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Journal articles on the topic 'Limit shapes'

Author: Grafiati

Published: 7 December 2024

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1

DeSALVO, STEPHEN, and IGOR PAK. "Limit Shapes via Bijections." Combinatorics, Probability and Computing 28, no. 2 (August 2, 2018): 187–240. http://dx.doi.org/10.1017/s0963548318000330.

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We compute the limit shape for several classes of restricted integer partitions, where the restrictions are placed on the part sizes rather than the multiplicities. Our approach utilizes certain classes of bijections which map limit shapes continuously in the plane. We start with bijections outlined in [43], and extend them to include limit shapes with different scaling functions.

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2

Pepelnjak, T., and B. Barisic. "Computer-assisted engineering determination of the formability limit for thin sheet metals by a modified Marciniak method." Journal of Strain Analysis for Engineering Design 44, no. 6 (August 1, 2009): 459–72. http://dx.doi.org/10.1243/03093247jsa503.

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Development of a new sheet-metal-forming technology in a digital environment demands accurate and reliable mechanical properties and forming limits of the selected material. It is essential to determine the forming limits for thin sheets and foils. Implementation of the Marciniak procedure with strip-shaped specimens defining the left-hand side of the forming limit diagram (FLD) results in tearing outside the observed area of the specimen. Therefore, new shapes of test pieces were designed with a strip-shaped central area and enlarged outer areas, which were in contact with the die during the forming process. The radius of the specimen enlargement enabled a co-axial contact of its edge and direction of the material flow over the die radius during the forming process. The shape of the redesigned geometry of the specimen was analysed using the finite element (FE) program ABAQUS to minimize undesired stress concentrations at the die radius. Finally, strain paths variations due to shape change were analysed. The new specimen concept was verified on TS-275 tinplate steel with a thickness of 0.24 mm. By implementing the necessary redesigned specimen shapes and by analysis of the tearing limit of the TS-275 material, the forming limit curve for the tinplate material under investigation was constructed.

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3

Okounkov, Andrei. "Limit shapes, real and imagined." Bulletin of the American Mathematical Society 53, no. 2 (August 20, 2015): 187–216. http://dx.doi.org/10.1090/bull/1512.

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4

Bocini, Saverio, and Jean-Marie Stéphan. "Non-probabilistic fermionic limit shapes." Journal of Statistical Mechanics: Theory and Experiment 2021, no. 1 (January 6, 2021): 013204. http://dx.doi.org/10.1088/1742-5468/abcd34.

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5

Johansson, Kurt. "Edge fluctuations of limit shapes." Current Developments in Mathematics 2016, no. 1 (2016): 47–110. http://dx.doi.org/10.4310/cdm.2016.v2016.n1.a2.

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6

Vassiliev, Nikolai, Vasilii Duzhin, and Artem Kuzmin. "Modeling of bumping routes in the RSK algorithm and analysis of their approach to limit shapes." Information and Control Systems, no. 6 (December 27, 2022): 2–9. http://dx.doi.org/10.31799/1684-8853-2022-6-2-9.

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Introduction: The RSK algorithm establishes an equivalence of finite sequences of elements of linearly ordered sets and pairs of Young tableaux P and Q of the same shape. Of particular interest is the study of the asymptotic limit, i. e., the limit shape of the so-called bumping routes formed by the boxes of tableau P affected in a single iteration of the RSK algorithm. The exact formulae for these limit shapes were obtained by D. Romik and P. Śniady in 2016. However, the problem of investigating the dynamics of the approach of bumping routes to their limit shapes remains insufficiently studied. Purpose: To study the dynamics of distances between the bumping routes and their limit shapes in Young tableaux with the help of computer experiments. Results: We have obtained a large number of experimental bumping routes through a series of computer experiments for Young tableaux P of sizes up to 4·106, filled with real numbers in the range [0, 1] and sets of inserted values α Î [0.1, 0.15, … , 0.85]. We have compared these bumping routes in the L2 metric with the corresponding limit shapes and have calculated the average distances and variances of their deviations from the limit shapes. We present an empirical formula for the rate of approach of discretized bumping routes to their limit shapes. Also, the experimental parameters of the normal distributions of the deviations of the bumping routes are obtained for various input values.

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7

Jeswiet, J., and D. Young. "Forming limit diagrams for single-point incremental forming of aluminium sheet." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 219, no. 4 (April 1, 2005): 359–64. http://dx.doi.org/10.1243/095440505x32210.

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The single-point incremental forming (SPIF) process is described. The maximum draw angle for SPIF is defined and specific values are given for 3003-0 and 5754-0 aluminium. Forming limit diagrams (FLDs) are developed for incremental forming of aluminium sheet, using SPIF. Five distinct shapes are used to define the forming limits: a hemisphere, a straight-sided cone, a hyperbolic-sided cone, a pyramid, and a shape with five lobes. Strains of more than 300 per cent have been achieved for all shapes.

