complex_problems – Specialized Plugin Workflows

Complex problems package with pluggable, problem-specific workflows.

class complex_problems.ProblemDescriptor(id, name, description)[source]

Bases: object

Display metadata for a complex problem.

Parameters:
id: str
name: str
description: str
complex_problems.get_problem_descriptors()[source]

Get all problem descriptors.

Return type:

dict[str, ProblemDescriptor]

complex_problems.open_problem_dialog(problem_id, parent)[source]

Open a registered complex problem dialog by id.

Return type:

None

Parameters:

  • problem_id (str)

  • parent (Tk | Toplevel)

Registry and dialog

Registry and lazy loader for complex problem plugins.

class complex_problems.problem_registry.ProblemRegistration(module_path, symbol_name='PROBLEM')[source]

Bases: object

Module path and symbol name for a problem plugin.

Parameters:

  • module_path (str)

  • symbol_name (str)

module_path: str
symbol_name: str
class complex_problems.problem_registry.ProblemRegistry(registrations)[source]

Bases: object

Lazy plugin registry for complex problems.

Parameters:

registrations (tuple[ProblemRegistration, ...])

get_descriptors()[source]

Return descriptors keyed by problem id.

Return type:

dict[str, ProblemDescriptor]

open_problem_dialog(problem_id, parent)[source]

Open the dialog for a registered problem id.

Return type:

None

Parameters:

  • problem_id (str)

  • parent (Tk | Toplevel)

complex_problems.problem_registry.open_problem_dialog(problem_id, parent)[source]

Open a registered complex problem dialog by id.

Return type:

None

Parameters:

  • problem_id (str)

  • parent (Tk | Toplevel)

complex_problems.problem_registry.get_problem_descriptors()[source]

Get all problem descriptors.

Return type:

dict[str, ProblemDescriptor]

Dialog for selecting which complex problem to solve.

class complex_problems.complex_problems_dialog.ComplexProblemsDialog(parent)[source]

Bases: object

Window for selecting a complex problem to solve.

Parameters:

parent (Tk | Toplevel) – Parent window.

Common helpers

Shared helpers for complex problem plugins.

complex_problems.common.compile_scalar_expression(expression, *, variables, parameters=None)[source]

Compile a scalar expression into a callable.

Parameters:

  • expression (str) – User expression.

  • variables (tuple[str, ...]) – Allowed variable names expected at call-time.

  • parameters (dict[str, float] | None) – Constant parameter map available in namespace.

Return type:

Callable[..., float]

Returns:

Callable returning a float from the expression evaluation.

complex_problems.common.run_solver_with_loading(*, parent, message, task, on_success, error_title='Solver Error', poll_ms=100)[source]

Run a blocking solver task on a daemon thread with a loading dialog.

Return type:

None

Parameters:
complex_problems.common.add_how_to_config_section(parent, scroll, *, problem_id, pad, wraplength=760)[source]

Add a standard collapsed ‘How to configure’ block for a problem dialog.

Return type:

None

Parameters:
complex_problems.common.parse_float(value, *, name)[source]

Parse a floating-point value from text.

Return type:

float

Parameters:
complex_problems.common.parse_int(value, *, name)[source]

Parse an integer value from text.

Return type:

int

Parameters:
complex_problems.common.parse_positive_float(value, *, name, min_value=0.0)[source]

Parse a positive floating-point value.

Return type:

float

Parameters:
complex_problems.common.parse_positive_int(value, *, name, min_value=1)[source]

Parse a strictly positive integer.

Return type:

int

Parameters:

Background execution helper for long-running complex-problem solvers.

complex_problems.common.background.run_solver_with_loading(*, parent, message, task, on_success, error_title='Solver Error', poll_ms=100)[source]

Run a blocking solver task on a daemon thread with a loading dialog.

Return type:

None

Parameters:

Safe expression helpers for complex-problem user inputs.

complex_problems.common.expression.compile_scalar_expression(expression, *, variables, parameters=None)[source]

Compile a scalar expression into a callable.

Parameters:

  • expression (str) – User expression.

  • variables (tuple[str, ...]) – Allowed variable names expected at call-time.

  • parameters (dict[str, float] | None) – Constant parameter map available in namespace.

Return type:

Callable[..., float]

Returns:

Callable returning a float from the expression evaluation.

UI helpers for rendering shared complex-problem documentation blocks.

complex_problems.common.problem_doc_ui.add_how_to_config_section(parent, scroll, *, problem_id, pad, wraplength=760)[source]

Add a standard collapsed ‘How to configure’ block for a problem dialog.

Return type:

None

Parameters:

Small parsing helpers for UI numeric fields.

complex_problems.common.validation.parse_int(value, *, name)[source]

Parse an integer value from text.

