Solve the one-dimensional problem using the shooting method. More...

#include <shooting.hpp>

Collaboration diagram for BubbleProfiler::Shooting:

Public Types
enum	Solver_options : unsigned int { Compute_action = 0x01, Compute_profile = 0x02 }

Public Member Functions
void	set_bisection_precision_bits (int b)

void	set_action_arrived_rel (double tol)

void	set_shooting_abs_tol (double tol)

void	set_shooting_rel_tol (double tol)

void	set_action_abs_tol (double tol)

void	set_action_rel_tol (double tol)

void	set_drho_frac (double frac)

void	set_evolve_change_rel (double frac)

void	set_bisect_lambda_max (double l)

void	set_max_iterations (int i)

void	set_max_periods (double p)

void	set_f_y_max (double f)

void	set_f_y_min (double f)

void	set_y_max (double y)

void	solve (const std::function< double(double)> &potential_, const std::function< double(double)> &potential_first_, const std::function< double(double)> &potential_second_, double false_min_, double true_min_, double barrier_, int dim_=3, unsigned int options=(Solver_options::Compute_action\|Solver_options::Compute_profile))

void	solve (const Potential &potential, double false_min_, double true_min_, double barrier_, int dim_=3, unsigned int options=(Solver_options::Compute_action\|Solver_options::Compute_profile))

const Field_profiles &	get_bubble_profile () const

double	get_euclidean_action () const

double	quadratic_potential_solution (double) const

double	quadratic_potential_solution (double, double) const

Private Types
using	evolve_type = boost::array< double, 3 >

using	state_type = boost::array< double, 2 >

using	error_stepper_type = boost::numeric::odeint::runge_kutta_dopri5< state_type >

using	controlled_stepper_type = boost::numeric::odeint::controlled_runge_kutta< error_stepper_type >

Private Member Functions
void	initialize_potential_parameters (const std::function< double(double)> &potential_, const std::function< double(double)> &potential_first_, const std::function< double(double)> &potential_second_, double false_min_, double true_min_, double barrier_, int dim_)

void	ode (const state_type &x, state_type &dxdt, double rho)
	ODE for bounce solution. More...

double	calculate_roll_time (double lambda, double dVdphi, double d2Vdphi2) const
	Find the (dimensionless) time at which the field changes by a small amount, \(m \hat\rho\). More...

double	calculate_roll_velocity (double lambda, double y, double dVdphi, double d2Vdphi2) const
	Find velocity \(\hat\phi(\hat\rho)\). More...

evolve_type	evolve (double lambda) const
	Uses an approximation solution to evolve the system forward until the field changes by a required amount. More...

double	bubble_scale () const
	Characteristic scale of bubble. More...

double	energy (double phi, double dot_phi) const

double	shoot (double lambda)
	Performs a single shot of our shooting method. More...

double	unmap (double lambda) const

double	shooting ()
	Solve for \(\phi_0\) by bisection. More...

double	integrand (double dot_phi, double rho) const
	Action integrand from kinetic term without pre-factor. More...

double	action (double lambda)

double	interior (double lambda)

Field_profiles	calculate_bubble_profile (double lambda)

Private Attributes
int	dim {3}

double	lambda_sol {0.}

double	euclidean_action {0.}

Field_profiles	profiles {}

bool	action_computed {false}

bool	profile_computed {false}

controlled_stepper_type	shoot_stepper {}

controlled_stepper_type	action_stepper {}

double	drho_guess {0.}

double	scale {0.}

double	barrier {0.}

double	false_min {0.}

double	true_min {1.}

double	sign_min {1.}

double	p_barrier {0.}

double	p_false_min {0.}

double	p_true_min {0.}

std::function< double(double)>	potential {nullptr}

std::function< double(double)>	potential_first {nullptr}

std::function< double(double)>	potential_second {nullptr}

int	shoot_bisect_bits {5}

double	action_arrived_rel {1.e-3}

double	shoot_ode_abs {1.e-4}

double	shoot_ode_rel {1.e-4}

double	action_ode_abs {1.e-6}

double	action_ode_rel {1.e-6}

double	drho_frac {1.e-3}

double	evolve_change_rel {1.e-2}

double	bisect_lambda_max {5.}

int	iter_max {100000}

double	periods_max {1.e2}

double	f_y_max {1.e6}

double	f_y_min {1.e-3}

double	y_max {1.e1}

Detailed Description

Solve the one-dimensional problem using the shooting method.

