{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,6]],"date-time":"2024-09-06T08:02:45Z","timestamp":1725609765985},"publisher-location":"Basel","reference-count":41,"publisher":"Birkh\u00e4user Basel","isbn-type":[{"type":"print","value":"9783034899598"},{"type":"electronic","value":"9783034892445"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1996]]},"DOI":"10.1007\/978-3-0348-9244-5_2","type":"book-chapter","created":{"date-parts":[[2011,9,15]],"date-time":"2011-09-15T18:51:44Z","timestamp":1316112704000},"page":"7-18","source":"Crossref","is-referenced-by-count":3,"title":["The Crystalline Algorithm for Computing Motion by Curvature"],"prefix":"10.1007","author":[{"given":"Pedro Martins","family":"Gir\u00e3o","sequence":"first","affiliation":[]},{"given":"Robert V.","family":"Kohn","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"2_CR1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4310\/jdg\/1214457030","volume":"42","author":"F Almgren","year":"1995","unstructured":"F. Almgren and J.E. Taylor, Flat flow is motion by crystalline curvature for curves with crystalline energies, J. Diff. Geom. 42 (1995) 1\u201322.","journal-title":"J. Diff. Geom."},{"key":"2_CR2","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1137\/0331020","volume":"31","author":"F Almgren","year":"1993","unstructured":"F. Almgren, J.E. Taylor, and L. Wang, Curvature driven flows: a variational approach, SIAM J. Cont. Opt. 31 (1993) 387\u2013437.","journal-title":"SIAM J. Cont. Opt."},{"key":"2_CR3","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1016\/S0021-9991(83)71112-5","volume":"106","author":"R Almgren","year":"1993","unstructured":"R. Almgren, Variational Algorithms and pattern formation in dendritic solidification, J. Comp. Phys. 106 (1993) 337\u2013354.","journal-title":"J. Comp. Phys."},{"key":"2_CR4","doi-asserted-by":"publisher","first-page":"1511","DOI":"10.1137\/S0036139993259908","volume":"55","author":"R Almgren","year":"1995","unstructured":"R. Almgren, Crystalline Saffman-Taylor fingers, SIAM J. Appl. Math. 55 (1995) 1511\u20131535.","journal-title":"SIAM J. Appl. Math."},{"key":"2_CR5","doi-asserted-by":"publisher","first-page":"1937","DOI":"10.1080\/03605309508821158","volume":"20","author":"S Angenent","year":"1995","unstructured":"S. Angenent, D. Chopp, and T. Emanen, A computed example of nonuniqueness of mean curvature flow in \u211d3, Comm. Part. Diff. Eqns. 20 (1995) 1937\u20131958.","journal-title":"Comm. Part. Diff. Eqns."},{"key":"2_CR6","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1007\/BF01041068","volume":"108","author":"S Angenent","year":"1989","unstructured":"S. Angenent and M. Gurtin, Multiphase thermomechanics with interfacial structure 2. Evolution of an isothermal interface, Arch. Rat. Mech. Anal. 108 (1989) 323\u2013391.","journal-title":"Arch. Rat. Mech. Anal."},{"key":"2_CR7","unstructured":"S. Angenent, T. Emanen, and J.J.L. Velazquez, Nonuniqueness in geometric heat flows, in preparation."},{"key":"2_CR8","doi-asserted-by":"publisher","first-page":"484","DOI":"10.1137\/0732020","volume":"32","author":"G Barles","year":"1995","unstructured":"G. Barles and C. Georgelin, A simple proof of convergence for an approximation scheme for computing motion by mean curvature, SIAM J. Numer. Anal. 32 (1995) 484\u2013500.","journal-title":"SIAM J. Numer. Anal."},{"key":"2_CR9","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1137\/0331021","volume":"31","author":"G Barles","year":"1993","unstructured":"G. Barles, H.M. Soner, and P.E. Souganides, Front propagation and phase field theory, SIAM J. Cont. Opt. 31 (1993) 439\u2013469.","journal-title":"SIAM J. Cont. Opt."},{"key":"2_CR10","doi-asserted-by":"publisher","first-page":"1005","DOI":"10.1103\/PhysRevE.50.1005","volume":"50","author":"E Ben-Jacob","year":"1994","unstructured":"E. Ben-Jacob, R. Kupferman, and O. Schochet, Numerical study of a morphology diagram in the large undercooling limit using a phase field model, Phys. Rev. E 50 (1994) 1005ff.","journal-title":"Phys. Rev. E"},{"key":"2_CR11","doi-asserted-by":"publisher","first-page":"4309","DOI":"10.1016\/0956-7151(95)00134-H","volume":"43","author":"WC Carter","year":"1995","unstructured":"W.C. Carter, A.R. Roosen, J.W. Cahn and J.E. Taylor, Shape evolution by surface diffusion and surface attachment limited kinetics on completely faceted surfaces, Acta Metall, et Mater. 43 (1995) 4309\u20134324.","journal-title":"Acta Metall"},{"key":"2_CR12","doi-asserted-by":"crossref","first-page":"749","DOI":"10.4310\/jdg\/1214446564","volume":"33","author":"Y-G Chen","year":"1991","unstructured":"Y.-G. Chen, Y. Giga, and S. Goto, Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations, J. Diff. Geom. 33 (1991) 749\u2013786.","journal-title":"J. Diff. Geom."},{"key":"2_CR13","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1512\/iumj.1993.42.42024","volume":"42","author":"LC Evans","year":"1993","unstructured":"L.C. Evans, Convergence of an algorithm for mean curvature flow, Indiana Univ. Math. J. 42 (1993) 533\u2013557.","journal-title":"Indiana Univ. Math. J."},{"key":"2_CR14","doi-asserted-by":"publisher","first-page":"1097","DOI":"10.1002\/cpa.3160450903","volume":"45","author":"LC Evans","year":"1992","unstructured":"L.C. Evans, H.M. Soner, and P.E. Souganides, Phase transitions and generalized motion by mean curvature, Comm. Pure Appl. Math. 45 (1992) 1097\u20131123.","journal-title":"Comm. Pure Appl. Math."},{"key":"2_CR15","doi-asserted-by":"crossref","first-page":"635","DOI":"10.4310\/jdg\/1214446559","volume":"33","author":"LC Evans","year":"1991","unstructured":"L.C. Evans and J. Spruck, Motion of level sets by mean curvature, J. Diff. Geom. 33 (1991) 635\u2013681.","journal-title":"J. Diff. Geom."},{"key":"2_CR16","first-page":"47","volume-title":"Proc. First World Congress of Nonlinear Analysts","author":"T Fukui","year":"1995","unstructured":"T. Fukui and Y. Giga, Motion of a graph by nonsmooth weighted curvature, in Proc. First World Congress of Nonlinear Analysts, V. Lakshmikantham, ed., W. de Gruyter, 1995, Vol. I, 47\u201356."},{"key":"2_CR17","doi-asserted-by":"crossref","first-page":"69","DOI":"10.4310\/jdg\/1214439902","volume":"23","author":"M Gage","year":"1986","unstructured":"M. Gage and R.S. Hamilton, The heat equation shrinking convex plane curves, J. Diff. Geom. 23 (1986) 69\u201395.","journal-title":"J. Diff. Geom."},{"key":"2_CR18","doi-asserted-by":"publisher","first-page":"886","DOI":"10.1137\/0732041","volume":"32","author":"PM Gir\u00e3o","year":"1995","unstructured":"P.M. Gir\u00e3o, Convergence of a crystalline algorithm for the motion of a simple closed convex curve by weighted curvature, SIAM J. Numer. Anal. 32 (1995) 886\u2013899.","journal-title":"SIAM J. Numer. Anal."},{"key":"2_CR19","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/s002110050017","volume":"67","author":"PM Gir\u00e3o","year":"1994","unstructured":"P.M. Gir\u00e3o and R.V. Kohn, Convergence of a crystalline algorithm for the heat equation in one dimension and for the motion of a graph by weighted curvature, Numer. Math. 67 (1994) 41\u201370.","journal-title":"Numer. Math."},{"key":"2_CR20","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198536949.001.0001","volume-title":"Thermomechanics of Evolving Phase Boundaries","author":"M Gurtin","year":"1993","unstructured":"M. Gurtin, Thermomechanics of Evolving Phase Boundaries, Oxford Univ. Press (1993)."},{"key":"2_CR21","doi-asserted-by":"publisher","first-page":"312","DOI":"10.1006\/jcph.1994.1170","volume":"114","author":"TY Hou","year":"1994","unstructured":"T.Y. Hou, J.S. Lowengrub, and M.J. Shelley, Removing the stiffness from interfacial flows with surface tension, J. Comp. Phys. 114 (1994) 312\u2013338","journal-title":"J. Comp. Phys."},{"key":"2_CR22","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1080\/10586458.1994.10504577","volume":"3","author":"R Kobayashi","year":"1994","unstructured":"R. Kobayashi, A numerical approach to three-dimensional dendritic solidification, Experimental Math. 3 (1994) 59\u201381.","journal-title":"Experimental Math"},{"key":"2_CR23","doi-asserted-by":"publisher","first-page":"334","DOI":"10.1006\/jcph.1994.1105","volume":"112","author":"B Merriman","year":"1994","unstructured":"B. Merriman, J. Bence, and S. Osher, Motion of multiple junctions: a level set approach, J. Comp. Phys. 112 (1994) 334\u2013363.","journal-title":"J. Comp. Phys."},{"key":"2_CR24","doi-asserted-by":"publisher","first-page":"296","DOI":"10.1006\/jcph.1996.0025","volume":"123","author":"RH Nochetto","year":"1996","unstructured":"R.H. Nochetto, M. Paolini, and C. Verdi, A dynamic mesh algorithm for curvature dependent evolving interfaces, J. Comp. Phys. 123 (1996) 296\u2013310.","journal-title":"J. Comp. Phys."},{"key":"2_CR25","doi-asserted-by":"crossref","unstructured":"R.H. Nochetto and C. Verdi, Convergence past singularities for a fully discrete approximation of curvature driven interfaces, submitted to SIAM J. Numer. Anal.","DOI":"10.1137\/S0036142994269526"},{"key":"2_CR26","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1016\/0021-9991(88)90002-2","volume":"79","author":"S Osher","year":"1988","unstructured":"S. Osher and J. Sethian, Fronts propagating with curvature dependent speed, J. Comp. Phys. 79 (1988) 12\u201349.","journal-title":"J. Comp. Phys."},{"key":"2_CR27","doi-asserted-by":"publisher","first-page":"244","DOI":"10.1017\/S0334270000009152","volume":"35","author":"S Roberts","year":"1993","unstructured":"S. Roberts, A line element algorithm for curve flow problems in the plane, J. Austral. Math. Soc. Ser. B 35 (1993) 244\u2013261.","journal-title":"J. Austral. Math. Soc. Ser. B"},{"key":"2_CR28","unstructured":"A.R. Roosen, Crystalline curvature and flat flow in a diffusion field, preprint."},{"key":"2_CR29","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1557\/PROC-237-25","volume":"237","author":"AR Roosen","year":"1992","unstructured":"A.R. Roosen and J. Taylor, Simulation of crystal growth with faceted interfaces, in Mater. Res. Soc. Symposium Proceedings Vol. 237 (1992) 25\u201336.","journal-title":"in Mater. Res. Soc. Symposium Proceedings"},{"key":"2_CR30","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1006\/jcph.1994.1153","volume":"114","author":"AR Roosen","year":"1994","unstructured":"A.R. Roosen and J. Taylor, Modeling crystal growth in a diffusion field using fully faceted interfaces, J. Comp. Phys. 114 (1994) 113\u2013128.","journal-title":"J. Comp. Phys."},{"key":"2_CR31","doi-asserted-by":"crossref","first-page":"131","DOI":"10.4310\/jdg\/1214444092","volume":"31","author":"J Sethian","year":"1990","unstructured":"J. Sethian, A review of recent numerical algorithms for hypersurfaces moving with curvature-dependent speed, J. Diff. Geom. 31 (1990) 131\u2013161","journal-title":"J. Diff. Geom."},{"key":"2_CR32","unstructured":"H.M. Soner, Ginzburg-Landau equation and motion by mean curvature, I. Convergence; II. Arbitrary initial data, J. Geom. Anal., in press."},{"key":"2_CR33","first-page":"321","volume-title":"Differential Geometry, Pitman Monographs Surveys Pure Appl. Math. 52, Longman Scientific","author":"JE Taylor","year":"1991","unstructured":"J.E. Taylor, Constructions and conjectures in crystalline nondifferential geometry, in Differential Geometry, Pitman Monographs Surveys Pure Appl. Math. 52, Longman Scientific (1991) 321\u2013336."},{"key":"2_CR34","volume-title":"Computing Optimal Geometries","author":"JE Taylor","year":"1991","unstructured":"J.E. Taylor, Motion by crystalline curvature, in Computing Optimal Geometries, J.E. Taylor, ed., Selected Lectures in Mathematics, Amer. Math. Soc, Providence (1991) 63ff."},{"key":"2_CR35","doi-asserted-by":"publisher","first-page":"1475","DOI":"10.1016\/0956-7151(92)90091-R","volume":"40","author":"JE Taylor","year":"1992","unstructured":"J.E. Taylor, Mean curvature and weighted mean curvature, Acta Metall, et Mater. 40 (1992) 1475\u20131485.","journal-title":"Acta Metall"},{"key":"2_CR36","first-page":"417","volume-title":"Differential Geometry","author":"JE Taylor","year":"1993","unstructured":"J.E. Taylor, Motion of curves by crystalline curvature, including triple junctions and boundary points, in Differential Geometry, R. Greene and S.T. Yau, eds., Proc. Symp. Pure Math. Vol. 54, Amer. Math. Soc. (1993) 417\u2013438."},{"key":"2_CR37","doi-asserted-by":"publisher","first-page":"1443","DOI":"10.1016\/0956-7151(92)90090-2","volume":"40","author":"JE Taylor","year":"1992","unstructured":"J.E. Taylor, J. Cahn, and C. Handwerker, Geometric models of crystal growth, Acta Metall, et Mater. 40 (1992) 1443\u20131474.","journal-title":"Acta Metall"},{"issue":"5","key":"2_CR38","first-page":"596","volume":"31","author":"AR Umantsev","year":"1986","unstructured":"A.R. Umantsev, V.V. Vinogradov, and V.T. Borisov, Modeling the evolution of a dendritic structure, Sov. Phys. Crystallogr. 31 no. 5 (1986) 596\u2013599.","journal-title":"Sov. Phys. Crystallogr."},{"key":"2_CR39","doi-asserted-by":"crossref","unstructured":"N.J. Walkington, Algorithms for computing motion by mean curvature, SIAM J. Numer. Anal., in press.","DOI":"10.1137\/S0036142994262068"},{"key":"2_CR40","doi-asserted-by":"publisher","first-page":"7424","DOI":"10.1103\/PhysRevA.45.7424","volume":"45","author":"AA Wheeler","year":"1992","unstructured":"A.A. Wheeler, W.J. Boettinger, and G.B. McFadden, Phase field model for isothermal phase transitions in binary alloys, Phys. Rev. A 45 (1992), 7424\u20137439.","journal-title":"Phys. Rev. A"},{"key":"2_CR41","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1016\/0167-2789(93)90242-S","volume":"66","author":"AA Wheeler","year":"1993","unstructured":"A.A. Wheeler, B.T. Murray, and R.J. Schaefer, Computation of dendrites using a phase field model, Physica D 66 (1993) 243\u2013262.","journal-title":"Physica D"}],"container-title":["Variational Methods for Discontinuous Structures"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-0348-9244-5_2.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,11]],"date-time":"2024-04-11T17:40:30Z","timestamp":1712857230000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-0348-9244-5_2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996]]},"ISBN":["9783034899598","9783034892445"],"references-count":41,"URL":"https:\/\/doi.org\/10.1007\/978-3-0348-9244-5_2","relation":{},"subject":[],"published":{"date-parts":[[1996]]}}}