Documentation

Submodules

Time integration

This submodule can be used to integrate in time new or already existing simulation.

diffenix.time_integration.new_simulation(consts_params: dict | None = None, directory_params: str | None = None) → tuple[str, dict[str, Any]][source]

Add directories/files needed to save the new simulation

Parameters

consts_paramsdict, optional

The dictionary with all constantes and parameter for the simulation, default use the globals values defined in: Constantes.py

directory_paramsstr, optional

The path to a directory containing several .npz files for a given set of constants. The first non integrated set of constant will be used for this new simulation

Returns

tuple[str, dict[str, Any]]: the name of the new simulation’s directory the dictionary with all the constants

diffenix.time_integration.restart(number: int | str, tf: float64 = np.float64(100.0), save_time_step: float64 = np.float64(0.1), rtol: float64 | None = None, method: str | None = None, integrate_only_surface_density: bool = False) → Sol[source]

Restart the simulation number

Parameters

numberint: The number of the simulation to be restarted

tf : np.float64, optional, default = 10 Myr

save_time_stepnp.float64, optional, default = 0.1 Myr: The time-steps to save the simulation
integrate_only_surface_densitybool, optional, default=False: To integrate only the evolution of surfaces densitys

Returns

Sol: The integrated solution

diffenix.time_integration.time_integration(tf: float64 = np.float64(100.0), save_time_step: float64 = np.float64(0.1), consts_params: dict | None = None, directory_params: str | None = None, integrate_only_surface_density: bool = False) → Sol[source]

Build a new simulation and integrate it until tf

Parameters

tf : np.float64, optional, default = 10 Myr

save_time_stepnp.float64, optional, default = 0.1 Myr: The time-steps to save the simulation
consts_paramsdict, optional: The dictionary with all constantes and parameter for the simulation, default use the globals values defined in Constantes.py
directory_paramsstr, optional: The path to a directory containing several .npz files for a given set of constants. The first non integrated set of constant will be used for this new simulation
integrate_only_surface_densitybool, optional, default=False: To integrate only the evolution of surfaces densitys

Returns

Sol: The new simulation

Systems

All of the operations related to the gas evolution are mades in this submodule. The object Sol contain all the informations nedded to run the simulation and the results. It also have dedicated plot method that generate several Phenigraph Graphique that can be modified after by the user.

class diffenix.systems.Sol(filename: str = '', consts: dict | None = None, directory='', mdot_st: float64 = np.float64(1e-20), mus0: ndarray | None = None, mass_fracs0: ndarray | None = None, noms_mus0: ndarray[str] | None = None)[source]

Bases: object

The object contains all the information needed tu run and exploits a viscous diffusion simulation. It can be saved into a compressed .npz file. This object can generate phenigraph’s Graphique to analyze the results.

add_planets_to_graph(graph: Graphique, name_planets: list | ndarray | None = None, show: bool = False) → None[source]

Add a gray-shaded area for each planet representing there influence zone (the zone where they accrete) to a given Graphique (assuming the x-axis is in code unit)

Parameters

graphg.Graphique: The Graphique to which represent the planets
name_planetslist[str] | np.ndarray[str], optional, default=None: A list with the planet’s name, if not None, the gray shaded area will be replaced by colored shaded area (one for each planet) and the label will be name_planets
showbool, default=False: To show the Graphique after the operation

Returns

None

calc_flux_radmc(temporal_size: int = 50, size_grid: int = 20, incl: float64 = 13, phi: float64 = 59.0) → None[source]

calc_single_flux_radmc(i: int, directory: str | None = None, size_grid: int = 128, incl: float64 = 13, phi: float64 = 59.0) → ndarray[float64][source]

Parameters

i: int: The index at which the surface density is plotted
directorystr, default=self.directory+’/’+i: The directory where the configuration are stored
size_gridint, default=128: The size of the spatial grid (the water surface density is interpolated on it)

Returns

np.ndarray[np.float64]: The spatially integrated luminosity flux

compteur: int = 0

constantes() → dict[source]

All the constants needed for the integration

Returns

dictdict

A dictionary with all the constantes :

C_L : np.float64, 1/6371009 m -> au: length conversion factor
C_M : np.float64, 1/(5.9722*1e24) kg -> Mearth : mass conversion factor
C_t : np.float64, 1 / (3600 * 24 * 365.25 * 1e6) : s-> 1 Myr : time conversion factor
Ts : np.float64, Surface temperature of the central star
Ms : np.float64, Mass of the central star
Rs : np.float64, Radius of the central star
Ls : np.float64, Luminosity of the central star
a_in : np.float64, Inner radius of the integration domain
a0 : np.float64,
a_out : np.float64, Outer radius of the integration domain
T0 : np.float64, Temperature at a0
mH_init : np.float64, The initial hydrogen mass
AB_mdot_st_init : np.float64, The gas mass generation rate that generate the initial steady state
AB_Mbelt : np.float64, Asteroid belt’s size
AB_Abelt : np.float64, Asteroids albedo
AB_a0 : np.float64, Asteroid belt’s central radius
AB_delta_r : np.float64, Half of asteroid belt size
AB_K : np.float64, Thermal diffusion coefficient in asteroids
AB_Phi : np.float64, Porosity
AB_rp : np.float64, Asteroid’s pore radius
AB_f_ice : np.float64, Ice to total mass ratio
AB_rho_refr : np.float64, Refractory’s materials density in asteroids
AB_rho_ice : np.float64 Ice density
AB_sublimation_model : str, {“none”, “thermal_full”, “constant_rate”} The model use to estimate

the gas generation rate for the asteroid belt :

none : No gas is produced
thermal_full : the gas is produced by sublimation : all sublimation, thermal diffusion and molecular

diffusion are take into acompte

constant_rate : The gas is produced at a constant rate of const_mdot

AB_const_mdot : np.float64, The gass mass generation rate for a constant_rate sublimation model
AB_SD_amax : np.double, Maximum size of asteroids
AB_SD_abig : np.double, Intermediate size
AB_SD_amed : np.double, Medium size for size distribution
AB_SD_amin : np.double, Minimal size
AB_SD_qh : np.double, Power slope of the distribution between abig and amax
AB_SD_qm : np.double, Power slope of the distribution between amed and abig
AB_SD_ql : np.double, Power slope of the distribution between amin and amed
AB_s_min: np.float64 = np.double(316) * C_L # Minimum size for collision model
AB_sb: np.float64 = np.double(316) * C_L # Intermediate size for collision model
AB_s_max: np.float64 = np.double(316) * C_L # Maximum size for collision model
AB_e: np.float64 = np.double(0.075) # Eccentricity
AB_i: np.float64 = AB_e / np.double(2.) # Inclination
AB_As: np.float64 = np.double(5.) * C_E / C_M # Massique energy to disrupt the asteroids
AB_bs: np.float64 = np.double(-0.1)
AB_bg: np.float64 = np.double(0.5)
AB_t0_diss: np.float64 = 10 * Gyr # Belt’s lifetime before dissipation
AB_t1_diss: np.float64 = 10 * Gyr # Dissipation timescale
KB_mdot_st_init : np.float64, The gas mass generation rate that generate the initial steady state
KB_Mbelt : np.float64, Kuiper belt’s mass
KB_Abelt : np.float64, KBO’s albedo
KB_a0 : np.float64, Kuiper belt central radius
KB_delta_r : np.float64, Half of Kuiper belt size
KB_K : np.float64, Thermal diffusion coefficient in KBO
KB_Phi : np.float64, KBO’s porosity
KB_rp : np.float64, KBO’s pore’s radius
KB_f_ice : np.float64, Initial ice to total mass ratio in KBO
KB_rho_refr : np.float64, Refractory’s materials density in KBO
KB_rho_ice : np.float64, Ice density
KB_sublimation_model : str, {“none”, “thermal_full”, “constant_rate”} The model use to estimate the

gas generation rate for the Kuiper belt:

none : No gas is produced

thermal_full : the gas is produced by sublimation : all sublimation, thermal diffusion and molecular

