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Biophysics & Medical Physics

Equivalent Dose

A radiation protection dose quantity weighing absorbed dose by the specific biological effectiveness factor w_R of the radiation type.

H = D × w_R (Radiation Weighting Factor w_R) Sv (Sievert = J/kg) or rem Mathematical & Computational Physics

Error Propagation

The mathematical evaluation of how uncertainties in measured input variables propagate into the final calculated physical quantity.

σ_f² = ∑ (∂f / ∂x_i)² σ_x_i² + 2 ∑ (∂f/∂x_i)(∂f/∂x_j) Cov(x_i, x_j) Uncertainty Units Classical Mechanics

Escape Velocity

The minimum speed required for a ballistic object to escape a massive body's gravitational field without further propulsion.

v_esc = √(2 G M / R) m/s Mathematical & Computational Physics

Euler Method

A basic first-order numerical procedure for solving ordinary differential equations with a given initial value.

y_(n+1) = y_n + h f(t_n, y_n) First-Order Numerical ODE Integration Mathematical & Computational Physics

Euler-Lagrange Equation

The fundamental partial differential equation of the calculus of variations that a function must satisfy to make a functional stationary.

(d / dt) (∂L / ∂q̇_i) - (∂L / ∂q_i) = 0 Calculus of Variations Equation Astrophysics, Cosmology & Relativity

Event Horizon

The boundary surrounding a black hole beyond which escape velocity exceeds the speed of light, preventing any matter or signal from…

R_s = 2 G M / c² km or m (Boundary Radius) Condensed Matter & Materials Physics

Exciton

A neutral quasiparticle consisting of a conduction electron bound to a valence band hole by electrostatic Coulomb attraction.

E_exciton = E_g - E_b (where E_b = μ e⁴ / (8 ε² h² n²)) eV (Binding Energy) Astrophysics, Cosmology & Relativity

Exoplanet

A planet situated outside the Solar System that orbits a star, stellar remnant, or brown dwarf.

Transit Depth ΔF / F = (R_planet / R_star)² Earth Masses (M_⊕) or Jupiter Masses (M_J) Quantum & Atomic Physics

Expectation Value

The probabilistic average or expected value of many physical measurements performed on an ensemble of identically prepared quantum states.

⟨A⟩ = ∫ ψ* Â ψ dx / ∫ ψ* ψ dx Same as measured quantity Condensed Matter & Materials Physics

Extrinsic Semiconductor

A semiconductor whose electrical conductivity is dominated by intentional impurity dopants rather than thermal excitation across the band…

n p = n_i² (Mass Action Law) cm⁻³ (Dopant Carrier Density) Electromagnetism & Electronics

Faraday's Law of Induction

Maxwell's third equation stating that a time-varying magnetic flux through a closed conductive loop induces an electromotive force (EMF)…

E = -dΦ_B / dt, ∇ × E = -∂B/∂t V (Volts) Mathematical & Computational Physics

Fast Fourier Transform (FFT)

An efficient algorithm that computes the Discrete Fourier Transform (DFT) of a sequence in O(N log N) operations instead of O(N²).

Cooley-Tukey Divide-and-Conquer: O(N log N) vs O(N²) Computational FFT Algorithm Condensed Matter & Materials Physics

Fatigue

The progressive structural weakening and microcrack failure of a material subjected to repeated cyclic loading stresses below its ultimate…

Basquin's Relation: S_a = σ'_f (2 N_f)^b Cycles to Failure N_f Optics

Fermat's Principle

The fundamental principle stating that light traveling between two points follows the path that requires the stationary (usually minimum)…

Optical Path Length L = ∫ n(s) ds = extremum s (or m) Quantum & Atomic Physics

Fermi Energy

The highest occupied kinetic energy state of non-interacting fermions in a quantum system at absolute zero temperature (0 K).

E_F = (ℏ² / (2 m)) (3 π² n)^(2/3) eV or Joules Condensed Matter & Materials Physics

Fermi Level

The thermodynamic Fermi-Dirac chemical potential representing the energy level at which the probability of electron occupancy is exactly…

f(E) = 1 / (e^((E - E_F) / (k_B T)) + 1) eV (Chemical Potential) Astrophysics, Cosmology & Relativity

Fermi Paradox

The apparent contradiction between high probabilistic estimates for the existence of extraterrestrial civilizations and the complete lack…

Enrico Fermi: 'Where is everybody?' Astronomical Paradox Quantum & Atomic Physics

Fermions

Subatomic particles possessing half-integer intrinsic spin that obey Fermi-Dirac statistics and the Pauli Exclusion Principle.

Spin = ½, ³/₂, ⁵/₂... Dimensionless Particle Class Electromagnetism & Electronics

Ferromagnetism

A strong magnetic phenomenon in which atomic magnetic moments spontaneously align parallel into localized magnetic domains, producing…

μ_r ≫ 1 (μ_r ~ 1,000–100,000) Dimensionless Nuclear & Particle Physics

Feynman Diagram

Visual pictorial representations of mathematical expressions describing the quantum interaction and scattering behavior of subatomic…

Pictorial matrix elements M_fi in QFT perturbational expansions Calculational Diagram Biophysics & Medical Physics

Fick's Laws of Diffusion

Physical laws describing solute diffusion mass transport across biological concentration gradients.

1st: J = -D (dC / dx); 2nd: ∂C / ∂t = D (∂²C / ∂x²) mol/(m²·s) (Flux J) & m²/s (Diffusion Coefficient D) Plasma Physics

Field-Reversed Configuration (FRC)

A high-beta compact toroid magnetic confinement concept where a closed-poloidal-field plasma torus is sustained inside a simple linear…

Average Beta ⟨β⟩ ≈ 1 (High-Beta Compact Toroid) Dimensionless High Beta ⟨β⟩ ~ 0.9 Quantum & Atomic Physics

Fine Structure

The small splitting of atomic spectral lines resulting from relativistic mass corrections and spin-orbit coupling.

E_fine ~ α² E_n, α ≈ 1 / 137 eV (Energy Splitting) Mathematical & Computational Physics

Finite Difference Method

A numerical method for solving differential equations by approximating derivatives with finite difference quotients on a discretized grid.

f'(x) ≈ (f(x + h) - f(x - h)) / (2 h), f''(x) ≈ (f(x+h) - 2f(x) + f(x-h)) / h² Grid Discretization Method