Return type:

int

Parameters:
complex_problems.common.validation.parse_positive_int(value, *, name, min_value=1)[source]

Parse a strictly positive integer.

Return type:

int

Parameters:
complex_problems.common.validation.parse_float(value, *, name)[source]

Parse a floating-point value from text.

Return type:

float

Parameters:
complex_problems.common.validation.parse_positive_float(value, *, name, min_value=0.0)[source]

Parse a positive floating-point value.

Return type:

float

Parameters:

Problem documentation metadata

Shared documentation metadata for complex-problem UIs.

class complex_problems.problem_docs.ProblemDoc(problem_type, extended_description, equation_summary, config_options_summary, visualizations_summary)[source]

Bases: object

Structured help content for a complex problem.

Parameters:

  • problem_type (str)

  • extended_description (str)

  • equation_summary (str | None)

  • config_options_summary (tuple[str, ...])

  • visualizations_summary (tuple[str, ...])

problem_type: str
extended_description: str
equation_summary: str | None
config_options_summary: tuple[str, ...]
visualizations_summary: tuple[str, ...]
complex_problems.problem_docs.get_problem_doc(problem_id)[source]

Return help content for the given problem id.

Return type:

ProblemDoc

Parameters:

problem_id (str)

complex_problems.problem_docs.get_all_problem_docs()[source]

Return all problem-doc entries.

Return type:

dict[str, ProblemDoc]

coupled_oscillators

Coupled harmonic oscillators plugin package.

complex_problems.coupled_oscillators.build_ode_function(n_oscillators, masses, k_coupling, boundary='fixed', coupling_types=None, nonlinear_coeff=0.0, nonlinear_fput_alpha=0.0, nonlinear_quartic=0.0, nonlinear_quintic=0.0, k_2nn=0.0, k_3nn=0.0, k_4nn=0.0, external_amplitude=0.0, external_frequency=1.0)[source]

Build the RHS for coupled oscillators with optional nonlinear terms.

Return type:

Callable[[float, ndarray], ndarray]

Parameters:
complex_problems.coupled_oscillators.solve_coupled_oscillators(n_oscillators, masses, k_coupling, boundary='fixed', coupling_types=None, nonlinear_coeff=0.0, nonlinear_fput_alpha=0.0, nonlinear_quartic=0.0, nonlinear_quintic=0.0, k_2nn=0.0, k_3nn=0.0, k_4nn=0.0, external_amplitude=0.0, external_frequency=1.0, t_min=0.0, t_max=30.0, n_points=None, y0=None, method=None)[source]

Solve the coupled oscillators system.

Return type:

CoupledOscillatorsResult

Parameters:

Physics model for coupled harmonic oscillators.

complex_problems.coupled_oscillators.model.build_ode_function(n_oscillators, masses, k_coupling, boundary='fixed', coupling_types=None, nonlinear_coeff=0.0, nonlinear_fput_alpha=0.0, nonlinear_quartic=0.0, nonlinear_quintic=0.0, k_2nn=0.0, k_3nn=0.0, k_4nn=0.0, external_amplitude=0.0, external_frequency=1.0)[source]

Build the RHS for coupled oscillators with optional nonlinear terms.

Return type:

Callable[[float, ndarray], ndarray]

Parameters:
complex_problems.coupled_oscillators.model.compute_normal_modes(n_oscillators, masses, k_coupling, boundary='fixed', k_2nn=0.0, k_3nn=0.0, k_4nn=0.0)[source]

Compute normal modes and angular frequencies for the linearized system.

Return type:

tuple[ndarray, ndarray]

Parameters:

Solver for coupled harmonic oscillators.

class complex_problems.coupled_oscillators.solver.CoupledOscillatorsResult(x, y, n_oscillators, masses, k_coupling, M_modes, omega_modes, has_modes, metadata=<factory>)[source]

Bases: object

Result from solving coupled oscillators.

Parameters:
x: ndarray
y: ndarray
n_oscillators: int
masses: ndarray
k_coupling: ndarray
M_modes: ndarray
omega_modes: ndarray
has_modes: bool
metadata: dict[str, Any]
complex_problems.coupled_oscillators.solver.solve_coupled_oscillators(n_oscillators, masses, k_coupling, boundary='fixed', coupling_types=None, nonlinear_coeff=0.0, nonlinear_fput_alpha=0.0, nonlinear_quartic=0.0, nonlinear_quintic=0.0, k_2nn=0.0, k_3nn=0.0, k_4nn=0.0, external_amplitude=0.0, external_frequency=1.0, t_min=0.0, t_max=30.0, n_points=None, y0=None, method=None)[source]

Solve the coupled oscillators system.