diffusion are take into acompte

constant_rate : The gas is produced at a constant rate of const_mdot

KB_const_mdot : np.float64, The gass mass generation rate for a constant_rate sublimation model
KB_SD_amax : np.double, Maximum size of KBO
KB_SD_abig : np.double, Intermediate size
KB_SD_amed : np.double, Medium size
KB_SD_amin : np.double, Minimal size
KB_SD_qh : np.double, Power slope of the distribution between abig and amax
KB_SD_qm : np.double, Power slope of the distribution between amed and abig
KB_SD_ql : np.double, Power slope of the distribution between amin and amed
KB_s_min: np.float64 = np.double(316) * C_L # Minimum size for collision model
KB_sb: np.float64 = np.double(316) * C_L # Intermediate size for collision model
KB_s_max: np.float64 = np.double(316) * C_L # Maximum size for collision model
KB_e: np.float64 = np.double(0.075) # Eccentricity
KB_i: np.float64 = KB_e / np.double(2.) # Inclination
KB_As: np.float64 = np.double(5.) * C_E / C_M # Massique energy to disrupt the asteroids
KB_bs: np.float64 = np.double(-0.1)
KB_bg: np.float64 = np.double(0.5)
KB_t0_diss: np.float64 = 10 * Gyr # Belt’s lifetime before dissipation
KB_t1_diss: np.float64 = 10 * Gyr # Dissipation timescale
a_planet : list[np.double], planet’s semi-major axis
m_planet : list[np.double], planet’s masses
f_accr : np.float64, Hydrodynamic accretion efficiency
t0 : The dissipation time of the protoplanetary disc
IT_s : int, number of spatial steps
dip : int, half of the number of sink cells for a given planets to model the accretion
rtol : np.float64, Relative tolerance for temporal integration
atolnp.float64, Absolute tolerance for temporal integration (by default too small hence to
relative tolerance will always be the limiting factor)
method_root : str, ‘LSODA’,’BDF’,’DOP853’,’RK45’ : Temporal integration method_root

get_final_mass_fractions(y: ndarray, tps: float64, step: int = 1, x: float64 | None = None) → ndarray[source]

Transform the result get by solve_ivp for the integration of the mass fractions to the format of self.sigmas

Parameters

ynp.ndarray: result of solve_ivp
tpsnp.ndarray: times associated with y
stepint, optional, default=: Only the tps[::step] will be saved
xnp.ndarray, optional, default: self.x: The radial coordinate

Returns

None

get_final_surface_densitys(y: ndarray, tps: ndarray, step: int = 1) → None[source]

Save into this Sol the result of a temporal integration contain in ys. This save a fraction of y in self.f (fraction given by step) and calculate some test variable such as the flux at the planets levels or the variables needed to calculate the mass conservation (inner and outer flux, total mass produced…)

Parameters

ynp.ndarray: result of solve_ivp = sigma * (r ** (2 + pls_temp))
tpsnp.ndarray: times associated with y
stepint, optional, default=: Only the tps[::step] will be saved

Returns

None

graph_image_surface_density(species: int | ndarray | list[int] = 9223372036854775807, plot_sigma_crit: bool = True, vmin: float64 | str = np.float64(1e-10), vmax: float64 | str | None = None, size_time: int = 500, size_radius: int = 1000, color_sigma_crit_h2o: str | tuple = 'w', color_sigma_crit_co: str | tuple = 'g', cmap: str = 'inferno', nb_levels: int = 10, color_min: str | tuple | None = None, color_max: str | tuple | None = None, plot_planets: bool = True, planets_names: list[str] | None = None, show: bool = True, save: bool = False, directory: str | None = None, plot_label_levels: bool = True, **kwargs_ax) → Graphique[source]

Build a Graphique that represant the evolution of surface density as function of time and radius

Parameters

speciesstr | int, optional

The specie for which the surface density is represanted, default the total surface density is represanted

plot_sigma_critbool, optional, default = True

To plot a specific level line at the critical surface density

vminnp.float64 | str , optional, {“auto”, np.loat64}, default = 1e-10 * Mearth / Myr

The minimum value of surface density to represant in the result (below it will be considered as saturated) If “auto”, the minimal value will be the minimal value of the surface density represanted

vmaxnp.float64 | str, optional, {“auto”, np.loat64},

The maximum value of surface density to represant in the result (above it will be considered as saturated) Default, v_max is not considered like for “auto” where the maximal value will be the maximal value of the surface density represanted

size_timeint, optional, default=1000

The image’s size for the time coordinate (x-axis)

size_radiusint, optional, default=1000

The image’s size for the radius coordinate (y-axis)

color_sigma_crit_h2ostr, optional, default = “w”

The color of the level line associated with the critical surface density of water

color_sigma_crit_costr, optional, default = “g”

The color of the level line associated with the critical surface density of CO

cmapstr, optional, default = “inferno”

The colormap used for the image

nb_levelsint, optional, default=10

The number of levels in the image: The number of levels to plot in addition to the image

color_minstr | tuple, optional

The color associated with the minimum value for a default cmap

color_maxstr | tuple, optional

The color associated with the maximum value for a default cmap

plot_planetsbool, optional, default = True

Whether or not to plot a grey shaded era that delimitate the planet’s sink cell’s era

planets_nameslist[str], optional

A list of names for the planets to write close to the grey shadeds eras

plot_label_levelsbool, optional, default=False

To plot (or not) labels for the contours (if True, labels are only plot every two levels)

showbool, optional, default = True

Whether to show the image

savebool, optional, default = False

Whether to save the image (if True, both the Graphique and the png image will be saved)

directorystr, optional

The directory to save the Graphique, default=self.directory

Returns

g.Graphique

graph_surface_density(times: ndarray | None = None, idx: ndarray | None = None, species: int | ndarray | list[int] = 9223372036854775807, plot_mean_volumique_density: bool = False, include_last_index: bool = False, plot_sigma_crit: bool = True, name_planets: ndarray[str] | list[str] | None = None, show: bool = True, save: bool = False, directory: str | None = None, lw: float64 = 2.0, **args_ax) → Graphique[source]

Create a Graphique of surface density as a function of radius for different time for given species

Parameters

timesnp.ndarray, optional,: table of the times we want to show the surface density. If None and idx is None, an arbitrary subset of self.tps will be taken
idxnp.ndarray, optional: index table of self.tps we want to show the surface density. If None, an arbitrary subset of self.tps will be taken
speciesint | str | np.ndarray | list[int] | list[str], optional, default: plot all species: the species we want to show (if -1 plot the total surface density), if < number of species plot the species associated with self.mu[species] else plot all the species if str, the specie associated with this name is plotted
plot_mean_volumique_densitybool, optional, default=False: If True plot the volumique density instead of the surface density
include_last_indexbool, optional, default=False: Systematically include the last surface density (even if self.tps[-1] is not in time)
plot_sigma_critbool, optional, default=True: To plot a line at the critical surface density to shield the main molecule
name_planets: The planet’s names. If not None (default), plot a vertical line at the planet’s positions
showbool, optional, default=True: To show the Graphique before returning it
savebool, optional, default=False: To save the Graphique
directorystr, optional, default=self.directory: The directory of the Graphique
lwint, optional, default=2: The line-weight of surface density
args_axdict: additional keywords argument for the generation of the axis associated with the graphique (ex

x_lim=[1,100])

Returns

g.Graphique: the requested Graphique

graphs(plot_planets=True, planets_names: list[str] | None = None, show: bool = True, save: bool = False, directory: str | None = None) → list[Graphique][source]

graphs_accretion(name_planets: list[str] | ndarray[str] | None = None, show: bool = False, directory: str | None = None, save: bool = False, times: ndarray[float64] | None = None, absolute: bool = False, include_last_index: bool = True) → list[Graphique][source]

initialization(mus0: ndarray, mass_fracs0: ndarray, nom_mus0) → None[source]: Initialize the solution with a steady state of the first element generated by a 10**-10 Mearth/Myr gas generation rate The radii are linearly spaced between a_min and a_max with IT_s points

