383 research outputs found
An eleventh century gospel book from Le Cateau
No full textAlexander Jonathan J. G., Cahn Walter. An eleventh century gospel book from Le Cateau. In: Scriptorium, Tome 20 n°2, 1966. pp. 248-264
Travelling waves for the spatially discretized bistable Allen-Cahn equation
No full textWe analyze the spatially discretized version of the Allen-Cahn partial differential equation. The second order derivative is numerically approximated by a weighted infinite sum. The coefficients of this sum as well as the function f in the differential equation have got freedom inside determined restrictions. For this spatially discretized variation of the Allen-Cahn partial differential equation, we prove the existence of a travelling wave solution.Applied Mathematic
Finite Element Analysis of Cahn-Hilliard equations: Mass transfer of an oil-soluble chemical for water control
No full textTwo models have been constructed and physically motivated based on the (system of) Cahn-Hilliard equation(s) and Stefan problem in order to describe the behavior of fluids in a hypothetical mixture. A finite element method is developed to solve the Cahn-Hilliard equations based on a mixed formulation where reduction of the forthorder spatial derivative is applied. The method is also extended to multiple species. Furthermore, mass conservation and energy decrease for the (system of) Cahn-Hilliard equation(s) as well as the Stefan problem are demonstrated mathematically. Then, all proved mathematical subjects have been verified by the numerical aspects for the purpose of approving the numerical results. The Cahn-Hilliard equations with a diffuse interface has been compared to a Stefan problem with a sharp interface and a reasonable agreement is obtained. To find out the advantages and disadvantages, the results and assumptions are discussed at the end for both models.Civil Engineering and GeosciencesGeoscience & EngineeringPetroleum Engineering and Geoscience
A note on the Cahn solute drag model
No full text<p>This document is a note on the Cahn solute drag model based on recent work in the literature. The solute drag models, in general, predict the magnitude of retardation of grain boundary migration due to solute segregation. An overview of classical solute drag model by Cahn is first presented. This is followed by some notes on the model, including a modified phenomenological model proposed by the author and a discussion on the solute drag model for the case of solutes with inhibited diffusion at the boundary. A C code that was used to solve the Cahn model numerically is included and available for download on github</p
Existence of solutions for two types of generalized versions of the Cahn-Hilliard equation
No full textsummary:We show existence of solutions to two types of generalized anisotropic Cahn-Hilliard problems: In the first case, we assume the mobility to be dependent on the concentration and its gradient, where the system is supplied with dynamic boundary conditions. In the second case, we deal with classical no-flux boundary conditions where the mobility depends on concentration , gradient of concentration and the chemical potential . The existence is shown using a newly developed generalization of gradient flows by the author and the theory of Young measures
Numerical methods for the implementation of the Cahn-Hilliard equation in one dimension and dynamic boundary condition in two dimensions
No full textThis project can be divided into two parts. The goal of the first part is to numerically implement the Cahn-Hilliard equation in one dimension both explicitly and implicitly. This will be done using Matlab. The goal of the second part is to validate the coupled Cahn-Hilliard-Navier-Stokes equation and the dynamic boundary condition for moving contact lines of (Carlson et al, 2011, p.9) by considering a two-dimensional spreading droplet case. This will be done using the CFD software OpenFOAM. In Chapter 1, the theory of positive and negative diffusion, including the normal diffusion equation and the Cahn-Hilliard equation, are discussed. Some background is given regarding the thermodynamics of the Cahn-Hilliard equation and its steady-state solution. After that, the theory of the coupled Cahn-Hilliard-Navier-Stokes equation, the dynamic boundary condition for moving contact lines and the case which is implemented in OpenFOAM, are discussed. In Chapters 2 and 3, the diffusion equation and the Cahn-Hilliard equation are implemented in one dimension, using the Euler Forward scheme. In implementing the Cahn-Hilliard equation, two different discretizations are used, of which only one gives the desired results. Next, an extensive stability analysis is done, using a linearization of the Cahn-Hilliard equation as well as numerical experiments. The stability condition is increasingly severe with increasing interface width. Regarding the results of the evolving interface, a qualitative analysis is done which discusses three subjects: the deviation of the solutions with the steady-state solution, the interface width for different parameters and grid sizes and the interface overshoot, which is an unphysical appearence. In Chapter 4, two semi-implicit methods and one implicit iterative method, are discussed. The implementations of the two semi-implicit methods, Implicit-Explicit (ImEx) and Modified Furihata, are succesful and their stability conditions are better than the stability condition of the Euler Forward scheme, for most interface widths. The results regarding the evolving interface are nearly identical to the results of the Euler Forward scheme, therefore the qualitative analysis is also similar. The implicit iterative method, which involves the use of the G\^ateaux derivative, has not been succesfully implemented, eventhough two different discretizations are used. The results regarding the evolving interface are behaving in a positive diffusive way, which results in a flattening interface with time. In Chapter 5, the coupled Cahn-Hilliard-Navier-Stokes equation and a dynamic boundary condition for moving contact lines are used to model a spreading droplet on a flat surface. The implemented model is validated using different cases in which the steady-state contact angle and the friction factor of the surface varies. Next, parametric studies are done regarding the interface width, the surface tension and the ratio of the surface tension and the friction factor. The conclusions are that the modeled system differs too much from the system in literature to make an absolute comparison but, qualitatively, the model behaves as expected.Transport PhenomenaChemical EngineeringApplied Science
Gradient estimates of the Finslerian Allen-Cahn equation
No full textIn this manuscript, we study bounded positive solutions to the Finslerian Allen-Cahn equation. The Allen-Cahn equation is widely applied and connected to many mathematical branches. We find the Finslerian Allen-Cahn equation is also an Euler-Lagrange equation to a Liapunov entropy functional. We prove the global gradient estimates of its positive solutions on compact Finsler metric measure spaces adopting the lower bounds of the weighted Ricci curvature. Moreover, as application of a new comparison theorem developed by the author, we also get a local gradient estimates on noncompact forward complete Finsler metric measure spaces with locally finite misalignment, combining with the bounds of some non-Riemannian curvatures and the lower bound mixed weighted Ricci curvature. At last, we give a Liouville type theorem of such solutions.arXiv admin note: text overlap with arXiv:2312.0661
Dare More, Do More, Live More: Living Fearlessly Beyond Cancer
No full textLu Ann Cahn is the author of the inspirational memoir I Dare Me, an entertaining look back on a year that changed everything for her. The book grew out of a blog called Year of Firsts, which chronicled this veteran journalist, mother and survivor’s daily adventures as she pushed herself to try something new for every single day – an effort to get her life “unstuck,” as her daughter put it.
