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Journal articles on the topic 'Shape functional'

Author: Grafiati

Published: 6 September 2023

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1

Kolehmainen, J., H. Häkkinen, M. Manninen, and M. Koskinen. "Linear Nuclei: A Density Functional Interpretation." International Journal of Modern Physics E 06, no. 03 (September 1997): 507–13. http://dx.doi.org/10.1142/s0218301397000287.

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We show that linear shape isomers of small even-even nuclei exist with nearly any internucleon interactions. The shapes of the linear isomers look like chains of alpha-particles, but single-particle spectrum reveals that alpha-particle interpretation is not needed. Indeed, the same shapes are obtained even with noninteracting particles in a rectangular cavity. Linear shape isomers are shown to exist also in metal clusters.

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2

Zhao, Pengwei, and Zhipan Li. "Spectroscopies of rod- and pear-shaped nuclei in covariant density functional theory." International Journal of Modern Physics E 27, no. 10 (October 2018): 1830007. http://dx.doi.org/10.1142/s0218301318300072.

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The spectroscopic properties play a crucial role in understanding the structure of nuclei, in particular, the shape and shape transitions of nuclei. In recent years, the exotic shapes of nuclear systems, such as the rod and pear shapes, have attracted a lot of attention. Covariant density functional theory (CDFT) has become a standard tool for nuclear structure calculations, and it provides a global and accurate description of nuclear ground states and excitations. In the present paper, we briefly review the recent progress in covariant density functional theory (DFT) for spectroscopic properties of the rod- and pear-shaped nuclei with the cranking calculations in a rotating mean field and the collective Hamiltonian method beyond mean field. The novel linear-chain structure of alpha clustering is discussed with the cranking approach, and low lying spectra of pear-shaped nuclei are illustrated with the quadrupole–octupole collective Hamiltonian.

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3

Helander, Sami, Petra Laketa, Pauliina Ilmonen, Stanislav Nagy, Germain Van Bever, and Lauri Viitasaari. "Integrated shape-sensitive functional metrics." Journal of Multivariate Analysis 189 (May 2022): 104880. http://dx.doi.org/10.1016/j.jmva.2021.104880.

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4

Delecroix, Michel, Michel Simioni, and Christine Thomas-agnan. "Functional estimation under shape constraints." Journal of Nonparametric Statistics 6, no. 1 (January 1996): 69–89. http://dx.doi.org/10.1080/10485259608832664.

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5

Plotnikov, P. I., and J. Sokolowski. "Shape Derivative of Drag Functional." SIAM Journal on Control and Optimization 48, no. 7 (January 2010): 4680–706. http://dx.doi.org/10.1137/090758179.

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6

Xu, Li, and Yili Hong. "Functional and Shape Data Analysis." Journal of Quality Technology 49, no. 4 (October 2017): 419–20. http://dx.doi.org/10.1080/00224065.2017.11918007.

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7

Shin, Su-Mi, Hye-In Park, and A.-Young Sung. "Development of Functional Ophthalmic Materials Using Natural Materials and Gold Nanoparticles." Micromachines 13, no. 9 (September 1, 2022): 1451. http://dx.doi.org/10.3390/mi13091451.

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Ginsenoside, known as a natural substance, is a saponin component in ginseng and has various effects, such as antibacterial, antioxidant, and anti-inflammatory effects. In addition, gold nanoparticles can realize various optical and physical properties according to particle size and shape. For polymer polymerization, ginsenoside and gold nanoparticles were used as additives and copolymerized with a basic silicone hydrogel material. As gold nanoparticles, spherical and rod-shaped particles were used, and basic physical properties, such as water content, refractive index, and wettability of the prepared ophthalmic lenses, were measured. As a result of measuring the physical properties of the resulting polymer, it was found that the contact angle decreased by about 1.6% to 83.1% as the addition ratio of ginsenoside increased. In addition, as the addition ratio of metal nanoparticles increased, the refractive index was found to increase regardless of the shape of the nanoparticles. In addition, in the case of water content, the spherical shape gradually decreased according to the addition ratio, while the rod shape gradually increased according to the addition ratio. Therefore, it was found that the addition of ginsenoside, known as a saponin-based natural substance, has excellent wettability, and gold nanoparticles with different shapes have different properties. Thus, it is judged that the resulting copolymer can be utilized as a variety of highly functional ophthalmic polymer materials with high refractive index and high wettability.

