повний текст джерелаАнотація:
Sub-Riemannian geometry is the natural setting for studying dynamical systems, as noise often has a lower dimension than the dynamics it enters. This makes sub-Riemannian geometry an important field of study. In this thesis, we analysis some of the aspects of sub-Riemannian diffusion processes on manifolds. We first focus on studying the small-time asymptotics of sub-Riemannian diffusion bridges. After giving an overview of recent work by Bailleul, Mesnager and Norris on small-time fluctuations for the bridge of a sub-Riemannian diffusion, we show, by providing a specific example, that, unlike in the Riemannian case, small-time fluctuations for sub-Riemannian diffusion bridges can exhibit exotic behaviours, that is, qualitatively different behaviours compared to Brownian bridges. We further extend the analysis by Bailleul, Mesnager and Norris of small-time fluctuations for sub-Riemannian diffusion bridges, which assumes the initial and final positions to lie outside the sub-Riemannian cut locus, to the diagonal and describe the asymptotics of sub-Riemannian diffusion loops. We show that, in a suitable chart and after a suitable rescaling, the small-time diffusion loop measures have a non-degenerate limit, which we identify explicitly in terms of a certain local limit operator. Our analysis also allows us to determine the loop asymptotics under the scaling used to obtain a small-time Gaussian limit for the sub-Riemannian diffusion bridge measures by Bailleul, Mesnager and Norris. In general, these asymptotics are now degenerate and need no longer be Gaussian. We close by reporting on work in progress which aims to understand the behaviour of Brownian motion conditioned to have vanishing $N$th truncated signature in the limit as $N$ tends to infinity. So far, it has led to an analytic proof of the stand-alone result that a Brownian bridge in $\mathbb{R}^d$ from $0$ to $0$ in time $1$ is more likely to stay inside a box centred at the origin than any other Brownian bridge in time $1$.
2
Kearney, Dominic. "Turbulent diffusion in channels of complex geometry." Thesis, Loughborough University, 2000. https://dspace.lboro.ac.uk/2134/7275.
Повний текст джерелаАнотація:
This thesis examines turbulent diffusion processes in rectangular and compound open channels, with particular attention to the effect of secondary flow and the relationship between eddy viscosity and eddy diffusivity. Three dimensional velocities and concentration were measured using 3 component Laser Doppler Velocimetry (LDV) combined with Laser Induced Fluorescence (LIF) from three laboratory flumes: one rectangular simple channel and a deep and a shallow compound channel. (Continues...).
3
DE, PONTI NICOLÒ. "Optimal transport: entropic regularizations, geometry and diffusion PDEs." Doctoral thesis, Università degli studi di Pavia, 2019. http://hdl.handle.net/11571/1292130.
Повний текст джерела
4
Glaser, Jens, Masashi Degawa, Inka Lauter, Rudolf Merkel, and Klaus Kroy. "Tube geometry and brownian dynamics in semiflexible polymer networks." Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-188856.
Повний текст джерела
5
Glaser, Jens, Masashi Degawa, Inka Lauter, Rudolf Merkel, and Klaus Kroy. "Tube geometry and brownian dynamics in semiflexible polymer networks." Diffusion fundamentals 11 (2009) 7, S. 1-2, 2009. https://ul.qucosa.de/id/qucosa%3A13927.
Повний текст джерела
6
Cai, Li-Dong. "Scale-based surface understanding using diffusion smoothing." Thesis, University of Edinburgh, 1991. http://hdl.handle.net/1842/6587.
Повний текст джерелаАнотація:
The research discussed in this thesis is concerned with surface understanding from the viewpoint of recognition-oriented, scale-related processing based on surface curvatures and diffusion smoothing. Four problems below high level visual processing are investigated: 1) 3-dimensional data smoothing using a diffusion process; 2) Behaviour of shape features across multiple scales, 3) Surface segmentation over multiple scales; and 4) Symbolic description of surface features at multiple scales. In this thesis, the noisy data smoothing problem is treated mathematically as a boundary value problem of the diffusion equation instead of the well-known Gaussian convolution, In such a way, it provides a theoretical basis to uniformly interpret the interrelationships amongst diffusion smoothing, Gaussian smoothing, repeated averaging and spline smoothing. It also leads to solving the problem with a numerical scheme of unconditional stability, which efficiently reduces the computational complexity and preserves the signs of curvatures along the surface boundaries. Surface shapes are classified into eight types using the combinations of the signs of the Gaussian curvature K and mean curvature H, both of which change at different scale levels. Behaviour of surface shape features over multiple scale levels is discussed in terms of the stability of large shape features, the creation, remaining and fading of small shape features, the interaction between large and small features and the structure of behaviour of the nested shape features in the KH sign image. It provides a guidance for tracking the movement of shape features from fine to large scales and for setting up a surface shape description accordingly. A smoothed surface is partitioned into a set of regions based on curvature sign homogeneity. Surface segmentation is posed as a problem of approximating a surface up to the degree of Gaussian and mean curvature signs using the depth data alone How to obtain feasible solutions of this under-determined problem is discussed, which includes the surface curvature sign preservation, the reason that a sculptured surface can be segmented with the KH sign image alone and the selection of basis functions of surface fitting for obtaining the KH sign image or for region growing. A symbolic description of the segmented surface is set up at each scale level. It is composed of a dual graph and a geometrical property list for the segmented surface. The graph describes the adjacency and connectivity among different patches as the topological-invariant properties that allow some object's flexibility, whilst the geometrical property list is added to the graph as constraints that reduce uncertainty. With this organisation, a tower-like surface representation is obtained by tracking the movement of significant features of the segmented surface through different scale levels, from which a stable description can be extracted for inexact matching during object recognition.
7
Lyytik�inen, Katja Johanna. "Control of complex structural geometry in optical fibre drawing." University of Sydney. School of Physics and the Optical Fibre Technology Centre, 2004. http://hdl.handle.net/2123/597.
Повний текст джерелаАнотація:
Drawing of standard telecommunication-type optical fibres has been optimised in terms of optical and physical properties. Specialty fibres, however, typically have more complex dopant profiles. Designs with high dopant concentrations and multidoping are common, making control of the fabrication process particularly important. In photonic crystal fibres (PCF) the inclusion of air-structures imposes a new challenge for the drawing process. The aim of this study is to gain profound insight into the behaviour of complex optical fibre structures during the final fabrication step, fibre drawing. Two types of optical fibre, namely conventional silica fibres and PCFs, were studied. Germanium and fluorine diffusion during drawing was studied experimentally and a numerical analysis was performed of the effects of drawing parameters on diffusion. An experimental study of geometry control of PCFs during drawing was conducted with emphasis given to the control of hole size. The effects of the various drawing parameters and their suitability for controlling the air-structure was studied. The effect of air-structures on heat transfer in PCFs was studied using computational fluid dynamics techniques. Both germanium and fluorine were found to diffuse at high temperature and low draw speed. A diffusion coefficent for germanium was determined and simulations showed that most diffusion occurred in the neck-down region. Draw temperature and preform feed rate had a comparable effect on diffusion. The hole size in PCFs was shown to depend on the draw temperature, preform feed rate and the preform internal pressure. Pressure was shown to be the most promising parameter for on-line control of the hole size. Heat transfer simulations showed that the air-structure had a significant effect on the temperature profile of the structure. It was also shown that the preform heating time was either increased or reduced compared to a solid structure and depended on the air-fraction.
8
Lyytikäinen, Katja Johanna. "Control of complex structural geometry in optical fibre drawing." Thesis, The University of Sydney, 2004. http://hdl.handle.net/2123/597.
Повний текст джерелаАнотація:
Drawing of standard telecommunication-type optical fibres has been optimised in terms of optical and physical properties. Specialty fibres, however, typically have more complex dopant profiles. Designs with high dopant concentrations and multidoping are common, making control of the fabrication process particularly important. In photonic crystal fibres (PCF) the inclusion of air-structures imposes a new challenge for the drawing process. The aim of this study is to gain profound insight into the behaviour of complex optical fibre structures during the final fabrication step, fibre drawing. Two types of optical fibre, namely conventional silica fibres and PCFs, were studied. Germanium and fluorine diffusion during drawing was studied experimentally and a numerical analysis was performed of the effects of drawing parameters on diffusion. An experimental study of geometry control of PCFs during drawing was conducted with emphasis given to the control of hole size. The effects of the various drawing parameters and their suitability for controlling the air-structure was studied. The effect of air-structures on heat transfer in PCFs was studied using computational fluid dynamics techniques. Both germanium and fluorine were found to diffuse at high temperature and low draw speed. A diffusion coefficent for germanium was determined and simulations showed that most diffusion occurred in the neck-down region. Draw temperature and preform feed rate had a comparable effect on diffusion. The hole size in PCFs was shown to depend on the draw temperature, preform feed rate and the preform internal pressure. Pressure was shown to be the most promising parameter for on-line control of the hole size. Heat transfer simulations showed that the air-structure had a significant effect on the temperature profile of the structure. It was also shown that the preform heating time was either increased or reduced compared to a solid structure and depended on the air-fraction.
