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Journal articles on the topic 'Evolving surfaces'

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Published: 8 June 2024

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1

Kovács, Balázs. "High-order evolving surface finite element method for parabolic problems on evolving surfaces." IMA Journal of Numerical Analysis 38, no. 1 (March 19, 2017): 430–59. http://dx.doi.org/10.1093/imanum/drx013.

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2

Bojsen-Hansen, Morten, Hao Li, and Chris Wojtan. "Tracking surfaces with evolving topology." ACM Transactions on Graphics 31, no. 4 (August 5, 2012): 1–10. http://dx.doi.org/10.1145/2185520.2185549.

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3

Dziuk, G., and C. M. Elliott. "Finite elements on evolving surfaces." IMA Journal of Numerical Analysis 27, no. 2 (April 1, 2007): 262–92. http://dx.doi.org/10.1093/imanum/drl023.

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4

Bruce, J. W., P. J. Giblin, and F. Tari. "Parabolic curves of evolving surfaces." International Journal of Computer Vision 17, no. 3 (March 1996): 291–306. http://dx.doi.org/10.1007/bf00128235.

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5

Chen, Sheng-Gwo, and Jyh-Yang Wu. "Discrete Conservation Laws on Evolving Surfaces." SIAM Journal on Scientific Computing 38, no. 3 (January 2016): A1725—A1742. http://dx.doi.org/10.1137/151003453.

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6

Plantinga, Simon, and Gert Vegter. "Computing contour generators of evolving implicit surfaces." ACM Transactions on Graphics 25, no. 4 (October 2006): 1243–80. http://dx.doi.org/10.1145/1183287.1183288.

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7

Gao, Laiyuan, and Yuntao Zhang. "Evolving convex surfaces to constant width ones." International Journal of Mathematics 28, no. 11 (October 2017): 1750082. http://dx.doi.org/10.1142/s0129167x17500823.

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Given an [Formula: see text]-dimensional convex surface [Formula: see text] in the Euclidean space [Formula: see text], this initial surface can be deformed into a convex surface with constant width by a new evolution model which preserves the convexity of the evolving surface, provided that the initial principal curvatures satisfy a [Formula: see text]-pinching condition. Some examples of the flow are also constructed via spherical harmonic expansion of the support function.

8

Lang, Lukas F., and Otmar Scherzer. "Optical flow on evolving sphere-like surfaces." Inverse Problems and Imaging 11, no. 2 (March 2017): 305–38. http://dx.doi.org/10.3934/ipi.2017015.

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9

Jiao, Xiangmin, Andrew Colombi, Xinlai Ni, and John Hart. "Anisotropic mesh adaptation for evolving triangulated surfaces." Engineering with Computers 26, no. 4 (December 9, 2009): 363–76. http://dx.doi.org/10.1007/s00366-009-0170-1.

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10

Wang, Chuan, and Hui Xia. "Numerical evidence of persisting surface roughness when deposition stops." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 1 (January 1, 2022): 013202. http://dx.doi.org/10.1088/1742-5468/ac4041.

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Abstract Do evolving surfaces become flat or not with time evolving when material deposition stops? As one qualitative exploration of this interesting issue, modified stochastic models for persisting roughness have been proposed by Schwartz and Edwards (2004 Phys. Rev. E 70 061602). In this work, we perform numerical simulations on the modified versions of Edwards–Wilkinson (EW) and Kardar–Parisi–Zhang (KPZ) systems when the angle of repose is introduced. Our results show that the evolving surface always presents persisting roughness during the flattening process, and sand dune-like morphology could gradually appear, even when the angle of repose is very small. Nontrivial scaling properties and differences of evolving surfaces between the modified EW and KPZ systems are also discussed.

11

Barreira, R., C. M. Elliott, and A. Madzvamuse. "The surface finite element method for pattern formation on evolving biological surfaces." Journal of Mathematical Biology 63, no. 6 (January 28, 2011): 1095–119. http://dx.doi.org/10.1007/s00285-011-0401-0.