She went on this year long adventure while working her full time “day job” as an 8-time Emmy award-winning journalist with NBC10 News in Philadelphia. Cahn’s journey eventually led to a major career change. In December 2014, she left her 40 year career in broadcast news to dare audiences across the country and to help launch the next generation of communicators at Temple University. Cahn is the Director of Career Services for Temple’s School of Media and Communication.
Cahn is well known in Philadelphia where she worked for WCAU-TV for 27 years. She filled many roles —breaking news reporter, anchor and entertainment show host – but is most well known for her years as a hard-charging investigative reporter with a talent for uncovering scandals and scams. In 2005, Lu Ann won a National Emmy for her undercover investigative story “Dirty Little Secret” about an illegal bar run by elected officials in their dry town
In 1991 Cahn made local and national news when she publicly told her story of battling breast cancer after a missed diagnosis when she was only 35. Her 1992 special report “Breast Cancer: My Personal Story” won her a national Clarion award and two Mid Atlantic Regional Emmys.
Cahn also had surgery for ulcerative colitis and kidney cancer. She regularly speaks on behalf of Living Beyond Breast Cancer, other area cancer support groups and the Crohn’s and Colitis Foundation of America. She hopes her survivor experience inspires others.
Earlier in her career Cahn worked at stations in Jacksonville, Florida; Chattanooga, Tennessee; Huntsville, Alabama; Little Rock, Arkansas; Charlotte, North Carolina; and Miami, Florida.
A native of Columbus, Ohio, Cahn grew up in Atlanta and graduated Phi Beta Kappa from the University of Georgia. She is married to NBC10 Photojournalist Phil Houser. They’re proud of their daughter Alexa, who dared herself to start her own company and is now managing electronic artists in the music business.
Presentation: 1:07:3
A generalization of the Allen–Cahn equation
No full textThis is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The version of record: Miranville, A.; Quintanilla, R. A generalization of the Allen–Cahn equation. "IMA Journal of Applied Mathematics", 01 Abril 2015, vol. 80, núm. 2, p. 410-430 is available online at:http://imamat.oxfordjournals.org/content/80/2/410.Our aim in this paper is to study generalizations of the Allen–Cahn equation based on a modification of the Ginzburg–Landau free energy proposed in S. Torabi et al. (2009, A new phase-field model for strongly anisotropic systems. Proc. R. Soc. A, 465, 1337–1359). In particular, the free energy contains an additional term called Willmore regularization. We prove the existence, uniqueness and regularity of solutions, as well as the existence of the global attractor. Furthermore, we study the convergence to the Allen–Cahn equation, when the Willmore regularization goes to zero. We finally study the spatial behaviour of solutions in a semi-infinite cylinder, assuming that such solutions exist.Peer ReviewedPostprint (author’s final draft
A generalization of the Allen–Cahn equation
No full textThis is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The version of record: Miranville, A.; Quintanilla, R. A generalization of the Allen–Cahn equation. "IMA Journal of Applied Mathematics", 01 Abril 2015, vol. 80, núm. 2, p. 410-430 is available online at:http://imamat.oxfordjournals.org/content/80/2/410.Our aim in this paper is to study generalizations of the Allen–Cahn equation based on a modification of the Ginzburg–Landau free energy proposed in S. Torabi et al. (2009, A new phase-field model for strongly anisotropic systems. Proc. R. Soc. A, 465, 1337–1359). In particular, the free energy contains an additional term called Willmore regularization. We prove the existence, uniqueness and regularity of solutions, as well as the existence of the global attractor. Furthermore, we study the convergence to the Allen–Cahn equation, when the Willmore regularization goes to zero. We finally study the spatial behaviour of solutions in a semi-infinite cylinder, assuming that such solutions exist.Peer Reviewe
- …
