Journal articles: 'Mullins-Sekerka'

1

Rigos, A. A., and J. M. Deutch. "Concentration effects on the Mullins–Sekerka instability." Journal of Chemical Physics 86, no. 12 (June 15, 1987): 7119–25. http://dx.doi.org/10.1063/1.452361.

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2

Fehribach, Joseph D. "Mullins–Sekerka stability analysis for melting-freezing waves in helium." European Journal of Applied Mathematics 5, no. 1 (March 1994): 21–37. http://dx.doi.org/10.1017/s0956792500001273.

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This paper considers the stability of melt-solid interfaces to eigenfunction perturbations for a system of equations which describe the melting and freezing of helium. The analysis is carried out in both planar and spherical geometries. The principal results are that when the melt is freezing, under certain far-field conditions, the interface is stable in the sense of Mullins and Sekerka. On the other hand, when the solid is melting (at least when the melting is sufficiently fast), the interface is unstable. In some circumstances these instabilities are oscillatory, with amplitude and growth rate increasing with surface tension and frequency. The last section considers the original problem of Mullins and Sekerka in the present notation.

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3

Antonopoulou, Dimitra, Ĺubomír Baňas, Robert Nürnberg, and Andreas Prohl. "Numerical approximation of the stochastic Cahn–Hilliard equation near the sharp interface limit." Numerische Mathematik 147, no. 3 (February 17, 2021): 505–51. http://dx.doi.org/10.1007/s00211-021-01179-7.

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AbstractWe consider the stochastic Cahn–Hilliard equation with additive noise term $$\varepsilon ^\gamma g\, {\dot{W}}$$ ε γ g W ˙ ($$\gamma >0$$ γ > 0 ) that scales with the interfacial width parameter $$\varepsilon $$ ε . We verify strong error estimates for a gradient flow structure-inheriting time-implicit discretization, where $$\varepsilon ^{-1}$$ ε - 1 only enters polynomially; the proof is based on higher-moment estimates for iterates, and a (discrete) spectral estimate for its deterministic counterpart. For $$\gamma $$ γ sufficiently large, convergence in probability of iterates towards the deterministic Hele–Shaw/Mullins–Sekerka problem in the sharp-interface limit $$\varepsilon \rightarrow 0$$ ε → 0 is shown. These convergence results are partly generalized to a fully discrete finite element based discretization. We complement the theoretical results by computational studies to provide practical evidence concerning the effect of noise (depending on its ’strength’ $$\gamma $$ γ ) on the geometric evolution in the sharp-interface limit. For this purpose we compare the simulations with those from a fully discrete finite element numerical scheme for the (stochastic) Mullins–Sekerka problem. The computational results indicate that the limit for $$\gamma \ge 1$$ γ ≥ 1 is the deterministic problem, and for $$\gamma =0$$ γ = 0 we obtain agreement with a (new) stochastic version of the Mullins–Sekerka problem.

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Chung, C. A., W. Z. Chien, and Y. H. Hsieh. "Morphological Instabilities in Time Periodic Crystallization." Journal of Mechanics 23, no. 4 (December 2007): 295–302. http://dx.doi.org/10.1017/s1727719100001349.

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AbstractA linear stability analysis is performed on the interface that forms during directional solidification of a dilute binary alloy in the presence of time-periodic growth rates. The basic state, in which the flat crystal-melt interface advances at a steady rate with an oscillation superimposed, is solved analytically by expanding the governing equations in terms of the assumed-small amplitude of modulation. We find that there is a frequency window of stabilization, in which the Mullins-Sekerka instability can be stabilized synchronously. Outside of the window, large input frequencies may destabilize the Mullins-Sekerka mode. The subharmonic mode, which occurs with small wave numbers, is stabilized with increasing the frequency. As for the modulation amplitude, larger amplitude tends to reduce the synchronous mode while enhance the subharmonic mode.

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5

Ma, Feiyao, and Lihe Wang. "Schauder type estimates of linearized Mullins-Sekerka problem." Communications on Pure & Applied Analysis 11, no. 3 (2012): 1037–50. http://dx.doi.org/10.3934/cpaa.2012.11.1037.

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6

Novick-Cohen, A. "A Stefan/Mullins-Sekerka Type Problem with Memory." Journal of Integral Equations and Applications 9, no. 2 (June 1997): 113–41. http://dx.doi.org/10.1216/jiea/1181076000.