Returns

None

interp_sigma(t: float64) → float64 | ndarray[float64][source]

Return surface density

Parameters

iint, optional: The index at wich calculate sigma

Returns

np.float64 | np.ndarray

mass_conservation() → ndarray[source]

Calculate the mass conservation in the whole system

Returns

np.ndarray: An array fo size self.diag[“time”], equal to zero only if the mass is conserved

mass_flux(i: int | ndarray = 9223372036854775807) → ndarray[source]

The mass flux for the temporal index(s) i of tps/f

Parameters

iint | np.ndarray, optional, default: the radial speed is calculated for every index: The temporal index(s) from which calculate the radial speed

Returns

np.ndarray: The mass flux

momentum_conservation() → ndarray[source]

Calculate the momentum conservation in the whole system

Returns

np.ndarray: An array fo size self.diag[“time”], equal to zero only if the mass is conserved

radial_speed(i: int | ndarray = 9223372036854775807) → ndarray[source]

The radial speed for the temporal index(s) i of tps/f

Parameters

iint | np.ndarray, optional, default: the radial speed is calculated for every index: The temporal index(s) from which calculate the radial speed

Returns

np.ndarray: The radial speed

radmc_setup(i: int, directory: str | None = None, size_grid: int = 128) → None[source]

Generate the configuration file for radmc3d for the surface density at time self.tps[i]

Parameters

i: int: The index at which the surface density is plotted
directorystr, default=self.directory+’/’+i: The directory where the configuration are stored
size_gridint, default=128: THe size of the spatial grid (the water surface density is interpolated on it)

Returns

None

save(filename: str = '', directory: str = './') → None[source]

Save the object in the compressed format .npz

Parameters

filenamestr, optional, default=self.filename: The name of the .npz file
directorystr, optional, default=self.filename: The name of the directory of the .npz file. If there is any “/” in filename, then it will be assumed that filename contains the whole path to the file and directory will be ignored

Returns

None

sigma(i: int = 9223372036854775807) → float64 | ndarray[float64][source]

Return surface density

Parameters

iint, optional: The index at wich calculate sigma

Returns

np.float64 | np.ndarray

split_y(y: ndarray) → ndarray[source]

Split y the argument of the time integration system in n lists, n the number of chemical elements

Parameters

ynp.ndarray: The array to be reshaped

Returns

np.ndarray: masses_fractions(y)

time_integration(tf: float64, dtmax: float64 = np.float64(inf), build_graphs: bool = False, integrate_only_surface_density: bool = False) → None[source]

Time integration of surface density and mass fraction until tf The surface density is integrated first Steps of 0.3 Myr are made to save the result

Parameters

tfnp.float64

The final integration time

dtmaxnp.float64, optional, default=the maximum timestep to keep a stable spatial integration of surface

density: The maximum timestep

build_graphsbool, optional, default=True

To build and save surface density and accretions Graphiques

integrate_only_surface_densitybool, optional, default=False

To integrate only the evolution of surfaces densitys

Returns

None

total_mass() → ndarray[source]: Calculate the total mass as a function of time

Returns

turbulent_speed(i: int | ndarray = 9223372036854775807) → ndarray[source]

The turbulent speed for the temporal index(s) i of mass_fractions

Parameters

iint | np.ndarray, optional, default:the turbulence speed is calculated for every index: The temporal index(s) from which calculate the radial speed

Returns

np.ndarray: The turbulent speeds

update_constantes(dic: dict) → None[source]

Update all the constants needed for the integration

Parameters

dic: dict

A dictionary with all the constantes :

C_L : np.float64, 1/6371009 m -> au: length conversion factor
C_M : np.float64, 1/(5.9722*1e24) kg -> Mearth : mass conversion factor
C_t : np.float64, 1 / (3600 * 24 * 365.25 * 1e6) : s-> 1 Myr : time conversion factor
Ts : np.float64, Surface temperature of the central star
Ms : np.float64, Mass of the central star
Rs : np.float64, Radius of the central star
Ls : np.float64, Luminosity of the central star
a_in : np.float64, Inner radius of the integration domain
a0 : np.float64,
a_out : np.float64, Outer radius of the integration domain
T0 : np.float64, Temperature at a0
mH_init : np.float64, The initial hydrogen mass
AB_mdot_st_init : np.float64, The gas mass generation rate that generate the initial steady state
AB_Mbelt : np.float64, Asteroid belt’s size
AB_Abelt : np.float64, Asteroids albedo
AB_a0 : np.float64, Asteroid belt’s central radius
AB_delta_r : np.float64, Half of asteroid belt size
AB_K : np.float64, Thermal diffusion coefficient in asteroids
AB_Phi : np.float64, Porosity
AB_rp : np.float64, Asteroid’s pore radius
AB_f_ice : np.float64, Ice to total mass ratio
AB_rho_refr : np.float64, Refractory’s materials density in asteroids
AB_rho_ice : np.float64 Ice density
AB_sublimation_model : str, {“none”, “thermal_full”, “constant_rate”} The model use to estimate

the gas generation rate for the asteroid belt :

none : No gas is produced
thermal_full : the gas is produced by sublimation : all sublimation, thermal diffusion and molecular

diffusion are take into acompte

constant_rate : The gas is produced at a constant rate of const_mdot

AB_const_mdot : np.float64, The gass mass generation rate for a constant_rate sublimation model
AB_SD_amax : np.double, Maximum size of asteroids
AB_SD_abig : np.double, Intermediate size
AB_SD_amed : np.double, Medium size for size distribution
AB_SD_amin : np.double, Minimal size
AB_SD_qh : np.double, Power slope of the distribution between abig and amax
AB_SD_qm : np.double, Power slope of the distribution between amed and abig
AB_SD_ql : np.double, Power slope of the distribution between amin and amed
AB_s_min: np.float64 = np.double(316) * C_L # Minimum size for collision model
AB_sb: np.float64 = np.double(316) * C_L # Intermediate size for collision model
AB_s_max: np.float64 = np.double(316) * C_L # Maximum size for collision model
AB_e: np.float64 = np.double(0.075) # Eccentricity
AB_i: np.float64 = AB_e / np.double(2.) # Inclination
AB_As: np.float64 = np.double(5.) * C_E / C_M # Massique energy to disrupt the asteroids
AB_bs: np.float64 = np.double(-0.1)
AB_bg: np.float64 = np.double(0.5)
AB_t0_diss: np.float64 = 10 * Gyr # Belt’s lifetime before dissipation
AB_t1_diss: np.float64 = 10 * Gyr # Dissipation timescale
KB_mdot_st_init : np.float64, The gas mass generation rate that generate the initial steady state
KB_Mbelt : np.float64, Kuiper belt’s mass
KB_Abelt : np.float64, KBO’s albedo
KB_a0 : np.float64, Kuiper belt central radius
KB_delta_r : np.float64, Half of Kuiper belt size
KB_K : np.float64, Thermal diffusion coefficient in KBO
KB_Phi : np.float64, KBO’s porosity
KB_rp : np.float64, KBO’s pore’s radius
KB_f_ice : np.float64, Initial ice to total mass ratio in KBO
KB_rho_refr : np.float64, Refractory’s materials density in KBO
KB_rho_ice : np.float64, Ice density
KB_sublimation_model : str, {“none”, “thermal_full”, “constant_rate”} The model use to estimate the

gas generation rate for the Kuiper belt:

none : No gas is produced

thermal_full : the gas is produced by sublimation : all sublimation, thermal diffusion and molecular