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8

Bobek, Jiří, Jiří Šafka, Martin Seidl, and Jiří Habr. "Mechanical Properties of Metal-Plastic Composite with Internal Fractal Shape Reinforcing Structure." Defect and Diffusion Forum 368 (July 2016): 170–73. http://dx.doi.org/10.4028/www.scientific.net/ddf.368.170.

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This paper deals with mechanical properties research of innovative polymer multiphase metal and polymer composite materials consisting of matrix and isotropic or anisotropic oriented deterministic fractal shapes made by 3D printing. By creating of reinforcing internal structure consisting of deterministic fractal connected shapes is possible to gain unlimited mechanical properties directing. These fractal shapes - placed in multiphase system matrix – are significantly influencing whole material system mechanical properties mainly in case of stress on the limit of strength, proportional elongation on the limit of strength or tensile/ flexural modulus. Fractal shapes are also possible to properly locate, orient or shape modify according to potential material using with goal to gain maximal efficiency of fractal shapes occurrence. Producing of this multiphase system is realized by the help of 3D printing technology. Internal fractal shape structure is 3D printed from aluminium. This feature is in the next step over injected by polymer. So is possible to create any fractal shapes placed in polymer matrix which are by another technology unmanufacturable. Mechanical properties analyse is performed with respect to fractal shape type, fractal dimension, and fractal shape orientation.

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9

Fatkullin, Ibrahim, and Valeriy Slastikov. "Limit Shapes for Gibbs Ensembles of Partitions." Journal of Statistical Physics 172, no. 6 (July 13, 2018): 1545–63. http://dx.doi.org/10.1007/s10955-018-2117-7.

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10

Pittel, Boris, and Dan Romik. "Limit shapes for random square Young tableaux." Advances in Applied Mathematics 38, no. 2 (February 2007): 164–209. http://dx.doi.org/10.1016/j.aam.2005.12.005.

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11

Kenyon, Richard, and Andrei Okounkov. "Limit shapes and the complex Burgers equation." Acta Mathematica 199, no. 2 (2007): 263–302. http://dx.doi.org/10.1007/s11511-007-0021-0.

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12

Colomo, Filippo, Sylvie Corteel, Philippe Di Francesco, Jan de Gier, Vadim Gorin, and Tomohiro Sasamoto. "Limit shapes and fluctuations in statistical physics." Journal of Physics A: Mathematical and Theoretical 57, no. 44 (October 17, 2024): 440201. http://dx.doi.org/10.1088/1751-8121/ad8497.

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13

Zhu, Lei, and J. T. Boyle. "Optimal Shapes for Axisymmetric Pressure Vessels: A Brief Overview." Journal of Pressure Vessel Technology 122, no. 4 (July 17, 2000): 443–49. http://dx.doi.org/10.1115/1.1308572.

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This paper describes how optimal shapes for axisymmetric pressure vessels can be established based on maximizing limit pressure. This type of problem has been rarely examined in the literature due to the difficulty of evaluating limit loads. However, the “elastic compensation method” is used to approximate the limit load using elastic analysis alone, which opens the possibility of studying shape optimization based on limit pressure. The basic procedure, using a commercial finite element analysis system, is described and three example problems are examined. The aim is to investigate how much of an increase in load-carrying capacity could potentially be achieved if nonstandard pressure vessel shapes could be employed in practice. Of course, this may not be possible, but the results described here do contribute to a better understanding of the role shape plays in providing strength to a simple pressure vessel. [S0094-9930(00)00304-8]

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Krapivsky, P. L. "Stochastic dynamics of growing Young diagrams and their limit shapes." Journal of Statistical Mechanics: Theory and Experiment 2021, no. 1 (January 1, 2021): 013206. http://dx.doi.org/10.1088/1742-5468/abd025.

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Abstract We investigate a class of Young diagrams growing via the addition of unit cells and satisfying the constraint that the height difference between adjacent columns ⩾r. In the long time limit, appropriately re-scaled Young diagrams approach a limit shape that we compute for each integer r ⩾ 0. We also determine limit shapes of ‘diffusively’ growing Young diagrams satisfying the same constraint and evolving through the addition and removal of cells that proceed with equal rates.

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15

Wang, Chao, and Zhongzi Wang. "The limit shapes of midpoint polygons in ℝ3." Journal of Knot Theory and Its Ramifications 28, no. 10 (September 2019): 1950062. http://dx.doi.org/10.1142/s0218216519500627.

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For a polygon in the [Formula: see text]-dimensional Euclidean space, we give two kinds of normalizations of its [Formula: see text]th midpoint polygon by a homothetic transformation and an affine transformation, respectively. As [Formula: see text] goes to infinity, the normalizations will approach “regular” polygons inscribed in an ellipse and a generalized Lissajous curve, respectively, where the curves may be degenerate. The most interesting case is when [Formula: see text], where polygons with all its [Formula: see text]th midpoint polygons knotted are discovered and discussed. Such polygonal knots can be seen as a discrete version of the Lissajous knots.