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7

Dai, Shibin, Barbara Niethammer, and Robert L. Pego. "Crossover in coarsening rates for the monopole approximation of the Mullins–Sekerka model with kinetic drag." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 140, no. 3 (May 21, 2010): 553–71. http://dx.doi.org/10.1017/s030821050900033x.

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The Mullins–Sekerka sharp-interface model for phase transitions interpolates between attachment-limited and diffusion-limited kinetics if kinetic drag is included in the Gibbs–Thomson interface condition. Heuristics suggest that the typical length-scale of patterns may exhibit a crossover in coarsening rate from l(t) ˜ t1/2 at short times to l(t) ˜ t1/3 at long times. We establish rigorous, universal one-sided bounds on energy decay that partially justify this understanding in the monopole approximation and in the associated Lifshitz–Slyozov–Wagner mean-field model. Numerical simulations for the Lifshitz–Slyozov–Wagner model illustrate the crossover behaviour. The proofs are based on a method for estimating coarsening rates introduced by Kohn and Otto, and make use of a gradient-flow structure that the monopole approximation inherits from the Mullins–Sekerka model by restricting particle geometry to spheres.

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8

Escher, Joachim, and Gieri Simonett. "A Center Manifold Analysis for the Mullins–Sekerka Model." Journal of Differential Equations 143, no. 2 (March 1998): 267–92. http://dx.doi.org/10.1006/jdeq.1997.3373.

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9

Röger, Matthias. "Existence of Weak Solutions for the Mullins--Sekerka Flow." SIAM Journal on Mathematical Analysis 37, no. 1 (January 2005): 291–301. http://dx.doi.org/10.1137/s0036141004439647.

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10

Su, J. "Axisymmetric three-dimensional finger solutions in Mullins-Sekerka equation." IMA Journal of Applied Mathematics 69, no. 4 (August 1, 2004): 421–35. http://dx.doi.org/10.1093/imamat/69.4.421.

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11

Chugreeva, Olga, Felix Otto, and Maria Westdickenberg. "Relaxation to a planar interface in the Mullins–Sekerka problem." Interfaces and Free Boundaries 21, no. 1 (May 9, 2019): 21–40. http://dx.doi.org/10.4171/ifb/415.

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12

Karali, Georgia D., and Panayotis G. Kevrekidis. "Bubble interactions for the Mullins–Sekerka problem: Some case examples." Mathematics and Computers in Simulation 80, no. 4 (December 2009): 707–20. http://dx.doi.org/10.1016/j.matcom.2009.08.023.

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13

Zhang, Lei, and Suresh V. Garimella. "A modified Mullins–Sekerka stability analysis including surface energy effects." Journal of Applied Physics 74, no. 4 (August 15, 1993): 2494–500. http://dx.doi.org/10.1063/1.354688.

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14

Milic, Natasa. "On the Mullins-Sekerka model for phase transitions in mixtures." Quarterly of Applied Mathematics 49, no. 3 (January 1, 1991): 437–45. http://dx.doi.org/10.1090/qam/1121676.

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15

Misbah, C. "The Mullins-Sekerka instability in directional solidification of quasi-azeotropes." Journal de Physique 47, no. 6 (1986): 1077–90. http://dx.doi.org/10.1051/jphys:019860047060107700.

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16

Zhu, Jingyi, Xinfu Chen, and Thomas Y. Hou. "An Efficient Boundary Integral Method for the Mullins–Sekerka Problem." Journal of Computational Physics 127, no. 2 (September 1996): 246–67. http://dx.doi.org/10.1006/jcph.1996.0173.

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17

Caroli, B., C. Caroli, and B. Roulet. "The Mullins-Sekerka instability in directional solidification of thin samples." Journal of Crystal Growth 76, no. 1 (July 1986): 31–49. http://dx.doi.org/10.1016/0022-0248(86)90006-0.

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18

Alikakos, Nicholas D., Peter W. Bates, Xinfu Chen, and Giorgio Fusco. "Mullins-Sekerka motion of small droplets on a fixed boundary." Journal of Geometric Analysis 10, no. 4 (December 2000): 575–96. http://dx.doi.org/10.1007/bf02921987.

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19

LOUIS, E., O. PLA, L. M. SANDER, and F. GUINEA. "VARIATIONS ON THE THEME OF DIFFUSION-LIMITED GROWTH." Modern Physics Letters B 08, no. 28 (December 10, 1994): 1739–58. http://dx.doi.org/10.1142/s0217984994001667.

