Chord intercepts in a two-dimensional cell growth model

1989 ◽  
Vol 24 (9) ◽  
pp. 3107-3112 ◽  
Author(s):  
G. E. W. Schulze ◽  
L. O. Schwan ◽  
R. Willers
Keyword(s):  
Cell Growth ◽  
Growth Model ◽  
Two Dimensional ◽  
Cell Growth Model ◽  
Dimensional Cell

Chord intercepts in a two-dimensional cell growth model

1992 ◽  
Vol 27 (4) ◽  
pp. 947-955 ◽  
Author(s):  
G. E. W. Schulze ◽  
W. A. Schulze
Keyword(s):  
Cell Growth ◽  
Growth Model ◽  
Two Dimensional ◽  
Cell Growth Model ◽  
Dimensional Cell

Chord intercepts in a two-dimensional cell growth model

1989 ◽  
Vol 24 (9) ◽  
pp. 3101-3106 ◽  
Author(s):  
G. E. W. Schulze ◽  
H. -P. Wilbert
Keyword(s):  
Cell Growth ◽  
Growth Model ◽  
Two Dimensional ◽  
Cell Growth Model ◽  
Dimensional Cell

scholarly journals EIGENFUNCTIONS ARISING FROM A FIRST-ORDER FUNCTIONAL DIFFERENTIAL EQUATION IN A CELL GROWTH MODEL

2010 ◽  
Vol 52 (1) ◽  
pp. 46-58 ◽  
Author(s):  
BRUCE VAN BRUNT ◽  
M. VLIEG-HULSTMAN
Keyword(s):  
Differential Equation ◽  
Cell Growth ◽  
Growth Model ◽  
Uniqueness Result ◽  
First Order ◽  
Orthogonality Relations ◽  
A Cell ◽  
Functional Differential ◽  
Cell Growth Model ◽  
First Eigenfunction

AbstractA boundary-value problem for cell growth leads to an eigenvalue problem. In this paper some properties of the eigenfunctions are studied. The first eigenfunction is a probability density function and is of importance in the cell growth model. We sharpen an earlier uniqueness result and show that the distribution is unimodal. We then show that the higher eigenfunctions have nested zeros. We show that the eigenfunctions are not mutually orthogonal, but that there are certain orthogonality relations that effectively partition the set of eigenfunctions into two sets.

A functional partial differential equation arising in a cell growth model with dispersion

2017 ◽  
Vol 41 (4) ◽  
pp. 1541-1553 ◽  
Author(s):  
Messoud Efendiev ◽  
Bruce van Brunt ◽  
Graeme C. Wake ◽  
Ali Ashher Zaidi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Cell Growth ◽  
Growth Model ◽  
Partial Differential ◽  
A Cell ◽  
Cell Growth Model

scholarly journals Multiscale Modeling of Recrystallization

1998 ◽  
Vol 538 ◽  
Author(s):  
M.A. Miodownik ◽  
E.A. Holm ◽  
A.W. Godfrey ◽  
D.A. Hughes ◽  
R. Lesar
Keyword(s):  
Cell Growth ◽  
Multiscale Modeling ◽  
Growth Model ◽  
Layered Materials ◽  
Macroscopic Model ◽  
Structure Evolution ◽  
Dislocation Model ◽  
Size Evolution ◽  
A Cell ◽  
Cell Growth Model

AbstractWe propose a multi length scale approach to modeling recrystallization which links a dislocation model, a cell growth model and a macroscopic model. Although this methodology and linking framework will be applied to recrystallization, it is also applicable to other types of phase transformations in bulk and layered materials. Critical processes such as the dislocation structure evolution, nucleation, the evolution of crystal orientations into a preferred texture, and grain size evolution all operate at different length scales. In this paper we focus on incorporating experimental measurements of dislocation substructures, misorientation measurements of dislocation boundaries, and dislocation simulations into a mesoscopic model of cell growth. In particular, we show how feeding information from the dislocation model into the cell growth model can create realistic initial microstructures.

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