9
Chaudry, Qasim Ali. "Numerical Approximation of Reaction and Diffusion Systems in Complex Cell Geometry." Licentiate thesis, KTH, Numerical Analysis, NA, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-12099.
Повний текст джерелаАнотація:
The mathematical modelling of the reaction and diffusion mechanism of lipophilic toxic compounds in the mammalian cell is a challenging task because of its considerable complexity and variation in the architecture of the cell. The heterogeneity of the cell regarding the enzyme distribution participating in the bio-transformation, makes the modelling even more difficult. In order to reduce the complexity of the model, and to make it less computationally expensive and numerically treatable, Homogenization techniques have been used. The resulting complex system of Partial Differential Equations (PDEs), generated from the model in 2-dimensional axi-symmetric setting is implemented in Comsol Multiphysics. The numerical results obtained from the model show a nice agreement with the in vitro cell experimental results. The model can be extended to more complex reaction systems and also to 3-dimensional space. For the reduction of complexity and computational cost, we have implemented a model of mixed PDEs and Ordinary Differential Equations (ODEs). We call this model as Non-Standard Compartment Model. Then the model is further reduced to a system of ODEs only, which is a Standard Compartment Model. The numerical results of the PDE Model have been qualitatively verified by using the Compartment Modeling approach. The quantitative analysis of the results of the Compartment Model shows that it cannot fully capture the features of metabolic system considered in general. Hence we need a more sophisticated model using PDEs for our homogenized cell model.
Computational Modelling of the Mammalian Cell and Membrane Protein Enzymology
10
Chaudhry, Qasim Ali. "Numerical Approximation of Reaction and Diffusion Systems in Complex Cell Geometry." Licentiate thesis, KTH, Numerisk analys, NA, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-12099.
Повний текст джерелаАнотація:
The mathematical modelling of the reaction and diffusion mechanism of lipophilic toxic compounds in the mammalian cell is a challenging task because of its considerable complexity and variation in the architecture of the cell. The heterogeneity of the cell regarding the enzyme distribution participating in the bio-transformation, makes the modelling even more difficult. In order to reduce the complexity of the model, and to make it less computationally expensive and numerically treatable, Homogenization techniques have been used. The resulting complex system of Partial Differential Equations (PDEs), generated from the model in 2-dimensional axi-symmetric setting is implemented in Comsol Multiphysics. The numerical results obtained from the model show a nice agreement with the in vitro cell experimental results. The model can be extended to more complex reaction systems and also to 3-dimensional space. For the reduction of complexity and computational cost, we have implemented a model of mixed PDEs and Ordinary Differential Equations (ODEs). We call this model as Non-Standard Compartment Model. Then the model is further reduced to a system of ODEs only, which is a Standard Compartment Model. The numerical results of the PDE Model have been qualitatively verified by using the Compartment Modeling approach. The quantitative analysis of the results of the Compartment Model shows that it cannot fully capture the features of metabolic system considered in general. Hence we need a more sophisticated model using PDEs for our homogenized cell model.Computational Modelling of the Mammalian Cell and Membrane Protein Enzymology
11
Gilbert, Stephen Henry. "An investigation of ventricular geometry and architecture using diffusion tensor MRI." Thesis, University of Leeds, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.493550.
Повний текст джерелаАнотація:
Although the heart structure and function have been characterised for many years there is still a ,far from complete understanding of the inter-relation. Detailed understanding of normal and deranged cardiac function, both of excitation and contraction, requires the integration of knowledge of individual myocyte electrophysiology, cell interconnectivity, the 3D structural arrangement of myocytes and of the Purkinje system.
12
Sengupta, Anandraj. "Effect of specimen geometry on ultrasound diffusion in cement-based aggregates." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/22578.
Повний текст джерела
13
Hughes-Riley, Theodore, John Beau Webber, Michael Ian Newton, and Robert H. Morris. "Magnetic resonance relaxation measurements using open-geometry sensors to assess the clog state of constructed wetlands." Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-178572.
Повний текст джерелаАнотація:
Monitoring the T1 relaxation of wetland clog matter has previously been identified as a gauge of its clogged state [1]. Magnetic resonance (MR) sensors explored in other work have typically been of a bore-whole configuration, which may not be ideal in a wetland environment where the sensitive volume of the sensor may become physically clogged and therefore inoperable. This work investigates two open-geometry sensor designs and a short study is presented to determine the suitability of the sensors for monitoring the clog state of
wetlands. It was shown that a bar magnet geometry has a higher stray field than that of the four magnet surface sensor also presented, leading to a prohibitively short T2 eff. This means that the T1 values collected are notably shorter and not useful for distinguishing between clog state for the single magnet sensor. By contrast the four magnet surface sensor has a longer T2 eff, making it more suitable for T1 measurements; where T1= 915 ± 212 ms for a very thinly clogged sample, and T1= 127 ± 27 ms for a heavily clogged sample. This offers a clearly resolvable difference in the T1 values allowing the clogging state to be easily determined and making this sensor the desirable choice for long-term embedding.
14
Forney, David C. III. "Diffusion in an absorbing porous medium : from microscopic geometry to macroscopic transport." Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/40293.
Повний текст джерелаАнотація:
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2007.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (p. 71-73).
Two physical models of diffusion in absorbing porous media are proposed on two length scales. One models diffusion in the pore space of a random medium with absorbing interfaces while the other is a reaction diffusion model where particles are absorbed in the bulk. Typical particle traveling distances and a bulk absorption coefficient are described in terms of general geometrical characteristics of a random medium and the analytical relations are found to compare well with numerical experiments. For the case of geometries consisting of randomly placed cubes, absorption in the bulk scales with the solid fraction to the two-thirds power. The statistical distribution of reaction rates in these models is found to be inversely related to the reaction rate. A quasi-static Monte-Carlo model is also investigated. The more complex problem of microbial extracellular enzyme distributions in marine sediment was an inspiration for this work.
by David C. Forney, III.
S.M.
15
Seland, John Georg. "Dynamic correlations between inhomogeneous magnetic fields, internal gradients, diffusion and transverse relaxation, as a probe for pore geometry and heterogeneity." Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-178804.
Повний текст джерелаАнотація:
In this study we have applied 2D NMR experiments where the spatial inhomogeneous magnetic field (Bi) inside a porous sample is correlated to respectively internal gradient (G0), diffusion coefficient (D), and transverse relaxation time (T2) of a confined liquid. Experiments were performed on samples having different pore system geometry and heterogeneity, leading to different types of confinement of the liquid.
The results show that the correlation between G0 and Bi is more sensitive to the type of confinement, and thus also of the pore geometry and heterogeneity, compared to the corresponding correlations involving D and T2.
16
Canaguier-Durand, Antoine. "Multipolar scattering expansion for the Casimir effect in the sphere-plane geometry." Paris 6, 2011. http://www.theses.fr/2011PA066246.
Повний текст джерелаАнотація:
Nous évaluons l’interaction de Casimir entre un miroir plan et un miroir sphérique, à température arbitraire, en tenant compte de la réflexion imparfaite. Cela nous permet d’étudier la riche dépendance à la géométrie de l’effet Casimir, et d’estimer l’erreur faite par l’approximation de proximité (PFA), communément utilisée pour cette configuration sphère-plan qui est celle des expériences. Pour cette évaluation nous appliquons la méthode de diffusion, basée sur la théorie des réseaux optiques, à la géométrie sphère-plan. La température est prise en compte par la formule de Matsubara. La réflexion sur le plan est exprimée à l’aide d’ondes planes, celle sur la sphère à l’aide d’ondes sphériques, entraînant un développement multipolaire. Les indices (l,m) de ces dernières sont tronqués à une valeur maximale pour l’évaluation numérique. Nous étudions d’abord le cas de la température nulle. Les résultats numériques permettent de caractériser l’erreur des différentes méthodes d’approximation, en fonction du modèle utilisé pour les miroirs, et de mettre en évidence des corrélations entre les effets de géométrie et de conductivité finie. Nous analysons ensuite la dépendance de l’effet Casimir à la température. Pour des miroirs parfaits, nous observons des corrélations entre les effets thermiques et géométriques pouvant entraîner une contribution répulsive des photons thermiques à la force de Casimir. Ce phénomène peut être associé à l’apparition de valeurs négatives pour l’entropie. Enfin, pour des miroirs métalliques à température ambiante nous observons une grande variété de corrélations entre les effets de la géométrie, de la température et de la dissipation dans les métaux.
17
Hughes-Riley, Theodore, John Beau Webber, Michael Ian Newton, and Robert H. Morris. "Magnetic resonance relaxation measurements using open-geometry sensors to assess the clog state of constructed wetlands." Diffusion fundamentals 22 (2014) 3, S. 1-8, 2014. https://ul.qucosa.de/id/qucosa%3A13476.
