By Tracy Kompelien

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**Additional info for 3-D Shapes Are Like Green Grapes!**

**Example text**

University Press, Princeton (1996) 2. : Homogeneous nucleation: theory and experiment. J. : Condens. Matter 4, 7627 (1992) 3. : Nucleation of first-order phase transitions. Acc. Chem. Res. 31, 91 (1998) 4. : Nucleation: theory and applications to protein solutions and colloidal suspensions. J. : Condens. Matter 19, 033101 (2007) 5. : Freezing of a Lennard-Jones fluid: from nucleation to spinodal regime. Phys. Rev. Lett. 97, 105701 (2006) 6. : Crystalline nucleation in deeply quenched liquids. Phys.

To describe this further, assume again that D 0, and let k 2 be an integer. Äk 1 C Äk /. Äk 1 C Äk /. The stabilizing secondary bifurcation point for k D 2 can easily be seen in the upper right and lower left images of Fig. 4. It is the first secondary bifurcation point on the second bifurcation branch from the trivial solution, and the images show that its location in the - -parameter quadrant changes with . In fact, the points . ; / at which the stabilizing secondary bifurcation point for k D 2 can be observed are precisely the points on the blue curve in Fig.

The parameter denotes the average mass of the mixture, and the two remaining parameters > 0 and 0 are dimensionless interaction lengths. Informally, > 0 being small corresponds to short range repulsions being strong, inducing a strong compulsion to separate, while being large represents strong long range chain elasticity forces, inducing a strong compulsion to hold together. Notice that for D 0 the diblock copolymer model (2) reduces to the celebrated Cahn-Hilliard equation [6], which serves as a basic model for the phase separation phenomena spinodal decomposition [33, 34, 49, 50, 54] and nucleation [2, 3, 14].

### 3-D Shapes Are Like Green Grapes! by Tracy Kompelien

by Jeff

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