164,124 research outputs found
John W. Cahn
No full textJOHN W. CAHN
Inducted: 2007
Citation:
For the application of thermodynamic, crystallographic and kinetic principles to a wide range of materials-science problems in metals and ceramics including: solidification, solid state phase transformations, stress effects, capillary phenomena and the paradigm-breaking discovery of quasicrystals, metallic phases with long range orientational order but no translational symmetry.
Tenure: 1977-2006
Birth: 1928, Cologne, Germany
Education:
University of Michigan, Ann Arbor, BS (Chemistry), 1949
University of California, Berkeley, PhD (Physical Chemistry), 1953
Positions held:
Scientist, Center for Materials Science, 1977 - 1984
Senior NIST Fellow (Metallurgist), Materials Science and Engineering Laboratory, 1984 - 2006
NIST Scientist Emeritus, 2006-
Honors:
Bower Prize, Franklin Institute (2002)
Emil Heyn Medal, German Metallurgical Society (2001)
National Medal of Science (1999)
Bakhuis Roozeboom Lecturer and Gold Medal, Netherlands Academy of Science (1999)
Member, National Academy of Engineering (1998)
Harvey Prize, Israel Institute of Technology (1995)
Rockwell Medal; Hall of Fame for Engineering, Science and Technology (1994)
Michelson and Morley Prize, Case-Western University (1991)
Stratton Award, National Bureau of Standards (1986)
US Department of Commerce Gold Medal, (1984)
Fellow, Japan Society for the Promotion of Science (1981)
Fellow, American Academy of Arts and Sciences (1974)
Member, National Academy of Sciences (1973)
Honorary doctorates from Northwestern University and Evry University
Memberships:
Metallurgical Society of the American Institute of Mining, Metallurgical, and Petroleum Engineers
Fellow, Minerals, Metals, & Materials Society, and American Society for Metals, International
Publications:
Approximately 250 publications:
Cahn, J.W., "Thermodynamics of Solid and Fluid Surfaces," in Segregation to Interfaces, ASM Seminar Series, 3-23, (1978).
Allen, S.M. and Cahn, J.W., "A Microscopic Theory for Antiphase Boundary Motion and Its Application to Antiphase Domain Coarsening," Acta Metallurgica 27, 1085-1095 (1979).
Kikuchi, R. and Cahn, J.W., "Theory of Interphase and Antiphase Boundaries in FCC Alloys," Acta Metallurgica 27, 1337 (1979).
Moldover, M.R. and Cahn, J.W., “Interface Phase-Transition - Complete to Partial Wetting,” Science 207 (4435): 1073-1075 (1980).
Shechtman, D., Blech, I., Gratias, D., and Cahn, J.W., “Metallic Phase with Long-Range Orientational Order and No Translational Symmetry,” Physical Review Letters 53 (20): 1951-1953 (1984).
Larche, F.C. and Cahn, J.W., “The Interactions of Composition and Stress in Crystalline Solids,” Acta Metallurgica 33 (3): 331-357 (1985)
Stationary solutions for the Cahn-Hilliard equation
No full textWe study the Cahn-Hilliard equation in a bounded domain without any symmetry assumptions. We assume that the mean curvature of the boundary
has a nongenerate critical point. Then we show that there exists a spike-like stationary solution whose global maximum lies on the boundary. Our method is based on Lyapunov-Schmidt reduction and the Brouwer fixed-point theorem
On the stationary Cahn-Hilliard equation: Interior spike solutions
No full textWe study solutions of the stationary Cahn-Hilliard equation in a bounded smooth domain which have a spike in the interior. We show that a large class of interior points (the "nondegenerate peak" points) have the following property: there exist such solutions whose spike lies close to a given nondegenerate peak point. Our construction uses among others the methods of viscosity solution, weak convergence of measures and Liapunov-Schmidt reduction
On the Stationary Cahn-Hilliard Equation: Bubble Solutions
No full textWe study
stationary solutions of the Cahn--Hilliard equation in a bounded
smooth domain which have an interior spherical interface (bubbles).