Examples:: action.cpp, and scale.cpp.

Definition at line 44 of file shooting.hpp.

Member Typedef Documentation

using BubbleProfiler::Shooting::controlled_stepper_type = boost::numeric::odeint::controlled_runge_kutta<error_stepper_type>

private

Definition at line 121 of file shooting.hpp.

using BubbleProfiler::Shooting::error_stepper_type = boost::numeric::odeint::runge_kutta_dopri5<state_type>

private

Definition at line 119 of file shooting.hpp.

using BubbleProfiler::Shooting::evolve_type = boost::array<double, 3>

private

Definition at line 116 of file shooting.hpp.

using BubbleProfiler::Shooting::state_type = boost::array<double, 2>

private

Definition at line 117 of file shooting.hpp.

Member Enumeration Documentation

enum BubbleProfiler::Shooting::Solver_options : unsigned int

Enumerator
Compute_action
Compute_profile

Definition at line 46 of file shooting.hpp.

Member Function Documentation

double BubbleProfiler::Shooting::action ( double lambda )

private

Returns: Action, \(S\)

Definition at line 414 of file shooting.cpp.

References BubbleProfiler::Abs(), action_arrived_rel, action_stepper, BubbleProfiler::area_n_sphere(), dim, drho_guess, evolve(), false_min, integrand(), interior(), iter_max, ode(), periods_max, scale, sign_min, and unmap().

Referenced by solve().

double BubbleProfiler::Shooting::bubble_scale ( ) const

private

Characteristic scale of bubble.

Found from period of oscillation about barrier. We approximate the potential at the barrier by a quadratic such that

\[ T = \frac{2\pi}{\sqrt{-V^{\prime\prime}(\phi_b)}}. \]

Definition at line 277 of file shooting.cpp.

References barrier, potential_second, and BubbleProfiler::Sqrt().

Referenced by initialize_potential_parameters().

Field_profiles BubbleProfiler::Shooting::calculate_bubble_profile ( double lambda )

private

Returns: The bubble profile, \(\phi(\rho)\)

Definition at line 490 of file shooting.cpp.

References BubbleProfiler::Abs(), action_arrived_rel, action_ode_abs, action_ode_rel, drho_guess, evolve(), false_min, iter_max, ode(), periods_max, quadratic_potential_solution(), scale, sign_min, and unmap().

Referenced by solve().

double BubbleProfiler::Shooting::calculate_roll_time	(	double	lambda,
		double	dVdphi,
		double	d2Vdphi2
	)		const

private

Find the (dimensionless) time at which the field changes by a small amount, \(m \hat\rho\).

Returns: \(m \hat\rho\)

Parameters

lambda	\(\lambda\), related to \(\phi_0\)
dVdphi	\(\left.\frac{dV}{d\phi}\right\|_\lambda\)
d2Vdphi2	\(\left.\frac{d^2V}{d\phi^2}\right\|_\lambda\)

Definition at line 164 of file shooting.cpp.

References BubbleProfiler::Abs(), BubbleProfiler::approx_root_neg_4(), BubbleProfiler::approx_root_pos_4(), BubbleProfiler::asinc(), BubbleProfiler::asinch(), barrier, dim, evolve_change_rel, f_y_max, false_min, BubbleProfiler::Log(), true_min, and unmap().

Referenced by evolve().

double BubbleProfiler::Shooting::calculate_roll_velocity	(	double	lambda,
		double	y,
		double	dVdphi,
		double	d2Vdphi2
	)		const

private

Find velocity \(\hat\phi(\hat\rho)\).

Returns: \(\hat\phi(\hat\rho)\)

Parameters

lambda	\(\lambda\), related to \(\phi_0\)
y	\(y = m \hat\rho\)
dVdphi	\(\left.\frac{dV}{d\phi}\right\|_\lambda\)
d2Vdphi2	\(\left.\frac{d^2V}{d\phi^2}\right\|_\lambda\)

Definition at line 200 of file shooting.cpp.

