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Numerical Stability Mathematical & Computational Physics Algorithm Stability Property The property of a numerical algorithm ensuring that errors introduced during computation do not magnify uncontrollably over successive time steps. Von Neumann Stability Analysis: |G(k, Δt)| ≤ 1 Nutation Geophysics & Environmental Physics Arcseconds (17.2″ in longitude, 9.2″ in obliquity) Small periodic nodding oscillations superimposed upon Earth's long-term rotational axis precession. Principal Nutation Period T = 18.6 years, Amplitude = 9.2″ Ocean Acidification Geophysics & Environmental Physics pH Units (Logarithmic Scale) The ongoing long-term reduction in the pH of Earth's oceans caused by the absorption of anthropogenic carbon dioxide from the atmosphere. CO₂ + H₂O ⇌ H₂CO₃ ⇌ H⁺ + HCO₃⁻, H⁺ + CO₃²⁻ ⇌ HCO₃⁻ Ocean Currents Geophysics & Environmental Physics Sv (Sverdrups = 10⁶ m³/s) or m/s Continuous, directed large-scale movements of seawater generated by wind stress, Coriolis force, temperature, salinity differences, and tides. Geostrophic Ocean Flow: 2 Ω sin φ v_ocean = (1 / ρ) (dP / dx) Ohm's Law Electromagnetism & Electronics V = A · Ω An empirical relation stating that the electric current flowing through an ohmic conductor is directly proportional to the applied voltage and inversely proportional to resistance. V = I R, J = σ E Olbers' Paradox Astrophysics, Cosmology & Relativity Cosmological Paradox The apparent paradox that if the universe were static, infinite, and uniformly populated with stars, the night sky should be uniformly bright as the Sun. Night sky brightness J = ∫ 4 π I r² dr / (4 π r²) → ∞ (in static infinite universe) Open Organ Pipes Waves, Oscillations & Acoustics Hz A cylindrical acoustic pipe open at both ends, containing displacement antinodes at both openings. f_n = n v / (2 L) (n = 1, 2, 3, ...) Operational Amplifier (Op-Amp) Electromagnetism & Electronics V (Volts) A high-gain DC-coupled electronic voltage amplifier with differential inputs and single-ended output. V_out = A_OL (V_+ - V_-) Optical Axis Optics N/A The imaginary central straight line passing through the centers of curvature of all optical elements in a rotationally symmetric system. N/A Optical Fiber Optics dB/km A flexible, transparent glass or plastic fiber that transmits light signals across long distances via total internal reflection. NA = √(n_core² - n_cladding²) Optical Power Optics Diopters (D, m⁻¹) A measure of a lens or curved mirror's degree of light convergence or divergence, equal to the reciprocal of its focal length. P = 1 / f (in meters) Optical Tweezers Biophysics & Medical Physics pN (Piconewton Forces ~0.1–100 pN) A biophysical instrument using a strongly focused laser beam to trap, manipulate, and exert piconewton forces on microscopic dielectric particles or biological molecules. F_gradient = ½ α ∇(E²), Hooke's Law F = -k_trap x Orbital Angular Momentum Quantum & Atomic Physics J·s (Angular Momentum Units) The quantized angular momentum of a quantum particle associated with its orbital spatial motion around a central force field. |L| = √(l (l + 1)) ℏ, L_z = m_l ℏ Orbital Velocity Classical Mechanics m/s The speed required for a body to maintain a stable circular orbit around a primary gravitational mass at a given radius. v_orb = √(G M / r) Order of Magnitude Foundations of Physics Dimensionless An exponential estimate of the size of a quantity, expressed as the power of ten closest to the numerical value. 10^n Osmosis Biophysics & Medical Physics Pa or kPa (Osmotic Pressure) The net passive diffusion of solvent molecules (water) across a selectively permeable membrane from lower solute concentration toward higher solute concentration. Π = i C R T (van 't Hoff Equation) Overtones Waves, Oscillations & Acoustics Hz Any resonant frequency higher than the fundamental frequency in a musical sound. First Overtone = 2nd Harmonic (for strings) P-type Semiconductor Condensed Matter & Materials Physics cm⁻³ (Hole Concentration) An extrinsic semiconductor in which trivalent acceptor impurities create an excess concentration of positive holes as majority charge carriers. p ≈ N_A ≫ n, n p = n_i² Paleoclimatology Geophysics & Environmental Physics Geologic Climate History The scientific study of Earth's past climate conditions across geologic history using indirect environmental proxy records. Climate Proxies: Ice Cores, Tree Rings, Coral δ¹⁸O, Speleothems Paleomagnetism Geophysics & Environmental Physics Degrees (° Declination / Inclination) The study of the historical record and orientation of Earth's magnetic field preserved in iron-bearing minerals in rocks, sediments, or archaeological artifacts. Remanent Magnetization Vector (Declination & Inclination) Parallel Axis Theorem Classical Mechanics kg·m² A theorem stating that the moment of inertia about any axis parallel to a centroidal axis equals the centroidal moment of inertia plus mass times squared offset distance. I = I_cm + M d² Parallel Circuit Electromagnetism & Electronics Ω (Ohms) An electrical circuit topology in which components are connected across common voltage nodes, offering multiple parallel paths for current. 1 / R_total = (1/R₁) + (1/R₂) + (1/R₃), V_total = V₁ = V₂ = V₃ Parallel Computing Mathematical & Computational Physics Speedup Factor S(P) A computational architecture where large physical calculations are divided into smaller sub-tasks executed simultaneously across multiple processor cores or GPUs. Amdahl's Law Speedup S(P) = 1 / ((1 - p) + p / P) Paramagnetism Electromagnetism & Electronics Dimensionless (χ_m > 0) A weak form of magnetism in which materials with unpaired electrons are weakly attracted into an external magnetic field. χ_m = C / T (Curie's Law)