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Relevant bibliographies by topics / Mullins-Sekerka

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Academic literature on the topic 'Mullins-Sekerka'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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Journal articles on the topic "Mullins-Sekerka"

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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Mullins-Sekerka"

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Brown, Sarah M. "A numerical scheme for Mullins-Sekerka flow in three space dimensions /." Diss., CLICK HERE for online access, 2004. http://contentdm.lib.byu.edu/ETD/image/etd493.pdf.

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Brown, Sarah Marie. "A Numerical Scheme for Mullins-Sekerka Flow in Three Space Dimensions." BYU ScholarsArchive, 2004. https://scholarsarchive.byu.edu/etd/136.

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The Mullins-Sekerka problem, also called two-sided Hele-Shaw flow, arises in modeling a binary material with two stable concentration phases. A coarsening process occurs, and large particles grow while smaller particles eventually dissolve. Single particles become spherical. This process is described by evolving harmonic functions within the two phases with the moving interface driven by the jump in the normal derivatives of the harmonic functions at the interface. The harmonic functions are continuous across the interface, taking on values equal to the mean curvature of the interface. This dissertation reformulates the three-dimensional problem as one on the two-dimensional interface by using boundary integrals. A semi-implicit scheme to solve the free boundary problem numerically is implemented. Numerical analysis tasks include discretizing surfaces, overcoming node bunching, and dealing with topology change in a toroidal particle. A particle (node)-cluster technique is developed with the aim of alleviating excessive run time caused by filling the dense matrix used in solving a system of linear equations.

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Book chapters on the topic "Mullins-Sekerka"

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Xu, Jian-Jun. "Unidirectional Solidification and Mullins–Sekerka Instability." In Springer Series in Synergetics, 29–74. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-52663-8_2.

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Xu, Jian-Jun. "Unidirectional Solidification and the Mullins-Sekerka Instability." In Interfacial Wave Theory of Pattern Formation, 27–67. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-642-80435-9_2.

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Su, Jianzhong, and Bao Loc Tran. "Numerical Calculations for a Mullins-Sekerka Problem in 2D." In Integral Methods in Science and Engineering, 239–44. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-0-8176-8184-5_36.

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Röger, Matthias. "Existence of Weak Solutions for the Mullins-Sekerka Flow." In Free Boundary Problems, 361–68. Basel: Birkhäuser Basel, 2006. http://dx.doi.org/10.1007/978-3-7643-7719-9_35.

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Chen, Chieh, Catherine Kublik, and Richard Tsai. "An Implicit Boundary Integral Method for Interfaces Evolving by Mullins-Sekerka Dynamics." In Springer Proceedings in Mathematics & Statistics, 1–21. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-66764-5_1.

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Soner, H. M. "Convergence of the Phase-Field Equations to the Mullins-Sekerka Problem with Kinetic Undercooling." In Fundamental Contributions to the Continuum Theory of Evolving Phase Interfaces in Solids, 413–71. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-642-59938-5_15.

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"Overview of growth phenomena and the Mullins-Sekerka instability." In Nematic and Cholesteric Liquid Crystals, 553–95. CRC Press, 2005. http://dx.doi.org/10.1201/9780203023013.ch9b.

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"Chapter B.IX: Overview of growth phenomena and the Mullins-Sekerka instability." In Nematic and Cholesteric Liquid Crystals, 579–622. CRC Press, 2005. http://dx.doi.org/10.1201/9780203023013-18.

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Conference papers on the topic "Mullins-Sekerka"

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Jung, Jin-Young, and Michael M. Chen. "MORPHOLOGICAL INSTABILITY OF ALLOY SOLIDIFICATION-ASYMPTOTIC ANALYSIS AND GENERALIZATION OF THE MULLINS-SEKERKA THEORY." In International Heat Transfer Conference 11. Connecticut: Begellhouse, 1998. http://dx.doi.org/10.1615/ihtc11.980.

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Dhami, Harish Singh, and Koushik Viswanathan. "On the Formation of Spherical Particles in Surface Grinding." In ASME 2020 15th International Manufacturing Science and Engineering Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/msec2020-8278.

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Abstract Grinding swarf is conventionally of secondary interest to the process engineer. However, it has long been recognized that it is a useful indicator of process performance — the exact particle morphologies occurring in the swarf contain a wealth of information about the abrasive-workpiece interaction mechanics. In this work, we study the generation of perfectly spherical particles when grinding two plain carbon steels and a grade of stainless steel with an alumina wheel. Similar particles have also been reported in the wear community and several possible formation mechanisms have been discussed including chip curl resulting from electronic charge distributions; melting due to local flash temperatures in the grinding zone; and repeated abrasive wear of the workpiece surface. We postulate that the particles are likely formed as a result of an oxidation-melting-solidification route with small grinding chips. We present spectroscopy and X-ray diffraction data in support of this hypothesis — significant oxygen content, in the form of Fe3O4 was detected on the surface of the spheres. Electron micrographs also show remarkably robust dendrite-like structures on the surface of the particles, indicative of rapid solidification from the melt. Motivated by these results, we present model calculations to support our hypothesis. We first evaluate the initial temperature of chips exiting the grinding zone using a three-way heat partition model for dry grinding. An upper bound for the chip temperature is ∼ 600°C, well-below the melting point for the metal. Next, we show that the oxidation kinetics at this elevated temperature are such that the formation of a thin oxide layer (∼ 2μm) on the surface of an initially curled up chip, with size ∼ 50 μm comparable to the observed spheres, is enough to melt the entire chip on a timescale of 10−6 seconds. Surface tension then brings the molten chip into a perfectly spherical shape, followed by rapid solidification. We present a preliminary calculation of this solidification process, using a coupled heat conduction model along with a moving interphase interface. By making suitable approximations, we derive an ordinary differential equation describing the temporal evolution of the interface location. Coupling the interface velocity with a Mullins-Sekerka type instability analysis, we argue that solidification of these drops likely starts from a nucleated core in the drop interior, resulting in dendrite-type patterns on the outer surface. Our work is a preliminary attempt to put decades old observations of grinding swarf on a firm quantitative footing. The experimental evidence and related analysis presented here make a strong case for the oxidation-melting-solidification hypothesis for the formation of spherical particles in grinding swarf.

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