diffusion are take into acompte

constant_rate : The gas is produced at a constant rate of const_mdot

KB_const_mdot : np.float64, The gass mass generation rate for a constant_rate sublimation model
KB_SD_amax : np.double, Maximum size of KBO
KB_SD_abig : np.double, Intermediate size
KB_SD_amed : np.double, Medium size
KB_SD_amin : np.double, Minimal size
KB_SD_qh : np.double, Power slope of the distribution between abig and amax
KB_SD_qm : np.double, Power slope of the distribution between amed and abig
KB_SD_ql : np.double, Power slope of the distribution between amin and amed
KB_s_min: np.float64 = np.double(316) * C_L # Minimum size for collision model
KB_sb: np.float64 = np.double(316) * C_L # Intermediate size for collision model
KB_s_max: np.float64 = np.double(316) * C_L # Maximum size for collision model
KB_e: np.float64 = np.double(0.075) # Eccentricity
KB_i: np.float64 = KB_e / np.double(2.) # Inclination
KB_As: np.float64 = np.double(5.) * C_E / C_M # Massique energy to disrupt the asteroids
KB_bs: np.float64 = np.double(-0.1)
KB_bg: np.float64 = np.double(0.5)
KB_t0_diss: np.float64 = 10 * Gyr # Belt’s lifetime before dissipation
KB_t1_diss: np.float64 = 10 * Gyr # Dissipation timescale
a_planet : list[np.double], planet’s semi-major axis
m_planet : list[np.double], planet’s masses
f_accr : np.float64, Hydrodynamic accretion efficiency
t0 : The dissipation time of the protoplanetary disc
IT_s : int, number of spatial steps
dip : int, half of the number of sink cells for a given planets to model the accretion
rtol : np.float64, Relative tolerance for temporal integration
atolnp.float64, Absolute tolerance for temporal integration (by default too small hence to
relative tolerance will always be the limiting factor)
method_root : str, ‘LSODA’,’BDF’,’DOP853’,’RK45’ : Temporal integration method_root

Returns

None

y(i: int) → ndarray[source]

Return the masses fractions flatten into a one dimensional array for a given time (argument of the time integration system)

Parameters

iint: The index to which return the mass fraction

Returns

diffenix.systems.T(r: ndarray | float64, t: float64 = -1, Ms: float64 = np.float64(332942.6342051505)) → ndarray | float64[source]

Calculate and return the temperature at radius r

Parameters

rnp.ndarray: radius
tnp.ndarray: The current time

Returns

np.ndarray | np.float: The temperature

diffenix.systems.T0(t: float64 = -1, a0: float64 = np.float64(2.6499999999999995), Ms: float64 = np.float64(332942.6342051505)) → ndarray | float64[source]

Calculate and return the temperature at a0

Parameters

tnp.ndarray: The current time
a0np.float64: The distance to the central star at wich the temperature is calculated
Msnp.float64: The mass of the central star

Returns

np.ndarray | np.float: The temperature

diffenix.systems.boundary_conditions(ys: ndarray, sol: Sol) → ndarray[source]

Define the inner and outer boundary conditions for the surface density

Parameters

ysnp.ndarray: log of surface density
Nunp.ndarray: Viscosity
solSol: Associated Sol

Returns

np.ndarray

diffenix.systems.boundary_conditions_mf(ys: ndarray, sol: Sol) → ndarray[source]

Define the inner and outer boundary conditions for the mass fractions

Parameters

ysnp.ndarray: Mass fractions
Nunp.ndarray: Viscosity
solSol: Associated Sol

Returns

np.ndarray

diffenix.systems.mass_flux(sol: Sol, ys: ndarray, t: float64) → ndarray[source]

Calculate the total mass flux for a given sigma, sol and m_out

Parameters

solSol: Associated Sol
ysnp.ndarray: sigma * r ** (2 + pls_temp)
tnp.float64: time

Returns

np.ndarray: the radial speed

diffenix.systems.mass_frac_dot(t: float64, ys: ndarray, sol: Sol) → ndarray[source]

Calculate the gas generation and destruction rate relatively to each species, The accretion onto planet is not expected to have any influence onto the mass fraction

Parameters

tnp.float64: the current time
ysnp.ndarray: The mass fractions shape=(n_species, len(self.r))
solSol: Object Sol associated with the resolution

Returns

np.ndarray

diffenix.systems.mass_steady_state(sol: Sol, mdot: float64 | None = None, a0: float64 | None = None, mu: float64 | None = None) → float64[source]

Return the mass of a steady state disc where gas is produced at radius a0 with a mass generation rate mdot

Parameters

solSol: The associated Sol
mdotnp.float64: Mass input rate at a0, if mtot is not None, this parameter is ignored
a0np.float64, optional, default=sol.a0: The radius at wich the gas is produced
munp.float64: Mean molar mass, default sol.mu.mean()

Returns

np.ndarray: the surface density of the steady state

diffenix.systems.merge_y(y: ndarray) → ndarray[source]

Do the inverse operation of split_y

Parameters

ynp.ndarray: The array to be reshaped

Returns

np.ndarray: The new array

diffenix.systems.new_space_grid(old_grid: ndarray[float64], last_masse_frac: ndarray[float64]) → ndarray[float64][source]

diffenix.systems.radial_speed(sol: Sol, ys: ndarray, t: float64) → ndarray[source]

Calculate the radial speed for a given sigma, sol and m_out

Parameters

solSol: Associated Sol
ysnp.ndarray: sigma * r ** (2 + pls_temp)
tnp.float64: time

Returns

np.ndarray: the radial speed

diffenix.systems.sigma_dot(t: float64, ys: ndarray, phi: ndarray, sol: Sol) → ndarray[source]

Calculate the gas generation and destruction rate

Parameters

tnp.float64: the current time
ysnp.ndarray: sigma * (r**(2 + alpha_t))
phinp.ndarray: mass flux
solSol: Object Sol associated with the resolution

Returns

np.ndarray: sigma_dot

diffenix.systems.split_y(y: ndarray, len_radius: int, nb_species: int) → ndarray[source]

Split y the argument of the time integration system in n lists, n the number of chemical elements

Parameters

ynp.ndarray: The array to be reshaped
len_radiusint: The lenght of the radius array
nb_speciesint: The number of chemicals species

Returns

np.ndarray: masses_fractions(y)

diffenix.systems.steady_state(sol: Sol, mdot: float64 | None = None, mtot: float64 | None = None, a0: float64 | None = None, mu: float64 | None = None)[source]

Return the log of steady state for a given mdot

Parameters

solSol: The associated Sol
mdotnp.float64: Mass input rate at a0, if mtot is not None, this parameter is ignored
mtotnp.float64, optional: The disc’s total mass,
a0np.float64, optional, default=sol.a0: The radius at wich the gas is produced
munp.float64: Mean molar mass, default sol.mu.mean()

Returns

np.ndarray: the surface density of the steady state

diffenix.systems.system_mass_fraction(t: float64, y: array, sol: Sol, verbose: bool = True) → ndarray[source]

Define the system to integrate in time to get the evolution of mass fractions, the spatial differentiation is made here to estimate the spatial derivatives

Parameters

tnp.float64: The current time
ynp.ndarray: The one dimensional array of mass fractions (shape=(n_species*len(self.r)))
solSol: The associated Sol
verbosebool, optional, default=True: To print some information

Returns

np.ndarray: d(log(sigma)/dt

diffenix.systems.system_sigma_tot(t: float64, y: array, sol: Sol, verbose: bool = True) → ndarray[source]

Define the system to integrate in time to get the evolution of surface density. The spatial differentiation is made here to estimate the spatial derivatives

Parameters

tnp.float64: The current time
ynp.ndarray: The log of surface density
solSol: The associated Sol
verbosebool: To print some information

Returns

np.ndarray: d(log(sigma)/dt

diffenix.systems.turbulent_speed(y: ndarray, sol: Sol, t: float64) → ndarray[source]

Calculate the turbulent speed for a given sigma, sol and m_out

Parameters

ynp.ndarray: mass fractions at time t
solSol: Associated Sol
tnp.float64: time

Returns

np.ndarray: the radial speed

Solve asteroid belt

All of the operations related to the gas prodcution rate are made in this submodule. The Sol_ast_belt object is used by the Sol object of the system module to estimate the gas production rate

class diffenix.solve_asteroid_belt.Compteur[source]