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12

Lubich, Christian, and Dhia Mansour. "Variational discretization of wave equations on evolving surfaces." Mathematics of Computation 84, no. 292 (October 24, 2014): 513–42. http://dx.doi.org/10.1090/s0025-5718-2014-02882-2.

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13

Zipunova, Elizaveta Vyacheslavovna, Anton Valerievich Ivanov, and Evgeny Borisovich Savenkov. "Solution of Reynolds lubrication equation on evolving surfaces." Keldysh Institute Preprints, no. 13 (2020): 1–20. http://dx.doi.org/10.20948/prepr-2020-13.

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14

Gosálvez, M. A., Y. Xing, K. Sato, and R. M. Nieminen. "Atomistic methods for the simulation of evolving surfaces." Journal of Micromechanics and Microengineering 18, no. 5 (April 21, 2008): 055029. http://dx.doi.org/10.1088/0960-1317/18/5/055029.

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15

Kovács, Balázs. "Computing arbitrary Lagrangian Eulerian maps for evolving surfaces." Numerical Methods for Partial Differential Equations 35, no. 3 (December 17, 2018): 1093–112. http://dx.doi.org/10.1002/num.22340.

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16

Lübcke, Andrea, Zsuzsanna Pápa, and Matthias Schnürer. "Monitoring of Evolving Laser Induced Periodic Surface Structures." Applied Sciences 9, no. 17 (September 3, 2019): 3636. http://dx.doi.org/10.3390/app9173636.

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Laser induced periodic surface structures (LIPSS) are generated on titanium and silicon nitride surfaces by multiple femtosecond laser pulses. An optical imaging system is used to observe the backscattered light during the patterning process. A characteristic fringe pattern in the backscattered light is observed and evidences the surface modification. Experiments are complemented by finite difference time domain numerical simulations which clearly show that the periodic surface modulation leads to characteristic modulations in the coherently scattered light field. It is proposed that these characteristic fringe pattern can be used as a very fast and low-cost monitor of LIPSS formation formation during the manufacturing process.

17

Adil, Nazakat, Xufeng Xiao, and Xinlong Feng. "Numerical Study on an RBF-FD Tangent Plane Based Method for Convection–Diffusion Equations on Anisotropic Evolving Surfaces." Entropy 24, no. 7 (June 22, 2022): 857. http://dx.doi.org/10.3390/e24070857.

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In this paper, we present a fully Lagrangian method based on the radial basis function (RBF) finite difference (FD) method for solving convection–diffusion partial differential equations (PDEs) on evolving surfaces. Surface differential operators are discretized by the tangent plane approach using Gaussian RBFs augmented with two-dimensional (2D) polynomials. The main advantage of our method is the simplicity of calculating differentiation weights. Additionally, we couple the method with anisotropic RBFs (ARBFs) to obtain more accurate numerical solutions for the anisotropic growth of surfaces. In the ARBF interpolation, the Euclidean distance is replaced with a suitable metric that matches the anisotropic surface geometry. Therefore, it will lead to a good result on the aspects of stability and accuracy of the RBF-FD method for this type of problem. The performance of this method is shown for various convection–diffusion equations on evolving surfaces, which include the anisotropic growth of surfaces and growth coupled with the solutions of PDEs.

18

WATANABE, Yasunori, Shinichiro ISHIZAKI, and Yasuo NIIDA. "Lateral Instability of Overtopping Jets Evolving into Fingering Surfaces." Journal of Japan Society of Civil Engineers, Ser. B2 (Coastal Engineering) 66, no. 1 (2010): 76–80. http://dx.doi.org/10.2208/kaigan.66.76.

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19

Dees, Dennis W., and Charles W. Tobias. "Mass Transfer at Gas Evolving Surfaces: A Microscopic Study." Journal of The Electrochemical Society 134, no. 7 (July 1, 1987): 1702–13. http://dx.doi.org/10.1149/1.2100740.

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20

Carvalho, J. C. "Caries Process on Occlusal Surfaces: Evolving Evidence and Understanding." Caries Research 48, no. 4 (2014): 339–46. http://dx.doi.org/10.1159/000356307.