Повний текст джерелаАнотація:
Monitoring the T1 relaxation of wetland clog matter has previously been identified as a gauge of its clogged state [1]. Magnetic resonance (MR) sensors explored in other work have typically been of a bore-whole configuration, which may not be ideal in a wetland environment where the sensitive volume of the sensor may become physically clogged and therefore inoperable. This work investigates two open-geometry sensor designs and a short study is presented to determine the suitability of the sensors for monitoring the clog state of
wetlands. It was shown that a bar magnet geometry has a higher stray field than that of the four magnet surface sensor also presented, leading to a prohibitively short T2 eff. This means that the T1 values collected are notably shorter and not useful for distinguishing between clog state for the single magnet sensor. By contrast the four magnet surface sensor has a longer T2 eff, making it more suitable for T1 measurements; where T1= 915 ± 212 ms for a very thinly clogged sample, and T1= 127 ± 27 ms for a heavily clogged sample. This offers a clearly resolvable difference in the T1 values allowing the clogging state to be easily determined and making this sensor the desirable choice for long-term embedding.
18
Sarfaraz, Wakil. "The geometric influence of domain-size on the dynamics of reaction-diffusion systems with applications in pattern formation." Thesis, University of Sussex, 2018. http://sro.sussex.ac.uk/id/eprint/79452/.
Повний текст джерелаАнотація:
This thesis presents through a number of applications a self-contained and robust methodology for exploring mathematical models of pattern formation from the perspective of a dynamical system. The contents of this work applies the methodology to investigate the influence of the domain-size and geometry on the evolution of the dynamics modelled by reaction-diffusion systems (RDSs). We start with deriving general RDSs on evolving domains and in turn explore Arbitrary Lagrangian Eulerian (ALE) formulation of these systems. We focus on a particular RDS of activator-depleted class and apply the detailed framework consisting of the application of linear stability theory, domain-dependent harmonic analysis and the numerical solution by the finite element method to predict and verify the theoretically proposed behaviour of pattern formation governed by the evolving dynamics. This is achieved by employing the results of domain-dependent harmonic analysis on three different types of two-dimensional convex and non-convex geometries consisting of a rectangle, a disc and a flat-ring.
19
Seland, John Georg. "Dynamic correlations between inhomogeneous magnetic fields, internal gradients, diffusion and transverse relaxation, as a probe for pore geometry and heterogeneity." Diffusion fundamentals 22 (2014) 10, S. 1-5, 2014. https://ul.qucosa.de/id/qucosa%3A13490.
Повний текст джерелаАнотація:
In this study we have applied 2D NMR experiments where the spatial inhomogeneous magnetic field (Bi) inside a porous sample is correlated to respectively internal gradient (G0), diffusion coefficient (D), and transverse relaxation time (T2) of a confined liquid. Experiments were performed on samples having different pore system geometry and heterogeneity, leading to different types of confinement of the liquid.
The results show that the correlation between G0 and Bi is more sensitive to the type of confinement, and thus also of the pore geometry and heterogeneity, compared to the corresponding correlations involving D and T2.
20
Rieux, Frédéric. "Processus de diffusion discret : opérateur laplacien appliqué à l'étude de surfaces." Thesis, Montpellier 2, 2012. http://www.theses.fr/2012MON20201/document.
Повний текст джерелаАнотація:
Le contexte est la géométrie discrète dans Zn. Il s'agit de décrire les courbes et surfaces discrètes composées de voxels: les définitions usuelles de droites et plans discrets épais se comportent mal quand on passe à des ensembles courbes. Comment garantir un bon comportement topologique, les connexités requises, dans une situation qui généralise les droites et plans discrets?Le calcul de données sur ces courbes, normales, tangentes, courbure, ou des fonctions plus générales, fait appel à des moyennes utilisant des masques. Une question est la pertinence théorique et pratique de ces masques. Une voie explorée, est le calcul de masques fondés sur la marche aléatoire. Une marche aléatoire partant d'un centre donné sur une courbe ou une surface discrète, permet d'affecter à chaque autre voxel un poids, le temps moyen de visite. Ce noyau permet de calculer des moyennes et par là, des dérivées. L'étude du comportement de ce processus de diffusion, a permis de retrouver des outils classiques de géométrie sur des surfaces maillées, et de fournir des estimateurs de tangente et de courbure performants. La diversité du champs d'applications de ce processus de diffusion a été mise en avant, retrouvant ainsi des méthodes classiques mais avec une base théorique identique.} motsclefs{Processus Markovien, Géométrie discrète, Estimateur tangentes, normales, courbure, Noyau de diffusion, Analyse d'imagesThe context of discrete geometry is in Zn. We propose to discribe discrete curves and surfaces composed of voxels: how to compute classical notions of analysis as tangent and normals ? Computation of data on discrete curves use average mask. A large amount of works proposed to study the pertinence of those masks. We propose to compute an average mask based on random walk. A random walk starting from a point of a curve or a surface, allow to give a weight, the time passed on each point. This kernel allow us to compute average and derivative. The studied of this digital process allow us to recover classical notions of geometry on meshes surfaces, and give accuracy estimator of tangent and curvature. We propose a large field of applications of this approach recovering classical tools using in transversal communauty of discrete geometry, with a same theorical base
21
Prinsloo, Rian Hendrik. "Solution of the multigroup analytic nodal diffusion equations in 3-dimensional cylindrical geometry / Rian H. Prinsloo." Thesis, North-West University, 2006. http://hdl.handle.net/10394/1460.
Повний текст джерела
22
Duerigen, Susan. "Neutron transport in hexagonal reactor cores modeled by trigonal-geometry diffusion and simplified P3 nodal methods." Forschungszentrum Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:d120-qucosa-124665.
Повний текст джерелаАнотація:
The superior advantage of a nodal method for reactor cores with hexagonal fuel assemblies discretized as cells consisting of equilateral triangles is its mesh refinement capability. In this thesis, a diffusion and a simplified P3 (or SP3) neutron transport nodal method are developed based on trigonal geometry. Both models are implemented in the reactor dynamics code DYN3D. As yet, no other well-established nodal core analysis code comprises an SP3 transport theory model based on trigonal meshes. The development of two methods based on different neutron transport approximations but using identical underlying spatial trigonal discretization allows a profound comparative analysis of both methods with regard to their mathematical derivations, nodal expansion approaches, solution procedures, and their physical performance.
The developed nodal approaches can be regarded as a hybrid NEM/AFEN form. They are based on the transverse-integration procedure, which renders them computationally efficient, and they use a combination of polynomial and exponential functions to represent the neutron flux moments of the SP3 and diffusion equations, which guarantees high accuracy.
The SP3 equations are derived in within-group form thus being of diffusion type. On this basis, the conventional diffusion solver structure can be retained also for the solution of the SP3 transport problem.
The verification analysis provides proof of the methodological reliability of both trigonal DYN3D models. By means of diverse hexagonal academic benchmark and realistic detailed-geometry full-transport-theory problems, the superiority of the SP3 transport over the diffusion model is demonstrated in cases with pronounced anisotropy effects, which is, e.g., highly relevant to the modeling of fuel assemblies comprising absorber material.
23
Hofrichter, Julian. "On the Diffusion Approximation of Wright–Fisher Models with Several Alleles and Loci and its Geometry." Doctoral thesis, Universitätsbibliothek Leipzig, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-150016.
Повний текст джерелаАнотація:
The present thesis is located within the context of the diffusion approximation of Wright–Fisher models and the Kolmogorov equations describing their evolution. On the one hand, a full account of recombinational Wright–Fisher model is developed as well as their enhancement by other evolutionary mechanisms, including some information geometrical analysis. On the other hand, the thesis addresses several issues arising in the context of analytical solution schemes for such Kolmogorov equations, namely the inclusion of the entire boundary of the state space. For this, a hierarchical extension scheme is developed, both for the forward and the backward evolution, and the uniqueness of such extensions is proven.
First, a systematic approach to the diffusion approximation of recombinational two- or more loci Wright–Fisher models is presented. As a point of departure a specific Kolmogorov backward equation for the diffusion approximation of a recombinational two-loci Wright–Fisher model is chosen, to which – with the help of some information geometrical methods, i. e. by calculating the sectional curvatures of the corresponding statistical manifold (which is the domain equipped with the corresponding Fisher metric) – one succeeds to identify the underlying Wright–Fisher model. Accompanying this, for all methods and tools involved a suitable introduction is presented. Furthermore, the considerations span a separate analysis for the two most common underlying models (RUZ and RUG) as well as a comparison of the two models. Finally, transferring corresponding results for a simpler model described by Antonelli and Strobeck, solutions of the Kolmogorov equations are contrasted with Brownian motion in the same domain.
Furthermore, the perspective of the diffusion approximation of recombinational Wright–Fisher models is widened as the model underlying the Ohta–Kimura formula is subsequently extended by an integration of the concepts of natural fitness and mutation. Simultaneously, the corresponding extensions of the Ohta–Kimura formula are stated. Crucial for this is the development of a suitable fitness scheme, which is accomplished by a multiplicative aggregation of fitness values for pairs of gametes/zygotes. Furthermore, the model is generalised to have an arbitrary number of alleles and – in the following step – an arbitrary number of loci respectively. The latter involves an increased number of recombination modes, for which the concept of recombination masks is also implemented into the model. Another generalisation in terms of coarse-graining is performed via an application of schemata; this also affects the previously introduced concepts, specifically mask recombination, which are adapted accordingly. Eventually, a geometric analysis of linkage equilibrium states of the multi-loci Wright–Fisher models is carried out, relating to the concept of hierarchical probability distributions in information geometry, which concludes the considerations of recombinational Wright–Fisher models and their extensions.
