Relevant bibliographies by topics / Cahn-Hillard equation

Academic literature on the topic 'Cahn-Hillard equation'

Author: Grafiati
Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Cahn-Hillard equation"

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Theljani, Anis, Hamdi Houichet, and Anis Mohamed. "An adaptive Cahn-Hilliard equation for enhanced edges in binary image inpainting." Journal of Algorithms & Computational Technology 14 (January 2020): 174830262094143. http://dx.doi.org/10.1177/1748302620941430.

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We consider the Cahn-Hilliard equation for solving the binary image inpainting problem with emphasis on the recovery of low-order sets (edges, corners) and enhanced edges. The model consists in solving a modified Cahn-Hilliard equation by weighting the diffusion operator with a function which will be selected locally and adaptively. The diffusivity selection is dynamically adopted at the discrete level using the residual error indicator. We combine the adaptive approach with a standard mesh adaptation technique in order to well approximate and recover the singular set of the solution. We give some numerical examples and comparisons with the classical Cahn-Hillard equation for different scenarios. The numerical results illustrate the effectiveness of the proposed model.
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Songmu, Zheng. "Asymptotic behavior of solution to the Cahn-Hillard equation." Applicable Analysis 23, no. 3 (December 1986): 165–84. http://dx.doi.org/10.1080/00036818608839639.

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Radkevich, E., and M. Zakharchenko. "The Singular Limit Problem to the Extended Cahn–Hillard Equation." Journal of Mathematical Sciences 120, no. 3 (March 2004): 1424–41. http://dx.doi.org/10.1023/b:joth.0000016059.66277.da.

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Львов, П. Е., and В. В. Светухин. "Влияние флуктуаций на образование выделений вторых фаз на границах зерен." Физика твердого тела 61, no. 2 (2019): 357. http://dx.doi.org/10.21883/ftt.2019.02.47138.232.

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AbstractBased on the free energy density functional method (modified Cahn–Hillard–Cook equation), the formation kinetics of secondary phases in binary alloys is considered in the presence of composition fluctuations and with inclusion of the grain boundaries influences. It is revealed that the existence of grain boundaries and the fluctuations at the initial stage of the phase transition can lead to the appearance of anomalous growth rate of the average precipitate size due to a competition of various decomposition mechanisms.
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Nastar, Maylise. "Beyond the Cahn-Hilliard Equation: a Vacancy-Based Kinetic Theory." Solid State Phenomena 172-174 (June 2011): 321–30. http://dx.doi.org/10.4028/www.scientific.net/ssp.172-174.321.

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A Self-Consistent Mean Field (SCMF) kinetic theory including an explicit description ofthe vacancy diffusion mechanism is developed. The present theory goes beyond the usual local equi-librium hypothesis. It is applied to the study of the early time spinodal decomposition in alloys. Theresulting analytical expression of the structure function highlights the contribution of the vacancydiffusion mechanism. Instead of the single amplification rate of the Cahn-Hillard linear theory, thelinearized SCMF kinetic equations involve three constant rates, first one describing the vacancy re-laxation kinetics, second one related to the kinetic coupling between local concentrations and paircorrelations and the third one representing the spinodal amplification rate. Starting from the same va-cancy diffusion model, we perform kineticMonte Carlo simulations of a Body Centered Cubic (BCC)demixting alloy. The resulting spherically averaged structure function is compared to the SCMF pre-dictions. Both qualitative and quantitative agreements are satisfying.
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王, 乙竹. "Regularity Criteria for the Navier-Stokes-Cahn-Hillard Equation in the Morrey-Campanato Space." Advances in Applied Mathematics 10, no. 06 (2021): 2095–104. http://dx.doi.org/10.12677/aam.2021.106219.

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Hernandez, Alvaro, and Michal Kowalczyk. "Nondegeneracy and the Jacobi fields of rotationally symmetric solutions to the Cahn-Hillard equation." Indiana University Mathematics Journal 68, no. 4 (2019): 1047–87. http://dx.doi.org/10.1512/iumj.2019.68.7718.

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Sigala-García, Darío A., Víctor M. López-Hirata, Maribel L. Saucedo-Muñoz, Héctor J. Dorantes-Rosales, and José D. Villegas-Cárdenas. "Phase-Field Simulation of Spinodal Decomposition in Mn-Cu Alloys." Metals 12, no. 7 (July 19, 2022): 1220. http://dx.doi.org/10.3390/met12071220.

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The spinodal decomposition was studied in the aged Mn-40 at. %Cu, Mn-30 at. %Cu, Mn-20 at. %Cu alloys using a phase-field model based on the Cahn–Hillard equation, considering a subregular solution model and the energy contribution of the magnetic behavior. The simulations were performed at aging temperatures of 300, 400, and 500 °C for times from 1 to 240 min. The growth kinetics of the Mn concentration profiles with time indicated clearly that the phase decomposition of the supersaturated solid solution γ into a mixture of Mn-rich γ′ and Cu-rich γ phases occurred by the spinodal decomposition mechanism. Moreover, the phase decomposition at the early stages of aging exhibited the characteristic morphology of spinodal decomposition, an interconnected and percolated microstructure of the decomposed phases. The most rapid growth kinetics of spinodal decomposition occurred for the aging of Mn-20 and 30 at. %Cu alloys because of the higher driving force. The presence of the phase decomposition is responsible for the increase in hardness, as well as the improvement of the damping capacity of Mn-Cu alloys.
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李, 亚楠. "Finite Element Method for the Modified Cahn-Hilliard Equation with the Concentration Mobility and the Logarithmic Potential." Advances in Applied Mathematics 09, no. 09 (2020): 1383–93. http://dx.doi.org/10.12677/aam.2020.99164.

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Polat, M., A. O. Çelebı, and N. Çali⋅kan. "Global attractors for the 3D viscous Cahn–Hillard equations in an unbounded domain." Applicable Analysis 88, no. 8 (August 2009): 1157–71. http://dx.doi.org/10.1080/00036810903156172.

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Book chapters on the topic "Cahn-Hillard equation"

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Shah, Kunjan, and Himanshu Patel. "A Novel Hybrid Approach to the Sixth-Order Cahn-Hillard Time-Fractional Equation." In Advances in Intelligent Systems and Computing, 65–77. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-15-9953-8_7.

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