References BubbleProfiler::Abs(), BubbleProfiler::BesselI(), BubbleProfiler::BesselJ(), BubbleProfiler::Cos(), BubbleProfiler::Cosh(), dim, evolve_change_rel, f_y_max, f_y_min, false_min, sign_min, BubbleProfiler::Sqrt(), and unmap().

Referenced by evolve().

double BubbleProfiler::Shooting::energy	(	double	phi,
		double	dot_phi
	)		const

private

Returns: Energy at \((\phi, \dot\phi)\)

Definition at line 283 of file shooting.cpp.

References p_false_min, and potential.

Referenced by shoot().

Shooting::evolve_type BubbleProfiler::Shooting::evolve ( double lambda ) const

private

Uses an approximation solution to evolve the system forward until the field changes by a required amount.

The required amount is specified by Shooting::rchange using:

\[ |\phi(\rho) - \phi_0| = Shooting::rchange |\phi_f - \phi_0|. \]

This method is used to avoid solving the ODE during the time period where friction dominates, which can be very slow, and avoids a singularity at \(\rho =0\).

Parameters

lambda \(\lambda\)

Returns: \((\hat\rho, \phi(\hat\rho), \dot\phi(\hat\rho))\)

Definition at line 251 of file shooting.cpp.

References BubbleProfiler::Abs(), calculate_roll_time(), calculate_roll_velocity(), evolve_change_rel, false_min, potential_first, potential_second, sign_min, BubbleProfiler::Sqrt(), and unmap().

Referenced by action(), calculate_bubble_profile(), interior(), and shoot().

const Field_profiles & BubbleProfiler::Shooting::get_bubble_profile ( ) const

Bubble profile, i.e., \(\phi(\rho)\)

Definition at line 48 of file shooting.cpp.

References profile_computed, and profiles.

Referenced by BubbleProfiler::Shooting_profile_guesser::calculate_field_profiles(), BubbleProfiler::run_shooting_profiler(), set_y_max(), and BubbleProfiler::solve_shooting().

double BubbleProfiler::Shooting::get_euclidean_action ( ) const

Euclidean action, \(S\)

Examples:: action.cpp, and scale.cpp.

Definition at line 40 of file shooting.cpp.

References action_computed, and euclidean_action.

Referenced by action(), main(), BubbleProfiler::run_shooting_profiler(), set_y_max(), and BubbleProfiler::solve_shooting().

void BubbleProfiler::Shooting::initialize_potential_parameters	(	const std::function< double(double)> &	potential_,
		const std::function< double(double)> &	potential_first_,
		const std::function< double(double)> &	potential_second_,
		double	false_min_,
		double	true_min_,
		double	barrier_,
		int	dim_
	)

private

Definition at line 56 of file shooting.cpp.

References barrier, bubble_scale(), dim, drho_frac, drho_guess, false_min, p_barrier, p_false_min, p_true_min, potential, potential_first, potential_second, scale, BubbleProfiler::Sign(), sign_min, and true_min.

Referenced by solve().

double BubbleProfiler::Shooting::integrand	(	double	dot_phi,
		double	rho
	)		const

private

Action integrand from kinetic term without pre-factor.

We use a trick that

\[ I = \int d\rho \rho^{d-1} \left[ \frac12 \dot\phi^2 + V(\phi) - V(\phi_f)\right] \equiv I_1 + I_2 \]

but by the fact that action is stationary under \(\rho \to a \rho\)

\[ d I_2 = (2 - d) I_1 \]

such that

\[ I = I_1 + I_2 = \frac{2}{d} I_1 = \frac{1}{d} \int d\rho \dot\phi^2 \rho^{d-1} \]

Parameters

dot_phi	\(\dot\phi\)
rho	\(\rho\)

Returns: Action without prefactor

Definition at line 409 of file shooting.cpp.

References dim.

Referenced by action().

double BubbleProfiler::Shooting::interior ( double lambda )

private

Returns: Action without prefactor for interior of bubble

Definition at line 616 of file shooting.cpp.

References BubbleProfiler::Abs(), BubbleProfiler::BesselI(), BubbleProfiler::BesselJ(), BubbleProfiler::Cos(), BubbleProfiler::Cosh(), dim, evolve(), evolve_change_rel, false_min, potential_first, potential_second, BubbleProfiler::Sin(), BubbleProfiler::Sinh(), BubbleProfiler::Sqrt(), unmap(), and y_max.