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16

Borodin, Alexei, and Fabio Toninelli. "Two-dimensional anisotropic KPZ growth and limit shapes." Journal of Statistical Mechanics: Theory and Experiment 2018, no. 8 (August 17, 2018): 083205. http://dx.doi.org/10.1088/1742-5468/aad6b4.

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17

Petrov, F. "Limit shapes of young diagrams. Two elementary approaches." Journal of Mathematical Sciences 166, no. 1 (March 2, 2010): 63–74. http://dx.doi.org/10.1007/s10958-010-9845-9.

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18

Reshetikhin, Nicolai, and Ananth Sridhar. "Limit Shapes of the Stochastic Six Vertex Model." Communications in Mathematical Physics 363, no. 3 (September 21, 2018): 741–65. http://dx.doi.org/10.1007/s00220-018-3253-2.

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19

Boedec, G., M. Jaeger, and M. Leonetti. "Settling of a vesicle in the limit of quasispherical shapes." Journal of Fluid Mechanics 690 (December 20, 2011): 227–61. http://dx.doi.org/10.1017/jfm.2011.427.

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AbstractVesicles are drops of radius of a few tens of micrometres bounded by an impermeable lipid membrane of approximately 4 nm thickness in a viscous fluid. The salient characteristics of such a deformable object are a membrane rigidity governed by flexion due to curvature energy and a two-dimensional membrane fluidity characterized by a local membrane incompressibility. This provides unique properties with strong constraints on the internal volume and membrane area. Yet, when subjected to external stresses, vesicles exhibit a large deformability. The deformation of a settling vesicle in an infinite flow is studied theoretically, assuming a quasispherical shape and expanding all variables of the problem onto spherical harmonics. The contribution of thermal fluctuations is neglected in this analysis. A system of equations describing the temporal evolution of the shape is derived with this formalism. The final shape and the settling velocity are then determined and depend on two dimensionless parameters: the Bond number and the excess area. This simultaneous study leads to three stationary shapes, an egg-like shape already observed in an analogous experimental configuration in the limit of weak flow magnitude (Chatkaew, Georgelin, Jaeger & Leonetti, Phys. Rev. Lett, 2009, vol. 103(24), 248103), a parachute-like shape and a non-trivial non-axisymmetrical shape. The final shape depends on the initial conditions: prolate or oblate vesicle and orientation compared with gravity. The analytical solution in the small deformation regime is compared with numerical results obtained with a three-dimensional code. A very good agreement between numerical and theoretical results is found.

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20

Lu, Hua Xi, Hai Feng Jiang, Ping Ying Liang, and Bi Tao Wu. "Influence of Dynamic Soil-Structure Interaction on Fundamental Period for Frame Structures." Applied Mechanics and Materials 90-93 (September 2011): 1618–26. http://dx.doi.org/10.4028/www.scientific.net/amm.90-93.1618.

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By using of the approximate value of T proposed in FEMA450, the equations of the approximate effective fundamental period are derived for circular mat foundations supported at the surface, embedded foundations of circular shape and embedded foundations of arbitrary shapes, respectively. It is found that the limit values of of Veletsos are not uniform, and excessive for structures with h/r > 9, but too small for embedded deeply foundations. In this paper the uniform limit value of is 1.10 for all structures, and the conditions of consideration of SSI are given for ordinary reinforced concrete frame structures with circular mat foundations supported at the surface, embedded foundations of circular shape, and embedded foundations of arbitrary shapes, respectively.

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21

Bobek, Jiří, Jiří Šafka, Jiří Habr, and Martin Seidl. "3D Printing of Fractal Deterministic Shapes into Polymer Matrix with Respect to Final Composite Mechanical Properties." Applied Mechanics and Materials 693 (December 2014): 207–12. http://dx.doi.org/10.4028/www.scientific.net/amm.693.207.

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This paper deals with mechanical properties research of innovative polymer multiphase composite materials consisting of matrix and isotropic or anisotropic oriented deterministic fractal shapes made by 3D printing. Standard polymer composite materials consisting for example of polypropylene matrix and glass fibres have mechanical properties which depend mainly on matrix-fibre interface strength, fibre length, fibre strength and fibres orientation. [1] In case of under critical fibre length is fibres orientation stochastic in for example injection moulded composites. So is possible to say that mechanical properties of these (standard) composites with short fibres are isotropic and thus all direction limited. However by creating of reinforcing internal structure consisting of deterministic fractal connected shapes is possible to gain unlimited mechanical properties directing. These fractal shapes – placed in multiphase system matrix – are significantly influencing whole material system mechanical properties mainly in case of stress on the limit of strength, proportional elongation on the limit of strength or tensile/ flexural modulus. Fractal shapes are also possible to properly locate, orient or shape modify according to potential material using with goal to gain maximal efficiency of fractal shapes occurrence. Producing of this multiphase system is realized by the help of two component 3D printing technology. So is possible to create any fractal shapes placed in polymer matrix which are by another technology unmanufacturable. Mechanical properties analyse is performed with respect to fractal shape type, fractal dimension, fractal shape orientation and shear and tensile strength of matrix.