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8

Cao, Dongliang, Paul Roetzer, and Florian Bernard. "Unsupervised Learning of Robust Spectral Shape Matching." ACM Transactions on Graphics 42, no. 4 (July 26, 2023): 1–15. http://dx.doi.org/10.1145/3592107.

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We propose a novel learning-based approach for robust 3D shape matching. Our method builds upon deep functional maps and can be trained in a fully unsupervised manner. Previous deep functional map methods mainly focus on predicting optimised functional maps alone, and then rely on off-the-shelf post-processing to obtain accurate point-wise maps during inference. However, this two-stage procedure for obtaining point-wise maps often yields sub-optimal performance. In contrast, building upon recent insights about the relation between functional maps and point-wise maps, we propose a novel unsupervised loss to couple the functional maps and point-wise maps, and thereby directly obtain point-wise maps without any post-processing. Our approach obtains accurate correspondences not only for near-isometric shapes, but also for more challenging non-isometric shapes and partial shapes, as well as shapes with different discretisation or topological noise. Using a total of nine diverse datasets, we extensively evaluate the performance and demonstrate that our method substantially outperforms previous state-of-the-art methods, even compared to recent supervised methods. Our code is available at https://github.com/dongliangcao/Unsupervised-Learning-of-Robust-Spectral-Shape-Matching.

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Vellanki, Pratibha, Santu Rana, Sunil Gupta, David Rubin de Celis Leal, Alessandra Sutti, Murray Height, and Svetha Venkatesh. "Bayesian Functional Optimisation with Shape Prior." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 1617–24. http://dx.doi.org/10.1609/aaai.v33i01.33011617.

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Real world experiments are expensive, and thus it is important to reach a target in a minimum number of experiments. Experimental processes often involve control variables that change over time. Such problems can be formulated as functional optimisation problem. We develop a novel Bayesian optimisation framework for such functional optimisation of expensive black-box processes. We represent the control function using Bernstein polynomial basis and optimise in the coefficient space. We derive the theory and practice required to dynamically adjust the order of the polynomial degree, and show how prior information about shape can be integrated. We demonstrate the effectiveness of our approach for short polymer fibre design and optimising learning rate schedules for deep networks.

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10

Courty, F., and A. Dervieux. "Multilevel functional preconditioning for shape optimisation." International Journal of Computational Fluid Dynamics 20, no. 7 (August 2006): 481–90. http://dx.doi.org/10.1080/10618560600839415.

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11

Morton, Andrew R., Nergiz Dogan-Artun, Zachary J. Faber, Graham MacLeod, Cynthia F. Bartels, Megan S. Piazza, Kevin C. Allan, et al. "Functional Enhancers Shape Extrachromosomal Oncogene Amplifications." Cell 179, no. 6 (November 2019): 1330–41. http://dx.doi.org/10.1016/j.cell.2019.10.039.

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12

Epifanio, Irene, and Noelia Ventura-Campos. "Functional data analysis in shape analysis." Computational Statistics & Data Analysis 55, no. 9 (September 2011): 2758–73. http://dx.doi.org/10.1016/j.csda.2011.04.003.

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13

Tachibana, Akitomo. "Shape wave in density functional theory." International Journal of Quantum Chemistry 34, no. 4 (October 1988): 309–23. http://dx.doi.org/10.1002/qua.560340402.

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14

Schmidt, C., K. Neuking, and G. Eggeler. "Functional Fatigue of Shape Memory Polymers." Advanced Engineering Materials 10, no. 10 (October 2008): 922–27. http://dx.doi.org/10.1002/adem.200800213.

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15

Kamangar, Sarfaraz, Govindaraju Kalimuthu, Irfan Anjum Badruddin, A. Badarudin, N. J. Salman Ahmed, and T. M. Yunus Khan. "Numerical Investigation of the Effect of Stenosis Geometry on the Coronary Diagnostic Parameters." Scientific World Journal 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/354946.