Referenced by action().

void BubbleProfiler::Shooting::ode	(	const state_type &	x,
		state_type &	dxdt,
		double	rho
	)

private

ODE for bounce solution.

Rewrite second-order as two coupled first order equations,

\[ \dot\phi = \chi \]

and

\[ \dot\chi = -\frac{2}{\rho} \phi + V^\prime(\phi) \]

Parameters

x	\((\phi, \chi)\)
dxdt	\((\dot\phi, \dot\chi)\)
rho	\(\rho\)

Definition at line 158 of file shooting.cpp.

References dim, and potential_first.

Referenced by action(), calculate_bubble_profile(), and shoot().

double BubbleProfiler::Shooting::quadratic_potential_solution ( double rho ) const

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 572 of file shooting.cpp.

References lambda_sol.

Referenced by calculate_bubble_profile(), BubbleProfiler::Shooting_profile_guesser::calculate_field_profiles(), and set_y_max().

double BubbleProfiler::Shooting::quadratic_potential_solution	(	double	rho,
		double	lambda
	)		const

Returns: Quadratic solution \(\phi(\rho)\)

Definition at line 577 of file shooting.cpp.

References BubbleProfiler::Abs(), BubbleProfiler::BesselI(), BubbleProfiler::BesselJ(), dim, potential_first, potential_second, BubbleProfiler::Sin(), BubbleProfiler::Sinh(), BubbleProfiler::Sqrt(), true_min, and unmap().

void BubbleProfiler::Shooting::set_action_abs_tol ( double tol )

inline

Absolute tolerance in ODE solver for action integral

Examples:: action.cpp.

Definition at line 60 of file shooting.hpp.

References action_ode_abs.

Referenced by action(), main(), and BubbleProfiler::run_shooting_profiler().

void BubbleProfiler::Shooting::set_action_arrived_rel ( double tol )

inline

Relative tolerance for judging when \(\phi \approx \phi_f\)

Examples:: action.cpp.

Definition at line 54 of file shooting.hpp.

References action_arrived_rel.

Referenced by action(), main(), and BubbleProfiler::run_shooting_profiler().

void BubbleProfiler::Shooting::set_action_rel_tol ( double tol )

inline

Relative tolerance in ODE solver for action integral

Examples:: action.cpp.

Definition at line 62 of file shooting.hpp.

References action_ode_rel.

Referenced by action(), main(), and BubbleProfiler::run_shooting_profiler().

void BubbleProfiler::Shooting::set_bisect_lambda_max ( double l )

inline

Maximum value of \(\lambda\)

Examples:: action.cpp.

Definition at line 74 of file shooting.hpp.

References bisect_lambda_max.

Referenced by action(), main(), and BubbleProfiler::run_shooting_profiler().

void BubbleProfiler::Shooting::set_bisection_precision_bits ( int b )

inline

Bits of precision in bisection of \(\phi_0\)

Examples:: action.cpp.

Definition at line 52 of file shooting.hpp.

References shoot_bisect_bits.

Referenced by action(), main(), BubbleProfiler::run_shooting_profiler(), and BubbleProfiler::solve_shooting().

void BubbleProfiler::Shooting::set_drho_frac ( double frac )

inline

The initial ODE step size, \(d\rho\), is this fraction of the bubble scale

Examples:: action.cpp.

Definition at line 64 of file shooting.hpp.

References drho_frac.

Referenced by action(), main(), and BubbleProfiler::run_shooting_profiler().

void BubbleProfiler::Shooting::set_evolve_change_rel ( double frac )

inline

The EOM is integrated analytically until

\[ \frac{\left|\phi(\hat\rho) - \phi_0 \right|}{\left|\phi_f - \phi_0\right|}, \]

changes by this amount.

Definition at line 72 of file shooting.hpp.

References evolve_change_rel.

Referenced by BubbleProfiler::run_shooting_profiler().

void BubbleProfiler::Shooting::set_f_y_max ( double f )

inline

Threshold for asymptotic approximation in analytic evolution

Examples:: action.cpp.

Definition at line 80 of file shooting.hpp.

References f_y_max.