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21

Voigt, Axel. "Dynamics of evolving surfaces with small corner energy regularization." Nonlinear Analysis: Theory, Methods & Applications 63, no. 5-7 (November 2005): e1179-e1184. http://dx.doi.org/10.1016/j.na.2005.03.038.

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22

Diodati, P., and F. Marchesoni. "Time-evolving statistics of cavitation damage on metallic surfaces." Ultrasonics Sonochemistry 9, no. 6 (November 2002): 325–29. http://dx.doi.org/10.1016/s1350-4177(02)00084-6.

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23

Elliott, Charles M., and Vanessa Styles. "An ALE ESFEM for Solving PDEs on Evolving Surfaces." Milan Journal of Mathematics 80, no. 2 (November 11, 2012): 469–501. http://dx.doi.org/10.1007/s00032-012-0195-6.

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24

Hou, Yong, Junying Min, Nan Guo, Jianping Lin, John E. Carsley, Thomas B. Stoughton, Heinrich Traphöner, Till Clausmeyer, and A. Erman Tekkaya. "Investigation of evolving yield surfaces of dual-phase steels." Journal of Materials Processing Technology 287 (January 2021): 116314. http://dx.doi.org/10.1016/j.jmatprotec.2019.116314.

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25

Kim, Hyundong, Ana Yun, Sungha Yoon, Chaeyoung Lee, Jintae Park, and Junseok Kim. "Pattern formation in reaction–diffusion systems on evolving surfaces." Computers & Mathematics with Applications 80, no. 9 (November 2020): 2019–28. http://dx.doi.org/10.1016/j.camwa.2020.08.026.

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26

Bruce, J. W., P. J. Giblin, and F. Tari. "Ridges, crests and sub-parabolic lines of evolving surfaces." International Journal of Computer Vision 18, no. 3 (June 1996): 195–210. http://dx.doi.org/10.1007/bf00123141.

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27

Han, Dong, and Min Xia. "The three kinds of degree distributions and nash equilibrium on the limiting random network." Stochastics and Dynamics 20, no. 05 (December 30, 2019): 2050033. http://dx.doi.org/10.1142/s0219493720500331.

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A generalized dynamically evolving random network and a game model taking place on the evolving network are presented. We show that there exists a high-dimensional critical curved surface of the parameters related the probabilities of adding or removing vertices or edges such that the evolving network may exhibit three kinds of degree distributions as the time goes to infinity when the parameters belong to the super-critical, critical and sub-critical curved surfaces, respectively. Some sufficient conditions are given for the existence of a regular Nash equilibrium which depends on the three kinds of degree distributions in the game model on the limiting random network.

28

Tomek, Lukáš, and Karol Mikula. "Discrete duality finite volume method with tangential redistribution of points for surfaces evolving by mean curvature." ESAIM: Mathematical Modelling and Numerical Analysis 53, no. 6 (October 18, 2019): 1797–840. http://dx.doi.org/10.1051/m2an/2019040.

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We propose a new discrete duality finite volume method for solving mean curvature flow of surfaces in ℝ3. In the cotangent scheme, which is widely used discretization of Laplace–Beltrami operator, a two-dimensional surface is usually approximated by a triangular mesh. In the cotangent scheme the unknowns are the vertices of the triangulation. A finite volume around each vertex is constructed as a surface patch bounded by a piecewise linear curve with nodes in the midpoints of the neighbouring edges and a representative point of each adjacent triangle. The basic idea of our new approach is to include the representative points into the numerical scheme as supplementary unknowns and generalize discrete duality finite volume method from ℝ2 to 2D surfaces embedded in ℝ3. To improve the quality of the mesh we use an area-oriented tangential redistribution of the grid points. We derive the numerical scheme for both closed surfaces and surfaces with boundary, and present numerical experiments. Surface evolution models are applied to construction of minimal surfaces with given set of boundary curves.

29

Dziuk, Gerhard, and Charles M. Elliott. "Finite element methods for surface PDEs." Acta Numerica 22 (April 2, 2013): 289–396. http://dx.doi.org/10.1017/s0962492913000056.