Subsequently, the discussion of analytical solution schemes for the Kolmogorov equations corresponding to the diffusion approximation of Wright–Fisher models is ushered in, which represents the second part of the thesis. This is started with the simplest setting of a 1-dimensional Wright–Fisher model, for which the solution strategy for the corresponding Kolmogorov forward equation given by M. Kimura is recalled. From this, one may construct a unique extended solution which also accounts for the dynamics of the model on lower-dimensional entities of the state space, i. e. configurations of the model where one of the alleles no longer exists in the population, utilising the concept of (boundary) flux of a solution; a discussion of the moments of the distribution confirms the findings. A similar treatment is then carried out for the corresponding Kolmogorov backward equation, yielding analogous results of existence and uniqueness for an extended solution. For the latter in particular, a corresponding account of the configuration on the boundary turns out to be crucial, which is also reflected in the probabilistic interpretation of the backward solution. Additionally, the long-term behaviour of solutions is analysed, and a comparison between such solutions of the forward and the backward equation is made.
Next, it is basically aimed to transfer the results obtained in the previous chapter to the subsequent increasingly complicated setting of a Wright–Fisher model with 1 locus and an arbitrary number of alleles: With solution schemes for the interior of the state space (i. e. not encompassing the boundary) already existing in the literature, an extension scheme for a successive determination of the solution on lower-dimensional entities of the domain is developed. This scheme, again, makes use of the concept of the (boundary) flux of solutions, and one may therefore show that this extended solution fulfils additional properties regarding the completeness of the diffusion approximation with respect to the boundary. These properties may be formulated in terms of the moments of the distribution, and their connection to the underlying Wright–Fisher model is illustrated. Altogether, stipulating such a moments condition, existence and uniqueness of an extended solution on the entire domain are shown. Furthermore, the corresponding Kolmogorov backward equation is examined, for which similarly a (backward) extension scheme is presented, which allows extending a solution in a domain (perceived as a boundary instance of a larger domain) to all adjacent higher-dimensional entities of the larger domain along a certain path. This generalises the integration of boundary data observed in the previous chapter; in total, the existence of a solution of the Kolmogorov backward equation in the entire domain is shown for arbitrary boundary data.
Of particular interest to the discussion are stationary solutions of the Kolmogorov backward equation as they describe eventual hit probabilities for a certain target set of the model (in accordance with the probabilistic interpretation of solutions of the backward equation). The presented backward extension scheme allows the construction of solutions for all relevant cases, reconfirming some results by R. A. Littler for the stationary case, but now providing a previously missing systematic derivation. Eventually, the hitherto missing uniqueness assertion for this type of solutions is established by means of a specific iterated transformation which resolves the critical incompatibilities of solutions by a successive blow-up while the domain is converted from a simplex into a cube. Then – under certain additional assumptions on the regularity of the transformed solution – the uniqueness directly follows from general principles. Lastly, several other aspects of the blow-up scheme are discussed; in particular, it is illustrated in what way the required extra regularity relates to reasonable additional properties of the underlying Wright–Fisher model.
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Curantz, Camille. "Morphogenesis of skin pattern geometry in birds." Electronic Thesis or Diss., Sorbonne université, 2020. https://accesdistant.sorbonne-universite.fr/login?url=https://theses-intra.sorbonne-universite.fr/2020SORUS027.pdf.
Повний текст джерелаАнотація:
Les motifs naturels constituent l’un des traits les plus variés des populations d’animaux sauvages. Leur mise en place nécessite une réponse différentielle des cellules d’un tissu naïf à des signaux de position moléculaires ou mécaniques. Dans quelles mesures ces processus contribuent à la variation naturelle de ces motifs demeurent flou. Chez l’oiseau, les plumes ne sont pas distribuées de façon homogène mais prennent une organisation spatiale typique définie par leur taille, leur espacement et la régularité de leur implantation. Leur positionnement est causé par des mécanismes d’auto-organisation moléculaires et cellulaires qui coopèrent dans le temps et l’espace dans la peau en développement. Nous avons montré que l’émergence des follicules de plumes implique une régionalisation précoce de la peau en domaines compétents. La position et largeur de ces domaines forment un pré-pattern spécifique à chaque espèce étudiée qui influence la géométrie finale du pattern. L’étude comparative de la géométrie locale des follicules à l’intérieur de ces domaines compétents a montré que la variation de l’amplitude de l’anisotropie des cellules corrèle avec des variations de régularité du motif cutané. J’ai ensuite montré par des expériences de perturbation de l’architecture cellulaire du tissue que l’anisotropie des cellules du derme avant la formation des follicules peut être assimilé à un marquer de l’état de compétence des cellules à former un pattern régulier. Ces résultats montrent que la morphologie du tissu contraint la réponse cellulaire aux informations de position et qu’elle contribue à la mise en place de la diversité de la géométrie des motifs cutanés dans la natureNatural patterns constitute one of the most diverse features observed in wild animals. The development of such patterns requires a series of morphogenetic events involving a differential response of a naïve tissue to chemical and mechanical positional cues. To what extent these processes contribute to the shape of the natural variation remains unclear. In birds, feather primordia are implanted in typical geometries which vary between birds in primordia size, spacing and pattern regularity. It has been shown that the development of the feather array surely involves self-organising processes. Such processes rely on molecular and cellular factors that cumulate and cooperate temporally and spatially in the developing skin. We showed that the patterning of feather primordia involves prior regionalisation of the skin into competent domains forming a specie-specific pre-pattern that influences the resulting pattern. The comparative description of the local variation of the feather array in these birds according to their initial competent domains shows that variation in the amplitude of dermal cell anisotropy correlates with variation in pattern regularity. Using ex vivo perturbations of skin architecture by an inhibitor of actin filament polymerisation, I showed that the anisotropy of dermal cells prior to feather primordia formation can be seen a readout of the competent state of the tissue to form a regular pattern. These results provide insights into the cellular basis of self-organisation and demonstrate that tissue morphology, constrain the cell response to the positional cues and contribute to shape the variation of the geometry of the feather array observed in nature
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Nardoni, Chiara. "Diffusion maps in the Subriemannian motion group and perceptual grouping." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/6971/.
Повний текст джерелаАнотація:
Il presente lavoro è motivato dal problema della constituzione di unità percettive a livello della corteccia visiva primaria V1. Si studia dettagliatamente il modello geometrico di Citti-Sarti con particolare attenzione alla modellazione di fenomeni di associazione visiva. Viene studiato nel dettaglio un modello di connettività. Il contributo originale risiede nell'adattamento del metodo delle diffusion maps, recentemente introdotto da Coifman e Lafon, alla geometria subriemanniana della corteccia visiva. Vengono utilizzati strumenti di teoria del potenziale, teoria spettrale, analisi armonica in gruppi di Lie per l'approssimazione delle autofunzioni dell'operatore del calore sul gruppo dei moti rigidi del piano. Le autofunzioni sono utilizzate per l'estrazione di unità percettive nello stimolo visivo. Sono presentate prove sperimentali e originali delle capacità performanti del metodo.
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Brahmachari, Aveek Shankar. "BLOGS: Balanced Local and Global Search for Non-Degenerate Two View Epipolar Geometry." [Tampa, Fla] : University of South Florida, 2009. http://purl.fcla.edu/usf/dc/et/SFE0003084.
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Guevara, Olivares Miguel. "Disentangling the short white matter connections using a fiber's geometry based dimensional reduction approach." Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPAST053.