Bases: object

This object can be used to estimate the number of calls for a function if given in parameter and incremented in the function (mutable object)

class diffenix.solve_asteroid_belt.SolrhoBelt(sublimation_model: str, Mbelt: float64, Ms: float64, a0: float64, delta_a: float64, tinit: float64, tmax: float64, rho_refr: float64, rho_ice: float64, f_ice: float64, A_ast: float64, K: float64, Its: int, Phi: float64, dmin: float64, sb: float64, dmax: float64, e: float64, i: float64, As: float64, bs: float64, bg: float64, Its_p: int, rp: float64, Itt: int, t0_diss: float64, t1_diss: float64, radius: ndarray[float64] | None = None, kwargs_N: dict | None = None, sig_dots: ndarray | None = None, tps: ndarray | None = None, m_init: float64 = np.float64(0.0), const_mdot: float64 = np.float64(0.0), **kwargs)[source]

Bases: object

const(prefix: str = '') → dict[source]

graph_image_surface_density(vmin: float64 | str = np.float64(1.0000000000000003e-10), vmax: float64 | str | None = None, size_time: int = 500, size_radius: int = 1000, cmap: str = 'inferno', nb_levels: int = 10, color_min: str | tuple | None = None, color_max: str | tuple | None = None, show: bool = True, save: bool = False, directory: str | None = None, plot_label_levels: bool = True, **kwargs_ax) → Graphique[source]

Build a Graphique that represant the evolution of surface density generation rate: as function of time and radius

Parameters

vminnp.float64 | str , optional, {“auto”, np.loat64}, default = 1e-10 * Mearth / Myr

The minimum value of surface density to represant in the result (below it will be considered as saturated) If “auto”, the minimal value will be the minimal value of the surface density represanted

vmaxnp.float64 | str, optional, {“auto”, np.loat64},

The maximum value of surface density to represant in the result (above it will be considered as saturated) Default, v_max is not considered like for “auto” where the maximal value will be the maximal value of the surface density represanted

size_timeint, optional, default=1000

The image’s size for the time coordinate (x-axis)

size_radiusint, optional, default=1000

The image’s size for the radius coordinate (y-axis)

cmapstr, optional, default = “inferno”

The colormap used for the image

nb_levelsint, optional, default=10

The number of levels in the image: The number of levels to plot in addition to the image

color_minstr | tuple, optional

The color associated with the minimum value for a default cmap

color_maxstr | tuple, optional

The color associated with the maximum value for a default cmap

plot_label_levelsbool, optional, default=False

To plot (or not) labels for the contours (if True, labels are only plot every two levels)

showbool, optional, default = True

Whether to show the image

savebool, optional, default = False

Whether to save the image (if True, both the Graphique and the png image will be saved)

directorystr, optional

The directory to save the Graphique, default=self.directory

Returns

g.Graphique

return_kwargsN(prefix: str = '') → dict[source]

diffenix.solve_asteroid_belt.linear_interp(t_new, t_old, values)[source]

diffenix.solve_asteroid_belt.mbelt_coll(t: float64, smin: float64 = np.float64(6.684587122268445e-20), smax: float64 = np.float64(2.673834848907378e-05), sb: float64 = np.float64(2.1123295306368286e-09), qp: float64 = np.float64(3.0), qs: float64 = np.float64(1.8333333333333333), qg: float64 = np.float64(1.67), e: float64 = np.float64(0.075), i: float64 | None = None, r: float64 | None = None, dr: float64 = np.float64(3.9999999999999996), As: float64 = np.float64(222498.51379990004), bs: float64 = np.float64(-0.1), bg: float64 = np.float64(0.5), M0: float64 = np.float64(0.01), Ms: float64 = np.float64(332942.6342051505), rho_ast: float64 = np.float64(1401463855786.2883), method_root: str = 'lm', st_est: float64 | ndarray | None = None) → float64 | ndarray[source]

Estimate the masse of a collisional belt as function of time (formula 38 of Löhne et al. 2008)

Parameters

tnp.float64: The time
sminnp.float64: Minimum size of bodys
smaxnp.float64: Maximum size of bodys
sbnp.float64: Medium size
qpnp.float64: Primordial slope as defined in Löhne et al. 2008
qsnp.float64: Intermediate slope
qgnp.float64: Slope for bodys in collisional regim
enp.float64: Eccentricity
inp.float64: Inclination
rnp.float64: Distance of the center of the belt to the central star
drnp.float64: Radial extension of the belt
Asnp.float64: Minimal disruption energy (see formula 1 of Löhne et al. 2008)
bsnp.float64: Slope of the massique disruption energy (see formula 1 of Löhne et al 2008)
bgnp.float64: Slope of the massique disruption energy (see formula 1 of Löhne et al. 2008)
M0np.float64: Initial belt’s mass
Msnp.float64: Central star’s mass
rho_astnp.float64: Density of asteroids/KBO
method_rootstr, optional, default=”lm”: The method for the root-finding routine used to find st the size such as tau(st)=t
st_estnp.float64: Estimation of st

Returns

np.float64 | np.ndarray: mbelt

References

Löhne et al. 2008

diffenix.solve_asteroid_belt.mdot_s(s: float64, t: ndarray, r: ndarray, consts: dict, It_d=300) → ndarray[source]

Compute the gas mass generation rate for a given bodie at differents radius

Parameters

s: np.float64: The size of the considered bodie
t: np.ndarray: The time at which evaluate the gas mass generation rate
r: np.ndarray: The distances from the central star at which evaluate the gas mass generation rate
constsdict: The dictionary of constants
It_dint: The number of iterations

Returns

np.ndarray: the gas mass generation rate as function of time and radius

diffenix.solve_asteroid_belt.mdot_s_l(rd: ndarray, t: ndarray, temp: ndarray, consts: dict) → ndarray[source]

Compute the gas mass generation for a given bodie

Parameters

rdnp.ndarray: The radial coordinates inside the asteroid / KBO
tnp.ndarray: The time
tempnp.ndarray: The array of temperature as function of rd and t calculated by thermal_diff
consts: dict: The dictionary of constants

Returns

np.ndarray: the gas mass generation rate as function of time

diffenix.solve_asteroid_belt.mdot_s_surf(s: float64, t: ndarray, r: ndarray, consts: dict, It_d=300) → ndarray[source]

Compute the gas mass generation rate for a given bodies at differents radius if the gas sublimate only at its surface

Parameters

s: np.float64: The size of the considered bodie
t: np.ndarray: The time at which evaluate the gas mass generation rate
r: np.ndarray: The distances from the central star at which evaluate the gas mass generation rate
constsdict: The dictionary of constants
It_dint: The number of iterations

Returns

np.ndarray: the gas mass generation rate as function of time and radius

diffenix.solve_asteroid_belt.mdot_s_vol(s: float64, t: ndarray, r: ndarray, consts: dict, It_d=300) → ndarray[source]

Compute the gas mass generation rate for a given bodies at differents radius if the gas sublimate in the whole volume neglecting thermal diffusion

Parameters

s: np.float64: The size of the considered bodie
t: np.ndarray: The time at which evaluate the gas mass generation rate
r: np.ndarray: The distances from the central star at which evaluate the gas mass generation rate
constsdict: The dictionary of constants
It_dint: The number of iterations

Returns

np.ndarray: the gas mass generation rate as function of time and radius

diffenix.solve_asteroid_belt.minit(r: ndarray, pinit: float64, rho_ice: float64, a0: float64, delta_a: float64, Mbelt: float64, kwargsN) → float64[source]

diffenix.solve_asteroid_belt.number_density(a, amax: float64, abig: float64, amed: float64, amin: float64, qh: float64, qm: float64, ql: float64, Mtot: float64 = np.float64(1.0), rho: float64 = np.float64(1.0)) → float64 | ndarray[source]

Return the number density of asteroid of size a

Parameters

anp.float64 | np.ndarray: The diameter(s) of asteroids
amaxnp.float64: The maximum diameter
abignp.float64: A reference diameter

amed : np.float64

aminnp.float64: The minimum diameter
qhnp.float64: The slope of distribution for the highest radius
qmnp.float64: The slope of distribution for medium seized asteroids
qlnp.float64: The slope of distribution for the smallest asteroids
Mtotnp.float64, optional, default=1: The total mass of the belt. The result is directly proportional to Mtot. number_density(Mtot)=Mtot*number_density(1.). It can be used to estimate the number density in a belt = sigma*number_density(1.) with sigma the surface density
rhonp.float64: The mean density of asteroids