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In this article we consider finite element methods for approximating the solution of partial differential equations on surfaces. We focus on surface finite elements on triangulated surfaces, implicit surface methods using level set descriptions of the surface, unfitted finite element methods and diffuse interface methods. In order to formulate the methods we present the necessary geometric analysis and, in the context of evolving surfaces, the necessary transport formulae. A wide variety of equations and applications are covered. Some ideas of the numerical analysis are presented along with illustrative numerical examples.

30

Tang, Bin, Ming Qiu Yao, Gang Tan, Prem Pal, Kazuo Sato, and Wei Su. "Smoothness Control of Wet Etched Si{100} Surfaces in TMAH+Triton." Key Engineering Materials 609-610 (April 2014): 536–41. http://dx.doi.org/10.4028/www.scientific.net/kem.609-610.536.

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The effect of galvanic interaction between the evolving facets of the etch front on the Si {100} surface smoothness during wet anisotropic etching in surfactant-added tetramethylammonium hydroxide (TMAH) is studied by etching different mask patterns. Triton X-100, with formula C14H22O(C2H4O)n, where n=9-10, is used as the surfactant. The different smoothness of wet etched Si {100} surfaces, evaluated by atomic force microscope (AFM) and optical microscope, indicates that the wet etched Si {100} surfaces could become extremely smooth after the onset of the electrochemical etching contribution. A model to account for the galvanic interaction between the evolving facets is proposed, demonstrating that the chemical etching can be significantly surpassed by the electrochemical etching when the relative area of the exposed {100} surfaces are relatively small in comparison to that of the developed {111} sidewalls. Additionally, silicon beams with smooth surfaces are presented in the fabrication of a sandwich micro accelerometer to avoid the risk of device invalidation. This study is useful for engineering applications where the fabrication of microstructures for high quality devices should contain smooth surfaces.

31

Beschle, Cedric Aaron, and Balázs Kovács. "Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces." Numerische Mathematik 151, no. 1 (April 5, 2022): 1–48. http://dx.doi.org/10.1007/s00211-022-01280-5.

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AbstractIn this paper, we consider a non-linear fourth-order evolution equation of Cahn–Hilliard-type on evolving surfaces with prescribed velocity, where the non-linear terms are only assumed to have locally Lipschitz derivatives. High-order evolving surface finite elements are used to discretise the weak equation system in space, and a modified matrix–vector formulation for the semi-discrete problem is derived. The anti-symmetric structure of the equation system is preserved by the spatial discretisation. A new stability proof, based on this structure, combined with consistency bounds proves optimal-order and uniform-in-time error estimates. The paper is concluded by a variety of numerical experiments.

32

CAETANO, D., and C. M. ELLIOTT. "Cahn–Hilliard equations on an evolving surface." European Journal of Applied Mathematics 32, no. 5 (June 16, 2021): 937–1000. http://dx.doi.org/10.1017/s0956792521000176.

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We describe a functional framework suitable to the analysis of the Cahn–Hilliard equation on an evolving surface whose evolution is assumed to be given a priori. The model is derived from balance laws for an order parameter with an associated Cahn–Hilliard energy functional and we establish well-posedness for general regular potentials, satisfying some prescribed growth conditions, and for two singular non-linearities – the thermodynamically relevant logarithmic potential and a double-obstacle potential. We identify, for the singular potentials, necessary conditions on the initial data and the evolution of the surfaces for global-in-time existence of solutions, which arise from the fact that integrals of solutions are preserved over time, and prove well-posedness for initial data on a suitable set of admissible initial conditions. We then briefly describe an alternative derivation leading to a model that instead preserves a weighted integral of the solution and explain how our arguments can be adapted in order to obtain global-in-time existence without restrictions on the initial conditions. Some illustrative examples and further research directions are given in the final sections.

33

Alphonse, Amal, and Charles M. Elliott. "A Stefan problem on an evolving surface." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 373, no. 2050 (September 13, 2015): 20140279. http://dx.doi.org/10.1098/rsta.2014.0279.