Return type:

CoupledOscillatorsResult

Parameters:

UI dialog for configuring and solving coupled harmonic oscillators.

class complex_problems.coupled_oscillators.ui.CoupledOscillatorsDialog(parent)[source]

Bases: object

Dialog for configuring coupled harmonic oscillators parameters.

Parameters:

parent (Tk | Toplevel) – Parent window.

Result dialog for coupled harmonic oscillators.

class complex_problems.coupled_oscillators.result_dialog.CoupledOscillatorsResultDialog(parent, *, result)[source]

Bases: object

Result window for coupled harmonic oscillators.

Shows tabs: Energy, Energy per mode, Animation, Heatmap, 3D Surface. Phase 1: Animation tab only. Phase 3 adds the rest.

Parameters:

membrane_2d

2D coupled-oscillator membrane complex problem.

complex_problems.membrane_2d.solve_membrane_2d(*, u0, v0=None, t_min=0.0, t_max=20.0, dt=0.02, mass=1.0, k_linear=1.0, boundary='fixed', integrator='verlet', alpha=0.0, beta=0.0, high_order_coeff=0.0, high_order_power=5)[source]

Solve the membrane dynamics for the provided initial fields.

Return type:

Membrane2DResult

Parameters:

Physical model helpers for the 2D nonlinear membrane.

complex_problems.membrane_2d.model.laplacian_2d(u, *, boundary)[source]

Compute the discrete 2D Laplacian.

Return type:

ndarray

Parameters:
complex_problems.membrane_2d.model.apply_fixed_boundary(u, v=None)[source]

Clamp edges to zero in-place for fixed boundaries.

Return type:

None

Parameters:
complex_problems.membrane_2d.model.acceleration_field(u, *, mass, k_linear, boundary, alpha=0.0, beta=0.0, high_order_coeff=0.0, high_order_power=5)[source]

Compute acceleration field from linear and nonlinear membrane terms.

Return type:

ndarray

Parameters:
complex_problems.membrane_2d.model.build_initial_displacement(*, nx, ny, shape, amplitude, sigma, mode_x=1, mode_y=1, center_x=0.5, center_y=0.5, custom_fn=None, random_seed=0, boundary='fixed')[source]

Create an initial displacement field.

Return type:

ndarray

Parameters:
complex_problems.membrane_2d.model.compute_energy_terms(u, v, *, mass, k_linear, boundary, alpha=0.0, beta=0.0, high_order_coeff=0.0, high_order_power=5)[source]

Compute kinetic, potential, total energies.

Return type:

tuple[float, float, float]

Parameters:
complex_problems.membrane_2d.model.compute_fft_power_2d(u)[source]

Compute shifted 2D power spectrum of a field.

Return type:

tuple[ndarray, ndarray, ndarray]

Parameters:

u (ndarray)

Solver for a 2D nonlinear membrane (coupled oscillator grid).

class complex_problems.membrane_2d.solver.Membrane2DResult(t, displacement, velocity, kinetic_energy, potential_energy, total_energy, kx, ky, spectrum_power, metadata=<factory>, magnitudes=<factory>)[source]

Bases: object

Result bundle for the membrane solver.

Parameters:
t: ndarray
displacement: ndarray
velocity: ndarray
kinetic_energy: ndarray
potential_energy: ndarray
total_energy: ndarray
kx: ndarray
ky: ndarray
spectrum_power: ndarray
metadata: dict[str, Any]
magnitudes: dict[str, float]
complex_problems.membrane_2d.solver.solve_membrane_2d(*, u0, v0=None, t_min=0.0, t_max=20.0, dt=0.02, mass=1.0, k_linear=1.0, boundary='fixed', integrator='verlet', alpha=0.0, beta=0.0, high_order_coeff=0.0, high_order_power=5)[source]

Solve the membrane dynamics for the provided initial fields.

Return type:

Membrane2DResult

Parameters:

UI dialog for configuring a 2D nonlinear membrane simulation.

complex_problems.membrane_2d.ui.resolve_optional_membrane_terms(selected_labels, *, alpha_text, beta_text, high_coeff_text, high_power_text)[source]

Resolve optional membrane nonlinear terms from selected labels.

Return type:

tuple[float, float, float, int]

Parameters:

  • selected_labels (set[str])

  • alpha_text (str)

  • beta_text (str)

  • high_coeff_text (str)

  • high_power_text (str)

class complex_problems.membrane_2d.ui.Membrane2DDialog(parent)[source]

Bases: object

Configuration dialog for the membrane problem.

Parameters:

parent (tk.Tk | tk.Toplevel)

Result dialog for the 2D nonlinear membrane.

class complex_problems.membrane_2d.result_dialog.Membrane2DResultDialog(parent, *, result)[source]

Bases: object

Result window for membrane simulations.

