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Plasma Physics

H-mode Confinement

High-confinement operating regime in tokamaks characterized by a steep edge pressure barrier (pedestal) and doubled energy confinement time.

Energy Confinement Time τ_E(H-mode) ≈ 2 × τ_E(L-mode) s (Energy Confinement Time τ_E) Nuclear & Particle Physics

Hadrons

Subatomic composite particles made of quarks and gluons held together by the strong nuclear force.

Strongly interacting composite particles (Baryons & Mesons) Composite Particle Class Nuclear & Particle Physics

Half-Life

The time required for half the radioactive nuclei in a given sample to undergo spontaneous radioactive decay.

t_½ = ln(2) / λ ≈ 0.693 / λ, N(t) = N₀ (½)^(t / t_½) Seconds, Hours, or Years Electromagnetism & Electronics

Hall Effect

The production of a transverse electric potential difference (Hall voltage) across a current-carrying conductor in an orthogonal magnetic…

V_H = (I B) / (n q t), R_H = 1 / (n q) V (Hall Voltage), m³/C (Hall Coefficient) Plasma Physics

Hall Effect Thruster

A electric space propulsion plasma engine that accelerates ions across an electrostatic potential drop using trapped electrons in an…

F_thrust = ṁ v_exhaust, v_ex = √(2 e V_acc / m_ion) N or mN (Thrust) & s (Specific Impulse ~1500–3000 s) Mathematical & Computational Physics

Hamiltonian Formalism

A formulation of classical mechanics describing system dynamics in 2N-dimensional phase space using position q_i and canonical momentum p_i.

H(q, p, t) = ∑ p_i q̇_i - L, q̇_i = ∂H / ∂p_i, ṗ_i = -∂H / ∂q_i Joules (Energy) Condensed Matter & Materials Physics

Hardness

A material's resistance to localized plastic surface deformation induced by mechanical scratching, abrasion, or indentation.

H = Load / Indentation Surface Area (Mohs, Vickers, Rockwell) MPa or GPa (Mohs scale 1 to 10) Waves, Oscillations & Acoustics

Harmonics

Resonant frequencies of a system that are integer multiples of its fundamental frequency.

f_n = n f1 (where n = 1, 2, 3, ...) Hz Astrophysics, Cosmology & Relativity

Hawking Radiation

Thermal blackbody radiation predicted to be emitted by black holes due to quantum field fluctuations near the event horizon.

T_H = ℏ c³ / (8 π G M k_B), P = ℏ c⁶ / (15360 π G² M²) Kelvin (Blackbody Temperature T_H) Thermodynamics & Statistical Physics

Heat Engine

A physical device that converts thermal energy absorbed from a high-temperature heat source into mechanical work, discharging waste heat to…

W = Q_hot - Q_cold, η = W / Q_hot W (J/s) Quantum & Atomic Physics

Heisenberg Uncertainty Principle

A fundamental quantum limit stating that canonical conjugate physical variables (such as position and momentum, or energy and time) cannot…

Δx Δp ≥ ℏ / 2, ΔE Δt ≥ ℏ / 2 J·s (Action Units) Thermodynamics & Statistical Physics

Helmholtz Free Energy

A thermodynamic potential measuring maximum reversible work obtainable from a closed system at constant temperature and volume.

F = U - T S, dF = -S dT - P dV J Biophysics & Medical Physics

Hemodynamics

The physical study of blood flow dynamics, vascular resistance, and pressure relations within the circulatory system.

Q = ΔP / R_v, R_v = (8 η L) / (π r⁴) (Poiseuille Flow) L/min (Cardiac Output) & mmHg (Pressure) Mathematical & Computational Physics

Hermite Polynomials

A sequence of classical orthogonal polynomials satisfying Hermite's differential equation y'' - 2x y' + 2n y = 0.

H_n(x) = (-1)^n e^(x²) (d^n / dx^n) (e^(-x²)) Dimensionless Orthogonal Polynomials Astrophysics, Cosmology & Relativity

Hertzsprung-Russell (H-R) Diagram

A foundational scatter plot of stellar luminosity versus surface temperature (or spectral type) used to trace stellar evolution phases.

L ∝ R² T^4 (Plot of Absolute Magnitude vs Spectral Type) Luminosity (L_☉) vs Surface Temp (K) Mathematical & Computational Physics

Hessian Matrix

A square matrix of second-order partial derivatives of a scalar-valued function, describing local surface curvature and local extrema…

H_ij = ∂²f / (∂x_i ∂x_j) Second Derivative Matrix Nuclear & Particle Physics

Higgs Boson

An elementary scalar boson associated with the Higgs field that endows fundamental particles with rest mass via electroweak symmetry…

m_H ≈ 125.1 GeV/c², Spin = 0, Scalar Field φ GeV/c² (Mass Energy) Mathematical & Computational Physics

Hilbert Space

A complete abstract vector space possessing an inner product that allows length and angle to be defined for infinite-dimensional function…

⟨f, g⟩ = ∫ f*(x) g(x) dx, ||f|| = √(⟨f, f⟩) Complete Inner Product Space Optics

Holography

A technique for recording and reconstructing 3D wavefields by recording phase and amplitude interference patterns between object and…

I(x,y) = |E_ref + E_obj|² N/A Classical Mechanics

Hooke's Law

A law of elasticity stating that restoring force exerted by a spring or elastic material is proportional to its extension or compression…

F = -k x N (k in N/m) Astrophysics, Cosmology & Relativity

Hubble's Law

The cosmological observation that galaxies recede from Earth at velocities directly proportional to their proper distance.

v = H₀ d, H₀ ≈ 70 (km/s) / Mpc km/s/Mpc (Hubble Constant) Quantum & Atomic Physics

Hund's Rule of Maximum Multiplicity

A rule stating that when filling degenerate atomic orbitals, electrons occupy separate orbitals singly with parallel spins before pairing…

S_total = ∑ s_i (Maximized spin in degenerate orbitals) Dimensionless Rule Waves, Oscillations & Acoustics

Huygens-Fresnel Principle

The wave propagation principle asserting that every point on a wavefront acts as a secondary source of spherical wavelets.

New Wavefront = Envelope of Secondary Wavelets N/A Quantum & Atomic Physics

Hydrogen Spectrum

The set of discrete electromagnetic emission and absorption lines produced when the electron in a hydrogen atom transitions between energy…

1 / λ = R_H (1 / n_f² - 1 / n_i²) m⁻¹ (Wavenumber)