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We formulate a Stefan problem on an evolving hypersurface and study the well posedness of weak solutions given L 1 data. To do this, we first develop function spaces and results to handle equations on evolving surfaces in order to give a natural treatment of the problem. Then, we consider the existence of solutions for data; this is done by regularization of the nonlinearity. The regularized problem is solved by a fixed point theorem and then uniform estimates are obtained in order to pass to the limit. By using a duality method, we show continuous dependence, which allows us to extend the results to L 1 data.

34

Olshanskii, Maxim A., and Xianmin Xu. "A Trace Finite Element Method for PDEs on Evolving Surfaces." SIAM Journal on Scientific Computing 39, no. 4 (January 2017): A1301—A1319. http://dx.doi.org/10.1137/16m1099388.

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35

Lenz, Martin, Simplice Firmin Nemadjieu, and Martin Rumpf. "A Convergent Finite Volume Scheme for Diffusion on Evolving Surfaces." SIAM Journal on Numerical Analysis 49, no. 1 (January 2011): 15–37. http://dx.doi.org/10.1137/090776767.

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36

Suchde, Pratik, and Jörg Kuhnert. "A fully Lagrangian meshfree framework for PDEs on evolving surfaces." Journal of Computational Physics 395 (October 2019): 38–59. http://dx.doi.org/10.1016/j.jcp.2019.06.031.

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37

Chen, Meng, and Leevan Ling. "Kernel-based collocation methods for heat transport on evolving surfaces." Journal of Computational Physics 405 (March 2020): 109166. http://dx.doi.org/10.1016/j.jcp.2019.109166.

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38

Kirisits, Clemens, Lukas F. Lang, and Otmar Scherzer. "Optical Flow on Evolving Surfaces with Space and Time Regularisation." Journal of Mathematical Imaging and Vision 52, no. 1 (June 25, 2014): 55–70. http://dx.doi.org/10.1007/s10851-014-0513-4.

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39

Gang, Zhou, Dan Knopf, and Israel Sigal. "Neckpinch Dynamics for Asymmetric Surfaces Evolving by Mean Curvature Flow." Memoirs of the American Mathematical Society 253, no. 1210 (May 2018): 0. http://dx.doi.org/10.1090/memo/1210.

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40

Tuncer, Necibe, and Anotida Madzvamuse. "Projected Finite Elements for Systems of Reaction-Diffusion Equations on Closed Evolving Spheroidal Surfaces." Communications in Computational Physics 21, no. 3 (February 7, 2017): 718–47. http://dx.doi.org/10.4208/cicp.oa-2016-0029.

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AbstractThe focus of this article is to present the projected finite element method for solving systems of reaction-diffusion equations on evolving closed spheroidal surfaces with applications to pattern formation. The advantages of the projected finite element method are that it is easy to implement and that it provides a conforming finite element discretization which is “logically” rectangular. Furthermore, the surface is not approximated but described exactly through the projection. The surface evolution law is incorporated into the projection operator resulting in a time-dependent operator. The time-dependent projection operator is composed of the radial projection with a Lipschitz continuous mapping. The projection operator is used to generate the surface mesh whose connectivity remains constant during the evolution of the surface. To illustrate the methodology several numerical experiments are exhibited for different surface evolution laws such as uniform isotropic (linear, logistic and exponential), anisotropic, and concentration-driven. This numerical methodology allows us to study new reaction-kinetics that only give rise to patterning in the presence of surface evolution such as theactivator-activatorandshort-range inhibition; long-range activation.

41

Zhang, Jingxuan. "Adiabatic theory for the area-constrained Willmore flow." Journal of Mathematical Physics 63, no. 4 (April 1, 2022): 041503. http://dx.doi.org/10.1063/5.0076701.

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In this paper, we develop an adiabatic theory for the evolution of large closed surfaces under the area-constrained Willmore (ACW) flow in a three-dimensional asymptotically Schwarzschild manifold. We explicitly construct a map, defined on a certain four-dimensional manifold of barycenters, which characterizes key static and dynamical properties of the ACW flow. In particular, using this map, we find an explicit four-dimensional effective dynamics of barycenters, which serves as a uniform asymptotic approximation for the (infinite-dimensional) ACW flow, so long as the initial surface satisfies certain mild geometric constraints (which determine the validity interval). Conversely, given any prescribed flow of barycenters evolving according to this effective dynamics, we construct a family of surfaces evolving by the ACW flow, whose barycenters are uniformly close to the prescribed ones on a large time interval (whose size depends on the geometric constraints of initial configurations).

