List of Figures

1. A schematic representation of the Laplace Nebula Theory
2. Deriving the Roche limit dependence
3. Roche limit example for a polytrope with $\gamma =20$
4. Roche limit example for a polytrope with $\gamma=\frac{5}{3}$
5. A schematic representation of Jeans' Tidal Theory
6. Condensations forming in a filament
7. The characteristics of an elliptical orbit
8. A schematic representation of the capture mechanism
9. 1964 simulation of the Capture Theory
10. 1971 simulation of the Capture Theory
11. Comparison of simulation methods
12. One dimensional density profiles
13. Comparison of the kernels
14. Determining the distance to the $N_{N}^{th}$ particle
15. Deriving the hydrodynamical acceleration of particle $i$
16. Colliding streams of gas
17. Gravitational force calculation: Sphere-Sphere interaction
18. Gravitational force calculation: Particle $i$-Sphere $j$ interaction
19. Specific heat capacity as a function of temperature
20. Dependence on specific internal energy
21. Integration schemes
22. Improved embedded Euler scheme
23. An example of a tree data structure
24. An example of grid based resolution refinement
25. Schematic overview of a cluster-cluster force calculation
26. Schematic overview of a particle-cluster force calculation
27. Representations of a quad-tree
28. Spatial tree structure for the example in Section 2.1
29. Tree traversal for the example in Figure 3.5
30. Testing the multipole acceptability criteria
31. Gravitational force interactions required for a sample particle
32. Radiation incident perpendicular to one face of a cuboid
33. Low temperature opacities
34. Opacity as a function of temperature at constant density
35. Radiators and receivers
36. Radiation and absorption test scenario
37. Demonstrating erroneous grid absorption
38. Radiation tree construction
39. Example pruned radiation trees
40. Calculating the tree absorption properties
41. Example constrained random walks for uniform leaf depth
42. Power packet walk scenarios
43. Sub-square absorption example
44. Example constrained random walks for multiple leaf depths
45. Tree neighbour search
46. Example random walks demonstrating enhanced absorption
47. Example absorption softening
48. Radiation incident perpendicular to one face of a leaf
49. Stereo representations of HCP and BCC spherical structures
50. Main free-fall mass radii curves
51. Free-fall test: Uniform grid - point mass force
52. Free-fall test: Uniform grid - softened force
53. Free-fall test: Displaced grid - softened force
54. Comparison of experimental free-fall deviations
55. Comparison of density profiles
56. Oscillation of polytropes: Variable number of particles
57. Oscillation of polytropes: Variable viscosity
58. Comparison of experimental with theoretical luminosity
59. Point source absorption test
60. Equilibrium distribution of particle temperatures
61. Point source equilibrium temperature test
62. Evolved temperature distribution after one time-step
63. Temperature evolution during the course of the simulation
64. Contracting protoplanets: Comparison of resolution
65. Dynamic equilibrium temperature profiles
66. Contracting protoplanets: 1067 particles
67. Orbital components of a typical encounter
68. An example quasi-statically collapsing protostar encounter.
69. Tidal induced fragmentation followed by capture
70. An example near free-fall encounter: Without solar radiation
71. Enlarged areas of interest of the encounter in Figure 5.7
72. Fragmentation of the filament into protoplanets
73. An example near free-fall encounter: With solar radiation
74. Enlarged areas of interest of the encounter in Figure 5.10
75. Protoplanetary evolution
76. Point source radiation test scenario

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