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TitleStress-driven pattern formation in living and non-living matter
File Size33.9 MB
Total Pages94
Table of Contents
                            Abstract
Resume
Publications
Contents
1 Introduction & objectives
2 Scale selection in columnar jointing
	2.1 The internal stress of the cooling material
		2.1.1 The contraction length scale
		2.1.2 The column diameter
	2.2 A continuum model of columnar jointing
		2.2.1 Relating column width and system parameters
		2.2.2 A one-to-one relation?
		2.2.3 The scaling function
	2.3 Discussion
3 Collective dynamics and division processes in tissue
	3.1 A continuum model for collective motion of cells
	3.2 Capturing bulk motion of tissue
	3.3 Capturing the cell division process
	3.4 Discussion
4 Coupling between substrate curvature and texture
	4.1 The Free Energy Functional
	4.2 Geometrical setup
	4.3 Expansion of the free energy density
		4.3.1 The volume element
		4.3.2 The gradient squared
		4.3.3 The Laplacian squared
		4.3.4 Powers of the order parameter field
		4.3.5 The final two-dimensional free energy density
	4.4 Relaxation towards equilibrium
	4.5 A benchmark problem
	4.6 Future directions
		4.6.1 Minimum energy texture
		4.6.2 Curvature as an ordering field
		4.6.3 Ordering kinetics
		4.6.4 Numerical implementation
	4.7 Discussion
		4.7.1 Previous models of block copolymers on curved substrates
		4.7.2 Nematic approaches
5 Conclusion
A Appendix: Scale selection in columnar jointing
	A.1 Conductive cooling with latent heat
	A.2 Numerical simulations
		A.2.1 Discrete element simulations
		A.2.2 Finite element simulations
B Appendix: Collective dynamics and division processes in tissue
	B.1 Experiments on epithelial and endothelial tissues
		B.1.1 Epithelial cells
		B.1.2 Endothelial cells
	B.2 Convected derivatives
		B.2.1 Objective vectors and tensors
		B.2.2 Objective time derivatives
	B.3 Numerical simulations
		B.3.1 Dimensionless form
		B.3.2 Numerical scheme
		B.3.3 Fitting procedure
C Appendix: Coupling between substrate curvature and texture
	C.1 Functional derivative of the free energy
References
                        

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