42

Qi†, Xingying, Yuli Shang, and Lei Sui. "State of Osseointegrated Titanium Implant Surfaces in Topographical Aspect." Journal of Nanoscience and Nanotechnology 18, no. 12 (December 1, 2018): 8016–28. http://dx.doi.org/10.1166/jnn.2018.16381.

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Titanium is a primary metallic biomaterial widely used in dental implants because of its favorable mechanical properties and osseointegration capability. Currently, increasing interests have been taken in the interaction between titanium implant surface and surrounding bone tissue, particularly in surface topographical aspect. There are currently several techniques developed to modify surface topographies in the world market of dental implant. In this review, state of titanium implant surfaces in topographical aspect is presented from relatively smooth surfaces to rougher ones with microtopographies and/or nanotopographies. Each surface is summarized with basic elaborations, preparation methods, mechanisms for cellular responses and current availabilities. It has been demonstrated that rough surfaces evolving from micro- to nano-scale, especially hierarchical micro-and nanotopographies, are favorable for faster and stronger osseointegration. Further experimental and clinical investigations will aid in the optimization of surface topography and clinical selection of suitable implants.

43

Hayslip, A. R., J. T. Johnson, and G. R. Baker. "Further numerical studies of backscattering from time-evolving nonlinear sea surfaces." IEEE Transactions on Geoscience and Remote Sensing 41, no. 10 (October 2003): 2287–93. http://dx.doi.org/10.1109/tgrs.2003.814662.

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44

Dziuk, G., C. Lubich, and D. Mansour. "Runge-Kutta time discretization of parabolic differential equations on evolving surfaces." IMA Journal of Numerical Analysis 32, no. 2 (August 4, 2011): 394–416. http://dx.doi.org/10.1093/imanum/drr017.

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45

Lubich, C., D. Mansour, and C. Venkataraman. "Backward difference time discretization of parabolic differential equations on evolving surfaces." IMA Journal of Numerical Analysis 33, no. 4 (March 28, 2013): 1365–85. http://dx.doi.org/10.1093/imanum/drs044.

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46

Dziuk, G., and C. M. Elliott. "An Eulerian approach to transport and diffusion on evolving implicit surfaces." Computing and Visualization in Science 13, no. 1 (July 24, 2008): 17–28. http://dx.doi.org/10.1007/s00791-008-0122-0.

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47

Mansour, Dhia. "Gauss–Runge–Kutta time discretization of wave equations on evolving surfaces." Numerische Mathematik 129, no. 1 (May 9, 2014): 21–53. http://dx.doi.org/10.1007/s00211-014-0632-2.

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48

Myers, Jason C., and R. Lee Penn. "Evolving Surface Reactivity of Cobalt Oxyhydroxide Nanoparticles." Journal of Physical Chemistry C 111, no. 28 (July 2007): 10597–602. http://dx.doi.org/10.1021/jp071468s.

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49

Tuğ, Gül, Zehra Özdemi̇r, Selçuk Han Aydin, and Fai̇k Nejat Ekmekci̇. "Accretive growth kinematics in Minkowski 3-space." International Journal of Geometric Methods in Modern Physics 14, no. 05 (April 13, 2017): 1750069. http://dx.doi.org/10.1142/s0219887817500694.

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In this study, a model of accretive growth for arbitrary surfaces in three-dimensional Minkowski space is formulated by evolving a curve. An analytical approach to surfaces is also given in terms of a few parameters which are effective in the accretive growth of surfaces. The proposed method is visualized on some test surfaces and displayed in terms of figures.

50

Kovács, Balázs, Buyang Li, and Christian Lubich. "A convergent evolving finite element algorithm for Willmore flow of closed surfaces." Numerische Mathematik 149, no. 3 (November 2021): 595–643. http://dx.doi.org/10.1007/s00211-021-01238-z.

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