Parameters:

nonlinear_waves

Nonlinear wave propagation complex problem (NLSE and KdV).

complex_problems.nonlinear_waves.solve_nonlinear_waves(*, model_type, x_min, x_max, nx, t_min=0.0, t_max=10.0, dt=0.002, profile='sech', amplitude=1.0, sigma=0.3, center=0.0, custom_profile_fn=None, initial_phase_k=0.0, beta2=1.0, gamma=1.0, c=0.0, alpha=6.0, beta_disp=1.0)[source]

Solve nonlinear wave propagation for NLSE or KdV.

Return type:

NonlinearWavesResult

Parameters:

Model helpers for nonlinear wave solvers (NLSE and KdV).

complex_problems.nonlinear_waves.model.build_periodic_grid(x_min, x_max, nx)[source]

Build periodic spatial grid and spectral k-grid.

Return type:

tuple[ndarray, float, ndarray]

Parameters:
complex_problems.nonlinear_waves.model.build_initial_profile(x, *, profile, amplitude, sigma, center, custom_fn=None)[source]

Build real-valued initial profile.

Return type:

ndarray

Parameters:
complex_problems.nonlinear_waves.model.compute_nlse_invariants(psi, *, dx, k, beta2, gamma)[source]

Compute NLSE invariants: norm, momentum, hamiltonian (approx).

Return type:

tuple[float, float, float]

Parameters:
complex_problems.nonlinear_waves.model.compute_kdv_invariants(u, *, dx, k)[source]

Compute KdV invariants: mass, L2, and approximate Hamiltonian.

Return type:

tuple[float, float, float]

Parameters:

Pseudo-spectral solvers for nonlinear wave models (NLSE and KdV).

class complex_problems.nonlinear_waves.solver.NonlinearWavesResult(model_type, x, t, field, magnitude, phase, k, spectrum_power, invariants, metadata=<factory>, magnitudes=<factory>)[source]

Bases: object

Result bundle for nonlinear wave simulations.

Parameters:
model_type: str
x: ndarray
t: ndarray
field: ndarray
magnitude: ndarray
phase: ndarray | None
k: ndarray
spectrum_power: ndarray
invariants: dict[str, ndarray]
metadata: dict[str, Any]
magnitudes: dict[str, float]
complex_problems.nonlinear_waves.solver.solve_nonlinear_waves(*, model_type, x_min, x_max, nx, t_min=0.0, t_max=10.0, dt=0.002, profile='sech', amplitude=1.0, sigma=0.3, center=0.0, custom_profile_fn=None, initial_phase_k=0.0, beta2=1.0, gamma=1.0, c=0.0, alpha=6.0, beta_disp=1.0)[source]

Solve nonlinear wave propagation for NLSE or KdV.

Return type:

NonlinearWavesResult

Parameters:

UI dialog for nonlinear wave simulations (NLSE / KdV).

class complex_problems.nonlinear_waves.ui.NonlinearWavesDialog(parent)[source]

Bases: object

Configuration dialog for nonlinear wave propagation models.

Parameters:

parent (tk.Tk | tk.Toplevel)

Result dialog for nonlinear wave simulations (NLSE/KdV).

class complex_problems.nonlinear_waves.result_dialog.NonlinearWavesResultDialog(parent, *, result)[source]

Bases: object

Result window for nonlinear waves.

Parameters:

schrodinger_td

Time-dependent Schrodinger complex problem (1D/2D).

complex_problems.schrodinger_td.solve_schrodinger_td(*, dimension, x_min, x_max, nx, y_min=-10.0, y_max=10.0, ny=128, t_min=0.0, t_max=8.0, dt=0.002, hbar=1.0, mass=1.0, boundary='periodic', absorb_ratio=0.1, absorb_strength=1.0, potential_type='free', omega=1.0, v0=5.0, width=2.0, barrier_sigma=0.4, lattice_k=2.0, a_dw=1.0, b_dw=1.0, packet_type='gaussian', sigma=0.8, x0=0.0, y0=0.0, k0x=0.0, k0y=0.0, separation=2.0, custom_potential_fn_1d=None, custom_potential_fn_2d=None, custom_packet_fn_1d=None, custom_packet_fn_2d=None)[source]

Solve TDSE in 1D or 2D with split-operator spectral method.

Return type:

SchrodingerTDResult

Parameters:

Model helpers for TDSE (1D/2D) with configurable potentials.

complex_problems.schrodinger_td.model.normalize_wavefunction_1d(psi, dx)[source]

Normalize 1D wavefunction.

Return type:

ndarray

Parameters:
complex_problems.schrodinger_td.model.normalize_wavefunction_2d(psi, dx, dy)[source]

Normalize 2D wavefunction.

Return type:

ndarray

Parameters:
complex_problems.schrodinger_td.model.build_absorbing_mask_1d(nx, *, ratio=0.1, strength=1.0)[source]

Build a smooth 1D absorbing boundary mask.