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The instabilities arising in various growth systems based on diffussion-limited aggregation are discussed. It is shown that a linear analysis à la Mullins-Sekerka is useful as it gives a hint on the complexity of the patterns to be generated in the nonlinear regime. As the only general analytical technique which can be applied to all of them, it can provide simple classification schemes.

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20

NIETHAMMER, B., and J. J. L. VELÁZQUEZ. "HOMOGENIZATION IN COARSENING SYSTEMS II: STOCHASTIC CASE." Mathematical Models and Methods in Applied Sciences 14, no. 09 (September 2004): 1401–24. http://dx.doi.org/10.1142/s0218202504003660.

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In the earlier paper (Part I) we study the homogenization of the Mullins–Sekerka problem for deterministic particle distributions in the case that the effective range of particle interactions is smaller than the system size. Here we extend those results to the case of stochastic particle distributions. The main difficulty is that in this case particles collide with positive probability. We show, however, that colliding particles are few and do not influence the macroscopic behavior.

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21

Yi, Fahuai, Youshan Tao, and Zuhan Liu. "Quasi-stationary Stefan problem as limit case of Mullins-Sekerka problem." Science in China Series A: Mathematics 40, no. 2 (February 1997): 151–62. http://dx.doi.org/10.1007/bf02874434.

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22

Tokuda, Yuichiro, Jun Kojima, Kazukuni Hara, Hidekazu Tsuchida, and Shoichi Onda. "4H-SiC Bulk Growth Using High-Temperature Gas Source Method." Materials Science Forum 778-780 (February 2014): 51–54. http://dx.doi.org/10.4028/www.scientific.net/msf.778-780.51.

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Our latest results of SiC bulk growth by High-Temperature Gas Source Method are given in this paper. Based on Mullins-Sekerka instability, optimal growth conditions to preclude dendrite crystals, which are one of the pending issues for high-speed bulk growth, was studied. First, the simulation studies showed that high temperature gradient in a growing crystal is required for high-speed bulk growth without dendrite crystals. Second, high-speed bulk growth was demonstrated under high temperature gradient.

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23

NIETHAMMER, B., and J. J. L. VELÁZQUEZ. "HOMOGENIZATION IN COARSENING SYSTEMS I: DETERMINISTIC CASE." Mathematical Models and Methods in Applied Sciences 14, no. 08 (August 2004): 1211–33. http://dx.doi.org/10.1142/s021820250400360x.

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We study the homogenization limit of the Mullins–Sekerka problem which serves as a model for late-stage coarsening in a phase transformation. We consider the case that the screening length which describes the effective range of particle interactions is much smaller than the system size, which leads to homogenization problems in unbounded domains. The present paper deals with deterministic initial particle distributions which are in an average sense homogeneously distributed. Stochastic particle distributions will be considered in a second paper (Part II).

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24

MANZI, GUIDO, and ROSSANA MARRA. "A KINETIC MODEL OF INTERFACE MOTION." International Journal of Modern Physics B 18, no. 04n05 (February 20, 2004): 715–24. http://dx.doi.org/10.1142/s0217979204024331.

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We study a kinetic model for a system of two species of particles interacting via a repulsive long range potential and with a reservoir at fixed temperature. The interaction between the particles is modeled by a Vlasov term and the thermal bath by a Fokker–Planck term. We show that in the diffusive and sharp interface limit the motion of the interfaces at low temperature is described by a Stefan problem or a Mullins–Sekerka motion, depending on the time scale.

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25

Garroni, Adriana, and Barbara Niethammer. "Correctors and error estimates in the homogenization of a Mullins–Sekerka problem." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 19, no. 4 (2002): 371–93. http://dx.doi.org/10.1016/s0294-1449(01)00085-3.

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26

Xinfu, Chen, Hong Jiaxin, and Yi Fahuai. "Existance uniqueness and regularity of classical solutions of the mullins—sekerka problem." Communications in Partial Differential Equations 21, no. 11-12 (January 1996): 1705–27. http://dx.doi.org/10.1080/03605309608821243.

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27

Laxmanan, V. "Analysis of stability of a planar solid-liquid interface in a dilute binary alloy." Journal of Materials Research 5, no. 1 (January 1990): 223–28. http://dx.doi.org/10.1557/jmr.1990.0223.