Returns

np.float64 | np.ndarray: The number density of asteroids for diameter(s) a

diffenix.solve_asteroid_belt.sig_dot_full_diff(tps: ndarray, r: ndarray, const: dict, kwargsN: dict | None = None, It_d: int = 100) → ndarray[source]

Compute the gas surface density generation rate for a belt discribed into the const dictionary

Parameters

tpsnp.ndarray: The time at which evaluate the result
rnp.ndarray: The distance to the central star at which evaluate the solution
constdict: The dictionary of constants
kwargsNdict: The dictionary that defined the size distribution
It_dint: The number of depth steps for thermal diffusion integration

Returns

np.ndarray

diffenix.solve_asteroid_belt.sig_dot_sub_surf(tps: ndarray, r: ndarray, const: dict, kwargsN: dict | None = None, It_d: int = 100) → ndarray[source]

Compute the gas surface density generation rate for a belt discribed into the const dictionary if the sublimation append only at the surface of asteroids

Parameters

tpsnp.ndarray: The time at which evaluate the result
rnp.ndarray: The distance to the central star at which evaluate the solution
constdict: The dictionary of constants
kwargsNdict: The dictionary that defined the size distribution
It_dint: The number of depth steps for thermal diffusion integration

Returns

np.ndarray

diffenix.solve_asteroid_belt.sig_dot_sub_vol(tps: ndarray, r: ndarray, const: dict, kwargsN: dict | None = None, It_d: int = 100) → ndarray[source]

Compute the gas surface density generation rate for a belt discribed into the const dictionary if the sublimation append only at the surface of asteroids

Parameters

tpsnp.ndarray: The time at which evaluate the result
rnp.ndarray: The distance to the central star at which evaluate the solution
constdict: The dictionary of constants
kwargsNdict: The dictionary that defined the size distribution
It_dint: The number of depth steps for thermal diffusion integration

Returns

np.ndarray

diffenix.solve_asteroid_belt.sigma_dot(Mbelt: float64, r: ndarray, tps: ndarray, a0: float64, delta_a: float64, tinit: float64, tmax: float64, f_ice: float64, rho_refr: float64, rho_ice: float64, Abelt: float64, K: float64, Its: int, Phi: float64, dmin: float64, dmax: float64, Its_p: int, rp: float64, Itt: int, kwargsN: dict, **kwargs) → ndarray[source]

Estimate the surface density mass generation rate for asteroids of diameters d at the distance r of the central star and of diameter d in a belt of mass Mbelt during the time times_loc

Parameters

Mbeltnp.float64: The total belt’s mass
rnp.ndarray: The distance to the central star
pnp.ndarray: The asteroids/KBO diameters
tpsnp.ndarray: The time
a0np.float64: The belt’s semi-major axis
delta_anp.float64: The (half) size pf the belt
tinitnp.float64: The initial time
tmaxnp.float64: The maximum time
f_icenp.float64: The initial ice to refractory mass ratio
rho_refrnp.float64: The asteroids/KBO density
rho_icenp.float64: The asteroids/KBO ice density
Abeltnp.float64: The asteroids/KBO albedo
Knp.float64: The thermal diffusion coefficient
Itsnp.float64: The number of spatial steps
Phinp.float64: The porosity (dimensionless number)
dminnp.float64: The minimum diameters
dmaxnp.float64: The maximum diameters
Its_pnp.float64: The number of diameters steps
rpnp.float64: The pore’s radius
Ittnp.float64: The number of time steps
kwargsNdict: The directory with all informations to build the belt’s size number distribution

kwargs : dict

Returns

np.ndarray

diffenix.solve_asteroid_belt.sigmap_rho(t: ~numpy.float64 | ~numpy.ndarray, rr: ~numpy.ndarray, pp: ~numpy.ndarray, consts: dict, comp: ~diffenix.solve_asteroid_belt.Compteur = <diffenix.solve_asteroid_belt.Compteur object>) → ndarray[source]

Calculate and return the gas generation rate at depth p, radius r and time t. This doesn’t take into acompte the limited amonth of material

Parameters

tnp.ndarray | np.float64: The current time
rnp.ndarray | np.float64: The distance to the central star (semi-major axis)
pnp.ndarray | np.float64: The depth into the asteroid/KBO
constsdict: The constantes
compCompteur, optional: To estimate the number of iterations

Returns

np.ndarray | np.float64

diffenix.solve_asteroid_belt.tau_diff(pp: ndarray, rr: ndarray, t: float64 | ndarray, consts: dict) → ndarray[source]

Calculate the diffusion timescale at time t and depth p

Parameters

p: np.ndarray: The depth at which the gas is realised
r: np.ndarray: The distance from the central star at which the gas is realised
t: np.ndarray: The time at which the gas is realised
consts: All the necessary constants

Returns

np.ndarray: The time needed for the gas to go at the surface

diffenix.solve_asteroid_belt.temp_belt(r: ndarray | float64, t: float64 | ndarray, consts: dict) → ndarray | float64[source]

Calculate and return the temperature at radius r and time t

Parameters

rnp.ndarray | np.float64: radius
tnp.ndarray | np.float64: the current time
constsdict: the constantes

Returns

np.ndarray | np.float64

diffenix.solve_asteroid_belt.thermal_diff(d: float64, consts: dict, It_d: int = 300, t: ndarray | None = None) → tuple[ndarray, ndarray, ndarray][source]

Compute the thermal diffusion equation into a bodi of radius d as a function of time assuming the bodi to be at the distance a_0 from the central star. To get the temperatures at others location r, one must multiplie the result by (r / a0) ** (-1/2)

Parameters

dnp.float64: The size of the bodi
constsdict: The dictionary of constant parameters
It_dint: The number of spatials steps
tnp.ndarray: the times at which evaluate the solution

Returns

np.ndarray

Numerical methods

Some numericals operation that need to be redifined for the numerical integration such as the seconde derivative of an array of the special first derivative of the advection-diffusion equation of a given speed v.

class diffenix.numericals_methods.SolutionED(x, y: list | ndarray, itérations: int = -1)[source]: Bases: object

diffenix.numericals_methods.gradient(y: ndarray[float64], dx: float64 = np.float64(1.0), axis: int = -1, radial_speed: ndarray[float64] | None = None) → ndarray[float64][source]

diffenix.numericals_methods.gradient2(y: ndarray[float64], dx: float64 = np.float64(1.0), axis: int = -1) → ndarray[float64][source]

diffenix.numericals_methods.gradient_d(y: ndarray[float64], dx: float64 = np.float64(1.0), axis: int = -1) → ndarray[float64][source]

diffenix.numericals_methods.gradient_g(y: ndarray[float64], dx: float64 = np.float64(1.0), axis: int = -1) → ndarray[float64][source]

diffenix.numericals_methods.gradient_weno5(y: ndarray, dx: float64 = 1.0, axis: int = -1) → ndarray[source]

Compute the spatial derivative of y following the WENO discretization scheme, robust to discontinuity, along a specified axis.