Return type:

ndarray

Parameters:
complex_problems.schrodinger_td.model.build_absorbing_mask_2d(nx, ny, *, ratio=0.1, strength=1.0)[source]

Build 2D absorbing mask as outer product of 1D masks.

Return type:

ndarray

Parameters:
complex_problems.schrodinger_td.model.potential_1d(x, *, potential_type, omega=1.0, v0=5.0, width=2.0, barrier_sigma=0.3, lattice_k=2.0, a_dw=1.0, b_dw=1.0, custom_fn=None)[source]

Build 1D potential profile.

Return type:

ndarray

Parameters:
complex_problems.schrodinger_td.model.potential_2d(X, Y, *, potential_type, omega=1.0, v0=5.0, width=2.0, barrier_sigma=0.3, lattice_k=2.0, a_dw=1.0, b_dw=1.0, custom_fn=None)[source]

Build 2D potential surface.

Return type:

ndarray

Parameters:
complex_problems.schrodinger_td.model.initial_packet_1d(x, *, packet_type, sigma, x0, k0x, separation=2.0, custom_fn=None)[source]

Build initial 1D packet.

Return type:

ndarray

Parameters:
complex_problems.schrodinger_td.model.initial_packet_2d(X, Y, *, packet_type, sigma, x0, y0, k0x, k0y, separation=2.0, custom_fn=None)[source]

Build initial 2D packet.

Return type:

ndarray

Parameters:

Split-operator spectral solver for time-dependent Schrodinger equation.

class complex_problems.schrodinger_td.solver.SchrodingerTDResult(dimension, x, y, t, psi, magnitude, phase, potential, kx, ky, spectrum_power, invariants, metadata=<factory>, magnitudes=<factory>)[source]

Bases: object

Result bundle for TDSE simulations.

Parameters:
dimension: int
x: ndarray
y: ndarray | None
t: ndarray
psi: ndarray
magnitude: ndarray
phase: ndarray
potential: ndarray
kx: ndarray
ky: ndarray | None
spectrum_power: ndarray
invariants: dict[str, ndarray]
metadata: dict[str, Any]
magnitudes: dict[str, float]
complex_problems.schrodinger_td.solver.solve_schrodinger_td(*, dimension, x_min, x_max, nx, y_min=-10.0, y_max=10.0, ny=128, t_min=0.0, t_max=8.0, dt=0.002, hbar=1.0, mass=1.0, boundary='periodic', absorb_ratio=0.1, absorb_strength=1.0, potential_type='free', omega=1.0, v0=5.0, width=2.0, barrier_sigma=0.4, lattice_k=2.0, a_dw=1.0, b_dw=1.0, packet_type='gaussian', sigma=0.8, x0=0.0, y0=0.0, k0x=0.0, k0y=0.0, separation=2.0, custom_potential_fn_1d=None, custom_potential_fn_2d=None, custom_packet_fn_1d=None, custom_packet_fn_2d=None)[source]

Solve TDSE in 1D or 2D with split-operator spectral method.

Return type:

SchrodingerTDResult

Parameters:

UI dialog for configuring time-dependent Schrödinger simulations.

class complex_problems.schrodinger_td.ui.SchrodingerTDDialog(parent)[source]

Bases: object

Configuration dialog for TDSE in 1D and 2D.

Parameters:

parent (tk.Tk | tk.Toplevel)

Result dialog for time-dependent Schrodinger simulations.

class complex_problems.schrodinger_td.result_dialog.SchrodingerTDResultDialog(parent, *, result)[source]

Bases: object

Result window for TDSE 1D/2D.

Parameters:

antenna_radiation

Antenna radiation complex problem plugin.

complex_problems.antenna_radiation.solve_antenna_radiation(*, antenna_type='dipole', frequency_hz=1000000000.0, transmit_power_w=10.0, efficiency=0.9, observation_distance_m=50.0, n_theta=181, n_phi=360, length_lambda=0.5, loop_radius_lambda=0.1, patch_length_lambda=0.5, patch_width_lambda=0.4, array_elements=8, array_spacing_lambda=0.5, array_phase_deg=0.0, array_steer_theta_deg=90.0)[source]

Solve a far-field antenna radiation case.

Return type:

AntennaRadiationResult

Parameters:

  • antenna_type (str)

  • frequency_hz (float)

  • transmit_power_w (float)

  • efficiency (float)

  • observation_distance_m (float)

  • n_theta (int)

  • n_phi (int)

  • length_lambda (float)

  • loop_radius_lambda (float)

  • patch_length_lambda (float)

  • patch_width_lambda (float)

  • array_elements (int)

  • array_spacing_lambda (float)

  • array_phase_deg (float)

  • array_steer_theta_deg (float)

Model helpers for far-field antenna radiation patterns.

complex_problems.antenna_radiation.model.build_angular_grid(n_theta, n_phi)[source]

Build theta/phi angular grids.