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22

Koh, C. G., and S. T. Quek. "Limit Loads of Buried Pipelines With Asymmetric Initial Imperfections." Journal of Pressure Vessel Technology 112, no. 4 (November 1, 1990): 392–96. http://dx.doi.org/10.1115/1.2929894.

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The effect of asymmetric imperfection on the limit-load response of pipelines buried in shallow trenches is investigated. The pipeline is modeled as a long beam resting on a rigid foundation and a small strain, large displacement formulation is used. Three different asymmetric imperfection shapes for the beam are considered and the corresponding limit loads are compared with that for a symmetric imperfection. It is found that the shape of initial imperfection plays an important role. The difference between limit loads based on a symmetric imperfection and a nonsymmetric imperfection can be quite significant.

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23

Hachiuma, Ryo, and Hideo Saito. "Pose Estimation of Primitive-Shaped Objects from a Depth Image Using Superquadric Representation." Applied Sciences 10, no. 16 (August 6, 2020): 5442. http://dx.doi.org/10.3390/app10165442.

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This paper presents a method for estimating the six Degrees of Freedom (6DoF) pose of texture-less primitive-shaped objects from depth images. As the conventional methods for object pose estimation require rich texture or geometric features to the target objects, these methods are not suitable for texture-less and geometrically simple shaped objects. In order to estimate the pose of the primitive-shaped object, the parameters that represent primitive shapes are estimated. However, these methods explicitly limit the number of types of primitive shapes that can be estimated. We employ superquadrics as a primitive shape representation that can represent various types of primitive shapes with only a few parameters. In order to estimate the superquadric parameters of primitive-shaped objects, the point cloud of the object must be segmented from a depth image. It is known that the parameter estimation is sensitive to outliers, which are caused by the miss-segmentation of the depth image. Therefore, we propose a novel estimation method for superquadric parameters that are robust to outliers. In the experiment, we constructed a dataset in which the person grasps and moves the primitive-shaped objects. The experimental results show that our estimation method outperformed three conventional methods and the baseline method.

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24

Reshetikhin, Nicolai, and Ananth Sridhar. "Integrability of Limit Shapes of the Six Vertex Model." Communications in Mathematical Physics 356, no. 2 (September 1, 2017): 535–65. http://dx.doi.org/10.1007/s00220-017-2983-x.

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25

Borodin, Alexei, Alexey Bufetov, and Grigori Olshanski. "Limit shapes for growing extreme characters of $U(\infty)$." Annals of Applied Probability 25, no. 4 (August 2015): 2339–81. http://dx.doi.org/10.1214/14-aap1050.

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26

Vershik, A. M. "Limit Shapes of Typical Geometric Configurations and Their Applications." Journal of Mathematical Sciences 119, no. 2 (January 2004): 165–77. http://dx.doi.org/10.1023/b:joth.0000008755.71555.1f.

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27

Vershik, A. M. "Statistical mechanics of combinatorial partitions, and their limit shapes." Functional Analysis and Its Applications 30, no. 2 (April 1996): 90–105. http://dx.doi.org/10.1007/bf02509449.

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28

Huang, Ruqi, Panos Achlioptas, Leonidas Guibas, and Maks Ovsjanikov. "Limit Shapes – A Tool for Understanding Shape Differences and Variability in 3D Model Collections." Computer Graphics Forum 38, no. 5 (August 2019): 187–202. http://dx.doi.org/10.1111/cgf.13799.

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29

Cohen, Caroline, Baptiste Darbois Texier, Etienne Reyssat, Jacco H. Snoeijer, David Quéré, and Christophe Clanet. "On the shape of giant soap bubbles." Proceedings of the National Academy of Sciences 114, no. 10 (February 21, 2017): 2515–19. http://dx.doi.org/10.1073/pnas.1616904114.

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We study the effect of gravity on giant soap bubbles and show that it becomes dominant above the critical sizeℓ=a2/e0, wheree0is the mean thickness of the soap film anda=γb/ρgis the capillary length (γbstands for vapor–liquid surface tension, andρstands for the liquid density). We first show experimentally that large soap bubbles do not retain a spherical shape but flatten when increasing their size. A theoretical model is then developed to account for this effect, predicting the shape based on mechanical equilibrium. In stark contrast to liquid drops, we show that there is no mechanical limit of the height of giant bubble shapes. In practice, the physicochemical constraints imposed by surfactant molecules limit the access to this large asymptotic domain. However, by an exact analogy, it is shown how the giant bubble shapes can be realized by large inflatable structures.

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30

Ding, Chao, and Hou-Duo Qi. "A Computable Characterization of the Extrinsic Mean of Reflection Shapes and Its Asymptotic Properties." Asia-Pacific Journal of Operational Research 32, no. 01 (February 2015): 1540005. http://dx.doi.org/10.1142/s0217595915400059.