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The question of stability of a planar solid-liquid interface in undercooled pure and alloy melts has been reconsidered without the restrictive assumption of no heat flow in the solid made in earlier works. The modified analysis indicates that provided the thermal gradient on the solid side of the interface, Gs, is positive, stability can be achieved in an undercooled alloy melt for growth rates R>Ra, whereas a recent analysis by Trivedi and Kurz, which assumes Gs = 0, suggests that stability is possible only if R>Ra + Rat. Here Ra is the familiar absolute stability limit of Mullins and Sekerka and Rat, is the absolute stability limit in an undercooled pure melt, as identified by Trivedi and Kurz. The absolute stability criterion for steady-state planar growth in an undercooled alloy melt is thus the same as derived earlier by Mullins and Sekerka for directional solidification. Relaxing the restrictive assumption of Gs = 0 also reveals that there is a regime of stability for low growth rates and low supercoolings. Stability is possible under these conditions if Gs>0, and the bath undercooling ΔTb < ΔTO + ΔTh/2, where ΔTO is the freezing range of the alloy and ΔTh is the hypercooling limit for the pure melt. For large supercoolings, Gs < 0, and the interface will be unstable with respect to large wavelength perturbations, even if R > Ra + Rat.

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28

Acerbi, E., N. Fusco, V. Julin, and M. Morini. "Nonlinear stability results for the modified Mullins–Sekerka and the surface diffusion flow." Journal of Differential Geometry 113, no. 1 (September 2019): 1–53. http://dx.doi.org/10.4310/jdg/1567216953.

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29

GLASNER, KARL. "Rapid growth and critical behaviour in phase field models of solidification." European Journal of Applied Mathematics 12, no. 1 (February 2001): 39–56. http://dx.doi.org/10.1017/s0956792501004351.

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Rapid solidification fronts are studied using a phase field model. Unlike slow moving solutions which approximate the Mullins–Sekerka free boundary problem, different limiting behaviour is obtained for rapidly moving fronts. A time-dependent analysis is carried out for various cases and the leading order behaviour of solidification front solutions is derived to be one of several travelling wave problems. An analysis of these problems is conducted, leading to expressions for front speeds in certain limits. The dynamics leading to these travelling wave solutions is derived, and conclusions about stability are drawn. Finally, a discussion is made of the relationship to other solidification models.

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30

Merchant, G. J., and S. H. Davis. "Kinetic Effects in Directional Solidification." Applied Mechanics Reviews 43, no. 5S (May 1, 1990): S76—S78. http://dx.doi.org/10.1115/1.3120855.

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Mullins and Sekerka showed for fixed temperature gradient that the planar interface is linearly stable for all pulling speeds V above some critical value, the absolute stability limit. Near this limit, where solidification rates are rapid, the assumption of local equilibrium at the interface may be violated. We incorporate nonequilibrium effects into a linear stability analysis of the planar front by allowing the segregation coefficient and interface temperature to depend on V in a thermodynamically-consistent way. In addition to the steady cellular mode, we find a new branch of long-wavelength time-periodic states. Under certain conditions there exists a stability window separating the steady and oscillatory branches.

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31

ESCHER, Joachim, and Yasumasa NISHIURA. "Smooth unique solutions for a modified Mullins-Sekerka model arising in diblock copolymer melts." Hokkaido Mathematical Journal 31, no. 1 (February 2002): 137–49. http://dx.doi.org/10.14492/hokmj/1350911774.

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32

Stoth, Barbara E. E. "Convergence of the Cahn–Hilliard Equation to the Mullins–Sekerka Problem in Spherical Symmetry." Journal of Differential Equations 125, no. 1 (February 1996): 154–83. http://dx.doi.org/10.1006/jdeq.1996.0028.

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33

Carlen, E. A., M. C. Carvalho, and E. Orlandi. "Approximate Solutions of the Cahn-Hilliard Equation via Corrections to the Mullins-Sekerka Motion." Archive for Rational Mechanics and Analysis 178, no. 1 (April 21, 2005): 1–55. http://dx.doi.org/10.1007/s00205-005-0366-5.

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34

Carlen, E. A., M. C. Carvalho, and E. Orlandi. "Approximate Solutions of the Cahn-Hilliard Equation via Corrections to the Mullins-Sekerka Motion." Archive for Rational Mechanics and Analysis 180, no. 3 (April 5, 2006): 511. http://dx.doi.org/10.1007/s00205-006-0433-6.