Return type:

tuple[ndarray, ndarray]

Parameters:
complex_problems.antenna_radiation.model.pattern_dipole(theta_grid, *, length_lambda)[source]

Approximate thin-wire dipole power pattern.

Return type:

ndarray

Parameters:
complex_problems.antenna_radiation.model.pattern_small_loop(theta_grid, *, radius_lambda)[source]

Small-loop-like power pattern.

Return type:

ndarray

Parameters:
complex_problems.antenna_radiation.model.pattern_patch(theta_grid, phi_grid, *, length_lambda, width_lambda)[source]

Simple aperture-model patch-like power pattern.

Return type:

ndarray

Parameters:
complex_problems.antenna_radiation.model.pattern_uniform_linear_array(theta_grid, *, n_elements, spacing_lambda, phase_deg, steer_theta_deg)[source]

Uniform linear array factor power (array axis z, theta from z).

Return type:

ndarray

Parameters:
complex_problems.antenna_radiation.model.antenna_pattern(*, antenna_type, theta, phi, length_lambda, loop_radius_lambda, patch_length_lambda, patch_width_lambda, array_elements, array_spacing_lambda, array_phase_deg, array_steer_theta_deg)[source]

Build raw non-normalized power pattern on theta-phi mesh.

Return type:

ndarray

Parameters:
complex_problems.antenna_radiation.model.normalize_pattern(p)[source]

Normalize pattern to max=1.

Return type:

ndarray

Parameters:

p (ndarray)

complex_problems.antenna_radiation.model.compute_directivity(p_norm, theta, phi)[source]

Compute directivity map from normalized pattern.

Return type:

ndarray

Parameters:
complex_problems.antenna_radiation.model.estimate_beamwidth_deg(theta, cut_power)[source]

Estimate -3 dB beamwidth from a theta cut.

Return type:

float

Parameters:
complex_problems.antenna_radiation.model.estimate_aperture_lambda(*, antenna_type, length_lambda, loop_radius_lambda, patch_length_lambda, patch_width_lambda, array_elements, array_spacing_lambda)[source]

Estimate largest physical dimension in wavelengths.

Return type:

float

Parameters:

  • antenna_type (str)

  • length_lambda (float)

  • loop_radius_lambda (float)

  • patch_length_lambda (float)

  • patch_width_lambda (float)

  • array_elements (int)

  • array_spacing_lambda (float)

complex_problems.antenna_radiation.model.to_db10(x, *, floor_db=-80.0)[source]

Convert linear values to dB with floor.

Return type:

ndarray

Parameters:
complex_problems.antenna_radiation.model.wrap_angle_deg(angle)[source]

Wrap angle to [-180, 180).

Return type:

float

Parameters:

angle (float)

complex_problems.antenna_radiation.model.degrees(rad)[source]

Radians to degrees.

Return type:

ndarray

Parameters:

rad (ndarray)

complex_problems.antenna_radiation.model.wavelength_from_frequency(frequency_hz)[source]

Compute free-space wavelength.

Return type:

float

Parameters:

frequency_hz (float)

complex_problems.antenna_radiation.model.far_field_distance_min(wavelength, aperture_lambda)[source]

Fraunhofer minimum far-field distance.

Return type:

float

Parameters:
complex_problems.antenna_radiation.model.e_from_power_density(power_density)[source]

Convert power density to RMS electric field magnitude.

Return type:

ndarray

Parameters:

power_density (ndarray)

complex_problems.antenna_radiation.model.h_from_e_field(e_rms)[source]

Convert RMS electric field to RMS magnetic field.

Return type:

ndarray

Parameters:

e_rms (ndarray)

complex_problems.antenna_radiation.model.compute_reaction_metrics(*, directivity, gain, theta, phi, p_norm)[source]

Compute scalar quality metrics from solved patterns.

Return type:

dict[str, float]

Parameters:

Analytical far-field solver for antenna radiation patterns.

class complex_problems.antenna_radiation.solver.AntennaRadiationResult(antenna_type, theta, phi, pattern_norm, directivity, directivity_db, gain, gain_db, power_density, e_rms, h_rms, theta_cut_db, phi_cut_db, metadata=<factory>, magnitudes=<factory>)[source]

Bases: object

Result bundle for antenna radiation problem.

