Electromagnetic Analysis Ontology

flow "ElectromagneticAnalysisOntology" v1.0

SOURCE_URL := "https://kirethresearch.org/booksai-core/ontologies/calculus-analysis-ontologies/scientific-applications/electromagnetic-analysis-ontology.html"
DOMAIN := "Mathematical Ontologies"
CATEGORY := "Calculus and Analysis Ontologies"
SUBCATEGORY := "Scientific Applications"
ENTITY := "Electromagnetic Analysis"

ELECTROMAGNETIC_ANALYSIS := {
 type: AppliedFieldAnalysisFramework,
 purpose: "Analyse electric and magnetic fields, sources, materials, waves, energy transfer and boundary interactions using Maxwell equations, vector calculus and computational methods."
}

CONCEPTS := {
 ELECTRIC_FIELD, MAGNETIC_FIELD, ELECTRIC_DISPLACEMENT,
 MAGNETIC_FLUX_DENSITY, CHARGE_DENSITY, CURRENT_DENSITY,
 MAXWELL_EQUATIONS, POTENTIAL, PERMITTIVITY, PERMEABILITY,
 CONDUCTIVITY, ELECTROMAGNETIC_WAVE, POYNTING_VECTOR,
 IMPEDANCE, BOUNDARY_CONDITION
}

# ---------- FIELDS ----------
E -> ELECTRIC_FIELD
D -> ELECTRIC_DISPLACEMENT
B -> MAGNETIC_FLUX_DENSITY
H -> MAGNETIC_FIELD_INTENSITY
rho -> CHARGE_DENSITY
J -> CURRENT_DENSITY

# ---------- MAXWELL EQUATIONS ----------
div(D) = rho
div(B) = 0
curl(E) = -partial_B/partial_t
curl(H) = J + partial_D/partial_t

MAXWELL_EQUATIONS
 -> govern(ELECTROMAGNETIC_FIELDS)

# ---------- MATERIAL RELATIONS ----------
linear_isotropic_medium:

D = epsilon*E
B = mu*H
J = sigma*E

epsilon -> PERMITTIVITY
mu -> PERMEABILITY
sigma -> CONDUCTIVITY

CONSTITUTIVE_RELATIONS
 -> connect(FIELDS_TO_MATERIAL_PROPERTIES)

# ---------- CHARGE CONSERVATION ----------
partial_rho/partial_t
+
div(J)
=
0

CONTINUITY_EQUATION
 -> CONSERVATION_OF_CHARGE

# ---------- ELECTROSTATICS ----------
partial/partial_t = 0

curl(E)=0

therefore locally:

E = -grad(phi)

-div(epsilon*grad(phi))
=
rho

rho=0
 -> LAPLACE_EQUATION

rho!=0
 -> POISSON_EQUATION

# ---------- MAGNETOSTATICS ----------
steady_currents:

curl(H)=J
div(B)=0

because div(B)=0:

B = curl(A)

A -> VECTOR_POTENTIAL

# ---------- ELECTROMAGNETIC WAVES ----------
source_free_homogeneous_medium:

LAPLACIAN(E)
-
mu*epsilon*partial_squared_E/partial_t_squared
=
0

LAPLACIAN(H)
-
mu*epsilon*partial_squared_H/partial_t_squared
=
0

wave_speed:

v = 1/sqrt(mu*epsilon)

vacuum:

c = 1/sqrt(mu_0*epsilon_0)

# ---------- PLANE WAVE ----------
plane_wave
 -> transverse(E,H,PROPAGATION_DIRECTION)

E perpendicular_to H

PROPAGATION_DIRECTION
 -> parallel_to(E cross H)

intrinsic_impedance:

eta = sqrt(mu/epsilon)

for simple lossless medium:

|E|/|H| = eta

# ---------- PHASOR ANALYSIS ----------
sinusoidal_fields
 -> COMPLEX_PHASORS

partial/partial_t
 -> i*omega
   under(exp(i*omega*t)_convention)

PHASOR_CONVENTION
 -> must_be_preserved

# ---------- ENERGY ----------
energy_density:

u_em
=
1/2*(E dot D + B dot H)

for linear nondispersive medium

POYNTING_VECTOR:

S = E cross H

POYNTING_THEOREM:

partial_u_em/partial_t
+
div(S)
=
-J dot E

POYNTING_THEOREM
 -> electromagnetic_energy_balance

# ---------- FORCE ----------
Lorentz_force:

F
=
q*(E + v cross B)

force_density:

f
=
rho*E + J cross B

MAXWELL_STRESS_TENSOR
 -> field_force_and_momentum_flux

# ---------- BOUNDARY CONDITIONS ----------
interface:

n dot (D_2-D_1)
=
rho_surface

n dot (B_2-B_1)
=
0

n cross (E_2-E_1)
=
0
 under ordinary nonsingular interface assumptions

n cross (H_2-H_1)
=
J_surface

BOUNDARY_CONDITIONS
 -> derived_from(MAXWELL_INTEGRAL_LAWS)

# ---------- REFLECTION / TRANSMISSION ----------
normal_incidence_simple_media:

reflection_coefficient:

Gamma
=
(eta_2-eta_1)/(eta_2+eta_1)

IMPEDANCE_MISMATCH
 -> REFLECTION

TRANSMISSION
 -> depends_on(MATERIAL_IMPEDANCES_AND_NORMALISATION)

# ---------- LOSS ----------
lossy_medium
 -> complex_propagation_constant

gamma
=
alpha+i*beta

alpha -> ATTENUATION
beta -> PHASE_CONSTANT

good_conductor_skin_depth:

delta
approx
sqrt(2/(omega*mu*sigma))

under standard approximation

# ---------- DISPERSION ----------
epsilon=epsilon(omega)
mu=mu(omega)

-> DISPERSIVE_MEDIUM

phase_velocity
 -/> necessarily(group_velocity)

FREQUENCY_DEPENDENT_MATERIAL
 -> pulse_dispersion

# ---------- POLARISATION ----------
POLARISATION
 -> orientation_and_phase_relation_of(E_COMPONENTS)

types:
 LINEAR
 CIRCULAR
 ELLIPTICAL

# ---------- WAVEGUIDES ----------
BOUNDARIES
 -> constrain(FIELD_MODES)

modes:
 TE
 TM
 TEM_WHERE_SUPPORTED

CUTOFF_FREQUENCY
 -> separates(PROPAGATING_AND_EVANESCENT_MODES)

# ---------- RESONANCE ----------
bounded_domain
 -> EIGENMODES

RESONANT_FREQUENCY
 -> Maxwell_boundary_eigenvalue

QUALITY_FACTOR
 -> stored_energy_relative_to_loss

# ---------- NUMERICAL METHODS ----------
methods:
 FDTD
 FEM
 METHOD_OF_MOMENTS
 BOUNDARY_ELEMENT
 SPECTRAL_METHOD

FDTD
 -> subject_to(COURANT_STABILITY)

FEM
 -> supports(COMPLEX_GEOMETRY_AND_MATERIALS)

OPEN_DOMAIN
 -> requires(
 ABSORBING_BOUNDARY,
 PML,
 RADIATION_CONDITION
)

# ---------- VALIDATION ----------
NUMERICAL_FIELD_SOLUTION
 -> verify(
 MESH_CONVERGENCE,
 TIME_STEP,
 ENERGY_BALANCE,
 DIVERGENCE_CONSTRAINTS,
 BOUNDARY_TREATMENT
)

compare_with:
 ANALYTIC_SOLUTION
 BENCHMARK
 MEASUREMENT

# ---------- APPLICATIONS ----------
ELECTROMAGNETIC_ANALYSIS
 -> ANTENNAS
 -> MICROWAVES
 -> OPTICS
 -> PHOTONICS
 -> MOTORS
 -> GENERATORS
 -> TRANSFORMERS
 -> EMC
 -> WIRELESS_COMMUNICATION
 -> MEDICAL_IMAGING

# ---------- RELATION GRAPH ----------
CHARGE -> sources(ELECTRIC_FIELD)
CURRENT -> sources(MAGNETIC_FIELD)
TIME_VARYING_B -> induces(ELECTRIC_FIELD)
TIME_VARYING_D -> contributes_to(MAGNETIC_FIELD)
MAXWELL_EQUATIONS -> generate(ELECTROMAGNETIC_WAVES)
CONSTITUTIVE_RELATIONS -> encode(MATERIAL_RESPONSE)
POYNTING_VECTOR -> represents(ENERGY_FLOW)
BOUNDARIES -> generate(REFLECTION_TRANSMISSION_AND_MODES)

# ---------- SEMANTIC EQUIVALENCE ----------
SEMANTIC_EQUIVALENCE := {
 "electromagnetic analysis" ~= "mathematical analysis of electromagnetic fields, sources, materials and waves",
 "electric potential" ~= "scalar potential generating electrostatic electric field through its negative gradient",
 "Poynting vector" ~= "electromagnetic energy-flux vector",
 "intrinsic impedance" ~= "plane-wave electric-to-magnetic field ratio in a medium",
 "skin depth" ~= "characteristic penetration depth in an attenuating conductor",
 "phasor analysis" ~= "frequency-domain representation of sinusoidal electromagnetic fields"
}

# ---------- CONSTRAINTS ----------
CONSTRAINTS := {
 E_D_B_H_are_distinct_fields: true,
 constitutive_relations_are_material_models: true,
 phasor_sign_depends_on_time_convention: true,
 plane_wave_formulas_require_plane_wave_assumptions: true,
 dispersive_lossy_media_require_complex_frequency_dependent_properties: true,
 wave_equations_must_retain_Maxwell_constraints: true,
 numerical_results_require_mesh_time_boundary_and_constraint_validation: true
}

# ---------- CONFIDENCE ----------
CONFIDENCE := {
 core_definition: 0.99,
 Maxwell_relation: 0.99,
 potential_relation: 0.99,
 wave_energy_relation: 0.99,
 boundary_relation: 0.99,
 numerical_relation: 0.99,
 semantic_equivalence: 0.97
}

# ---------- RECURSIVE REASONING ----------
RECURSIVE_REASONING(query):
 identify(geometry_sources_fields_materials_frequency_and_units)
 -> classify(electrostatic_magnetostatic_quasistatic_or_wave_problem)
 -> apply(Maxwell_equations_and_constitutive_relations)
 -> identify(boundary_interface_and_open_domain_conditions)
 -> derive(potential_wave_energy_force_or_impedance_relations)
 -> analyse(reflection_transmission_modes_dispersion_and_polarisation)
 -> choose(analytic_or_numerical_method)
 -> compute(fields_flux_power_force_or_response)
 -> verify(divergence_energy_mesh_time_step_and_boundary_consistency)
 -> validate(reference_solution_or_measurement)
 -> return(semantic_result)

# ---------- AI CONSUMPTION ----------
AI_CONSUMPTION := {
 parse_as: "typed electromagnetic-analysis semantic graph",
 primary_entity: ELECTROMAGNETIC_ANALYSIS,
 preserve: [
  geometry, sources, fields, material_properties,
  frequency, boundary_conditions, phasor_convention, units
 ],
 infer_through: [
  Maxwell_equations, potentials, waves, energy_flux,
  impedance, reflection, transmission, modes, numerical_methods
 ],
 avoid: [
  conflating_E_D_B_H,
  ignoring_dispersion_or_loss,
  mixing_phasor_conventions,
  applying_plane_wave_formulas_to_near_fields,
  discarding_divergence_constraints,
  accepting_simulation_without_convergence_validation
 ]
}

# ---------- UPDATE MODEL ----------
UPDATE_MODEL(new_information):
 validate(new_information)
 -> identify(electromagnetic_analysis_context)
 -> compare(existing_relations)
 -> preserve(field_source_material_frequency_boundary_and_convention_invariants)
 -> update(affected_entities)
 -> update(affected_edges)
 -> recompute(CONFIDENCE)
 -> regenerate(FLOW_HASH)

# ---------- FLOW HASH ----------
FLOW_HASH := hash(
 SOURCE_URL
 + ENTITY
 + CONCEPTS
 + ELECTROMAGNETIC_ANALYSIS
 + ELECTRIC_FIELD
 + MAGNETIC_FIELD
 + MAXWELL_EQUATIONS
 + POTENTIAL
 + ELECTROMAGNETIC_WAVE
 + POYNTING_VECTOR
 + IMPEDANCE
 + BOUNDARY_CONDITION
 + SEMANTIC_EQUIVALENCE
 + CONSTRAINTS
)

# ---------- EXECUTION ----------
INPUT(query)
 -> ELECTROMAGNETIC_ANALYSIS
 -> PROBLEM_IDENTIFICATION
 -> REGIME_CLASSIFICATION
 -> MAXWELL_MATERIAL_ANALYSIS
 -> BOUNDARY_ANALYSIS
 -> FIELD_RELATION_DERIVATION
 -> WAVE_INTERFACE_MODE_ANALYSIS
 -> METHOD_SELECTION
 -> RESPONSE_COMPUTATION
 -> VERIFICATION
 -> VALIDATION
 -> RECURSIVE_REASONING(query)
 -> CONFIDENCE
 -> OUTPUT(semantic_result)

END FLOW