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The reflection shapes of configurations in ℜm with k landmarks consist of all the geometric information that is invariant under compositions of similarity and reflection transformations. By considering the corresponding Schoenberg embedding, we embed the reflection shape space into the Euclidean space of all (k - 1) by (k - 1) real symmetric matrices. In this paper, we provide a computable formula of the extrinsic mean of the reflection shapes in arbitrary dimensions. Moreover, the asymptotic analysis of the extrinsic mean of the reflection shapes is studied. By using the differentiability of spectral operators, we obtain a central limit theorem of the sample extrinsic mean of the reflection shapes. As a direct application, the two-example hypothesis test of the reflection shapes is also derived.

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31

Arai, Yasuhiko. "Microshape Measurement Method Using Speckle Interferometry Based on Phase Analysis." Photonics 8, no. 4 (April 8, 2021): 112. http://dx.doi.org/10.3390/photonics8040112.

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A method for the measurement of the shape of a fine structure beyond the diffraction limit based on speckle interferometry has been reported. In this paper, the mechanism for measuring the shape of the fine structure in speckle interferometry using scattered light as the illumination light is discussed. Furthermore, by analyzing the phase distribution of the scattered light from the surface of the measured object, this method can be used to measure the shapes of periodic structures and single silica microspheres beyond the diffraction limit.

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32

Sasikumar, M., and V. Sundareswaran. "Influence of Projectile Nose Shape on Ballistic Limit and Damage to Glass/Vinyl Ester Composite Plates." Advanced Composites Letters 20, no. 5 (September 2011): 096369351102000. http://dx.doi.org/10.1177/096369351102000502.

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In the recent past, the substantial structural strength, light weight and stiffness properties of polymer based composite materials find its application in aircraft and automotive structures at prodigious rate. Fibre glass Reinforced Plastic (FRP) composites are partially elastic and brittle. The present study evaluates the ballistic limit, energy absorbed and the damage area caused by different projectile nose shapes on the composite plates made of glass fibre and vinyl ester resin with the orientation of (0/90)s. The number of plies in the plates is varied to 4, 6 and 8 and thus lead to different thicknesses. The projectile nose geometry is varied (hemispherical, conical, truncated conical, ogival and truncated ogival) to have realistic effect on the impact. The influence of projectile nose shape over ballistic limit is found experimentally and compared with the analytical predictions by H. M. Wen [ 5 , 6 ]. The ballistic limit, perforation mechanism, energy absorption at ballistic limit and the damage area at ballistic limit velocity has been studied. The influence of thickness of the composite plate over the ballistic limit have also been discussed. It is found that the truncated conical nose shaped projectile resulted in highest ballistic limit and largest damage area dominated by delamination. Experimental results showed that the analytical method [ 5 , 6 ] could satisfactorily predict the ballistic limit.

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33

MENG, FANXIN, WEIJIAN CHEN, DALIN ZHANG, and HUI MA. "EXPERIMENTAL AND NUMERICAL INVESTIGATION OF ICE ACCRETION ON AIRFOIL." International Journal of Modern Physics: Conference Series 19 (January 2012): 227–36. http://dx.doi.org/10.1142/s2010194512008793.

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Open Circuit Icing Research Tunnel was developed to test the ice shape under simulated icing conditions. Standard icing blade technique was used to measure liquid water content (LWC) in the icing tunnel test section. The uniformity of liquid water content was assessed by accreting ices on aluminum cylinder bars. Mean volumetric diameter (MVD) of the spray cloud was determined by soot-coated slide and verified through the limits of impingement. Ice accretion tests were performed on a NACA0012 wing model in typical rime and glaze conditions. Results were compared to ice shapes numerically predicted by Messinger method in the same conditions. It is indicated that good overall agreement is achieved in both icing shape and impingement limit.

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34

Lehmann, Kevin K. "Two-photon absorption line shapes in the transit-time limit." Journal of Chemical Physics 154, no. 10 (March 14, 2021): 104105. http://dx.doi.org/10.1063/5.0040868.

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35

Keating, David, Nicolai Reshetikhin, and Ananth Sridhar. "Integrability of Limit Shapes of the Inhomogeneous Six Vertex Model." Communications in Mathematical Physics 391, no. 3 (March 1, 2022): 1181–207. http://dx.doi.org/10.1007/s00220-022-04334-9.

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36

Goncharova, Elena, and Alexander Ovseevich. "LIMIT SHAPES OF REACHABLE SETS FOR LINEAR IMPULSE CONTROL SYSTEMS." IFAC Proceedings Volumes 38, no. 1 (2005): 42–47. http://dx.doi.org/10.3182/20050703-6-cz-1902.00407.

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37

Vershik, A. M. "Random permutations, limit shapes and asymptotic problems of partition theory." Advances in Applied Probability 24, no. 4 (December 1992): 772. http://dx.doi.org/10.1017/s0001867800024769.

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38

Romik, Dan, and Piotr Śniady. "Limit shapes of bumping routes in the Robinson-Schensted correspondence." Random Structures & Algorithms 48, no. 1 (September 8, 2014): 171–82. http://dx.doi.org/10.1002/rsa.20570.