We show that a large class of interior points
(the ``nondegenerate peak'' points)
have the following property: there exists such a
solution whose bubble center lies close to a given nondegenerate peak point.
Our construction uses among others the Liapunov-Schmidt
reduction method and exponential asymptotics
Cahn Bros.
No full textRecto: [imprinted] Fragrant Ivory Polish, Whitens the Teeth, Fleming's Crudoform Liniment for Rheumatism and Pain, Price 25 cents, Sold by All Druggists. Verso: [imprinted] Cahn Bros. Dry Goods, Clothing, Boots, Shoes & Hats, 635 & 637 Elm St. Dallas, Texas. [paragraphs not transcribed]
Solutions for the Cahn-Hilliard Equation With Many Boundary Spike Layers
No full textIn this paper we
construct new classes of stationary solutions for the Cahn-Hilliard
equation
by a novel approach.
One of the results is as follows:
Given a positive integer K and a (not necessarily nondegenerate) local
minimum point of the mean curvature of the boundary then there are
boundary
K-spike solutions
whose peaks all approach this point.
This implies that for any smooth and bounded domain there
exist boundary K-spike solutions.
The central ingredient of our analysis is the novel derivation and
exploitation of a reduction of the energy to finite dimensions (Lemma 3.5),
where the variables are closely related to the peak loations
Computational methods for Cahn-Hilliard variational inequalities
No full textWe consider the non-standard fourth order parabolic Cahn-Hilliard variational inequality with constant as well as non-constant diffusional mobility. We propose a primal-dual active set method as solution technique for the discrete variational inequality given by a (semi-)implicit Euler discretization in time and linear finite elements in space. We show local convergence of the method by reinterpretation as a semi-smooth Newton method. The discrete saddle point system arising in each iteration step is handled by either a Gauss-Seidel type method, the application of a multi-frontal direct solver or a preconditioned conjugate gradient method applied to the Schur complement. Finally we show the efficiency of the method and the preconditioning with several numerical simulations
Multi-interior-spike solutions for the Cahn-Hilliard equation with arbitrarily many peaks
No full textWe study the Cahn-Hilliard equation in a bounded smooth
domain without any symmetry
assumptions. We prove that for any fixed positive integer K there
exist interior --spike solutions
whose peaks have maximal possible distance from the boundary and
from one another. This implies that for any bounded and smooth
domain there
exist interior K-peak solutions.
The central ingredient of our analysis is the novel derivation
and exploitation of a reduction of the energy to finite dimensions
(Lemma 5.5) with variables which are closely related to the location of
the peaks.
We do not assume nondegeneracy of the points of
maximal distance to the boundary but can do with a global condition instead
which in many cases is weaker
Numerical analysis of a coupled pair of Cahn-Hilliard equations
No full textA mathematical analysis has been carried out for a coupled pair of Cahn-Hilliard equations, which appear in modelling a phase separation on a thin film of binary liquid mixture coating substrate, which is wet by one component. Existence and uniqueness are proved for a weak formulation of the problem, which possesses a Lyapunov functional. Regularity results are presented for the weak formulation. A fully practical piecewise linear finite element approximation is proposed where existence and uniqueness of the numerical solution, and its convergence to the solution of the continuous problem are proven. An error bound between the discrete and continuous solutions is given in three space dimensions. A practical algorithm for solving the resulting algebraic problem at each time step is suggested and its convergence is proven. Finally, linear stability analysis for one space dimension is presented, and some numerical simulations in one and two spaces dimension are exhibited
Optimal energy growth lower bounds for a class of solutions to the vectorial Allen-Cahn equation
No full textWe prove optimal lower bounds for the growth of the energy over balls of minimizers to the vectorial Allen-Cahn energy in two spatial dimensions, as the radius tends to infinity. In the case of radially symmetric solutions, we can prove a stronger result in all dimensions
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