Referenced by action(), main(), and BubbleProfiler::run_shooting_profiler().

void BubbleProfiler::Shooting::set_f_y_min ( double f )

inline

Threshold for asymptotic approximation in analytic evolution

Examples:: action.cpp.

Definition at line 82 of file shooting.hpp.

References f_y_min.

Referenced by action(), main(), and BubbleProfiler::run_shooting_profiler().

void BubbleProfiler::Shooting::set_max_iterations ( int i )

inline

Maximum number of iterations of shooting method

Examples:: action.cpp.

Definition at line 76 of file shooting.hpp.

References iter_max.

Referenced by action(), main(), and BubbleProfiler::run_shooting_profiler().

void BubbleProfiler::Shooting::set_max_periods ( double p )

inline

Maximum number periods before the ODE integration aborts

Examples:: action.cpp.

Definition at line 78 of file shooting.hpp.

References periods_max.

Referenced by action(), main(), and BubbleProfiler::run_shooting_profiler().

void BubbleProfiler::Shooting::set_shooting_abs_tol ( double tol )

inline

Absolute tolerance in ODE solver for a shot

Examples:: action.cpp.

Definition at line 56 of file shooting.hpp.

References shoot_ode_abs.

Referenced by action(), main(), and BubbleProfiler::run_shooting_profiler().

void BubbleProfiler::Shooting::set_shooting_rel_tol ( double tol )

inline

Relative tolerance in ODE solver for a shot

Examples:: action.cpp.

Definition at line 58 of file shooting.hpp.

References shoot_ode_rel.

Referenced by action(), main(), and BubbleProfiler::run_shooting_profiler().

void BubbleProfiler::Shooting::set_y_max ( double y )

inline

Threshold for asymptotic approximation in analytic evolution

Examples:: action.cpp.

Definition at line 84 of file shooting.hpp.

References get_bubble_profile(), get_euclidean_action(), potential, quadratic_potential_solution(), solve(), and y_max.

Referenced by action(), main(), and BubbleProfiler::run_shooting_profiler().

double BubbleProfiler::Shooting::shoot ( double lambda )

private

Performs a single shot of our shooting method.

Evolves field from an initial guess for \(\phi_0\), given by \(\lambda\) and tests whether it under or over shoots the false vacuum.

Parameters

lambda \(\lambda\)

Returns: Whether overshot or undershot

Definition at line 288 of file shooting.cpp.

References BubbleProfiler::Abs(), drho_guess, energy(), evolve(), false_min, iter_max, ode(), periods_max, scale, shoot_stepper, sign_min, and unmap().

Referenced by shooting().

double BubbleProfiler::Shooting::shooting ( )

private

Solve for \(\phi_0\) by bisection.

Bisect between over and under shots, beginning from the interval \((\phi_b, \phi_t)\).

Returns: \(\lambda\) corresponding to \(\phi_0\)

Definition at line 380 of file shooting.cpp.

References bisect_lambda_max, iter_max, shoot(), and shoot_bisect_bits.

Referenced by solve().

void BubbleProfiler::Shooting::solve	(	const std::function< double(double)> &	potential_,
		const std::function< double(double)> &	potential_first_,
		const std::function< double(double)> &	potential_second_,
		double	false_min_,
		double	true_min_,
		double	barrier_,
		int	dim_ = `3`,
		unsigned int	options = `(Solver_options::Compute_action \| Solver_options::Compute_profile)`
	)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Solver that accepts potential and first and second derivatives

Examples:: action.cpp, and scale.cpp.

Definition at line 81 of file shooting.cpp.

References action(), action_computed, action_ode_abs, action_ode_rel, action_stepper, calculate_bubble_profile(), euclidean_action, initialize_potential_parameters(), lambda_sol, profile_computed, profiles, shoot_ode_abs, shoot_ode_rel, shoot_stepper, and shooting().

Referenced by action(), main(), BubbleProfiler::run_shooting_profiler(), set_y_max(), solve(), BubbleProfiler::Shooting_profile_guesser::solve_one_dimensional(), and BubbleProfiler::solve_shooting().

void BubbleProfiler::Shooting::solve	(	const Potential &	potential,
		double	false_min_,
		double	true_min_,
		double	barrier_,
		int	dim_ = `3`,
		unsigned int	options = `(Solver_options::Compute_action \| Solver_options::Compute_profile)`
	)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Solver that accepts a Potential object

Definition at line 128 of file shooting.cpp.