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39

Plazzotta, Giacomo, and Caroline Colijn. "Asymptotic frequency of shapes in supercritical branching trees." Journal of Applied Probability 53, no. 4 (December 2016): 1143–55. http://dx.doi.org/10.1017/jpr.2016.70.

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Abstract The shapes of branching trees have been linked to disease transmission patterns. In this paper we use the general Crump‒Mode‒Jagers branching process to model an outbreak of an infectious disease under mild assumptions. Introducing a new class of characteristic functions, we are able to derive a formula for the limit of the frequency of the occurrences of a given shape in a general tree. The computational challenges concerning the evaluation of this formula are in part overcome using the jumping chronological contour process. We apply the formula to derive the limit of the frequency of cherries, pitchforks, and double cherries in the constant-rate birth‒death model, and the frequency of cherries under a nonconstant death rate.

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40

Yang, Liu, KyoungOk Kim, and Masayuki Takatera. "Effect of the fabric dimension on limits of the drape coefficient." Textile Research Journal 90, no. 3-4 (August 21, 2019): 442–59. http://dx.doi.org/10.1177/0040517519868175.

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The effects of fabric dimension on drape deformation are analyzed using a model of a circular segment cantilever for infinite shear stiffness (upper limit) and the deflection of strip cantilevers in radial directions for zero shear stiffness (lower limit). The drape shapes are determined by nondimensional parameters K and K′ in addition to the parameters m and m′, which are given by the ratio of the fabric radius and segment cantilever length, respectively. K and K′ are given by the segment cantilever length for the upper limit and by the differences between the radii of the fabric and support disk for the lower limit, with weights, and bending rigidity. The drape coefficient (DC) limits of fabrics are theoretically obtained using the model in three cases according to the relationship of m and m′. Even for different fabrics, the drape shapes are similar for the same m and K, or m′ and K′, in each case. The effects of dimension on fabric drape are therefore clarified theoretically. The obtained limits are experimentally verified for eight woven fabrics and one sheet. It is found that the DCs of samples are between the two theoretical curves of limits, although there are variations even for the same K or K′. The variations might be due to depressions between adjacent nodes or the presence of double-curvature deformation due to lower shear stiffness. The effects of dimensions in the drape test considering bending rigidity for infinite and zero shear stiffness are thus clarified theoretically and experimentally.

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41

Xin, Gangtao, Pingyi Fan, and Khaled B. Letaief. "Why Shape Coding? Asymptotic Analysis of the Entropy Rate for Digital Images." Entropy 25, no. 1 (December 27, 2022): 48. http://dx.doi.org/10.3390/e25010048.

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This paper focuses on the ultimate limit theory of image compression. It proves that for an image source, there exists a coding method with shapes that can achieve the entropy rate under a certain condition where the shape-pixel ratio in the encoder/decoder is O(1/logt). Based on the new finding, an image coding framework with shapes is proposed and proved to be asymptotically optimal for stationary and ergodic processes. Moreover, the condition O(1/logt) of shape-pixel ratio in the encoder/decoder has been confirmed in the image database MNIST, which illustrates the soft compression with shape coding is a near-optimal scheme for lossless compression of images.

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Ni, Yanshuo, He Zhang, Junfeng Li, Hexi Baoyin, and Jiaye Hu. "The Shape Entropy of Small Bodies." Mathematics 11, no. 4 (February 9, 2023): 878. http://dx.doi.org/10.3390/math11040878.

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The irregular shapes of small bodies usually lead to non-uniform distributions of mass, which makes dynamic behaviors in the vicinities of small bodies different to that of planets. This study proposes shape entropy (SE) as an index that compares the shapes of small bodies and spheres to describe the shape of a small body. The results of derivation and calculation of SE in two-dimensional and three-dimensional cases show that: SE is independent of the size of geometric figures but depends on the shape of the figures; the SE difference between a geometric figure and a circle or a sphere, which is the limit of SE value, reflects the difference between this figure and a circle or a sphere. Therefore, the description of shapes of small bodies, such as near-spherical, ellipsoid, and elongated, can be quantitatively described via a continuous index. Combining SE and the original inertia index, describing the shape of small bodies, can define the shapes of small bodies and provide a reasonably simple metric to describe a complex shape that is applicable to generalized discussion and analysis rather than highly detailed work on a specific, unique, polyhedral model.

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Wang, Long, De’an Sun, and Lin Li. "Three-dimensional stability of compound slope using limit analysis method." Canadian Geotechnical Journal 56, no. 1 (January 2019): 116–25. http://dx.doi.org/10.1139/cgj-2017-0345.

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This paper investigates three-dimensional (3D) stability of a compound soil slope with two inclination angles using the limit analysis method. The current limit analysis involves the toe-failure, face-failure, and base-failure mechanisms of the slope, all of which are possible 3D failure mechanisms. By reducing the current compound slope to a simple slope, the validity and efficiency of the present analysis are examined by comparing the current results with published solutions. The 3D stability of a compound soil slope is studied schematically for a wide range of parameters, and the stability charts are presented. The effects of slope shape (i.e., concave and convex shapes) and depth coefficient on the slope stability are investigated graphically. The graphs of critical failure surfaces are also presented to demonstrate the effects of slope shape and depth coefficient on the failure mechanism of a compound soil slope.