Повний текст джерелаАнотація:
L'étude de la substance blanche superficielle (SBS) a souvent été laissée de côté car elle est difficile à accéder et très variable. Des méthodes d'acquisition de meilleure qualité et le développement de nouveaux outils d'analyse ont facilité son étude à partir de l'IRM de diffusion et la tractographie. La connectivité du cortex et son plissement sont fortement liés, en particulier pour les fibres en U qui contournent les sillons. Comme la morphologie des motifs du plissement est spécifique à chaque être humain, la configuration des fibres sous-jacentes devrait l'être aussi. Un pipeline pour démêler les différentes configurations des connexions de la SBS et pour caractériser leur relation avec d'autres structures a été conçu. Une méthode pour définir les faisceaux courts à partir de tractographies a d’abord été élaborée selon une approche hybride, en extrayant les fibres reliant deux régions d'intérêt puis en les regroupant en faisceaux reproductibles d'un sujet à l'autre. Une transformation affine fondée sur l’IRM T1 et une base de données de tractographie déterministe ont été utilisées. Cela a permis de générer un atlas des faisceaux du cerveau entier, utilisé pour segmenter les faisceaux de nouveaux sujets, afin de réaliser des études cliniques sur des connexions spécifiques. Cet atlas a été comparé à deux autres atlas publics afin d'évaluer la reproductibilité des faisceaux. Un grand nombre de faisceaux ont été trouvé similaires entre les trois atlas. La définition des faisceaux de la SBS n’étant pas encore consensuelle, une sur-segmentation peut être néanmoins observée d’un atlas à l’autre. Cependant, une plus grande granularité que celle de ces atlas est souhaitable pour étudier la variabilité de leurs configurations entre les individus. Le niveau de démêlage escompté a été obtenu en utilisant une ISOMAP, un algorithme de réduction de dimension, pour stratifier la population en fonction de la géométrie des fibres locales avant la définition des faisceaux. Pour chaque région étudiée, les fibres contournant un sulcus spécifique ont été ciblées et des ROI ont été sélectionnées en conséquence. Ces régions correspondent aux sillons central, temporal supérieur, cingulaire et au gyrus précentral. La méthode a été appliquée sur les données de tractographie probabiliste de 816/897 sujets de la base HCP. Pour chaque région, les fibres ont été extraites puis utilisées dans le calcul de l’ISOMAP, qui à son tour a été utilisé pour diviser la population en dix groupes. Dans chaque groupe, la méthode d'identification des faisceaux courts a été appliquée, afin d'obtenir des faisceaux reproductibles. Ceux-ci ont ensuite été automatiquement mis en correspondance avec ceux des autres groupes, sur la base d'une distance entre centroïdes. Un principe d'hystérésis a été utilisé pour récupérer certains faisceaux précédemment rejetés. Afin d'identifier les faisceaux à l'origine des différences reflétées par les dimensions de l'ISOMAP, une distance «faisceau à tractogramme» pour chaque paire de sujets a été corrélée à leur position dans l’ISOMAP. Une corrélation élevée a été observée entre les premières dimensions de l’ISOMAP fondée sur les fibres et de celle fondée sur la morphologie des sillons. Les faisceaux contribuant à cette dimension de l’ISOMAP montrent des transitions morphologiques cohérentes, et sont situés dans des zones où le sillon présente également des transitions de forme. De plus, les changements des faisceaux sont également spatialement corrélés aux changements des activations fonctionnelles. Ces résultats prouvent le lien entre le câblage cérébral et le plissement cortical. De plus, ils montrent qu'une délimitation plus fine des faisceaux permet de voir des différences qui, la plupart du temps, sont brouillées en raison du mélange des configurationsThe study of superficial white matter (SWM) has often been left aside, mainly because of its high variability. Higher quality acquisition methods and the development of new analysis tools have facilitated the study of SWM from diffusion MRI and tractography. Brain connectivity and cortical folding pattern must be strongly related, especially for short U-fibers, which circumvent the folds. As the folding patterns morphology is specific to each human being, so should be the underlying fibers configuration. In this work we created a pipeline to disentangle the short white matter connections into their different configurations and to characterize their relation with other structures.First a method to delineate short bundles from a tractography set was built using a hybrid approach, by extracting fibers connecting two cortical regions of interest (ROIs) (incorporating anatomical information) and then clustering them into bundles (considering their shape), reproducible across subjects. Subjects were aligned by a T1-based affine transformation and a deterministic tractography database (79 subjects) was used. This generated a whole brain streamline bundle atlas, which allows distance-based segmentation of the bundles in new subjects, in order to perform clinical studies over specific connections. The bundles obtained were compared against other two publicly available atlases (using alternative non-linear alignment across subjects), to evaluate their reproducibility given different methods and databases. A non-negligible number of bundles were found similar among the three atlases. As SWM bundle definition is still a subjective matter, over-segmentation can nevertheless occur. However, even greater granularity is required when aiming to classify the different bundle configurations. This level of disentanglement was achieved by an ISOMAP dimensionality reduction algorithm. It aimed to stratify the population based on their fibers using geometrical changes across subjects. For each region under study, the fibers surrounding a specific sulcus were targeted and therefore the ROIs were selected accordingly. These regions are: central sulcus, superior temporal sulcus, cingulate sulcus and precentral gyrus. The method was applied over 816/897 subjects of the S900 release of the HCP database and a preprocessed probabilistic tractography database. For each region the fibers were extracted, sampled and then used in the ISOMAP computation, which in turn was employed to split the population in ten groups. In each group a refined version of a short bundle identification method was applied, in order to obtain reproducible bundles. These were then automatically matched with their corresponding ones in the other groups, based on a centroid fiber distance. A Hysteresis principle was used to recover missing bundles (previously discarded) in each group. In order to identify the bundles driving the differences reflected on each ISOMAP dimension, the correlation of the fibers geometry with the subjects ISOMAP values was performed, by using a “bundle to tractogram” distance for each pair of subjects. The fiber-based ISOMAP values were also compared to a sulcus-based ones, obtaining a high correlation for the first dimension. The bundles showing correlation with the ISOMAP values show coherent morphological transitions along the groups, and are located in areas where the sulcus also exhibits differences in shape. Moreover, the bundles are also spatially correlated to changes in functional activations. These results prove the link between the brain wiring and the cortical folding pattern. Moreover, they evidence that a finer delineation of the bundles allow the detection of differences that most of the time are blurred out due to the mixing of configurations
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Dürigen, Susan [Verfasser], and R. [Akademischer Betreuer] Stieglitz. "Neutron Transport in Hexagonal Reactor Cores Modeled by Trigonal-Geometry Diffusion and Simplified P3 Nodal Methods / Susan Dürigen. Betreuer: R. Stieglitz." Karlsruhe : KIT-Bibliothek, 2013. http://d-nb.info/1034865706/34.
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Meco, Halim. "Solidification at the High and Low Rate Extreme." Washington, D.C. : Oak Ridge, Tenn. : United States. Dept. of Energy. Office of Science ; distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy, 2004. http://www.osti.gov/servlets/purl/835376-9UiMWH/webviewable/.
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Pezzi, Luigi. "Advanced numerical modeling of masonry vaulted structures based on BIM parametric geometry generation." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021.
Знайти повний текст джерелаАнотація:
Vaults are an architectural element which during construction history have been built with a great variety of different materials, shapes, and sizes. The shape of these structural elements was often dependent by the necessity to cover complex spaces, by the needed loading capacity, or by architectural aesthetics. Within this complex scenario masonry patterns generates also different effects on loading capacity, load percolation and stiffness of the structure. These effects were been extensively investigated, both with empirical observations and with modern numerical methods. While most of them focus on analyzing the load bearing capacity or the texture effect on vaulted structures, the aim of this analysis is to investigate on the effects of the variation of a single structural characteristic on the load percolation in the vault. Moreover, an additional purpose of the work is related to the coding of a parametrical model aiming at generating different masonry vaulted structures. Nevertheless, proposed script can generate different typology of vaulted structure basing on some structural characteristics, such as the span and the length to cover and the dimensions of the blocks.
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Di, Santo Dario. "Study of anabatic flows using large-eddy simulations in a simplified geometry." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/20762/.
Повний текст джерелаАнотація:
In the present work, the turbulent anabatic flow generated over a uniformly heated slope in neutral stratification is originally studied through a large-eddy simulation (LES) technique. The present study is, to the best of the author's knowledge, the first case of a LES applied to anabatic flows in neutral stratification. The simulation approach is succesfully validated against three data sets: experimental, DNS and theoretical. One of the primary objectives of the study is to characterise the instantaneous turbulent structures triggered by the vertical buoyancy force responsible for the increase the turbulent mixing in the boundary layer. Such structures are hardly detected in both field and laboratory experiments and cannot be reproduced by steady-state numerical simulations. A new expression of the characteristic length scale of the thermal boundary layer is proposed and applied to derive alternative scaling parameters. Three principal regions are detected in the near-surface temperature profiles: a conduction region that contains most of the temperature decrease, a convective region dominated by flow convection and an equilibrium region that is almost not influenced by the heated slope. The newly proposed length scale resulted to be linked to the evolution of instantaneous turbulent structures identified as Rayleigh-Taylor instabilities which are analyzed and described. Their characteristic frequency is determined through a spectral analysis and their geometric dimensions are studied and linked to the extension of the vertical mixing zone inside the convection region. Three simulations are performed at different Rayleigh numbers to understand if there is a critical value above which the anabatic flow results Rayleigh-independent. the sensitivity analysis is carried out concluding that the analyzed flows are not Rayleigh-independent.
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Hofrichter, Julian [Verfasser], Jürgen [Akademischer Betreuer] Jost, Jürgen [Gutachter] Jost, and Angela [Gutachter] Stevens. "On the Diffusion Approximation of Wright–Fisher Models with Several Alleles and Loci and its Geometry / Julian Hofrichter ; Gutachter: Jürgen Jost, Angela Stevens ; Betreuer: Jürgen Jost." Leipzig : Universitätsbibliothek Leipzig, 2014. http://d-nb.info/1238788602/34.
