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A curve shortening flow rule for closed embedded plane curves with a prescribed rate of change in enclosed area. [PDF]
Proc Math Phys Eng Sci, 2016 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.
Dallaston MC, McCue SW.
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Curve shortening flow coupled to lateral diffusion [PDF]
Numerische Mathematik, 2016 We present and analyze a semi-discrete finite element scheme for a system consisting of a geometric evolution equation for a curve and a parabolic equation on the evolving curve. More precisely, curve shortening flow with a forcing term that depends on a field defined on the curve is coupled with a diffusion equation for that field. The scheme is based
Pozzi, Paola, Stinner, Björn
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The Curve Shortening Flow in the Metric-Affine Plane [PDF]
Mathematics, 2020 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”
Vladimir Rovenski
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An Adaptive Moving Mesh Method for Forced Curve Shortening Flow. [PDF]
SIAM J Sci Comput, 2019 We propose a novel adaptive moving mesh method for the numerical solution of a forced curve shortening geometric evolution equation. Control of the mesh quality is obtained using a tangential mesh velocity derived from a mesh equidistribution principle, where a positive adaptivity measure or monitor function is approximately equidistributed along the ...
Mackenzie JA +3 more
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Curve shortening–straightening flow for non-closed planar curves with infinite length
Journal of Differential Equations, 2014 We consider a motion of non-closed planar curves with infinite length. The motion is governed by a steepest descent flow for the geometric functional which consists of the sum of the length functional and the total squared curvature. We call the flow shortening-straightening flow.
NOVAGA, MATTEO, Shinya Okabe
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Preoperative echocardiography predictive analytics for postinduction hypotension prediction
PLoS ONE, 2022 Purpose Hypotension is a risk factor for adverse perioperative outcomes. Preoperative transthoracic echocardiography has been extended for preoperative risk assessment before noncardiac surgery.
Manabu Yoshimura +3 more
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Geosciences, 2021 Unravelling the burial-deformation history of sedimentary rocks is prerequisite information to understand the regional tectonic, sedimentary, thermal, and fluid-flow evolution of foreland basins.
Aurélie Labeur +7 more
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International Journal of Advanced Robotic Systems, 2021 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 ...
Marcel Huptych, Sascha Röck
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Convergence of curve shortening flow to translating soliton [PDF]
American Journal of Mathematics, 2021 28 pages, 0 ...
Choi, Beomjun +2 more
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Nonconvex ancient solutions to curve shortening flow
Transactions of the American Mathematical Society, 2023 We construct an ancient solution to planar curve shortening. The solution is at all times compact and embedded. For t ≪ 0 t\ll 0 it is approximated by the rotating Yin-Yang soliton, truncated at a finite angle α ( t ) = − t \alpha (t) = -t , and ...
Zhang, Y, Olson, C, Khan, I, Angenent, S
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