... gases1.1
A completely dissociated hydrogen mix is an appropriate approximation for the temperatures considered by Jeans. A molecular hydrogen-helium mix of gases results in a coefficient equal to $2.1\times10^{21}$, see Equation 2.38 in Chapter 2 for further details.
... formed1.2
See Section 4.2 for an example of this type of behaviour.
... cloud1.3
See Golanski (1999) for recent modelling of this.
... investigation2.1
The major new additions are presented in Section 2.3, Section 2.9, and Section 2.11.
... mass2.2
For simplicity, the mass of the particles are assumed to be the same and constant in this discussion.
... neighbour2.3
The number of neighbours of a particle is a global constant, denoted conventionally by $N_{N}$.
... only2.4
Both hydrodynamic and gravitational forces are of this type, See Section 2.5 and Section 2.8.
... field2.5
See Section 2.10 for an example of this.
... two2.6
The vibrational energy has both kinetic and potential energy associated with it.
... clarity2.7
Less than $5\%$ of the total internal energy of the gas at the evaporation temperature of icy grains, $\approx 150K$, was absorbed.
... conservation2.8
Achieved by equating the change in kinetic energy to the change in internal energy.
... simulation2.9
See Serna et al. (1996) for further discussion on the $\nabla h$ terms.
... time-step2.10
When radiation transport is implemented, FSAL cannot be used, see Section 3.2.
... large3.1
Some implementations of SPH use values as large as $N_{N}=100$ in three dimensions.
... opacity3.2
Modelling stars and star formation for example.
... grid3.3
Although linear interpolation from surrounding grid cells could be used for this purpose, the properties of the grid cell in which the interparticle point resides in is used for computational speed.
...#tex2html_wrap_inline4919#3.4
If $\rho_{ig}$ in Equation 3.35 were to be expanded using Equation 3.9, the expected contribution of the specific internal energy from $i$ to $g$ would result: $u_{ig}$=$u_{i}$.
... fraction4.1
The packing fraction is a term used in crystallography, calculated by assuming that the particles are touching solid spheres. It is defined as the fraction of the volume of an infinite crystal structure, which is occupied by the spheres.
... density4.2
Setting the number of neighbours to $1$ produces a density profile across the system similar to that demonstrated in Figure 2.2(a) in Chapter 2, only more extreme.
... occur4.3
When a virtual layer of leafs is employed to attenuate the energy radiated from surface leafs, see Section 5.1 in Chapter 5, this virtual layer also attenuates energy received from point sources for consistency.
... time4.4
The actual optical depth across this body is around $\tau=1000$ at 25K raising to around $\tau=50000$ at 255K. This value of the time-step was determined by trial and error.
... material5.1
The most important assumptions, with respect to radiation transfer, are that the material is well mixed, its constituent gases and dust are in local thermal equilibrium, and that the material is grey (with respect to its opacity).
... originate5.2
For consistency, the virtual layer of leafs also attenuates radiation received from point sources.
... valid5.3
For example, if the grains responsible for the opacity at these temperatures are not in LTE with the gas, or that they have segregated to the centre of the body.
... magnitude5.4
See Figure 3.12 in Chapter 3.
... condensations5.5
In theory, a self contained condensation must contain at least $N_{N}$ particles. In practice, condensations tend not to form with less than around $3N_{N}$ particles contained in them.
... viscosity5.6
The artificial viscosity used in this implementation of SPH, is known to have problems associated with spurious transport of angular momentum, especially where rotating bodies modelled with a small number of particles are concerned(e.g., Navarro and Steinmetz, 1997; Lombardi et al., 1999).