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Ghanbarian-Alavijeh, Behzad. "Modeling Physical and Hydraulic Properties of Disordered Porous Media: Applications from Percolation Theory and Fractal Geometry." Wright State University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=wright1401380554.
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Sugar, Joshua D. "Mechanisms of microstructure development at metallic-interlayer/ceramic interfaces during liquid-film-assisted bonding." Berkeley, Calif. : Oak Ridge, Tenn. : Lawrence Berkeley National Laboratory ; distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy, 2003. http://www.osti.gov/servlets/purl/825347-j6A0Su/native/.
Повний текст джерелаАнотація:
Thesis (M.S.); Submitted to the University of California, Berkeley, CA (US); 1 Dec 2003.Published through the Information Bridge: DOE Scientific and Technical Information. "LBNL--54185" Sugar, Joshua D. USDOE Director. Office of Science. Basic Energy Sciences (US) 12/01/2003. Report is also available in paper and microfiche from NTIS.
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Kervil, Ronan. "Matière active et écoulements : jets de bactéries et nageurs interfaciaux." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSE1039/document.
Повний текст джерелаАнотація:
Cette thèse étudie quelques situations dans lesquelles un système actif, composé de particules auto-propulsées, est soumis à des contraintes extérieures. Dans un premier chapitre, nous étudions le comportement d'une assemblée de bactéries magnétotactiques —capables de s'aligner sur un champ magnétique extérieur— forcées au travers d'une constriction en forme de sablier. Nous caractérisons les propriétés dynamiques de ce système, à l'échelle individuelle mais également à celle de l'embouteillage formé et du jet émergeant. En particulier, nous montrons dans les zones concentrées en bactéries des couplages reliant densité en bactéries, vitesse de nage et forçage magnétique beaucoup plus complexes que ce qui avait été considéré jusqu'à maintenant dans les modèles théoriques.Le deuxième chapitre aborde un nouveau système actif constitué de disques de camphres posés à la surface de l'eau. Dans une première étape, nous avons étudié en détails les propriétés de nage individuelle de ces objets qui brisent spontanément la symétrie du système pour se mettre en mouvement. En particulier, nous montrons que les données recueillies peuvent être rationnalisées à l'aide d'une approche théorique très simple de ce problème couplé d'hydrodynamique et de transport de tensio-actif. Dans un troisième chapitre, nous avons abordé la dynamique d'une assemblée de ces nageurs interfaciaux interagissant via les champs hydrodynamiques et chimiques qu'ils génèrent. À concentration intermédiaire en nageurs, un régime de nage intermittente caractérisé par des bouffées pseudo-périodiques d'activité des nageurs apparaît. En utilisant des outils et concepts issus du domaine de la turbulence nous montrons que de façon remarquable, ce système très simple exhibe des comportements canoniques de la turbulence tels que prédits par Kolmogorov (1941), ouvrant ainsi des perspectives concrètes sur des analogies très riches entre turbulence et systèmes actifsThis work address different situations where active matter, made out of self-propelled particles, is submitted to external constraints.In a first part, we consider the response of magnetotactic bacteria –capable of swim alignment along magnetic field lines- directed through an hourglass shape geometry. We characterize the dynamic properties of the system, both at the individual bacteria scale and at the scale of the jammed region or of the induced outgoing jet. We show that in high density regions, couplings between the bacteria interactions, swim velocity and magnetic forcing take a much more complex form than had been considered so far in theoretical models.In a second chapter, we are addressing a new active system made out of camphor disks lying at the air-water interface. First of all, we study in details the individual swim properties of such particles, which spontaneously break the system symmetry to start moving. In particular, we show that all experimental data can be rationalized within the framework of a very simple model of this complex problem where hydrodynamic flows and surfactant transports are coupled through Marangoni stress.In a last chapter, we addressed the collective dynamics of an assembly of such interfacial swimmers that interact through the flow and chemical fields they generate. At intermediate swimmers concentrations, an intermittent swim regime appears characterized by pseudo-periodic activity bursts. Using tools and concepts from the turbulence domain, we show that, remarkably, this simple system exhibits dynamical properties matching the ones of canonical turbulence as predicted by Kolmogorov in the 40s. This demonstration opens up rich perspectives in the historical domain of turbulence together with in the emerging one of active matter
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Jacob, Dolly. "Investigation into reliability and performance of an implantable closed-loop insulin delivery device." Thesis, De Montfort University, 2014. http://hdl.handle.net/2086/11126.
Повний текст джерелаАнотація:
An implantable closed-loop insulin delivery device (INsmart device) containing a glucose responsive gel has been developed within the INsmart research group, over a period of 10 years, to mimic pancreas. In this thesis, the reliability and performance capability of the INsmart device was studied for future clinical use. Investigations into the device material compatibility with insulin solution, assessed by monitoring insulin loss and degradant formation over a period of 31 days using RP-HPLC have shown that stainless steel and titanium are the most compatible materials. Polycarbonate contributes to insulin loss after 11 days, resin might not be the best material and polyurethane is the least compatible for future device designs. To study insulin delivery mechanism and kinetics from the device, fluorescently labelled human insulin (FITC-insulin) was synthesised and characterised using RP-HPLC and MS, to produce a product with predominantly di-labelled conjugate (>75%) with no unreacted FITC or native insulin. Clinically used insulin analogues were also fluorescently labelled to produce predominantly di-labelled FITC-insulin conjugate with potential future biological and in vitro applications. The drug release mechanism from the glucose sensitive gel held in the INsmart device, studied using fluorescein sodium was determined as a Fickian diffusion controlled release mechanism. The diffusion coefficient (D) for FITC-insulin in the non-polymerised dex2M-conA gel (NP gel) determined using mathematical models, QSS and TL slope methods was 1.05 ± 0.02 x 10-11 m2/s and in the cross-linked dex500MA-conAMA gel (CL gel) was 0.75 ± 0.06 x 10-11 m2/s. In response to physiologically relevant glucose triggers in the NP gel, the diffusivity of FITC-insulin increases with increasing glucose concentrations, showing a second order polynomial fit, device thus showing glucose sensitivity and graded response, mimicking pancreas. Rheological measurements further confirmed the gel glucose responsiveness demonstrated by a third order polynomial fit between FITC-insulin D and the NP complex viscosity in response to increasing glucose concentration. The knowledge of FITC-insulin diffusion kinetics in the gel has aided in making some theoretical predictions for the capability and performance of the INsmart device. Alternate device geometry and design optimisation is also explored.
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Preusser, Tobias. "Anisotropic geometric diffusion in image and image sequence processing." [S.l. : s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=97051879X.
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SOUZA, LEANDRO CARLOS DE. "FEATURE PRESERVING MESH SIMPLIFICATION BASED ON MARKOV GEOMETRIC DIFFUSION." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2011. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=21556@1.
Повний текст джерелаАнотація:
PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROO uso de modelos computacionais baseados em malhas 3D se torna cada vez mais frequente em diversas áreas da computação como em jogos, animações e simuladores de realidade virtual, por exemplo. Entretanto, malhas que possuem uma grande quantidade de elementos exigem um alto poder computacional para serem manipuladas. A fim de resolver este problema são utilizados métodos de simplicação para reduzir o número de elementos, preservando a topologia que o modelo apresenta. Neste trabalho é introduzido um método de Difusão Geométrica Markoviana - difusão calculada na forma de probabilidades de transição e construída sobre um conjunto de pontos organizados geometricamente - aplicado na malha. Esse método combina uma estratégia baseada em uma Cadeia de Markov de base geométrica, que controla probabilisticamente o comportamento das normais na malha, com métodos de simplicação que são capazes de avaliar o impacto que a remoção de um elemento provoca na estrutura da malha. Métricas de avaliação são utilizadas para comparar o erro cometido em relação à malha original.
Computational models based on 3D meshes are ubiquitous in are such as game, animations and virtual reality. However, very large data sets are frequently produced, e.g. by scanners 3D and fluid dynamics simulations, wich require high computer power to be handled. Mesh simplification tecniques, preserving the topology and the geometry of the mesh, are then implemented to bring the datea to a size suited to be used in such areas. In this work we introduce a new tecnique wich we call Markov Geometric Diffusion based on probability transition matrix tecniques and built upon a data set organized geometricallyas a mesh. This method puts together a strategy based on a geometrically constructed Markov chain, wich control, in a probabilistic way, a normal vector field to the mesh, with a simplification method capable of estimating the impact of element removal in the mesh structure. Several error evaluation metrics are used tocompare the error of the simplified mesh with the original one.
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Lenglet, Christophe. "Geometric and variational methods for diffusion tensor MRI processing." Nice, 2006. http://www.theses.fr/2006NICE4083.
