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Journal articles on the topic 'Curve shortening'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Gage, Michael E. "Curve shortening on surfaces." Annales scientifiques de l'École normale supérieure 23, no. 2 (1990): 229–56. http://dx.doi.org/10.24033/asens.1603.

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2

Meijer, Kenneth, Henk J. Grootenboer, Bart F. J. M. Koopman, and Peter A. Huijing. "Fully Isometric Length-Force Curves of Rat Muscle Differ from Those during and after Concentric Contractions." Journal of Applied Biomechanics 13, no. 2 (1997): 164–81. http://dx.doi.org/10.1123/jab.13.2.164.

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The effect of various shortening histories on postshortening isometric length-force characteristics of rat medial gastrocnemlus (GM) was studied. Active muscle force and muscle geometry were analyzed after isotonic as well as isokinetic shortening. Active shortening significantly changed GM length-force characteristics (i.e., maximal muscle force, optimum muscle length, and active slack length). Muscle geometry did not change, which indicates that the observed changes in length-force curves are related to intracellular processes. Length-force curves valid during shortening, derived from postsh

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3

Stadler, Peter. "Curve shortening by short rulers." ESAIM: Proceedings and Surveys 46 (November 2014): 217–32. http://dx.doi.org/10.1051/proc/201446018.

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4

Nakayama, Kazuaki, Harvey Segur, and Miki Wadati. "A discrete curve-shortening equation." Methods and Applications of Analysis 4, no. 2 (1997): 162–72. http://dx.doi.org/10.4310/maa.1997.v4.n2.a6.

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5

Dziuk, Gerhard. "Discrete Anisotropic Curve Shortening Flow." SIAM Journal on Numerical Analysis 36, no. 6 (1999): 1808–30. http://dx.doi.org/10.1137/s0036142998337533.

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6

Stadler, Peter. "Curve shortening by short rulers." Journal of Difference Equations and Applications 22, no. 1 (2015): 22–36. http://dx.doi.org/10.1080/10236198.2015.1073724.

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7

Rademacher, Christine, and Hans-Bert Rademacher. "Solitons of Discrete Curve Shortening." Results in Mathematics 71, no. 1-2 (2016): 455–82. http://dx.doi.org/10.1007/s00025-016-0572-5.

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8

Dittberner, Friederike. "Curve Flows with a Global Forcing Term." Journal of Geometric Analysis 31, no. 8 (2021): 8414–59. http://dx.doi.org/10.1007/s12220-020-00600-1.

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AbstractWe consider embedded, smooth curves in the plane which are either closed or asymptotic to two lines. We study their behaviour under curve shortening flow with a global forcing term. We prove an analogue to Huisken’s distance comparison principle for curve shortening flow for initial curves whose local total curvature does not lie below $$-\pi $$ - π and show that this condition is sharp. With that, we can exclude singularities in finite time for bounded forcing terms. For immortal flows of closed curves whose forcing terms provide non-vanishing enclosed area and bounded length, we show

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9

Stanton, Marietta P. "Shortening the Case Management Learning Curve." Professional Case Management 14, no. 6 (2009): 278–81. http://dx.doi.org/10.1097/ncm.0b013e3181c3d424.

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10

Ma, Li, and Dezhong Chen. "Curve shortening in a Riemannian manifold." Annali di Matematica Pura ed Applicata 186, no. 4 (2006): 663–84. http://dx.doi.org/10.1007/s10231-006-0025-y.

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11

Rovenski, Vladimir. "The Curve Shortening Flow in the Metric-Affine Plane." Mathematics 8, no. 5 (2020): 701. http://dx.doi.org/10.3390/math8050701.

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We investigated, for the first time, the curve shortening flow in the metric-affine plane and prove that under simple geometric condition (when the curvature of initial curve dominates the torsion term) it shrinks a closed convex curve to a “round point” in finite time. This generalizes the classical result by M. Gage and R.S. Hamilton about convex curves in a Euclidean plane.