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The present study deals with the functional severity of a coronary artery stenosis assessed by the fractional flow reserve (FFR). The effects of different geometrical shapes of lesion on the diagnostic parameters are unknown. In this study, 3D computational simulation of blood flow in three different geometrical shapes of stenosis (triangular, elliptical, and trapezium) is considered in steady and transient conditions for 70% (moderate), 80% (intermediate), and 90% (severe) area stenosis (AS). For a given percentage AS, the variation of diagnostic parameters which are derived from pressure drop across the stenosis was found in three different geometrical shapes of stenosis and it was observed that FFR is higher in triangular shape and lower in trapezium shape. The pressure drop coefficient (CDP) was higher in trapezium shape and lower in triangular model whereas the LFC shows opposite trend. From the clinical perspective, the relationship between percentage AS and FFR is linear and inversely related in all the three models. A cut-off value of 0.75 for FFR was observed at 76.5% AS in trapezium model, 79.5% in elliptical model, and 82.7% AS for the triangular shaped model. The misinterpretation of the functional severity of the stenosis is in the region of 76.5%-82.7 % AS from different shapes of stenosis models.

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16

Hjelm, Joakim, Gerco H. van de Weerd, and Ferdinand A. Sibbing. "Functional link between foraging performance, functional morphology, and diet shift in roach (Rutilus rutilus)." Canadian Journal of Fisheries and Aquatic Sciences 60, no. 6 (June 1, 2003): 700–709. http://dx.doi.org/10.1139/f03-058.

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This study explores how feeding performance (size-dependent attack rate) and the diet shift from zooplankton to benthic macroinvertebrates in the fish species roach (Rutilus rutilus L.) is related to changes in functional morphology over ontogeny. The morphological changes included overall body shape and structures of the feeding apparatus. The foraging performance of roach on zooplankton, as a function of size, was hump-shaped with a maximum of ~160 mm, and the diet shift took place around 150 mm. Over ontogeny, roach body shape gradually changed from fusiform into high-bodied. The second principal component (PC2) of the feeding apparatus had a U-shaped relationship with body size, with a minimum at 140-mm total length, which is the inverse of that found for the foraging performance on zooplankton. We suggest that changes of the feeding apparatus affect prey intake during the early zooplanktivorous phases and at the final benthivorous feeding stage, whereas prey retention ability limits the maximum intake rate at a later phase of the zooplanktivorous feeding stage. Our results also suggest the presence of both positive and negative correlations in morphology between the feeding niches, which point to the occurrence of morphological trade-offs within ontogenetic niches.

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17

Lijue Xue, Lijue Xue. "Direct Manufacturing of Net-Shape Functional Components by Laser Consolidation Process(Invited Paper)." Chinese Journal of Lasers 36, no. 12 (2009): 3179–91. http://dx.doi.org/10.3788/cjl20093612.3179.

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18

Chen, Guancong, and Di Chen. "Heterogeneous Solid-State Plasticity of a Multi-Functional Metallo-Supramolecular Shape-Memory Polymer towards Arbitrary Shape Programming." Polymers 14, no. 8 (April 14, 2022): 1598. http://dx.doi.org/10.3390/polym14081598.

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Shape-memory polymers (SMPs) exhibit notable shape-shifting behaviors under environmental stimulations. In a specific shape-memory cycle, the material can be temporarily fixed at diverse geometries while recovering to the same permanent shape driven by the elastic network, which somewhat limits the versatility of SMPs. Via dynamic metallo-supramolecular interactions, herein, we report a multi-functional shape-memory polymer with tunable permanent shapes. The network is constructed by the metallic coordination of a four-armed polycaprolactone with a melting temperature of 54 °C. Owing to the thermo-induced stress relaxation through the bond exchange, the SMPs can be repeatedly programmed into different geometries in their solid state and show the self-welding feature. Via further welding of films crosslinked by different ions, it will present heterogeneous solid-state plasticity, and a more sophisticated shape can be created after the uniform thermal treatment. With elasticity and plasticity in the same network, the SMPs will display programmable shape-shifting behaviors. Additionally, the used material can be recast into a new film which retains the thermo-induced plasticity. Overall, we establish a novel strategy to manipulate the permanent shapes of SMPs through solid-state plasticity and develop a multi-functional shape-shifting material that has many practical applications.

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19

Lowe, T. W., M. I. G. Bloor, and M. J. Wilson. "The Automatic Functional Design of Hull Surface Geometry." Journal of Ship Research 38, no. 04 (December 1, 1994): 319–28. http://dx.doi.org/10.5957/jsr.1994.38.4.319.

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The surface geometry of a model yacht hull is generated using the partial differential equation (PDE) method, which enables the shape of the hull to be completely specified using only a small number of parameters while not overlimiting the range of shapes obtainable. This permits a computationally efficient search of the design parameter space for the hull form which optimizes some performance indicator. Here, hulls of low wave resistance are sought subject to certain imposed design constraints. The wave resistance is calculated using a panel method similar to that developed by Dawson. The effects on the hull shape of requiring reductions in approximations to the skin friction and form drags are also considered.

