uniform_sphere.hpp File Reference

A uniform sphere of cold particles: the configuration for scaling work. More...

#include "orrery/core/particle_data.hpp"
#include "orrery/core/random.hpp"
#include "orrery/core/types.hpp"

Go to the source code of this file.

Classes
struct	orrery::initial_conditions::UniformSphereParameters
	A sphere of uniform density to sample. More...

Functions
core::ParticleData	orrery::initial_conditions::make_uniform_sphere (const UniformSphereParameters &parameters, core::RandomSource &random)
	Sample count particles uniformly through the sphere, at rest.
core::Real	orrery::initial_conditions::uniform_sphere_potential_energy (const UniformSphereParameters &parameters)
	The potential energy of the model, -3 G M^2 / 5 R.

Detailed Description

A uniform sphere of cold particles: the configuration for scaling work.

Performance measurements need a configuration whose only interesting property is how many particles are in it. A Plummer sphere is not that: its density spans several orders of magnitude between the centre and the edge, so the tree depth in Phase 8 varies across the volume and a timing taken from it mixes the cost of the algorithm with the shape of the model. A uniform sphere has one density, a bounded radius, and a tree that is the same depth everywhere, which makes it the honest thing to quote a particles-per- second figure from.

It is also a physics test in its own right. The particles start at rest, so the configuration is the classic cold collapse: it has half the kinetic energy the virial theorem asks for at every radius, falls inward, and passes through a state dense enough to punish an integrator with a fixed timestep. That makes it the natural stress case for the energy conservation results, as against the Plummer sphere, which is the natural equilibrium case.

Its potential energy has a closed form, -3 G M^2 / 5 R, which is the simplest analytic check available on the potential energy diagnostic and needs no sampling theory to interpret.

Function Documentation

make_uniform_sphere()

core::ParticleData orrery::initial_conditions::make_uniform_sphere ( const UniformSphereParameters & parameters, core::RandomSource & random )

nodiscard

Sample count particles uniformly through the sphere, at rest.

Positions are recentred so the centre of mass is at the origin. The velocities are exactly zero and are left alone, since a configuration at rest is already in its own centre-of-mass frame.

Throws std::invalid_argument if the total mass or the radius is not positive.

uniform_sphere_potential_energy()

core::Real orrery::initial_conditions::uniform_sphere_potential_energy ( const UniformSphereParameters & parameters )

nodiscard

The potential energy of the model, -3 G M^2 / 5 R.

The continuum value. A finite sample scatters about it, and, as with the Plummer sphere, falls short of it by about one part in the count because a sample has no self-pairs.