Parameters

ynp.ndarray: The array to be derived
dxnp.float64, optional, default: 1.0: The space step, the space domain should be evenly spaced with dx
axisint, optional, default: -1: The axis along which to compute the derivative

Returns

np.ndarray: The order 1 spatial derivative of y at each point along the specified axis

diffenix.numericals_methods.grid_refine_inner_edge(x_orig: ndarray[float64], nlev: int, nspan: int) → ndarray[float64][source]

A simple grid refinement function

Parameters

x_orig: np.ndarray[np.float64]: The origi,al grid to be refined

nlev: int nspan: int

Returns

np.ndarray[np.float64]: The refined grid

diffenix.numericals_methods.linear_interpolation(x: ndarray[float64] | float64, y: ndarray[float64] | float64)[source]

Linear interpolation

Parameters

xnp.float64 | np.ndarray[np.float64]: The variable
ynp.float64 | np.ndarray[np.float64]: The datapoints asssociated with the variable x to be interpolated. Both x and y can be multisimensionals vectors

Returns

A function that returns the interpolated value

diffenix.numericals_methods.rk4(f: Callable, x0: float64 | ndarray | None = None, y0: float64 | ndarray | None = None, xf: float64 = np.float64(-1.0), dx_max: float64 | None = None, args: list | tuple | None = None, IT_s_max: int = 1000, f_dx: Callable | None = None) → SolutionED[source]

Global constants and functions

diffenix.Constantes.AB_Mbelt: np.float64 = np.float64(0.12): Total initial mass

diffenix.Constantes.AB_a0: np.float64 = np.float64(2.6499999999999995): Central radius

diffenix.Constantes.AB_delta_r: np.float64 = np.float64(0.7999999999999999): Radial extention above and below central redius (half of belt’s size)

diffenix.Constantes.C_E: np.float64 = np.float64(7.451140745450589e-21): j -> Mearth au**2 / Myr**2 : energy

diffenix.Constantes.C_F: np.float64 = np.float64(1.1146747898054189e-09): N -> Mearth au**2 / Myr : force

diffenix.Constantes.C_L: np.float64 = np.float64(6.684587122268445e-12): 1/6371009 # m -> au: length

diffenix.Constantes.C_Lum: np.float64 = np.float64(2.351401191886315e-07): W = j / s -> Mearth au**2 / Myr**3: Luminosity

diffenix.Constantes.C_M: np.float64 = np.float64(1.6744248350691536e-25): 1/5.9722*1e24 # kg -> Mearth : mass

diffenix.Constantes.C_rho: np.float64 = np.float64(560585542.3145154): kg/m3 -> Mearth / au**2: density

diffenix.Constantes.C_t: np.float64 = np.float64(3.168808781402895e-14): s-> 1 Myr : time

diffenix.Constantes.G: np.float64 = np.float64(118569165.93179607): 6.67430e-11 N m*2 kg**-2 : Gravitational constant

diffenix.Constantes.Gyr: np.float64 = np.float64(1000.0): One billion year in code unit

diffenix.Constantes.IT_s: int = 700: Spatials steps

diffenix.Constantes.KB_Mbelt: np.float64 = np.float64(0.01): Total initial mass

diffenix.Constantes.KB_a0: np.float64 = np.float64(43.99999999999999): Central radius

diffenix.Constantes.KB_delta_r: np.float64 = np.float64(7.999999999999999): Radial extention above and below central redius (half of belt’s size)

diffenix.Constantes.Myr: np.float64 = np.float64(1.0): One million year in code unit

diffenix.Constantes.Na: np.float64 = np.float64(6.0221407599999985e+23): Avogadro constant

diffenix.Constantes.Pi: np.float64 = np.float64(3.141592653589793): Pi double precision

diffenix.Constantes.Rgp: np.float64 = np.float64(6.195223119064738e-20): 8.31446261815324 J K−1 mol−1 : perfect gas constant

diffenix.Constantes.T0: np.float64 = np.float64(170.77404247983844): Reference temperature at a0

diffenix.Constantes.a_in: np.float64 = np.float64(0.049999999999999996): Inner radius

diffenix.Constantes.a_out: np.float64 = np.float64(499.99999999999994): outer radius

diffenix.Constantes.alpha: np.float64 = np.float64(0.001): viscous parameter

diffenix.Constantes.atol: np.float64 = np.float64(1e-250): Absolute tolerance for temporal integration (by default too small hence to

diffenix.Constantes.c: np.float64 = np.float64(63241077084.26627): 299792458 m/s Speed of light

diffenix.Constantes.chargement_constantes(consts_filename: str) → None[source]

Load all the constantes in const_filename

Parameters

consts_filenamestr: path to the .npz file containing all the constantes

Returns

diffenix.Constantes.constantes() → dict[str, float64 | str][source]

All the constants

Returns

dict

A dictionary with all the constants :

racine : str, The absolute path to the directory where all the results are saved
results : str, The relative path to racine of the directory (inside racine) where the simulations are saved
C_L : np.float64, 1/6371009 m -> au: length conversion factor
C_M : np.float64, 1/(5.9722*1e24) kg -> Mearth : mass conversion factor
C_t : np.float64, 1 / (3600 * 24 * 365.25 * 1e6) : s-> 1 Myr : time conversion factor
Ts : np.float64, Surface temperature of the central star
Ms : np.float64, Mass of the central star
Rs : np.float64, Radius of the central star
Ls : np.float64, Luminosity of the central star
a_in : np.float64, Inner radius of the integration domain
a0 : np.float64,
a_out : np.float64, Outer radius of the integration domain
T0 : np.float64, Temperature at a0
pls_temp : np.float64, the radial power slope of the temperature
mdot : np.float64, gas mass generation rate (if constant generation rate)
AB_Mbelt : np.float64, Asteroid belt’s size
AB_Abelt : np.float64, Asteroids albedo
AB_a0 : np.float64, Asteroid belt’s central radius
AB_delta_r : np.float64, Half of asteroid belt size
AB_K : np.float64, Thermal diffusion coefficient in asteroids
AB_Phi : np.float64, Porosity
AB_rp : np.float64, Asteroid’s pore radius
AB_f_ice : np.float64, Ice to total mass ratio
AB_rho_refr : np.float64, Refractory’s materials density in asteroids
AB_rho_ice : np.float64 Ice density
AB_sublimation_model : np.float64 Sublimation model in asteroid belt
AB_SD_amax : np.double, Maximum size of asteroids
AB_SD_abig : np.double, Intermediate size
AB_SD_amed : np.double, Medium size for size distribution
AB_SD_amin : np.double, Minimal size
AB_SD_qh : np.double, Power slope of the distribution between abig and amax
AB_SD_qm : np.double, Power slope of the distribution between amed and abig
AB_SD_ql : np.double, Power slope of the distribution between amin and amed
AB_s_min: np.float64 = np.double(316) * C_L # Minimum size for collision model
AB_sb: np.float64 = np.double(316) * C_L # Intermediate size for collision model
AB_s_max: np.float64 = np.double(316) * C_L # Maximum size for collision model
AB_e: np.float64 = np.double(0.075) # Eccentricity
AB_i: np.float64 = AB_e / np.double(2.) # Inclination
AB_As: np.float64 = np.double(5.) * C_E / C_M # Massique energy to disrupt the asteroids
AB_bs: np.float64 = np.double(-0.1)
AB_bg: np.float64 = np.double(0.5)
AB_t0_diss: np.float64 = 10 * Gyr # Belt’s lifetime before dissipation
AB_t1_diss: np.float64 = 10 * Gyr # Dissipation timescale
KB_Mbelt : np.float64, Kuiper belt’s mass
KB_Abelt : np.float64, KBO’s albedo
KB_a0 : np.float64, Kuiper belt central radius
KB_delta_r : np.float64, Half of Kuiper belt size
KB_K : np.float64, Thermal diffusion coefficient in KBO
KB_Phi : np.float64, KBO’s porosity
KB_rp : np.float64, KBO’s pore’s radius
KB_f_ice : np.float64, Initial ice to total mass ratio in KBO
KB_rho_refr : np.float64, Refractory’s materials density in KBO
KB_rho_ice : np.float64, Ice density
KB_sublimation_model : np.float64, Sublimation model in Kuiper belt
KB_SD_amax : np.double, Maximum size of KBO
KB_SD_abig : np.double, Intermediate size
KB_SD_amed : np.double, Medium size
KB_SD_amin : np.double, Minimal size
KB_SD_qh : np.double, Power slope of the distribution between abig and amax
KB_SD_qm : np.double, Power slope of the distribution between amed and abig
KB_SD_ql : np.double, Power slope of the distribution between amin and amed
KB_s_min: np.float64 = np.double(316) * C_L # Minimum size for collision model
KB_sb: np.float64 = np.double(316) * C_L # Intermediate size for collision model
KB_s_max: np.float64 = np.double(316) * C_L # Maximum size for collision model
KB_e: np.float64 = np.double(0.075) # Eccentricity
KB_i: np.float64 = KB_e / np.double(2.) # Inclination
KB_As: np.float64 = np.double(5.) * C_E / C_M # Massique energy to disrupt the asteroids
KB_bs: np.float64 = np.double(-0.1)
KB_bg: np.float64 = np.double(0.5)
KB_t0_diss: np.float64 = 10 * Gyr # Belt’s lifetime before dissipation
KB_t1_diss: np.float64 = 10 * Gyr # Dissipation timescale
a_planet : list[np.double], planet’s semi-major axis
m_planet : list[np.double], planet’s masses
f_accr : np.float64, Hydrodynamic accretion efficiency
t0 : The dissipation time of the protoplanetary disc
IT_s : int, number of spatial steps
dip : int, half of the number of sink cells for a given planets to model the accretion
rtol : np.float64, Relative tolerance for temporal integration
atolnp.float64, Absolute tolerance for temporal integration (by default too small hence to
relative tolerance will always be the limiting factor)
method_root : str, ‘LSODA’,’BDF’,’DOP853’,’RK45’ : Temporal integration method_root