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12

Dallaston, Michael C., and Scott W. McCue. "A curve shortening flow rule for closed embedded plane curves with a prescribed rate of change in enclosed area." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2185 (2016): 20150629. http://dx.doi.org/10.1098/rspa.2015.0629.

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Motivated by a problem from fluid mechanics, we consider a generalization of the standard curve shortening flow problem for a closed embedded plane curve such that the area enclosed by the curve is forced to decrease at a prescribed rate. Using formal asymptotic and numerical techniques, we derive possible extinction shapes as the curve contracts to a point, dependent on the rate of decreasing area; we find there is a wider class of extinction shapes than for standard curve shortening, for which initially simple closed curves are always asymptotically circular. We also provide numerical eviden

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13

Pozzi, Paola. "Anisotropic curve shortening flow in higher codimension." Mathematical Methods in the Applied Sciences 30, no. 11 (2007): 1243–81. http://dx.doi.org/10.1002/mma.836.

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14

Hsu, Yu-Wen. "Curve shortening flow and smooth projective planes." Communications in Analysis and Geometry 27, no. 6 (2019): 1281–324. http://dx.doi.org/10.4310/cag.2019.v27.n6.a4.

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15

Zhou, Hengyu. "Curve shortening flows in warped product manifolds." Proceedings of the American Mathematical Society 145, no. 10 (2017): 4503–16. http://dx.doi.org/10.1090/proc/13661.

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16

Edelen, Nick. "Noncollapsing of Curve-Shortening Flow in Surfaces." International Mathematics Research Notices 2015, no. 20 (2015): 10143–53. http://dx.doi.org/10.1093/imrn/rnu271.

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17

Rubinstein, Jacob, Peter Sternberg, and Joseph B. Keller. "Fast Reaction, Slow Diffusion, and Curve Shortening." SIAM Journal on Applied Mathematics 49, no. 1 (1989): 116–33. http://dx.doi.org/10.1137/0149007.

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18

Deckelnick, Klaus. "Weak solutions of the curve shortening flow." Calculus of Variations and Partial Differential Equations 5, no. 6 (1997): 489–510. http://dx.doi.org/10.1007/s005260050076.

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19

Pozzi, Paola, and Björn Stinner. "Curve shortening flow coupled to lateral diffusion." Numerische Mathematik 135, no. 4 (2016): 1171–205. http://dx.doi.org/10.1007/s00211-016-0828-8.

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20

Novaga, Matteo, and Shinya Okabe. "Curve shortening–straightening flow for non-closed planar curves with infinite length." Journal of Differential Equations 256, no. 3 (2014): 1093–132. http://dx.doi.org/10.1016/j.jde.2013.10.009.

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21

Angenent, S. B., and J. J. L. Vel�zquez. "Asymptotic shape of cusp singularities in curve shortening." Duke Mathematical Journal 77, no. 1 (1995): 71–110. http://dx.doi.org/10.1215/s0012-7094-95-07704-7.

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22

Halldorsson, Hoeskuldur P. "Self-similar solutions to the curve shortening flow." Transactions of the American Mathematical Society 364, no. 10 (2012): 5285–309. http://dx.doi.org/10.1090/s0002-9947-2012-05632-7.

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23

Eppstein, David, Sariel Har-Peled, and Gabriel Nivasch. "Grid Peeling and the Affine Curve-Shortening Flow." Experimental Mathematics 29, no. 3 (2018): 306–16. http://dx.doi.org/10.1080/10586458.2018.1466379.

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24

Abresch, U., and J. Langer. "The normalized curve shortening flow and homothetic solutions." Journal of Differential Geometry 23, no. 2 (1986): 175–96. http://dx.doi.org/10.4310/jdg/1214440025.

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25

Drugan, Gregory, Weiyong He, and Micah W. Warren. "Legendrian curve shortening flow in $\mathbb{R}^3$." Communications in Analysis and Geometry 26, no. 4 (2018): 759–85. http://dx.doi.org/10.4310/cag.2018.v26.n4.a4.