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35

Escher, J., and U. F. Mayer. "Loss of convexity for a modified Mullins–Sekerka model arising in diblock copolymer melts." Archiv der Mathematik 77, no. 5 (November 2001): 434–48. http://dx.doi.org/10.1007/pl00000515.

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36

Cristini, Vittorio, and John Lowengrub. "Three-dimensional crystal growth—II: nonlinear simulation and control of the Mullins–Sekerka instability." Journal of Crystal Growth 266, no. 4 (June 2004): 552–67. http://dx.doi.org/10.1016/j.jcrysgro.2004.02.115.

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37

Li, Shuwang, John S. Lowengrub, Perry H. Leo, and Vittorio Cristini. "Nonlinear stability analysis of self-similar crystal growth: control of the Mullins–Sekerka instability." Journal of Crystal Growth 277, no. 1-4 (April 2005): 578–92. http://dx.doi.org/10.1016/j.jcrysgro.2004.12.042.

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38

Soner, H. Mete. "Convergence of the phase-field equations to the mullins-sekerka problem with kinetic undercooling." Archive for Rational Mechanics and Analysis 131, no. 2 (1995): 139–97. http://dx.doi.org/10.1007/bf00386194.

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39

SZABÓ, G., A. SZOLNOKI, T. ANTAL, and I. BORSOS. "INTERFACE INSTABILITY IN DRIVEN LATTICE GASES." Fractals 01, no. 04 (December 1993): 954–58. http://dx.doi.org/10.1142/s0218348x93001015.

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In driven lattice-gas models, the enhanced material transport along the interfaces results in an instability of the planar interfaces and leads to the formation of multistrip states. To study the interfacial instability, Monte Carlo simulations are performed on different square lattice-gas models. The amplification rate of a periodic perturbation depends on the wave number k; it has a positive maximum at a characteristic value of k on the analogy of the Mullins-Sekerka instability. Significant differences have been found in the dependence of amplification rate on k when comparing the systems with nearest neighbor repulsive and nearest and next-nearest neighbor attractive interactions. The results agree qualitatively with theories neglecting the fluctuations.

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40

MAYER, UWE F. "A numerical scheme for moving boundary problems that are gradient flows for the area functional." European Journal of Applied Mathematics 11, no. 1 (February 2000): 61–80. http://dx.doi.org/10.1017/s0956792599003812.

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Many moving boundary problems that are driven in some way by the curvature of the free boundary are gradient flows for the area of the moving interface. Examples are the Mullins–Sekerka flow, the Hele-Shaw flow, flow by mean curvature, and flow by averaged mean curvature. The gradient flow structure suggests an implicit finite differences approach to compute numerical solutions. The proposed numerical scheme will allow us to treat such free boundary problems in both IR2 and IR3. The advantage of such an approach is the re-usability of much of the setup for all of the different problems. As an example of the method, we compute solutions to the averaged mean curvature flow that exhibit the formation of a singularity.

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41

Bronsard, Lia, Harald Garcke, and Barbara Stoth. "A multi-phase Mullins–Sekerka system: matched asymptotic expansions and an implicit time discretisation for the geometric evolution problem." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 128, no. 3 (1998): 481–506. http://dx.doi.org/10.1017/s0308210500021612.

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We propose a generalisation of the Mullins–Sekerka problem to model phase separation in multi-component systems. The model includes equilibrium equations in bulk, the Gibbs–Thomson relation on the interfaces, Young's law at triple junctions, together with a dynamic law of Stefan type. Using formal asymptotic expansions, we establish the relationship to a transition layer model known as the Cahn-Hilliard system. We introduce a notion of weak solutions for this sharp interface model based on integration by parts on manifolds, together with measure theoretical tools. Through an implicit time discretisation, we construct approximate solutions by stepwise minimisation. Under the assumption that there is no loss of area as the time step tends to zero, we show the existence of a weak solution.

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42

Style, Robert W., and M. Grae Worster. "Linear stability of a solid–vapour interface." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2116 (December 3, 2009): 1005–25. http://dx.doi.org/10.1098/rspa.2009.0496.

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We investigate a system consisting of a condensed phase in contact with its vapour. We derive similarity solutions for vapour and temperature profiles and calculate the condition for the presence of vapour supersaturation adjacent to the condensed phase. We analyse the linear stability of a solid–vapour interface with varying atmospheric conditions. The instability is qualitatively similar to the Mullins–Sekerka instability in binary alloys but the results highlight the important parameters for the solid/vapour problem. We derive the neutral stability condition and results are applied to frost flowers, which are small hoar-frost-like crystals that grow on sea ice, and to physical vapour deposition. The results are applicable to many problems in the wide field of condensed-phase/vapour systems.