diffenix.Constantes.dip: int = 10: half of the number of sink cells for a given planets to model the accretion

diffenix.Constantes.h: np.float64 = np.float64(1.5644973406367687e-67): 6.62607015e-34 J/s Planck constant

diffenix.Constantes.inf: np.float64 = np.float64(inf): infinite double precision

diffenix.Constantes.kb: np.float64 = np.float64(1.0287410019065611e-43): 1.380649e-23 J/K Boltzmann constant

diffenix.Constantes.kyr: np.float64 = np.float64(0.001): One thousand year in code unit

diffenix.Constantes.m_dot: np.float64 = np.float64(0.1): Gas generation rate (if constant generation rate)

diffenix.Constantes.method: str = 'RK45': ‘LSODA’,’BDF’,’DOP853’,’RK45’ : Temporal integration method_root

diffenix.Constantes.pls_temp: np.float64 = -0.5: Temperature distribution power slope

diffenix.Constantes.rtol: np.float64 = np.float64(1e-05): Relative tolerance for temporal integration

diffenix.Constantes.sigma: np.float64 = np.float64(298393456.15390253): 5.670374419 * 1e-8 W m-2 K-4 : Stefan-Boltzmann’s constant

diffenix.Constantes.t0: np.float64 = np.float64(5.0): Time at which the disc dissipates

diffenix.Constantes.update_constantes(dic: dict) → None[source]

Update all constates from a dictionary

Parameters

dicdict, optional, default=None

A dictionary with all the constants :

racine : str, The absolute path to the directory where all the results are saved
results : str, The relative path to racine of the directory (inside racine) where the simulations are saved
C_L : np.float64, 1/6371009 m -> au: length conversion factor
C_M : np.float64, 1/(5.9722*1e24) kg -> Mearth : mass conversion factor
C_t : np.float64, 1 / (3600 * 24 * 365.25 * 1e6) : s-> 1 Myr : time conversion factor
Ts : np.float64, Surface temperature of the central star
Ms : np.float64, Mass of the central star
Rs : np.float64, Radius of the central star
Ls : np.float64, Luminosity of the central star
a_in : np.float64, Inner radius of the integration domain
a0 : np.float64,
a_out : np.float64, Outer radius of the integration domain
T0 : np.float64, Temperature at a0
mdot : np.float64, gas mass generation rate (if constant generation rate)
AB_Mbelt : np.float64, Asteroid belt’s size
AB_Abelt : np.float64, Asteroids albedo
AB_a0 : np.float64, Asteroid belt’s central radius
AB_delta_r : np.float64, Half of asteroid belt size
AB_K : np.float64, Thermal diffusion coefficient in asteroids
AB_Phi : np.float64, Porosity
AB_rp : np.float64, Asteroid’s pore radius
AB_f_ice : np.float64, Ice to total mass ratio
AB_rho_refr : np.float64, Refractory’s materials density in asteroids
AB_rho_ice : np.float64 Ice density
AB_sublimation_model : np.float64 Sublimation model in asteroid belt
AB_SD_amax : np.double, Maximum size of asteroids
AB_SD_abig : np.double, Intermediate size
AB_SD_amed : np.double, Medium size for size distribution
AB_SD_amin : np.double, Minimal size
AB_SD_qh : np.double, Power slope of the distribution between abig and amax
AB_SD_qm : np.double, Power slope of the distribution between amed and abig
AB_SD_ql : np.double, Power slope of the distribution between amin and amed
AB_s_min: np.float64 = np.double(316) * C_L # Minimum size for collision model
AB_sb: np.float64 = np.double(316) * C_L # Intermediate size for collision model
AB_s_max: np.float64 = np.double(316) * C_L # Maximum size for collision model
AB_e: np.float64 = np.double(0.075) # Eccentricity
AB_i: np.float64 = AB_e / np.double(2.) # Inclination
AB_As: np.float64 = np.double(5.) * C_E / C_M # Massique energy to disrupt the asteroids
AB_bs: np.float64 = np.double(-0.1)
AB_bg: np.float64 = np.double(0.5)
AB_t0_diss: np.float64 = 10 * Gyr # Belt’s lifetime before dissipation
AB_t1_diss: np.float64 = 10 * Gyr # Dissipation timescale
KB_Mbelt : np.float64, Kuiper belt’s mass
KB_Abelt : np.float64, KBO’s albedo
KB_a0 : np.float64, Kuiper belt central radius
KB_delta_r : np.float64, Half of Kuiper belt size
KB_K : np.float64, Thermal diffusion coefficient in KBO
KB_Phi : np.float64, KBO’s porosity
KB_rp : np.float64, KBO’s pore’s radius
KB_f_ice : np.float64, Initial ice to total mass ratio in KBO
KB_rho_refr : np.float64, Refractory’s materials density in KBO
KB_rho_ice : np.float64, Ice density
KB_sublimation_model : np.float64, Sublimation model in Kuiper belt
KB_SD_amax : np.double, Maximum size of KBO
KB_SD_abig : np.double, Intermediate size
KB_SD_amed : np.double, Medium size
KB_SD_amin : np.double, Minimal size
KB_SD_qh : np.double, Power slope of the distribution between abig and amax
KB_SD_qm : np.double, Power slope of the distribution between amed and abig
KB_SD_ql : np.double, Power slope of the distribution between amin and amed
KB_s_min: np.float64 = np.double(316) * C_L # Minimum size for collision model
KB_sb: np.float64 = np.double(316) * C_L # Intermediate size for collision model
KB_s_max: np.float64 = np.double(316) * C_L # Maximum size for collision model
KB_e: np.float64 = np.double(0.075) # Eccentricity
KB_i: np.float64 = KB_e / np.double(2.) # Inclination
KB_As: np.float64 = np.double(5.) * C_E / C_M # Massique energy to disrupt the asteroids
KB_bs: np.float64 = np.double(-0.1)
KB_bg: np.float64 = np.double(0.5)
KB_t0_diss: np.float64 = 10 * Gyr # Belt’s lifetime before dissipation
KB_t1_diss: np.float64 = 10 * Gyr # Dissipation timescale
a_planet : list[np.double], planet’s semi-major axis
m_planet : list[np.double], planet’s masses
f_accr : np.float64, Hydrodynamic accretion efficiency
t0 : The dissipation time of the protoplanetary disc
IT_s : int, number of spatial steps
dip : int, half of the number of sink cells for a given planets to model the accretion
rtol : np.float64, Relative tolerance for temporal integration
atolnp.float64, Absolute tolerance for temporal integration (by default too small hence to
relative tolerance will always be the limiting factor)
method_root : str, ‘LSODA’,’BDF’,’DOP853’,’RK45’ : Temporal integration method_root

Returns

None

diffenix.Constantes.yr: np.float64 = np.float64(1e-06): One year in code unit

diffenix.Constantes.zero: np.float64 = np.float64(0.0)

double precision