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26

Yang, Yun Yan, and Xiao Xiang Jiao. "Curve Shortening Flow in Arbitrary Dimensional Euclidian Space." Acta Mathematica Sinica, English Series 21, no. 4 (2004): 715–22. http://dx.doi.org/10.1007/s10114-004-0426-z.

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27

Chou, Kai-Seng, and Xiao-Liu Wang. "The curve shortening problem under Robin boundary condition." Nonlinear Differential Equations and Applications NoDEA 19, no. 2 (2011): 177–94. http://dx.doi.org/10.1007/s00030-011-0123-4.

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28

Choi, Beomjun, Kyeongsu Choi, and Panagiota Daskalopoulos. "Convergence of curve shortening flow to translating soliton." American Journal of Mathematics 143, no. 4 (2021): 1043–77. http://dx.doi.org/10.1353/ajm.2021.0027.

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29

Huang, R. L. "Blow-up rates for the general curve shortening flow." Journal of Mathematical Analysis and Applications 383, no. 2 (2011): 482–89. http://dx.doi.org/10.1016/j.jmaa.2011.05.039.

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30

Arous, Gérard Ben, Allen Tannenbaum, and Ofer Zeitouni. "Stochastic approximations to curve-shortening flows via particle systems." Journal of Differential Equations 195, no. 1 (2003): 119–42. http://dx.doi.org/10.1016/s0022-0396(03)00166-9.

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31

Hall-Findlay, Elizabeth J. "A Simplified Vertical Reduction Mammaplasty: Shortening the Learning Curve." Plastic and Reconstructive Surgery 104, no. 3 (1999): 748–59. http://dx.doi.org/10.1097/00006534-199909010-00020.

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32

Hall-Findlay, Elizabeth J. "A Simplified Vertical Reduction Mammaplasty: Shortening the Learning Curve." Plastic and Reconstructive Surgery 104, no. 3 (1999): 760–61. http://dx.doi.org/10.1097/00006534-199909010-00021.

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33

Hall-Findlay, Elizabeth J. "A Simplified Vertical Reduction Mammaplasty: Shortening the Learning Curve." Plastic and Reconstructive Surgery 104, no. 3 (1999): 762–63. http://dx.doi.org/10.1097/00006534-199909010-00022.

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34

Hall-Findlay, Elizabeth J. "A Simplified Vertical Reduction Mammaplasty: Shortening the Learning Curve." Plastic & Reconstructive Surgery 104, no. 3 (1999): 748–59. http://dx.doi.org/10.1097/00006534-199909030-00020.

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35

Hammond, Dennis C. "A Simplified Vertical Reduction Mammaplasty: Shortening the Learning Curve." Plastic & Reconstructive Surgery 104, no. 3 (1999): 760–61. http://dx.doi.org/10.1097/00006534-199909030-00021.

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36

Spear, Scott L. "A Simplified Vertical Reduction Mammaplasty: Shortening the Learning Curve." Plastic & Reconstructive Surgery 104, no. 3 (1999): 762–63. http://dx.doi.org/10.1097/00006534-199909030-00022.

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37

Norbury, John, and Li-Chin Yeh. "Inhomogeneous fast reaction, slow diffusion and weighted curve shortening." Nonlinearity 14, no. 4 (2001): 849–62. http://dx.doi.org/10.1088/0951-7715/14/4/312.

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38

Es-Sarhir, Abdelhadi, and Max-K. von Renesse. "Ergodicity of Stochastic Curve Shortening Flow in the Plane." SIAM Journal on Mathematical Analysis 44, no. 1 (2012): 224–44. http://dx.doi.org/10.1137/100798235.

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39

Angenent, Sigurd, and Qian You. "Ancient solutions to curve shortening with finite total curvature." Transactions of the American Mathematical Society 374, no. 2 (2020): 863–80. http://dx.doi.org/10.1090/tran/8186.