References BubbleProfiler::Potential::get_number_of_fields(), BubbleProfiler::Potential::partial(), and solve().

double BubbleProfiler::Shooting::unmap ( double lambda ) const

private

Returns: \(\phi\) from \(\lambda\)

Definition at line 375 of file shooting.cpp.

References barrier, BubbleProfiler::Exp(), and true_min.

Referenced by action(), calculate_bubble_profile(), calculate_roll_time(), calculate_roll_velocity(), evolve(), interior(), quadratic_potential_solution(), and shoot().

Member Data Documentation

double BubbleProfiler::Shooting::action_arrived_rel {1.e-3}

private

Definition at line 167 of file shooting.hpp.

Referenced by action(), calculate_bubble_profile(), and set_action_arrived_rel().

bool BubbleProfiler::Shooting::action_computed {false}

private

Definition at line 131 of file shooting.hpp.

Referenced by get_euclidean_action(), and solve().

double BubbleProfiler::Shooting::action_ode_abs {1.e-6}

private

Definition at line 170 of file shooting.hpp.

Referenced by calculate_bubble_profile(), set_action_abs_tol(), and solve().

double BubbleProfiler::Shooting::action_ode_rel {1.e-6}

private

Definition at line 171 of file shooting.hpp.

Referenced by calculate_bubble_profile(), set_action_rel_tol(), and solve().

controlled_stepper_type BubbleProfiler::Shooting::action_stepper {}

private

Definition at line 136 of file shooting.hpp.

Referenced by action(), and solve().

double BubbleProfiler::Shooting::barrier {0.}

private

Location of the barrier, \(\phi_b\)

Definition at line 144 of file shooting.hpp.

Referenced by bubble_scale(), calculate_roll_time(), initialize_potential_parameters(), and unmap().

double BubbleProfiler::Shooting::bisect_lambda_max {5.}

private

Definition at line 174 of file shooting.hpp.

Referenced by set_bisect_lambda_max(), and shooting().

int BubbleProfiler::Shooting::dim {3}

private

Number of space-time dimensions, \(d\)

Definition at line 124 of file shooting.hpp.

Referenced by action(), calculate_roll_time(), calculate_roll_velocity(), initialize_potential_parameters(), integrand(), interior(), ode(), and quadratic_potential_solution().

double BubbleProfiler::Shooting::drho_frac {1.e-3}

private

Definition at line 172 of file shooting.hpp.

Referenced by initialize_potential_parameters(), and set_drho_frac().

double BubbleProfiler::Shooting::drho_guess {0.}

private

Guess of step size, \(d\rho\)

Definition at line 139 of file shooting.hpp.

Referenced by action(), calculate_bubble_profile(), initialize_potential_parameters(), and shoot().

double BubbleProfiler::Shooting::euclidean_action {0.}

private

Solution for Euclidean action, \(S\)

Definition at line 129 of file shooting.hpp.

Referenced by get_euclidean_action(), and solve().

double BubbleProfiler::Shooting::evolve_change_rel {1.e-2}

private

Definition at line 173 of file shooting.hpp.

Referenced by calculate_roll_time(), calculate_roll_velocity(), evolve(), interior(), and set_evolve_change_rel().

double BubbleProfiler::Shooting::f_y_max {1.e6}

private

Definition at line 177 of file shooting.hpp.

Referenced by calculate_roll_time(), calculate_roll_velocity(), and set_f_y_max().

double BubbleProfiler::Shooting::f_y_min {1.e-3}

private

Definition at line 178 of file shooting.hpp.

Referenced by calculate_roll_velocity(), and set_f_y_min().

double BubbleProfiler::Shooting::false_min {0.}

private

Location of the false minimum, \(\phi_f\)

Definition at line 146 of file shooting.hpp.

Referenced by action(), calculate_bubble_profile(), calculate_roll_time(), calculate_roll_velocity(), evolve(), initialize_potential_parameters(), interior(), and shoot().

int BubbleProfiler::Shooting::iter_max {100000}

private

Definition at line 175 of file shooting.hpp.

