Book contents
- Frontmatter
- Contents
- Preface
- Notation guide
- PART 1 Introduction
- 1 Interfaces in nature
- 2 Scaling concepts
- 3 Fractal concepts
- PART 2 Nonequilibrium roughening
- PART 3 Interfaces in random media
- PART 4 Molecular beam epitaxy
- PART 5 Noise
- PART 6 Advanced topics
- PART 7 Finale
- APPENDIX A Numerical recipes
- APPENDIX B Dynamic renormalization group
- APPENDIX C Hamiltonian description
- Bibliography
- Index
2 - Scaling concepts
Published online by Cambridge University Press: 23 December 2009
- Frontmatter
- Contents
- Preface
- Notation guide
- PART 1 Introduction
- 1 Interfaces in nature
- 2 Scaling concepts
- 3 Fractal concepts
- PART 2 Nonequilibrium roughening
- PART 3 Interfaces in random media
- PART 4 Molecular beam epitaxy
- PART 5 Noise
- PART 6 Advanced topics
- PART 7 Finale
- APPENDIX A Numerical recipes
- APPENDIX B Dynamic renormalization group
- APPENDIX C Hamiltonian description
- Bibliography
- Index
Summary
The formation of interfaces and surfaces is influenced by a large number of factors, and it is almost impossible to distinguish all of them. Nevertheless, a scientist always hopes that there is a small number of basic ‘laws’ determining the morphology and the dynamics of growth. The action of these basic laws can be described in microscopic detail through discrete growth models – models that mimic the essential physics but bypass some of the less essential details.
To this end, we introduce a simple model, ballistic deposition (BD), which generates a nonequilibrium interface that exemplifies many of the essential properties of a growth process. We shall use the BD model to introduce scaling concepts, a central theme of this book.
Ballistic deposition
Ballistic deposition was introduced as a model of colloidal aggregates, and early studies concentrated on the properties of the porous aggregate produced by the model. The nontrivial surface properties became a subject of scientific inquiry after the introduction of vapor deposition techniques.
It is simpler to define and study the BD model on a lattice, as in Fig. 2.1, but off-lattice versions have been investigated as well. A particle is released from a randomly chosen position above the surface, located at a distance larger than the maximum height of the interface. The particle follows a straight vertical trajectory until it reaches the surface, whereupon it sticks.
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- Information
- Fractal Concepts in Surface Growth , pp. 19 - 28Publisher: Cambridge University PressPrint publication year: 1995
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