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40

Epstein, C. L., and M. I. Weinstein. "A stable manifold theorem for the curve shortening equation." Communications on Pure and Applied Mathematics 40, no. 1 (1987): 119–39. http://dx.doi.org/10.1002/cpa.3160400106.

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41

Yang, Yunlong, and Jianbo Fang. "An application of the curve shortening flow on surfaces." Archiv der Mathematik 114, no. 5 (2020): 595–600. http://dx.doi.org/10.1007/s00013-020-01444-5.

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42

Haußer, Frank, and Axel Voigt. "A numerical scheme for regularized anisotropic curve shortening flow." Applied Mathematics Letters 19, no. 8 (2006): 691–98. http://dx.doi.org/10.1016/j.aml.2005.05.011.

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43

Au, Thomas Kwok-Keung. "On the saddle point property of Abresch–Langer curves under the curve shortening flow." Communications in Analysis and Geometry 18, no. 1 (2010): 1–21. http://dx.doi.org/10.4310/cag.2010.v18.n1.a1.

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44

Holroyd, S. M., and C. L. Gibbs. "Is there a shortening-heat component in mammalian cardiac muscle contraction?" American Journal of Physiology-Heart and Circulatory Physiology 262, no. 1 (1992): H200—H208. http://dx.doi.org/10.1152/ajpheart.1992.262.1.h200.

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It has been suggested that there is a shortening-heat component that is an extra liberation of heat on shortening above that due to the external work, which contributes to the total energy expenditure of the beating heart. The presence of a shortening heat component was studied in isolated papillary muscles from the right ventricle of rabbits killed by cervical dislocation. At the onset of a contraction, muscles were shortened from various initial lengths through fixed distances at near maximum velocity before being allowed to develop force at the new length; the heat production accompanying s

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45

Huptych, Marcel, and Sascha Röck. "Real-time path planning in dynamic environments for unmanned aerial vehicles using the curve-shortening flow method." International Journal of Advanced Robotic Systems 18, no. 1 (2021): 172988142096868. http://dx.doi.org/10.1177/1729881420968687.

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This article proposes a new algorithm for real-time path planning in dynamic environments based on space-discretized curve-shortening flows. The so-called curve-shortening flow method shares working principles with the well-established elastic bands method and overcomes some of its drawbacks concerning numerical robustness and parameterability. This is achieved by efficiently applying semi-implicit time integration for evolving the path and secondly by developing a methodology for setting the algorithm’s parameters based on physical quantities. Different short- and long-term validation scenari

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46

Angenent, Sigurd. "Curve shortening and the topology of closed geodesics on surfaces." Annals of Mathematics 162, no. 3 (2005): 1187–241. http://dx.doi.org/10.4007/annals.2005.162.1187.

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47

Angenent, Sigurd. "On the formation of singularities in the curve shortening flow." Journal of Differential Geometry 33, no. 3 (1991): 601–33. http://dx.doi.org/10.4310/jdg/1214446558.

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48

Daskalopoulos, Panagiota, Richard Hamilton, and Natasa Sesum. "Classification of compact ancient solutions to the curve shortening flow." Journal of Differential Geometry 84, no. 3 (2010): 455–64. http://dx.doi.org/10.4310/jdg/1279114297.

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49

Chou, Kai-Seng, and Guan-Xin Li. "Optimal systems and invariant solutions for the curve shortening problem." Communications in Analysis and Geometry 10, no. 2 (2002): 241–74. http://dx.doi.org/10.4310/cag.2002.v10.n2.a1.

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50

Smith, Stephen L., Mireille E. Broucke, and Bruce A. Francis. "Curve Shortening and the Rendezvous Problem for Mobile Autonomous Robots." IEEE Transactions on Automatic Control 52, no. 6 (2007): 1154–59. http://dx.doi.org/10.1109/tac.2007.899024.

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