Referenced by action(), calculate_bubble_profile(), set_max_iterations(), shoot(), and shooting().

double BubbleProfiler::Shooting::lambda_sol {0.}

private

Solution for \(\lambda\)

Definition at line 127 of file shooting.hpp.

Referenced by quadratic_potential_solution(), and solve().

double BubbleProfiler::Shooting::p_barrier {0.}

private

Potential at barrier, \(V(\phi_b)\)

Definition at line 152 of file shooting.hpp.

Referenced by initialize_potential_parameters().

double BubbleProfiler::Shooting::p_false_min {0.}

private

Potential at false minimum, \(V(\phi_f)\)

Definition at line 154 of file shooting.hpp.

Referenced by energy(), and initialize_potential_parameters().

double BubbleProfiler::Shooting::p_true_min {0.}

private

Potential at true minimum, \(V(\phi_t)\)

Definition at line 156 of file shooting.hpp.

Referenced by initialize_potential_parameters().

double BubbleProfiler::Shooting::periods_max {1.e2}

private

Definition at line 176 of file shooting.hpp.

Referenced by action(), calculate_bubble_profile(), set_max_periods(), and shoot().

std::function<double(double)> BubbleProfiler::Shooting::potential {nullptr}

private

Potential, \(V(\phi)\)

Definition at line 159 of file shooting.hpp.

Referenced by energy(), initialize_potential_parameters(), and set_y_max().

std::function<double(double)> BubbleProfiler::Shooting::potential_first {nullptr}

private

Derivative of potential, \(V^{\prime}(\phi)\)

Definition at line 161 of file shooting.hpp.

Referenced by evolve(), initialize_potential_parameters(), interior(), ode(), and quadratic_potential_solution().

std::function<double(double)> BubbleProfiler::Shooting::potential_second {nullptr}

private

Second derivative of potential, \(V^{\prime\prime}(\phi)\)

Definition at line 163 of file shooting.hpp.

Referenced by bubble_scale(), evolve(), initialize_potential_parameters(), interior(), and quadratic_potential_solution().

bool BubbleProfiler::Shooting::profile_computed {false}

private

Definition at line 132 of file shooting.hpp.

Referenced by get_bubble_profile(), and solve().

Field_profiles BubbleProfiler::Shooting::profiles {}

private

Definition at line 130 of file shooting.hpp.

Referenced by get_bubble_profile(), and solve().

double BubbleProfiler::Shooting::scale {0.}

private

Estimated scale of bubble

Definition at line 141 of file shooting.hpp.

Referenced by action(), calculate_bubble_profile(), initialize_potential_parameters(), and shoot().

int BubbleProfiler::Shooting::shoot_bisect_bits {5}

private

Definition at line 166 of file shooting.hpp.

Referenced by set_bisection_precision_bits(), and shooting().

double BubbleProfiler::Shooting::shoot_ode_abs {1.e-4}

private

Definition at line 168 of file shooting.hpp.

Referenced by set_shooting_abs_tol(), and solve().

double BubbleProfiler::Shooting::shoot_ode_rel {1.e-4}

private

Definition at line 169 of file shooting.hpp.

Referenced by set_shooting_rel_tol(), and solve().

controlled_stepper_type BubbleProfiler::Shooting::shoot_stepper {}

private

Definition at line 135 of file shooting.hpp.

Referenced by shoot(), and solve().

double BubbleProfiler::Shooting::sign_min {1.}

private

\(\textrm{sign}\,\phi_f - \phi_t\)

Definition at line 150 of file shooting.hpp.

Referenced by action(), calculate_bubble_profile(), calculate_roll_velocity(), evolve(), initialize_potential_parameters(), and shoot().

double BubbleProfiler::Shooting::true_min {1.}

private

Location of the true minimum, \(\phi_t\)

Definition at line 148 of file shooting.hpp.

Referenced by calculate_roll_time(), initialize_potential_parameters(), quadratic_potential_solution(), and unmap().

double BubbleProfiler::Shooting::y_max {1.e1}

private

Definition at line 179 of file shooting.hpp.

Referenced by interior(), and set_y_max().

The documentation for this class was generated from the following files:

/home/michael/bubbleprofiler_release/include/shooting.hpp
/home/michael/bubbleprofiler_release/src/shooting.cpp

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