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Bragin, Evgeniy, Ahmat El'kanov, Aleksandr Dolgalev, Yuriy Sergeev, and Vazgen Avanisyan. "COMPARATIVE ASSESSMENT OF STATIC STRENGTH OF IMPLANT-ABUTMENT CONNECTIONS OF VARIOUS IMPLANT SHAPES." Actual problems in dentistry 19, no. 1 (May 22, 2023): 121–25. http://dx.doi.org/10.18481/2077-7566-2023-19-1-121-125.

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Nowadays the problem of optimal restorative prosthetics on dental implants is of paramount importance for solving a number of clinically difficult cases and extends beyond the alternative treatment at the complete and partial adentia both on the upper and lower jaws. An essential factor here is understanding of the biomechanical behaviour of the implant-abutment interface, because an optimal implant-abutment interface simulates the biophysical behaviour of natural teeth and ensures the long-term function of the prosthetic restoration. The optimal method for assessing the implant-abutment junction is the static tensile strength method. The limit is determined by performing a single loading of the dental implant in the implant-abutment area. The aim of the study was to assess the implant-abutment deformation of demountable and non-demountable structures of the 4*10 cylindrical and cone-shaped dental implants with determination of their static strength limit. Materials and methods. Two brands of dental implants have been chosen as the objects of research – cylindrical implant LIKO M 4x10 and cone-shaped implant LIKO M DG 4x10. A subject of the research is the ultimate strength of the implant-abutment unit of demountable and non-dismountable abutment design. Results. Static loading tests with estimation of the deformation limit of the implant-abutment unit were carried out along with the comparative estimation of the strength of demountable and non-demountable abutment constructions of dental implants of various shapes. Conclusion. The carried out comparative analysis of the static strength makes it possible to optimise the process of orthopaedic treatment on dental implants taking into account the maximal limits of the loaded structures and to carry out the equilibrium load distribution.

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HEDGES, S. BLAIR. "At the lower size limit in snakes: two new species of threadsnakes (Squamata: Leptotyphlopidae: Leptotyphlops) from the Lesser Antilles." Zootaxa 1841, no. 1 (August 4, 2008): 1. http://dx.doi.org/10.11646/zootaxa.1841.1.1.

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Islands are viewed as natural evolutionary laboratories for terrestrial organisms because they have boundaries that limit dispersal and often reveal evolutionary patterns and mechanisms. One such pattern is that the smallest and largest species of different types of tetrapod animals are frequently found on islands. Here I describe two new diminutive species of snakes of the genus Leptotyphlops from the Lesser Antilles: one from Saint Lucia and the other from Barbados. The one from Barbados is the smallest species of snake and has a total adult length of approximately 100 mm. Limited evidence indicates a clutch size of one and a greatly elongated egg shape (length /width). Comparison of egg shapes in snakes indicates that the shape is a packaging phenomenon, related primarily to the shape of the available body cavity and clutch size. For a clutch size of one, expected egg shape is eight whereas expected egg shape drops to two at a clutch size of ten. The body shape of snakes, defined as snout-to-vent length divided by width, also varies and influences the shape of snake eggs. The smallest snakes are typically stout-bodied with shapes of 30–35 whereas the longest snakes usually are more elongate, with shapes of 45–50. The allometry of organ size also affects clutch size and shape, because the smallest snakes have the smallest proportion of body cavity space available for reproduction. The best explanation for the observation of body size extremes on islands is that colonizing species have adapted to open ecological niches that would otherwise be occupied on the mainland. Island colonists encounter novel environments and reduced interspecific competition, allowing species to evolve physical traits, including extremes in size, not normally seen on continents. However, the lower limit of adult size appears to be constrained by the allometry of morphology, physiology, and reproduction. The smallest tetrapods have small clutches, usually one egg or young, and offspring that are relatively large. In the smallest snakes, offspring are one-half of the length of adults, compared with 10% adult length in the case of large species of snakes. Thus the evolutionary tradeoff between number and size of offspring appears to have reached a size boundary in these species, limiting the evolution of yet smaller species.

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Kim, Soyeon, Dai-Soon Kwak, and In-Beom Kim. "Morphometric Analysis and Classification of the Cross-Sectional Shape of the C2 Lamina." BioMed Research International 2017 (2017): 1–7. http://dx.doi.org/10.1155/2017/7276946.