Parameters:
antenna_type: str
theta: ndarray
phi: ndarray
pattern_norm: ndarray
directivity: ndarray
directivity_db: ndarray
gain: ndarray
gain_db: ndarray
power_density: ndarray
e_rms: ndarray
h_rms: ndarray
theta_cut_db: ndarray
phi_cut_db: ndarray
metadata: dict[str, Any]
magnitudes: dict[str, float]
complex_problems.antenna_radiation.solver.solve_antenna_radiation(*, antenna_type='dipole', frequency_hz=1000000000.0, transmit_power_w=10.0, efficiency=0.9, observation_distance_m=50.0, n_theta=181, n_phi=360, length_lambda=0.5, loop_radius_lambda=0.1, patch_length_lambda=0.5, patch_width_lambda=0.4, array_elements=8, array_spacing_lambda=0.5, array_phase_deg=0.0, array_steer_theta_deg=90.0)[source]

Solve a far-field antenna radiation case.

Return type:

AntennaRadiationResult

Parameters:

  • antenna_type (str)

  • frequency_hz (float)

  • transmit_power_w (float)

  • efficiency (float)

  • observation_distance_m (float)

  • n_theta (int)

  • n_phi (int)

  • length_lambda (float)

  • loop_radius_lambda (float)

  • patch_length_lambda (float)

  • patch_width_lambda (float)

  • array_elements (int)

  • array_spacing_lambda (float)

  • array_phase_deg (float)

  • array_steer_theta_deg (float)

UI dialog for configuring antenna radiation simulations.

class complex_problems.antenna_radiation.ui.AntennaRadiationDialog(parent)[source]

Bases: object

Configuration dialog for antenna radiation patterns.

Parameters:

parent (tk.Tk | tk.Toplevel)

Result dialog for antenna radiation simulations.

class complex_problems.antenna_radiation.result_dialog.AntennaRadiationResultDialog(parent, *, result)[source]

Bases: object

Result window for antenna radiation problem.

Parameters:

aerodynamics_2d

Aerodynamics complex problem plugin.

complex_problems.aerodynamics_2d.solve_aerodynamics_2d(*, approximation='nonlinear_ns', nx=96, ny=64, lx=4.0, ly=2.0, t_max=2.0, dt=0.002, sample_every=10, rho=1.0, nu=0.01, u_inf=1.0, penalization=0.005, obstacle_shape='cylinder', obstacle_center_x=1.3, obstacle_center_y=1.0, obstacle_size_x=0.3, obstacle_size_y=0.3, obstacle_attack_deg=0.0)[source]

Solve 2D incompressible flow in a periodic box with an immersed obstacle.

Return type:

Aerodynamics2DResult

Parameters:

Geometry and field helpers for 2D aerodynamics.

complex_problems.aerodynamics_2d.model.build_periodic_domain(*, nx, ny, lx, ly)[source]

Build periodic domain coordinates and mesh.

Return type:

tuple[ndarray, ndarray, ndarray, ndarray, float, float]

Parameters:
complex_problems.aerodynamics_2d.model.rotate_coordinates(X, Y, *, center_x, center_y, angle_deg)[source]

Rotate coordinates around obstacle center.

Return type:

tuple[ndarray, ndarray]

Parameters:
complex_problems.aerodynamics_2d.model.build_obstacle_mask(*, shape, X, Y, center_x, center_y, size_x, size_y, attack_deg)[source]

Build obstacle mask and reference scales.

Return type:

tuple[ndarray, float, float]

Parameters:
complex_problems.aerodynamics_2d.model.ddx_periodic(f, dx)[source]

Periodic x-derivative.

Return type:

ndarray

Parameters:
complex_problems.aerodynamics_2d.model.ddy_periodic(f, dy)[source]

Periodic y-derivative.

Return type:

ndarray

Parameters:
complex_problems.aerodynamics_2d.model.laplacian_periodic(f, dx, dy)[source]

Periodic 2D Laplacian.

Return type:

ndarray

Parameters:
complex_problems.aerodynamics_2d.model.divergence_periodic(u, v, dx, dy)[source]

Periodic divergence.

Return type:

ndarray

Parameters:
complex_problems.aerodynamics_2d.model.vorticity_periodic(u, v, dx, dy)[source]

Periodic scalar vorticity.

Return type:

ndarray

Parameters:

2D incompressible aerodynamics solver with obstacle penalization.

class complex_problems.aerodynamics_2d.solver.Aerodynamics2DResult(x, y, t, u, v, pressure, speed, vorticity, obstacle_mask, drag_coeff, lift_coeff, metadata=<factory>, magnitudes=<factory>)[source]

Bases: object

Result bundle for 2D aerodynamics simulation.