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43

Le, Nam Q. "On the Convergence of the Ohta–Kawasaki Equation to Motion by Nonlocal Mullins–Sekerka Law." SIAM Journal on Mathematical Analysis 42, no. 4 (January 2010): 1602–38. http://dx.doi.org/10.1137/090768643.

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44

Ignés-Mullol, Jordi, and Patrick Oswald. "Growth and melting of the nematic phase: Sample thickness dependence of the Mullins-Sekerka instability." Physical Review E 61, no. 4 (April 1, 2000): 3969–76. http://dx.doi.org/10.1103/physreve.61.3969.

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45

Dai, Shibin, and Keith Promislow. "Geometric evolution of bilayers under the functionalized Cahn–Hilliard equation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2153 (May 8, 2013): 20120505. http://dx.doi.org/10.1098/rspa.2012.0505.

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We use a multi-scale analysis to derive a sharp interface limit for the dynamics of bilayer structures of the functionalized Cahn–Hilliard equation. In contrast to analysis based on single-layer interfaces, we show that the Stefan and Mullins–Sekerka problems derived for the evolution of single-layer interfaces for the Cahn–Hilliard equation are trivial in this context, and the sharp interface limit yields a quenched mean-curvature-driven normal velocity at O ( ε −1 ), whereas on the longer O ( ε −2 ) time scale, it leads to a total surface area preserving Willmore flow. In particular, for space dimension n =2, the constrained Willmore flow drives collections of spherically symmetric vesicles to a common radius, whereas for n =3, the radii are constant, and for n ≥4 the largest vesicle dominates.

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46

Abels, Helmut, and Mathias Wilke. "Well-posedness and qualitative behaviour of solutions for a two-phase Navier–Stokes-Mullins–Sekerka system." Interfaces and Free Boundaries 15, no. 1 (2013): 39–75. http://dx.doi.org/10.4171/ifb/294.

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47

Alikakos, Nicholas D., Giorgio Fusco, and Georgia Karali. "Ostwald ripening in two dimensions—the rigorous derivation of the equations from the Mullins–Sekerka dynamics." Journal of Differential Equations 205, no. 1 (October 2004): 1–49. http://dx.doi.org/10.1016/j.jde.2004.05.008.

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48

Ji, Shou Xun, Yun Wang, Douglas Watson, and Zhong Yun Fan. "Microstructural Characteristics of Diecast AlMgSiMn Alloy." Materials Science Forum 783-786 (May 2014): 234–39. http://dx.doi.org/10.4028/www.scientific.net/msf.783-786.234.

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Solidiﬁcation and microstructural characteristics of Al-5wt.%Mg-1.5wt.%Si-0.6wt.%Mn-0.2wt.%Ti alloy have been investigated in high pressure die casting. The average size of dendrites and fragmented dendrites of the primary α-Al phase formed in the shot sleeve is 43 m, and the globular α-Al grains formed inside the die cavity is 7.5 m. Solidification inside the die cavity also forms the lamellar Al-Mg2Si eutectic phase and the Fe-rich intermetallics. The size of the eutectic cells is about 10 m, in which the lamellar α-Al phase is 0.41 m thick. The Fe-rich intermetallic compound exhibits a compact morphology and is less than 2 m. Calculations using the Mullins and Sekerka stability criterion reveal that the solidiﬁcation of the primary α-Al phase inside the die cavity has completed before the spherical α-Al globules begin to lose their stability, but the α-Al grains formed in the shot sleeve exceed the limit of spherical growth and therefore exhibit a dendritic morphology.

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49

Qian, Ma. "Creation of semisolid slurries containing fine and spherical particles by grain refinement based on the Mullins–Sekerka stability criterion." Acta Materialia 54, no. 8 (May 2006): 2241–52. http://dx.doi.org/10.1016/j.actamat.2006.01.022.

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50

Barrett, John W., Harald Garcke, and Robert Nürnberg. "On stable parametric finite element methods for the Stefan problem and the Mullins–Sekerka problem with applications to dendritic growth." Journal of Computational Physics 229, no. 18 (September 2010): 6270–99. http://dx.doi.org/10.1016/j.jcp.2010.04.039.

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Journal articles on the topic 'Mullins-Sekerka'

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