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Relevant bibliographies by topics / Diffusion geometry

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Academic literature on the topic 'Diffusion geometry'

Author: Grafiati

Published: 11 March 2023

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Journal articles on the topic "Diffusion geometry"

1

Ambjørn, Jan, Konstantinos N. Anagnostopoulos, Lars Jensen, Takashi Ichihara, and Yoshiyuki Watabiki. "Quantum geometry and diffusion." Journal of High Energy Physics 1998, no. 11 (1998): 022. http://dx.doi.org/10.1088/1126-6708/1998/11/022.

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Kaloshin, Vadim, and Mark Levi. "Geometry of Arnold Diffusion." SIAM Review 50, no. 4 (2008): 702–20. http://dx.doi.org/10.1137/070703235.

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Shaw, R. S., N. Packard, M. Schroter, and H. L. Swinney. "Geometry-induced asymmetric diffusion." Proceedings of the National Academy of Sciences 104, no. 23 (2007): 9580–84. http://dx.doi.org/10.1073/pnas.0703280104.

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Hochgerner, Simon, and Tudor Ratiu. "Geometry of non-holonomic diffusion." Journal of the European Mathematical Society 17, no. 2 (2015): 273–319. http://dx.doi.org/10.4171/jems/504.

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De Lara, Michel. "On drift, diffusion and geometry." Journal of Geometry and Physics 56, no. 8 (2006): 1215–34. http://dx.doi.org/10.1016/j.geomphys.2005.06.012.

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SÖDERMAN, OLLE, and BENGT JÖNSSON. "Restricted Diffusion in Cylindrical Geometry." Journal of Magnetic Resonance, Series A 117, no. 1 (1995): 94–97. http://dx.doi.org/10.1006/jmra.1995.0014.

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Klaus, Colin James Stockdale, Krishnan Raghunathan, Emmanuele DiBenedetto, and Anne K. Kenworthy. "Analysis of diffusion in curved surfaces and its application to tubular membranes." Molecular Biology of the Cell 27, no. 24 (2016): 3937–46. http://dx.doi.org/10.1091/mbc.e16-06-0445.

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Diffusion of particles in curved surfaces is inherently complex compared with diffusion in a flat membrane, owing to the nonplanarity of the surface. The consequence of such nonplanar geometry on diffusion is poorly understood but is highly relevant in the case of cell membranes, which often adopt complex geometries. To address this question, we developed a new finite element approach to model diffusion on curved membrane surfaces based on solutions to Fick’s law of diffusion and used this to study the effects of geometry on the entry of surface-bound particles into tubules by diffusion. We show that variations in tubule radius and length can distinctly alter diffusion gradients in tubules over biologically relevant timescales. In addition, we show that tubular structures tend to retain concentration gradients for a longer time compared with a comparable flat surface. These findings indicate that sorting of particles along the surfaces of tubules can arise simply as a geometric consequence of the curvature without any specific contribution from the membrane environment. Our studies provide a framework for modeling diffusion in curved surfaces and suggest that biological regulation can emerge purely from membrane geometry.

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Gao, Tingran. "The diffusion geometry of fibre bundles: Horizontal diffusion maps." Applied and Computational Harmonic Analysis 50 (January 2021): 147–215. http://dx.doi.org/10.1016/j.acha.2019.08.001.

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Halle, Bertil, and Stefan Gustafsson. "Diffusion in a fluctuating random geometry." Physical Review E 55, no. 1 (1997): 680–86. http://dx.doi.org/10.1103/physreve.55.680.

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Ledoux, Michel. "The geometry of Markov diffusion generators." Annales de la faculté des sciences de Toulouse Mathématiques 9, no. 2 (2000): 305–66. http://dx.doi.org/10.5802/afst.962.

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Dissertations / Theses on the topic "Diffusion geometry"

1

Habermann, Karen. "Geometry of sub-Riemannian diffusion processes." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/271855.

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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 $1$.

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Kearney, Dominic. "Turbulent diffusion in channels of complex geometry." Thesis, Loughborough University, 2000. https://dspace.lboro.ac.uk/2134/7275.

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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...).

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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.

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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.

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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.

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Cai, Li-Dong. "Scale-based surface understanding using diffusion smoothing." Thesis, University of Edinburgh, 1991. http://hdl.handle.net/1842/6587.

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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.

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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.

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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.

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Lyytikäinen, Katja Johanna. "Control of complex structural geometry in optical fibre drawing." Thesis, The University of Sydney, 2004. http://hdl.handle.net/2123/597.

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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.

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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.

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<p>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.</p><br>Computational Modelling of the Mammalian Cell and Membrane Protein Enzymology

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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.

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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.<br>Computational Modelling of the Mammalian Cell and Membrane Protein Enzymology

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Books on the topic "Diffusion geometry"

1

ter Haar Romeny, Bart M., ed. Geometry-Driven Diffusion in Computer Vision. Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-017-1699-4.

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Romeny, Bart M. Haar. Geometry-Driven Diffusion in Computer Vision. Springer Netherlands, 1994.

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Haar Romeny, Bart M. ter., ed. Geometry-driven diffusion in computer vision. Kluwer Academic, 1994.

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Bakry, Dominique, Ivan Gentil, and Michel Ledoux. Analysis and Geometry of Markov Diffusion Operators. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-00227-9.

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Elworthy, K. David, Yves Le Jan, and Xue-Mei Li. On the Geometry of Diffusion Operators and Stochastic Flows. Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/bfb0103064.

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Antonelli, P. L. Fundamentals of Finslerian Diffusion with Applications. Springer Netherlands, 1999.

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The measurement of grain boundary geometry. Institute of Physics Pub., 1993.

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Denzler, Jochen. Higher-order time asymptotics of fast diffusion in Euclidean space: A dynamical systems methods. American Mathematical Society, 2014.

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Singh, Tej. Hexnem nodal neutronics code for two dimensional multi group diffusion calculations in hexagonal geometry. Bhabha Atomic Research Centre, 2005.

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Geiser, Juergen. Groundwater contamination: Discretization and simulation of systems for convection-diffusion-dispersion reactions. Nova Science Publishers, 2008.

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Book chapters on the topic "Diffusion geometry"

1

Elworthy, K. David, Yves Le Jan, and Xue-Mei Li. "Diffusion Operators." In The Geometry of Filtering. Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0176-4_1.

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Huisken, Gerhard. "Heat diffusion in geometry." In Geometric Analysis. American Mathematical Society, 2016. http://dx.doi.org/10.1090/pcms/022/01.

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Antonelli, P. L. "Finslerian Diffusion and Curvature." In Handbook of Finsler Geometry. Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-007-0942-3_15.

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Elworthy, K. David, Yves Le Jan, and Xue-Mei Li. "Decomposition of Diffusion Operators." In The Geometry of Filtering. Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0176-4_2.

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Candel, Alberto, and Lawrence Conlon. "Riemannian geometry and heat diffusion." In Graduate Studies in Mathematics. American Mathematical Society, 2003. http://dx.doi.org/10.1090/gsm/060/16.

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Farooq, Hamza, Yongxin Chen, Tryphon Georgiou, and Christophe Lenglet. "Brain Parcellation and Connectivity Mapping Using Wasserstein Geometry." In Computational Diffusion MRI. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-73839-0_13.

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Elworthy, K. David, Yves Le Jan, and Xue-Mei Li. "Projectible Diffusion Processes and Markovian Filtering." In The Geometry of Filtering. Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0176-4_4.

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Antonelli, P. L. "Diffusion on the Tangent and Indicatrix Bundles." In Handbook of Finsler Geometry. Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-007-0942-3_16.

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Dela Haije, Tom, and Aasa Feragen. "Conceptual Parallels Between Stochastic Geometry and Diffusion-Weighted MRI." In Mathematics and Visualization. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-56215-1_9.

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AbstractDiffusion-weighted magnetic resonance imaging (MRI) is sensitive to ensemble-averaged molecular displacements, which provide valuable information on e.g. structural anisotropy in brain tissue. However, a concrete interpretation of diffusion-weighted MRI data in terms of physiological or structural parameters turns out to be extremely challenging. One of the main reasons for this is the multi-scale nature of the diffusion-weighted signal, as it is sensitive to the microscopic motion of particles averaged over macroscopic volumes. In order to analyze the geometrical patterns that occur in (diffusion-weighted measurements of) biological tissue and many other structures, we may invoke tools from the field of stochastic geometry. Stochastic geometry describes statistical methods and models that apply to random geometrical patterns of which we may only know the distribution. Despite its many uses in geology, astronomy, telecommunications, etc., its application in diffusion-weighted MRI has so far remained limited. In this work we review some fundamental results in the field of diffusion-weighted MRI from a stochastic geometrical perspective, and discuss briefly for which other questions stochastic geometry may prove useful. The observations presented in this paper are partly inspired by the Workshop on Diffusion MRI and Stochastic Geometry held at Sandbjerg Estate (Denmark) in 2019, which aimed to foster communication and collaboration between the two fields of research.

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Poirier, Charles, Maxime Descoteaux, and Guillaume Gilet. "Accelerating Geometry-Based Spherical Harmonics Glyphs Rendering for dMRI Using Modern OpenGL." In Computational Diffusion MRI. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-87615-9_13.

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Conference papers on the topic "Diffusion geometry"

1

Mazuruk, K., and N. Ramachandran. "Volume diffusion growth kinetics and step geometry." In 37th Aerospace Sciences Meeting and Exhibit. American Institute of Aeronautics and Astronautics, 1999. http://dx.doi.org/10.2514/6.1999-951.

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Ehler, Martin, Frank Filbir, and Hrushikesh N. Mhaskar. "Learning Biomedical Data Locally using Diffusion Geometry Techniques." In Imaging and Signal Processing in Health Care and Technology. ACTAPRESS, 2012. http://dx.doi.org/10.2316/p.2012.771-036.

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Murphy, James M., and Mauro Maggioni. "Iterative active learning with diffusion geometry for hyperspectral images." In 2018 9th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS). IEEE, 2018. http://dx.doi.org/10.1109/whispers.2018.8747033.

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García, J., B. González, M. Marrero-Martin, I. Aldea, J. del Pino, and A. Hernández. "Influence of the diffusion geometry on PN integrated varactors." In Microtechnologies for the New Millennium, edited by Valentín de Armas Sosa, Kamran Eshraghian, and Félix B. Tobajas. SPIE, 2007. http://dx.doi.org/10.1117/12.721999.

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Liao, C., X. Zheng, Z. Liu, and C. Liu. "Multilevel adaptive technique for diffusion flames with complex geometry." In 32nd Joint Propulsion Conference and Exhibit. American Institute of Aeronautics and Astronautics, 1996. http://dx.doi.org/10.2514/6.1996-3127.

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Kumar, G. Naga Siva, Sushanta K. Mitra, and Subir Bhattacharjee. "Dielectrophoretic Mixing With Novel Electrode Geometry." In ASME 2009 Fluids Engineering Division Summer Meeting. ASMEDC, 2009. http://dx.doi.org/10.1115/fedsm2009-78260.

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Electrokinetic mixing of analytes at micro-scale is important in several biochemical applications like cell activation, DNA hybridization, protein folding, immunoassays and enzyme reactions. This paper deals with the modeling and numerical simulation of micromixing of two different types of colloidal suspensions based on principle of dielectrophoresis (DEP). A mathematical model is developed based on Laplace, Navier-Stokes, and convection-diffusion-migration equations to calculate electric field, velocity, and concentration distributions, respectively. Mixing of two colloidal suspensions is simulated in a three-dimensional computational domain using finite element analysis considering dielectrophoretic, gravitational and convective (advective)–diffusive forces. Phase shifted AC signal is applied to the alternating electrodes for achieving the mixing of two different colloidal suspensions. The results indicate that the electric field and DEP forces are maximum at the edges of the electrodes and become minimum elsewhere. As compared to curved edges, straight edges of electrodes have lower electric field and DEP forces. The results also indicate that DEP force decays exponentially along the height of the channel. The effect of DEP forces on the concentration profile is studied. It is observed that, the concentration of colloidal particles at the electrodes edges is very less compared to elsewhere. Mixing of two colloidal suspensions due to diffusion is observed at the interface of the two suspensions. The improvement in mixing after applying the repulsive DEP forces on the colloidal suspension is observed. Most of the mixing takes place across the slant edges of the triangular electrodes. The effect of electrode pairs and the mixing length on degree of mixing efficiency are also observed.

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Polk, Sam L., and James M. Murphy. "Multiscale Clustering of Hyperspectral Images Through Spectral-Spatial Diffusion Geometry." In IGARSS 2021 - 2021 IEEE International Geoscience and Remote Sensing Symposium. IEEE, 2021. http://dx.doi.org/10.1109/igarss47720.2021.9554397.

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Li, Zhifeng, Hongchun Wu, Chenghui Wan, and Tianliang Hu. "The Fast Three-Dimensional Space-Time Neutron Kinetic Model for Cartesian Geometry and Cylindrical Geometry." In 2016 24th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/icone24-60861.

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In order to raise computation speed on the premise of enough numerical accuracy, the Predictor-Corrector Improved Quasi-Static (PC-IQS) method and Nodal Green’s Function Method (NGFM) were combined to solve the three-dimensional space-time neutron diffusion kinetics problems for Cartesian geometry. In addition, the improved quasi-static method and the Krylov algorithm were applied to solve the three-dimensional space-time neutron diffusion kinetics problems for cylindrical geometry. Based on the proposed model, the program of three-dimensional neutron space-time kinetic code has been tested by the two-dimensional and three-dimensional transient numerical benchmarks. The numerical results obtained by this work were in good agreement with the reference solutions.

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Li, Yunzhao, Hongchun Wu, Liangzhi Cao, and Qichang Chen. "Exponential Function Expansion Nodal Diffusion Method." In 18th International Conference on Nuclear Engineering. ASMEDC, 2010. http://dx.doi.org/10.1115/icone18-29447.

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An exponential function expansion nodal diffusion method is proposed to take care of diffusion calculation in unstructured geometry. Transverse integral technique is widely used in nodal method in regular geometry, such as rectangular and hexagonal, while improper in arbitrary triangular geometry because of the mathematical singularity. In this paper, nodal response matrix is derived by expanding detailed nodal flux distribution into a sum of exponential functions, and nodal balance equation can be obtained by strict integral in the polygonal node. Numerical results illustrate that the exponential function expansion nodal method in rectangular and triangular block can solve neutron diffusion equation in regular and irregular geometry.

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Ahn, Woojin, SangHoon Shin, Reza Asadpour, et al. "Optimum filler geometry for suppression of moisture diffusion in molding compounds." In 2016 IEEE International Reliability Physics Symposium (IRPS). IEEE, 2016. http://dx.doi.org/10.1109/irps.2016.7574625.

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Reports on the topic "Diffusion geometry"

1

Coifman, Ronald, Andreas Coppi, Matthew Hirn, and Frederick Warner. Diffusion Geometry Based Nonlinear Methods for Hyperspectral Change Detection. Defense Technical Information Center, 2010. http://dx.doi.org/10.21236/ada524546.

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Ougouag, Abderrafi Mohammed-El-Ami, and William Knox Terry. Development of a Nodal Method for the Solution of the Neutron Diffusion Equation in General Cylindrical Geometry. Office of Scientific and Technical Information (OSTI), 2002. http://dx.doi.org/10.2172/910654.

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Gill, Daniel Fury. Behavior of the Diamond Difference and Low-Order Nodal Numerical Transport Methods in the Thick Diffusion Limit for Slab Geometry. Office of Scientific and Technical Information (OSTI), 2007. http://dx.doi.org/10.2172/903208.

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Zucker, Steven W. Neurobiologically Inspired Geometric Diffusion for Target Recognition. Defense Technical Information Center, 2012. http://dx.doi.org/10.21236/ada577270.

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Zucker, Steven W., and Ronald Coifman. Diffusion Maps and Geometric Harmonics for Automatic Target Recognition (ATR). Volume 2. Appendices. Defense Technical Information Center, 2007. http://dx.doi.org/10.21236/ada476293.

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Kirchhoff, Helmut, and Ziv Reich. Protection of the photosynthetic apparatus during desiccation in resurrection plants. United States Department of Agriculture, 2014. http://dx.doi.org/10.32747/2014.7699861.bard.

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Abstract:

In this project, we studied the photosynthetic apparatus during dehydration and rehydration of the homoiochlorophyllous resurrection plant Craterostigmapumilum (retains most of the photosynthetic components during desiccation). Resurrection plants have the remarkable capability to withstand desiccation, being able to revive after prolonged severe water deficit in a few days upon rehydration. Homoiochlorophyllous resurrection plants are very efficient in protecting the photosynthetic machinery against damage by reactive oxygen production under drought. The main purpose of this BARD project was to unravel these largely unknown protection strategies for C. pumilum. In detail, the specific objectives were: (1) To determine the distribution and local organization of photosynthetic protein complexes and formation of inverted hexagonal phases within the thylakoid membranes at different dehydration/rehydration states. (2) To determine the 3D structure and characterize the geometry, topology, and mechanics of the thylakoid network at the different states. (3) Generation of molecular models for thylakoids at the different states and study the implications for diffusion within the thylakoid lumen. (4) Characterization of inter-system electron transport, quantum efficiencies, photosystem antenna sizes and distribution, NPQ, and photoinhibition at different hydration states. (5) Measuring the partition of photosynthetic reducing equivalents between the Calvin cycle, photorespiration, and the water-water cycle. At the beginning of the project, we decided to use C. pumilum instead of C. wilmsii because the former species was available from our collaborator Dr. Farrant. In addition to the original two dehydration states (40 relative water content=RWC and 5% RWC), we characterized a third state (15-20%) because some interesting changes occurs at this RWC. Furthermore, it was not possible to detect D1 protein levels by Western blot analysis because antibodies against other higher plants failed to detect D1 in C. pumilum. We developed growth conditions that allow reproducible generation of different dehydration and rehydration states for C. pumilum. Furthermore, advanced spectroscopy and microscopy for C. pumilum were established to obtain a detailed picture of structural and functional changes of the photosynthetic apparatus in different hydrated states. Main findings of our study are: 1. Anthocyan accumulation during desiccation alleviates the light pressure within the leaves (Fig. 1). 2. During desiccation, stomatal closure leads to drastic reductions in CO2 fixation and photorespiration. We could not identify alternative electron sinks as a solution to reduce ROS production. 3. On the supramolecular level, semicrystalline protein arrays were identified in thylakoid membranes in the desiccated state (see Fig. 3). On the electron transport level, a specific series of shut downs occur (summarized in Fig. 2). The main events include: Early shutdown of the ATPase activity, cessation of electron transport between cyt. bf complex and PSI (can reduce ROS formation at PSI); at higher dehydration levels uncoupling of LHCII from PSII and cessation of electron flow from PSII accompanied by crystal formation. The later could severe as a swift PSII reservoir during rehydration. The specific order of events in the course of dehydration and rehydration discovered in this project is indicative for regulated structural transitions specifically realized in resurrection plants. This detailed knowledge can serve as an interesting starting point for rationale genetic engineering of drought-tolerant crops.

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