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20

Fu, Qiang, Xiaowu Chen, Xiaoyu Su, and Hongbo Fu. "Pose-Inspired Shape Synthesis and Functional Hybrid." IEEE Transactions on Visualization and Computer Graphics 23, no. 12 (December 1, 2017): 2574–85. http://dx.doi.org/10.1109/tvcg.2017.2739159.

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21

Tobushi, H., S. Hayashi, K. Okumura, and M. Endo. "Functional Properties of Polyurethane-Shape Memory Polymer." Proceedings of the JSME annual meeting 2000.3 (2000): 373–74. http://dx.doi.org/10.1299/jsmemecjo.2000.3.0_373.

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22

Epifanio, Irene. "Shape Descriptors for Classification of Functional Data." Technometrics 50, no. 3 (August 2008): 284–94. http://dx.doi.org/10.1198/004017008000000154.

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23

Belyaev, S., M. Evard, I. Lomakin, N. Resnina, V. Rubanik, V. Rubanik, and A. Volkov. "Functional Properties of Shape Memory Bimetal Plate." Materials Today: Proceedings 2 (2015): S723—S726. http://dx.doi.org/10.1016/j.matpr.2015.07.384.

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24

Waimann, Johanna, Philipp Junker, and Klaus Hackl. "Functional Fatigue in polycrystalline Shape Memory Alloys." PAMM 14, no. 1 (December 2014): 371–72. http://dx.doi.org/10.1002/pamm.201410173.

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25

Nicotra, Adrienne B., Andrea Leigh, C. Kevin Boyce, Cynthia S. Jones, Karl J. Niklas, Dana L. Royer, and Hirokazu Tsukaya. "The evolution and functional significance of leaf shape in the angiosperms." Functional Plant Biology 38, no. 7 (2011): 535. http://dx.doi.org/10.1071/fp11057.

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Angiosperm leaves manifest a remarkable diversity of shapes that range from developmental sequences within a shoot and within crown response to microenvironment to variation among species within and between communities and among orders or families. It is generally assumed that because photosynthetic leaves are critical to plant growth and survival, variation in their shape reflects natural selection operating on function. Several non-mutually exclusive theories have been proposed to explain leaf shape diversity. These include: thermoregulation of leaves especially in arid and hot environments, hydraulic constraints, patterns of leaf expansion in deciduous species, biomechanical constraints, adaptations to avoid herbivory, adaptations to optimise light interception and even that leaf shape variation is a response to selection on flower form. However, the relative importance, or likelihood, of each of these factors is unclear. Here we review the evolutionary context of leaf shape diversification, discuss the proximal mechanisms that generate the diversity in extant systems, and consider the evidence for each the above hypotheses in the context of the functional significance of leaf shape. The synthesis of these broad ranging areas helps to identify points of conceptual convergence for ongoing discussion and integrated directions for future research.

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Seguin, Brian, Yi-chao Chen, and Eliot Fried. "Closed Unstretchable Knotless Ribbons and the Wunderlich Functional." Journal of Nonlinear Science 30, no. 6 (May 22, 2020): 2577–611. http://dx.doi.org/10.1007/s00332-020-09630-z.

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Abstract In 1962, Wunderlich published the article “On a developable Möbius band,” in which he attempted to determine the equilibrium shape of a free standing Möbius band. In line with Sadowsky’s pioneering works on Möbius bands of infinitesimal width, Wunderlich used an energy minimization principle, which asserts that the equilibrium shape of the Möbius band has the lowest bending energy among all possible shapes of the band. By using the developability of the band, Wunderlich reduced the bending energy from a surface integral to a line integral without assuming that the width of the band is small. Although Wunderlich did not completely succeed in determining the equilibrium shape of the Möbius band, his dimensionally reduced energy integral is arguably one of the most important developments in the field. In this work, we provide a rigorous justification of the validity of the Wunderlich integral and fully formulate the energy minimization problem associated with finding the equilibrium shapes of closed bands, including both orientable and nonorientable bands with arbitrary number of twists. This includes characterizing the function space of the energy functional, dealing with the isometry and local injectivity constraints, and deriving the Euler–Lagrange equations. Special attention is given to connecting edge conditions, regularity properties of the deformed bands, determination of the parameter space needed to ensure that the deformation is surjective, reduction in isometry constraints, and deriving matching conditions and jump conditions associated with the Euler–Lagrange equations.

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27

Deckelnick, Klaus, Philip J. Herbert, and Michael Hinze. "A novel W^1,∞ approach to shape optimisation with Lipschitz domains." ESAIM: Control, Optimisation and Calculus of Variations 28 (2022): 2. http://dx.doi.org/10.1051/cocv/2021108.

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This article introduces a novel method for the implementation of shape optimisation with Lipschitz domains. We propose to use the shape derivative to determine deformation fields which represent steepest descent directions of the shape functional in the W1,∞-topology. The idea of our approach is demonstrated for shape optimisation of n-dimensional star-shaped domains, which we represent as functions defined on the unit (n − 1)-sphere. In this setting we provide the specific form of the shape derivative and prove the existence of solutions to the underlying shape optimisation problem. Moreover, we show the existence of a direction of steepest descent in the W1,∞− topology. We also note that shape optimisation in this context is closely related to the ∞−Laplacian, and to optimal transport, where we highlight the latter in the numerics section. We present several numerical experiments in two dimensions illustrating that our approach seems to be superior over a widely used Hilbert space method in the considered examples, in particular in developing optimised shapes with corners.

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28

Bacani, Jerico B., and Julius Fergy T. Rabago. "On the Second-Order Shape Derivative of the Kohn-Vogelius Objective Functional Using the Velocity Method." International Journal of Differential Equations 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/954836.

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The exterior Bernoulli free boundary problem was studied via shape optimization technique. The problem was reformulated into the minimization of the so-called Kohn-Vogelius objective functional, where two state variables involved satisfy two boundary value problems, separately. The paper focused on solving the second-order shape derivative of the objective functional using the velocity method with nonautonomous velocity fields. This work confirms the classical results of Delfour and Zolésio in relating shape derivatives of functionals using velocity method and perturbation of identity technique.

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29

Starodubtseva, Yu V., I. S. Starodubtsev, A. T. Ismail-Zadeh, I. A. Tsepelev, O. E. Melnik, and A. I. Korotkii. "A Method for Magma Viscosity Assessment by Lava Dome Morphology." Journal of Volcanology and Seismology 15, no. 3 (May 2021): 159–68. http://dx.doi.org/10.1134/s0742046321030064.

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Abstract Lava domes form when a highly viscous magma erupts on the surface. Several types of lava dome morphology can be distinguished depending on the flow rate and the rheology of magma: obelisks, lava lobes, and endogenic structures. The viscosity of magma nonlinearly depends on the volume fraction of crystals and temperature. Here we present an approach to magma viscosity estimation based on a comparison of observed and simulated morphological forms of lava domes. We consider a two-dimensional axisymmetric model of magma extrusion on the surface and lava dome evolution, and assume that the lava viscosity depends only on the volume fraction of crystals. The crystallization is associated with a growth of the liquidus temperature due to the volatile loss from the magma, and it is determined by the characteristic time of crystal content growth (CCGT) and the discharge rate. Lava domes are modeled using a finite-volume method implemented in Ansys Fluent software for various CCGTs and volcanic vent sizes. For a selected eruption duration a set of morphological shapes of domes (shapes of the interface between lava dome and air) is obtained. Lava dome shapes modeled this way are compared with the observed shape of the lava dome (synthesized in the study by a random modification of one of the calculated shapes). To estimate magma viscosity, the deviation between the observed dome shape and the simulated dome shapes is assessed by three functionals: the symmetric difference, the peak signal-to-noise ratio, and the structural similarity index measure. These functionals are often used in the computer vision and in image processing. Although each functional allows to determine the best fit between the modeled and observed shapes of lava dome, the functional based on the structural similarity index measure performs it better. The viscosity of the observed dome can be then approximated by the viscosity of the modeled dome, which shape fits best the shape of the observed dome. This approach can be extended to three-dimensional case studies to restore the conditions of natural lava dome growth.

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30

Mihalitsis, Michalis, and David Bellwood. "Functional implications of dentition-based morphotypes in piscivorous fishes." Royal Society Open Science 6, no. 9 (September 11, 2019): 190040. http://dx.doi.org/10.1098/rsos.190040.

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Teeth are crucial in elucidating the life history of vertebrates. However, most studies of teeth have focused on mammals. In heterodont mammals, tooth function is based on tooth shape and position along the jaw. However, the vast majority of vertebrates are homodont, and tooth function might not be based on the same principles (in homodonts, tooth shape is broadly similar along the jaw). We provide a quantitative framework and establish dentition-based morphotypes for piscivorous fishes. We then assess how these morphotypes relate to key functional feeding traits. We identified three broad morphotypes: edentulate, villiform and macrodont, with edentulate and villiform species displaying considerable functional overlap; macrodont species are more distinct. When analysing macrodonts exclusively, we found a major axis of variation between ‘front-fanged’ and ‘back-fanged’ species. The functional interpretations of this axis suggest that tooth-based functional decoupling could exist, even in homodont vertebrates, where teeth have similar shapes. This diversity is based not only on tooth shape but also solely on the position along the jaw.

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31

Yun, Jonghyun, Sanggoo Kang, Amin Darabnoush Tehrani, and Suyun Ham. "Image Analysis and Functional Data Clustering for Random Shape Aggregate Models." Mathematics 8, no. 11 (October 31, 2020): 1903. http://dx.doi.org/10.3390/math8111903.

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This study presents a random shape aggregate model by establishing a functional mixture model for images of aggregate shapes. The mesoscale simulation to consider heterogeneous properties concrete is the highly cost- and time-effective method to predict the mechanical behavior of the concrete. Due to the significance of the design of the mesoscale concrete model, the shape of the aggregate is the most important parameter to obtain a reliable simulation result. We propose image analysis and functional data clustering for random shape aggregate models (IFAM). This novel technique learns the morphological characteristics of aggregates using images of real aggregates as inputs. IFAM provides random aggregates across a broad range of heterogeneous shapes using samples drawn from the estimated functional mixture model as outputs. Our learning algorithm is fully automated and allows flexible learning of the complex characteristics. Therefore, unlike similar studies, IFAM does not require users to perform time-consuming tuning on their model to provide realistic aggregate morphology. Using comparative studies, we demonstrate the random aggregate structures constructed by IFAM achieve close similarities to real aggregates in an inhomogeneous concrete medium. Thanks to our fully data-driven method, users can choose their own libraries of real aggregates for the training of the model and generate random aggregates with high similarities to the target libraries.

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32

Méjri, Bochra. "Shape sensitivity analysis for identification of voids under Navier’s boundary conditions in linear elasticity." Journal of Inverse and Ill-posed Problems 27, no. 3 (June 1, 2019): 385–400. http://dx.doi.org/10.1515/jiip-2018-0029.

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Abstract This work is devoted to the study of the void identification problem from partially overdetermined boundary data in the 2D-elastostatic case. In a first part, a shape identifiability result from a Cauchy data is presented, i.e. with traction field and boundary displacement as measurements. Then this geometric inverse problem is tackled by the minimization of two cost functionals, an energy gap functional and an {L^{2}} -gap functional, which enable the reconstruction of voids under Navier’s boundary conditions. The shape derivatives of these cost functionals are computed for the purpose of sensitivity analysis.

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33

Bressan, Alberto, and Qing Sun. "On the optimal shape of tree roots and branches." Mathematical Models and Methods in Applied Sciences 28, no. 14 (December 30, 2018): 2763–801. http://dx.doi.org/10.1142/s0218202518500604.

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This paper introduces two classes of variational problems, determining optimal shapes for tree roots and branches. Given a measure [Formula: see text], describing the distribution of leaves, we introduce a sunlight functional [Formula: see text] computing the total amount of light captured by the leaves. On the other hand, given a measure [Formula: see text] describing the distribution of root hair cells, we consider a harvest functional [Formula: see text] computing the total amount of water and nutrients gathered by the roots. In both cases, we seek to maximize these functionals subject to a ramified transportation cost, for transporting nutrients from the roots to the trunk and from the trunk to the leaves. The main results establish various properties of these functionals, and the existence of optimal distributions. In particular, we prove the upper semicontinuity of [Formula: see text] and [Formula: see text], together with a priori estimates on the support of optimal distributions.

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34

Bacani, Jerico B. "On the shape gradient and shape Hessian of a shape functional subject to Dirichlet and Robin conditions." Applied Mathematical Sciences 8 (2014): 5387–97. http://dx.doi.org/10.12988/ams.2014.47583.

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35

Prakash, R., M. Hrizi, and A. A. Novotny. "A noniterative reconstruction method for solving a time-fractional inverse source problem from partial boundary measurements." Inverse Problems 38, no. 1 (December 1, 2021): 015002. http://dx.doi.org/10.1088/1361-6420/ac38b6.

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Abstract In this paper, a noniterative method for solving an inverse source problem governed by the two-dimensional time-fractional diffusion equation is proposed. The basic idea consists in reconstructing the geometrical support of the unknown source from partial boundary measurements of the associated potential. A Kohn–Vogelius type shape functional is considered together with a regularization term penalizing the relative perimeter of the unknown set of anomalies. Identifiability result is derived and uniqueness of a minimizer is ensured. The shape functional measuring the misfit between the solutions of two auxiliary problems containing information about the boundary measurements is minimized with respect to a finite number of ball-shaped trial anomalies by using the topological derivative method. In particular, the second-order topological gradient is exploited to devise an efficient and fast noniterative reconstruction algorithm. Finally, some numerical experiments are presented, showing different features of the proposed approach in reconstructing multiple anomalies of varying shapes and sizes by taking noisy data into account.

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36

Yampolsky, M., C. M. Salafia, O. Shlakhter, D. P. Misra, D. Haas, B. Eucker, and J. Thorp. "Variable placental thickness affects placental functional efficiency independent of other placental shape abnormalities." Journal of Developmental Origins of Health and Disease 2, no. 4 (May 9, 2011): 205–11. http://dx.doi.org/10.1017/s2040174411000195.

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Our previous work suggests that stressors that impact placental vascular growth result in a deformed chorionic surface shape, which reflects an abnormal placental three-dimensional shape. We propose to use variability of placental disk thickness as a reflector of deviations in placental vascular growth at the finer level of the fetal stems. We hypothesize that increased variability of thickness is associated with abnormal chorionic surface shape, but will be a predictor of reduced placental functional efficiency (smaller baby for a given placental weight) independent of shape. These measures may shed light on the mechanisms linking placental growth to risk of adult disease. The sample was drawn from the Pregnancy, Infection and Nutrition Study. In all, 94.6% of the cohort consented to placental examination. Of the 1023 delivered at term, those previously sectioned by the Pathology Department were excluded, leaving 587 (57%) cases with intact placentas that were sliced and photographed. The chorionic surface shape and the shape of a central randomly oriented placental slice were analyzed and measures were compared using correlation. Lower mean placental disk thickness and more variable disk thickness were each strongly and significantly correlated with deformed chorionic plate shapes. More variable disk thickness was strongly correlated with reduced placental efficiency independent of abnormal chorionic surface shape. Variability of placental disk thickness, simple to measure in a single randomly oriented central slice, may be an easily acquired measure that is an independent indicator of lowered placental efficiency, which may in turn program the infant and result in increased risk for development of adult diseases.

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37

Yan, Wenjing, Axia Wang, and Yichen Ma. "The Application of Shape Gradient for the Incompressible Fluid in Shape Optimization." Mathematical Problems in Engineering 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/728534.

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This paper is concerned with the numerical simulation for shape optimization of the Stokes flow around a solid body. The shape gradient for the shape optimization problem in a viscous incompressible flow is evaluated by the velocity method. The flow is governed by the steady-state Stokes equations coupled with a thermal model. The structure of continuous shape gradient of the cost functional is derived by employing the differentiability of a minimax formulation involving a Lagrange functional with the function space parametrization technique. A gradient-type algorithm is applied to the shape optimization problem. Numerical examples show that our theory is useful for practical purpose, and the proposed algorithm is feasible and effective.

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38

Zabarankin, Michael. "Minimum-resistance shapes in linear continuum mechanics." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2160 (December 8, 2013): 20130206. http://dx.doi.org/10.1098/rspa.2013.0206.

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A necessary optimality condition for the problem of the minimum-resistance shape for a rigid three-dimensional inclusion displaced in an unbounded isotropic elastic medium subject to a constraint on the volume of the inclusion is obtained through Betti's reciprocal work theorem. It generalizes Pironneau's optimality condition for the minimum-drag shape for a rigid body immersed into a uniform Stokes flow and is specialized for axisymmetric inclusions in axisymmetric and transversal translations. In both cases of translation, the three-dimensional displacement field is represented in terms of generalized analytic functions, and the three-dimensional elastostatics problem is reduced to boundary-integral equations (BIEs) via the generalized Cauchy integral formula. Minimum-resistance shapes are found in the semi-analytical form of functional series from an iterative procedure coupling the optimality condition and the BIEs. They are compared with the minimum-resistance spheroids and with the minimum-resistance spindle-shaped and lens-shaped bodies. Remarkably, in the axisymmetric translation, the minimum-resistance shapes transition from spindle-like shapes to almost prolate spheroidal shapes as the Poisson ratio changes from 1/2 to 0, whereas in the transversal translation, they are close to oblate spheroidal shapes for any Poisson ratio.

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39

Staicu, Ana-Maria, Ciprian M. Crainiceanu, Daniel S. Reich, and David Ruppert. "Modeling Functional Data with Spatially Heterogeneous Shape Characteristics." Biometrics 68, no. 2 (November 3, 2011): 331–43. http://dx.doi.org/10.1111/j.1541-0420.2011.01669.x.

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40

SAKUMA, Toshio. "Shape Memory Alloy Acting as Advanced Functional Materials." Journal of the Society of Mechanical Engineers 107, no. 1028 (2004): 508. http://dx.doi.org/10.1299/jsmemag.107.1028_508.

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41

Lejeune, Clément, Josiane Mothe, Adil Soubki, and Olivier Teste. "Shape-based outlier detection in multivariate functional data." Knowledge-Based Systems 198 (June 2020): 105960. http://dx.doi.org/10.1016/j.knosys.2020.105960.

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42

Nakamura, Katsuki, Ryuta Kawashima, Akitoshi Hanazawa, Yuko Sato, Motoaki Sugiura, Jobu Watanabe, Kazunori Sato, Yasuhiro Maeda, Yoshihiko Matsue, and Hiroshi Fukuda. "Functional MR imaging of cue-invariant shape perception." NeuroImage 13, no. 6 (June 2001): 917. http://dx.doi.org/10.1016/s1053-8119(01)92259-1.

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43

Abela, E., A. Federspiel, R. Wiest, M. Sturzenegger, C. Hess, and B. Weder. "Hemispheric functional asymmetry during explicit somatosensory shape discrimination." NeuroImage 47 (July 2009): S108. http://dx.doi.org/10.1016/s1053-8119(09)70962-0.

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44

Pagel, Kenny, Welf-Guntram Drossel, and Wolfgang Zorn. "Multi-functional Shape-Memory-Actuator with guidance function." Production Engineering 7, no. 5 (March 28, 2013): 491–96. http://dx.doi.org/10.1007/s11740-013-0463-5.

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45

Bedivan, D. M. "A boundary functional for optimal shape design problems." Applied Mathematics Letters 9, no. 1 (January 1996): 9–14. http://dx.doi.org/10.1016/0893-9659(95)00094-1.

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46

Collado, M., R. Cabás, J. San Juan, and I. López-Ferreño. "Functional Characterization of a Novel Shape Memory Alloy." Journal of Materials Engineering and Performance 23, no. 7 (June 18, 2014): 2321–26. http://dx.doi.org/10.1007/s11665-014-1104-7.

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47

Koval, Yu M. "Shape Memory Alloys – Powerful Class of Functional Materials." Nauka ta innovacii 1, no. 2 (March 30, 2005): 80–95. http://dx.doi.org/10.15407/scin1.02.080.

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48

Guo, Mengmeng, Jingyong Su, Li Sun, and Guofeng Cao. "Statistical regression analysis of functional and shape data." Journal of Applied Statistics 47, no. 1 (September 25, 2019): 28–44. http://dx.doi.org/10.1080/02664763.2019.1669541.

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49

Gurevich, Vsevolod V., and Eugenia V. Gurevich. "Extensive shape shifting underlies functional versatility of arrestins." Current Opinion in Cell Biology 27 (April 2014): 1–9. http://dx.doi.org/10.1016/j.ceb.2013.10.007.

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50

Bracken, Paul. "Shape equations for two-dimensional manifolds through a moving frame variational approach." International Journal of Geometric Methods in Modern Physics 16, no. 10 (October 2019): 1950155. http://dx.doi.org/10.1142/s021988781950155x.

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A variational approach is given which can be applied to functionals of a general form to determine a corresponding Euler–Lagrange or shape equation. It is the intention to formulate the theory in detail based on a moving frame approach. It is then applied to a functional of a general form which depends on both the mean and Gaussian curvatures as well as the area and volume elements of the manifold. Only the case of a two-dimensional closed manifold is considered. The first variation of the functional is calculated in terms of the variations of the basic variables of the manifold. The results of the first variation allow for the second variation of the functional to be evaluated.

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