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A thorough understanding of the morphology of the lamina of the second cervical vertebra (C2) is important for safe C2 translaminar screw placement. Although anatomical characteristics of the C2 lamina have been widely documented, individual differences in morphology have not been addressed. The aim of this study was to morphometrically analyze the cross-sectional shape of the C2 lamina and classify the shape to describe individual differences. Morphometric analysis was conducted on 145 three-dimensional C2 models based on computerized tomography images from Korean adult cadavers. Several parameters were measured on a cross-section image of the lamina model. Based on numerical criteria, all of the C2 lamina’s cross-sectional shapes could be categorized into three distinctive morphological types: pyriform, ellipse, and obpyriform shapes. We confirmed that most Koreans can accommodate C2 translaminar screw placement with a lower limit of the 95% confidence interval of thickness measured at 6.26 mm. Morphometric analysis suggested that the obpyriform-shaped lamina (4.48%) is likely to require screw trajectory adjustment to avoid cortical breakout of the screw. Our results will enhance current anatomical understanding of the C2 lamina and thus facilitate safer C2 translaminar screw placement.

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Vassiliev, Nikolay, Vasilii Duzhin, and Artem Kuzmin. "On the convergence of bumping routes to their limit shapes in the RSK algorithm: numerical experiments." Information and Control Systems, no. 6 (December 16, 2021): 2–9. http://dx.doi.org/10.31799/1684-8853-2021-6-2-9.

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Introduction: The Robinson — Schensted — Knuth (RSK) algorithm transforms a sequence of elements of a linearly ordered set into a pair of Young tableaux P, Q of the same shape. This transformation is based on the process of bumping and inserting elements in tableau P according to special rules. The trajectory formed by all the boxes of the tableau P shifted in the RSK algorithm is called the bumping route. D. Romik and P. Śniady in 2016 obtained an explicit formula for the limit shape of the bumping route, which is determined by its first element. However, the rate of convergence of the bumping routes to the limit shape has not been previously investigated either theoretically or by numerical experiments. Purpose: Carrying out computer experiments to study the dynamics of the bumping routes produced by the RSK algorithm on Young tableaux as their sizes increase. Calculation of statistical means and variances of deviations of bumping routes from their limit shapes in the L2 metric for various values fed to the input of the RSK algorithm. Results: A series of computer experiments have been carried out on Young tableaux, consisting of up to 10 million boxes. We used 300 tableaux of each size. Different input values (0.1, 0.3, 0.5, 0.7, 0.9) were added to each such tableau using the RSK algorithm, and the deviations of the bumping routes built from these values from the corresponding limit shapes were calculated. The graphs of the statistical mean values and variances of these deviations were produced. It is noticed that the deviations decrease in proportion to the fourth root of the tableau size n. An approximation of the dependence of the mean values of deviations on n was obtained using the least squares method.

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Jeswiet, J., David J. Young, and M. Ham. "Non-Traditional Forming Limit Diagrams for Incremental Forming." Advanced Materials Research 6-8 (May 2005): 409–16. http://dx.doi.org/10.4028/www.scientific.net/amr.6-8.409.

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Although not standard, Forming Limit Diagrams, FLD’s, are used throughout the automotive industry as a preliminary tool to determine if a sheet metal forming process is capable of forming a good part. FLD’s show a limited range of strains on the diagram; typically the range is 0 to 1 on the major strain axis. A new rapid prototyping process called Single Pont Incremental Forming, SPIF, experiences strains over 3. As FLD’s do not typically cover that level of strain, a new method for developing FLD’s is needed. Such a method is proposed in this paper. Research has been conducted with five different shapes, formed using Single Point Incremental Forming. The part shapes utilized contain the most common combinations of angles and curves observed in formed sheet metal products. The strains encountered in forming each of these parts are measured and the strain data is then plotted on the same FLD. These new FLD’s can then be utilized as a predictive tool for engineers to determine if their design can be produced using the SPIF process.

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Aggarwal, Amol. "Limit Shapes and Local Statistics for the Stochastic Six-Vertex Model." Communications in Mathematical Physics 376, no. 1 (December 2, 2019): 681–746. http://dx.doi.org/10.1007/s00220-019-03643-w.

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Parrish, W., and M. Hart. "Parallel Beam and Focusing X-ray Powder Diffractometry." Advances in X-ray Analysis 32 (1988): 481–88. http://dx.doi.org/10.1154/s0376030800020802.

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AbstractComparison of results using synchrotron radiation and X-ray tubes requires a knowledge of the fundamentally different profile shapes inherent in the methods. The varying asymmetric shapes and peak shifts in focusing geometry limit the accuracy and applications of the method and their origins are reviewed. Most o f the focusing aberrations such as specimen displacement, flat specimen and θ-2θ mis-setting do not occur in the parallel beam geometry. The X-ray optics used in synchrotron parallel beam methods produces narrow, symmetrical profiles which can be accurately fit with a pseudo-Voigt function, They have the same shape in the entire pattern. Only the width increases as tanθ due to wavelength dispersion but with higher resolution systems dispersion can be eliminated. The constant instrument function contribution to the experimental profile shape is an important advantage in studies involving profile shapes, e.g., small particle sizes and microstrains, and accurate integrated intensities. The absence of systematic errors leads to more precise lattice parameter determinations.

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