Повний текст джерелаАнотація:
Cette thèse est consacrée au développement d'outils de traitement pour l'Imagerie par Résonance Magnétique du Tenseur de Diffusion (IRM-TD). Cette technique d'IRM récente est d'une grande importance pour comprendre le fonctionnement du cerveau ou pour améliorer le diagnostic de pathologies neurologiques. Nous proposons des méthodes de traitement basées sur la géométrie Riemannienne, les équations aux dérivées partielles et les techniques de propagation de front. La première partie de ce travail est théorique. Après des rappels sur le système nerveux humain, l'IRM et la géométrie différentielle, nous étudions l'espace des lois normales multivariées. L'introduction d'une structure Riemannienne sur cet espace nous permet de définir des statistiques et des schémas numériques intrinsèques qui sont à la base des algorithmes proposés dans la seconde partie. Les propriétés de cet espace sont importantes pour l'IRM-TD car les tenseurs de diffusion sont les matrices de covariance de lois normales modélisant la diffusion des molécules d'eau en chaque voxel du milieu imagé. La seconde partie est méthodologique. Nous y introduisons des approches originales pour l'estimation et la régularisation d'IRM-TD. Puis nous montrons comment évaluer le degré de connectivité entre aires corticales et introduisons un modèle statistique d'évolution de surface permettant de segmenter ces images. Finalement, nous proposons une méthode de recalage non-rigide. La dernière partie de cette thèse est consacrée à l'analyse des connexions entre le cortex cérébral et les noyaux gris centraux, impliquées dans des tâches motrices, et à l'étude du réseau anatomo-fonctionnel du cortex visuel humainThis thesis deals with the development of new processing tools for Diffusion Tensor Magnetic Resonance Imaging (DT-MRI). This recent MRI technique is of utmost importance to acquire a better understanding of the brain mechanisms and to improve the diagnosis of neurological disorders. We introduce new algorithms relying on Riemannian geometry, partial differential equations and front propagation techniques. The first part of this work is theoretical. After a few reminders about the human nervous system, MRI and differential geometry, we study the space of multivariate normal distributions. The introduction of a Riemannian structure on that space allows us to define statistics and intrinsic numerical schemes that will constitute the core of the algorithms proposed in the second part. The properties of that space are important for DT-MRI since diffusion tensors are the covariance matrices of normal laws modeling the diffusion of water molecules at each voxel of the acquired volume. The second part of this thesis is methodological. We start with the introduction of original approaches for the estimation and regularization of DT-MRI. We then show how to evaluate the degree of connectivity between cortical areas. Next, we introduce a statistical surface evolution framework for the segmentation of those images. Finally, we propose a non-rigid registration method. The last part of this thesis is dedicated to the application of our tools to two important neuroscience problems: the analysis of the connections between the cerebral cortex and the basal ganglia, implicated in motor tasks, and the study of the anatomo-functional network of the human visual cortex
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GAMA, Fernando José de Almeida. "Acoplamento massa-energia na descrição de secagem de produtos cilíndricos." Universidade Federal de Campina Grande, 2014. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/458.
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Este trabalho tem como objetivo estudar o fenômeno da difusão transiente de transferência de calor e massa em sólidos com forma geométrica de um cilindro infinito. O estudo apresenta soluções para a equação de difusão com condição de contorno do terceiro tipo. Foram desenvolvidas ferramentas numéricas para a descrição da difusão de calor e massa em produtos com as formas mencionadas. Para as soluções numéricas propostas, a equação de difusão unidimensional foi discretizada usando o método dos volumes finitos, com uma formulação totalmente implícita, usando coordenadas cilíndricas. Para a solução numérica em coordenadas cilíndricas, foram desenvolvidos dois softwares na plataforma Windows, um para a migração de massa e outro para a propagação de calor, utilizando a linguagem de programação Fortran, opção Quick Win Application. O software foi validado usando-se soluções conhecidas para cilindros tanto com parâmetros termofísicos constantes quanto variáveis. Pode-se concluir que as ferramentas desenvolvidas foram adequadas para o estudo de problemas difusivos em geral. As ferramentas desenvolvidas foram usadas para descrever o processo de secagem de bananas inteiras. Na descrição, foram considerados volume e difusividade de calor e massa variáveis. Pode-se concluir que o modelo proposto para descrever o processo apresentou excelentes indicadores estatísticos na descrição da cinética de transferência de calor e massa. Pode-se concluir, também, que a exclusão do aquecimento do vapor nos cálculos efetuados não altera de forma significativa os resultados e que o uso do calor latente da água livre ao invés desta propriedade no produto não produz efeitos significativos. Por outro lado, o desprezo do calor latente de vaporização e a consideração da densidade e do calor específico do produto como propriedades constantes devem ser evitados.
This work aims to study the phenomenon of the transient diffusion of heat and mass in solids with geometric form of an infinite cylinder. The study presents solutions for the diffusion equation with boundary condition of the third kind. Numerical tools for describing the diffusion of heat and mass in the ways mentioned were developed. For the numerical solutions proposed, the one-dimensional diffusion equation was discretized using the finite volume method with a fully implicit formulation, using cylindrical coordinates. For the numerical solution in cylindrical coordinates, two software have been developed on the Windows platform, one for mass migration and one for the heat transfer, using the Fortran programming language, Quick Win Application option. The software was validated using solutions known for cylinders with both constant and variable thermophysical parameters. It can be concluded that the developed tools were appropriate for the study of diffusion problems in general. The above tools were used to describe the process of drying whole banana. In the description, we considered the volume and diffusivities with variables values. It can be concluded that the proposed model to describe the process showed excellent statistical indicators to describe the kinetics of heat and mass transfer. One can also conclude that the exclusion of the vapor heating in the calculations performed does not significantly alter the results. In addition that using the latent heat of free water instead of this property in the product does not produce significant effects. On the other hand, discard the latent heat of vaporization and the consideration of density and specific heat of the product as constant properties should be avoided.
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De, Zan Cecilia. "Some new results on reaction-diffusion equations and geometric flows." Doctoral thesis, Università degli studi di Padova, 2012. http://hdl.handle.net/11577/3422529.
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In this thesis we discuss the asymptotic behavior of the solutions of scaled reaction-diffusion equations in the unbounded domain Rn × (0 + ∞), in the cases when such a behavior is described in terms of moving interfaces.
As first class of asymptotic problems we consider the singular limit of bistable reaction-diffusion equations in the case when the velocity of the traveling wave equation depends on the space variable, i.e. cε = cε(x), and it satisfies, in some suitable sense, cε/ετ → α, as ε → 0+, where α is a discontinuous function and τ is an integer that can be equal to 0 or 1. The second part of the thesis concerns semilinear reaction-diffusion equations with diffusion term of type tr(Aε(x)D2uε), where tr denotes the trace operator, Aε = σεσtε for some matrix map σε : Rn → Rn×(m+n) and Aε converges to a degenerate matrix.
In order to establish such results rigorously, we modify and adapt to our problems the ”geometric approach” introduced by G. Barles and P. E. Souganidis for solving problems in Rn, and then partially revisited by G. Barles and F. Da Lio for reaction-diffusion equations in bounded domains. When it is possible we always consider the question of the well posedness of the Cauchy problems governing the motion of the fronts that describe the asymptotics we considerIn questa tesi discutiamo il comportamento asintotico delle soluzioni di equazioni di reazione-diffusione nel dominio illimitato Rn × (0,+∞) nei casi in cui tale comportamento sia descritto da un’interfaccia in movimento. Come primo tipo di problemi asintotici consideriamo il limite singolare di equazioni di reazione-diffusione bistabili nel caso in cui la velocità dell’onda viaggiante dipenda dalla variabile di stato, cioè cε = cε(x), e sia soddisfatto, al tendere di ε a zero e in qualche modo opportuno, cε/ετ → α, laddove α è una funzione discontinua e τ è un intero che può essere uguale a 0 o a 1. La seconda parte della tesi riguarda equazioni di reazione-diffusione semilineari e aventi termini di diffusione del tipo tr(Aε(x)D2uε), laddove tr denota l’operatore traccia, Aε = σεσtε per qualche funzione σε : Rn → Rn×(m+n) e Aε converge ad una matrice degenere. Al fine di provare tali risultati in modo rigoroso, abbiamo modificato e adattato "l’approccio geometrico" introdotto da G. Barles e P. E. Souganidis per risolvere problemi in Rn e in seguito parzialmente rivisto dallo stesso G. Barles assieme a F. Da Lio per equazioni di reazione-diffusione in domini limitati. Laddove possibile abbiamo sempre considerato la questione della buona posizione dei problemi di Cauchy che governano il moto dei fronti che descrivono le asintotiche da noi considerate
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Panagiotaki, E. "Geometric models of brain white matter for microstructure imaging with diffusion MRI." Thesis, University College London (University of London), 2011. http://discovery.ucl.ac.uk/1310435/.
Повний текст джерелаАнотація:
The research presented in this thesis models the diffusion-weighted MRI signal within brain white matter tissue. We are interested in deriving descriptive microstructure indices such as white matter axon diameter and density from the observed diffusion MRI signal. The motivation is to obtain non-invasive reliable biomarkers for early diagnosis and prognosis of brain development and disease. We use both analytic and numerical models to investigate which properties of the tissue and aspects of the diffusion process affect the diffusion signal we measure. First we develop a numerical method to approximate the tissue structure as closely as possible. We construct three-dimensional meshes, from a stack of confocal microscopy images using the marching cubes algorithm. The experiment demonstrates the technique using a biological phantom (asparagus). We devise an MRI protocol to acquire data from the sample. We use the mesh models as substrates in Monte-Carlo simulations to generate synthetic MRI measurements. To test the feasibility of the method we compare simulated measurements from the three-dimensional mesh with scanner measurements from the same sample and simulated measurements from an extruded mesh and much simpler parametric models. The results show that the three-dimensional mesh model matches the data better than the extruded mesh and the parametric models revealing the sensitivity of the diffusion signal to the microstructure. The second study constructs a taxonomy of analytic multi-compartment models of white matter by combining intra- and extra-axonal compartments from simple models. We devise an imaging protocol that allows diffusion sensitisation parallel and perpendicular to tissue fibres. We use the protocol to acquire data from two fixed rat brains, which allows us to fit, study and evaluate the models. We conclude that models which incorporate non-zero axon radius describe the measurements most accurately. The key observation is a departure of signals in the parallel direction from the two-compartment models, suggesting restriction, most likely from glial cells or binding of water molecules to the membranes. The addition of the third compartment can capture this departure and explain the data. The final study investigates the estimates using in vivo brain diffusion measurements. We adjust the imaging protocol to allow an in vivo MRI acquisition of a rat brain and compare and assess the taxonomy of models. We then select the models that best explain the in vivo data and compare the estimates with those from the ex vivo measurements to identify any discrepancies. The results support the addition of the third compartment model as per the ex vivo findings, however the ranking of the models favours the zero radius intra-axonal compartments.
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LOBRY, LAURENT. "Etude par diffusion de la lumiere d'un mouvement brownien en geometrie confinee." Nice, 1996. http://www.theses.fr/1996NICE4947.
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On etudie par la technique de diffusion de la lumiere le coefficient de diffusion de particules browniennes en geometrie confinee. De telles particules peuvent etre utilisees comme sonde pour caracteriser differents materiaux tels que des milieux poreux, des gels, des solutions en phase lamellaire, etc dans le cas de particules piegees, deux effets importants vont apparaitre: le coefficient de diffusion des particules va diminuer a cause des interactions hydrodynamiques particules-parois du milieu confinant. Pour des grandeurs de confinement de l'ordre de la longueur d'onde on mesure non plus un coefficient de diffusion reel, mais un coefficient effectif qui dependra de la valeur de qd ou q est la norme du vecteur diffusant et d la largeur du confinement suivant la direction de q. Nous avons confine des solutions colloidales de particules de latex dans un coin forme de deux prismes demi-cylindriques. La direction du vecteur diffusant est choisi perpendiculaire aux parois. L'angle d'incidence et la hauteur du faisceau determinent respectivement les valeurs de q et de d. Des etudes du ralentissement hydrodynamique ont ete faites pour differentes tailles de particules (de 70 a 300 nm) et largeurs de confinement (de 0. 2 a quelques m). Les resultats seront compares a une etude theorique du ralentissement d'une particule piegee entre deux parois que nous avons developpee par ailleurs. La mesure d'un coefficient de diffusion effectif fonction de qd a ete mise en evidence. En comparant les resultats experimentaux a la courbe theorique, il est possible de remonter aux longueurs des interactions electrostatiques particules-parois
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Mastrolia, P. "GRADIENT ESTIMATES AND LIOUVILLE THEOREMS FOR DIFFUSION-TYPE OPERATORS ON COMPLETE RIEMANNIAN MANIFOLDS." Doctoral thesis, Università degli Studi di Milano, 2011. http://hdl.handle.net/2434/153097.
Повний текст джерелаАнотація:
The aim of this work is twofold. The first main concern, the analytical one, is to study, using the method of gradient estimates, various Liouville-type theorems which are extensions of the classical Liouville Theorem for harmonic functions. We generalize the setting - from the Euclidean space to complete Riemannian manifolds - and the relevant operator - from the Laplacian to a general diffusion operator - and we also consider ``relaxed'' boundedness conditions (such as non-negativity, controlled growth and so on).
The second main concern is geometrical, and is deeply related to the first: we prove some triviality results for Einstein warped products and quasi-Einstein manifolds studying a specific Poisson equation for a particular, and geometrically relevant, diffusion operator.
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Manay, Siddharth. "Applications of anti-geometric diffusion of computer vision : thresholding, segmentation, and distance functions." Diss., Georgia Institute of Technology, 2003. http://hdl.handle.net/1853/33626.
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Al-Sawai, Wael. "Non-equilibrium Phase Transitions in Interacting Diffusions." Scholar Commons, 2018. https://scholarcommons.usf.edu/etd/7660.
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The theory of thermodynamic phase transitions has played a central role both in theoretical physics and in dynamical systems for several decades. One of its fundamental results is the classification of various physical models into equivalence classes with respect to the scaling behavior of solutions near the critical manifold. From that point of view, systems characterized by the same set of critical exponents are equivalent, regardless of how different the original physical models might be. For non-equilibrium phase transitions, the current theoretical framework is much less developed. In particular, an equivalent classification criterion is not available, thus requiring a specific analysis of each model individually. In this thesis, we propose a potential classification method for time-dependent dynamical systems, namely comparing the possible deformations of the original problem, and identifying dynamical systems which share the same deformation space. The specific model on which this procedure is developed is the Kuramoto model for interacting, disordered oscillators. Studied in the mean-field limit by a variety of methods, its associated synchronization phase transition appears as an appropriate model for cooperative phenomena ranging from coupled Josephson junctions to self-ordering patterns in biological and social systems. We investigate the geometric deformation of the dynamical system into the space of univalent maps of the unit disk, related to the Douady-Earle extension and the Denjoy-Wolff theory, and separately the algebraic deformation into the space of nonlinear sigma models for unitary operators. The results indicate that the Kuramoto model is representative for a large class of non-equilibrium synchronization models, with a rich phase-space diagram.
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Harley, Kristen E. "Canards in advection-reaction-diffusion systems in one spatial dimension." Thesis, Queensland University of Technology, 2014. https://eprints.qut.edu.au/79261/1/Kristen_Harley_Thesis.pdf.
Повний текст джерелаАнотація:
This thesis contains a mathematical investigation of the existence of travelling wave solutions to singularly perturbed advection-reaction-diffusion models of biological processes. An enhanced mathematical understanding of these solutions and models is gained via the identification of canards (special solutions of fast/slow dynamical systems) and their role in the existence of the most biologically relevant, shock-like solutions.
The analysis focuses on two existing models. A new proof of existence of a whole family of travelling waves is provided for a model describing malignant tumour invasion, while new solutions are identified for a model describing wound healing angiogenesis.
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Silva, Odair Pinheiro da. "Modelagem computacional da estabilização de sistemas subcríticos segundo o modelo unidimensional de difusão de nêutrons monoenergéticos." Universidade do Estado do Rio de Janeiro, 2014. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=6836.
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Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de JaneiroUm método numérico espectronodal (END) livre de erros de truncamento espacial é desenvolvido para problemas unidimensionais de difusão de nêutrons monoenergéticos em duas versões. Na versão de problemas de autovalor, o método gera soluções numéricas para o perfil do fluxo escalar e para o fator de multiplicação efetivo (k), que coincidem com a solução analítica dominante, afora os erros da aritmética finita computacional. Na versão de fonte fxa, o método também gera soluções numéricas analíticas para o problema de fonte fixa correspondente, onde a fonte de fissão, com dependência espacial, é obtida analiticamente, a partir da reconstrução espacial do fluxo escalar gerado pelo método END para problemas de autovalor. Alguns experimentos numéricos são apresentados para dois problemas modelos a fim de ilustrar a precisão do método.
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Roy, Samit. "A finite element analysis of adhesively bonded composite joints including geometric nonlinearity, nonlinear viscoelasticity, moisture diffusion and delayed failure." Diss., Virginia Polytechnic Institute and State University, 1987. http://hdl.handle.net/10919/88624.
Повний текст джерелаАнотація:
A two-dimensional finite-element computational procedure is developed for the accurate analysis of the strains and stresses in adhesively bonded joints. The large displacements and rotations experienced by the adherends and the adhesive are taken into account by invoking the updated Lagrangian description of motion. The adhesive layer is modeled using Schapery's nonlinear single integral constitutive law for uniaxial and multiaxial states of stress. Effect of temperature and stress level on the viscoelastic response is taken into account by a nonlinear shift factor definition. Penetrant sorption is accounted for by a nonlinear Fickean diffusion model in which the diffusion coefficient is dependent on the penetrant concentration and the dilatational strain. A delayed failure criterion based on the Reiner-Weisenberg failure theory has also been implemented in the finite element code. The applicability of the proposed models is demonstrated by several numerical examples.Doctor of Philosophy
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Ziegler, Kai U. [Verfasser]. "Experimentelle Untersuchung der Laufrad-Diffusor-Interaktion in einem Radialverdichter variabler Geometrie / Kai U Ziegler." Aachen : Shaker, 2003. http://d-nb.info/1170542824/34.
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