Parameters:
x: ndarray
y: ndarray
t: ndarray
u: ndarray
v: ndarray
pressure: ndarray
speed: ndarray
vorticity: ndarray
obstacle_mask: ndarray
drag_coeff: ndarray
lift_coeff: ndarray
metadata: dict[str, Any]
magnitudes: dict[str, float]
complex_problems.aerodynamics_2d.solver.solve_aerodynamics_2d(*, approximation='nonlinear_ns', nx=96, ny=64, lx=4.0, ly=2.0, t_max=2.0, dt=0.002, sample_every=10, rho=1.0, nu=0.01, u_inf=1.0, penalization=0.005, obstacle_shape='cylinder', obstacle_center_x=1.3, obstacle_center_y=1.0, obstacle_size_x=0.3, obstacle_size_y=0.3, obstacle_attack_deg=0.0)[source]

Solve 2D incompressible flow in a periodic box with an immersed obstacle.

Return type:

Aerodynamics2DResult

Parameters:

UI dialog for configuring 2D aerodynamics simulations.

class complex_problems.aerodynamics_2d.ui.Aerodynamics2DDialog(parent)[source]

Bases: object

Configuration dialog for 2D aerodynamic flow solver.

Parameters:

parent (tk.Tk | tk.Toplevel)

Result dialog for 2D aerodynamics simulations.

class complex_problems.aerodynamics_2d.result_dialog.Aerodynamics2DResultDialog(parent, *, result)[source]

Bases: object

Result window for 2D aerodynamics.

Parameters:

pipe_flow

Pipe flow complex problem plugin.

complex_problems.pipe_flow.solve_pipe_flow(*, model_type='steady', length=20.0, nx=256, profile='constant', d_in=0.08, d_out=0.05, d0=0.06, profile_amplitude=0.2, profile_waves=2.0, custom_diameter_fn=None, rho=1000.0, mu=0.001, roughness=1e-05, friction_model='auto', p_in=200000.0, p_out=190000.0, p_base=200000.0, p_amp=2000.0, p_freq_hz=2.0, wave_speed=200.0, damping=0.2, t_max=1.0, dt=0.0005, sample_every=10)[source]

Solve steady or transient 1D pipe flow.

Return type:

PipeFlowResult

Parameters:

Model helpers for 1D pipe flow.

complex_problems.pipe_flow.model.build_pipe_grid(length, nx)[source]

Build 1D pipe grid.

Return type:

tuple[ndarray, float]

Parameters:
complex_problems.pipe_flow.model.diameter_profile(x, *, profile, d_in, d_out, d0, amplitude, n_waves, custom_fn=None)[source]

Build diameter profile along x.

Return type:

ndarray

Parameters:
complex_problems.pipe_flow.model.area_from_diameter(diameter)[source]

Pipe cross-sectional area.

Return type:

ndarray

Parameters:

diameter (ndarray)

complex_problems.pipe_flow.model.reynolds_number(rho, mu, velocity, diameter)[source]

Compute Reynolds number profile.

Return type:

ndarray

Parameters:
complex_problems.pipe_flow.model.friction_factor(re, *, roughness, diameter, model)[source]

Compute Darcy friction factor.

Return type:

ndarray

Parameters:

Steady and transient 1D pipe-flow solvers.

class complex_problems.pipe_flow.solver.PipeFlowResult(model_type, x, t, diameter, area, pressure, velocity, reynolds, friction, flow_rate_mean, flow_rate_std, metadata=<factory>, magnitudes=<factory>)[source]

Bases: object

Result bundle for pipe-flow simulations.

Parameters:
model_type: str
x: ndarray
t: ndarray
diameter: ndarray
area: ndarray
pressure: ndarray
velocity: ndarray
reynolds: ndarray
friction: ndarray
flow_rate_mean: ndarray
flow_rate_std: ndarray
metadata: dict[str, Any]
magnitudes: dict[str, float]
complex_problems.pipe_flow.solver.solve_pipe_flow(*, model_type='steady', length=20.0, nx=256, profile='constant', d_in=0.08, d_out=0.05, d0=0.06, profile_amplitude=0.2, profile_waves=2.0, custom_diameter_fn=None, rho=1000.0, mu=0.001, roughness=1e-05, friction_model='auto', p_in=200000.0, p_out=190000.0, p_base=200000.0, p_amp=2000.0, p_freq_hz=2.0, wave_speed=200.0, damping=0.2, t_max=1.0, dt=0.0005, sample_every=10)[source]

Solve steady or transient 1D pipe flow.

Return type:

PipeFlowResult

Parameters:

UI dialog for configuring pipe-flow simulations.

class complex_problems.pipe_flow.ui.PipeFlowDialog(parent)[source]

Bases: object

Configuration dialog for steady and transient pipe flow.

Parameters:

parent (tk.Tk | tk.Toplevel)

Result dialog for pipe-flow simulations.

class complex_problems.pipe_flow.result_dialog.PipeFlowResultDialog(parent, *, result)[source]

Bases: object

Result window for steady/transient pipe flow.

Parameters: