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Mathematical & Computational Physics

Numerical Stability

The property of a numerical algorithm ensuring that errors introduced during computation do not magnify uncontrollably over successive time…

Von Neumann Stability Analysis: |G(k, Δt)| ≤ 1 Algorithm Stability Property
Geophysics & Environmental Physics

Nutation

Small periodic nodding oscillations superimposed upon Earth's long-term rotational axis precession.

Principal Nutation Period T = 18.6 years, Amplitude = 9.2″ Arcseconds (17.2″ in longitude, 9.2″ in obliquity)
Geophysics & Environmental Physics

Ocean Acidification

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⁻ pH Units (Logarithmic Scale)
Geophysics & Environmental Physics

Ocean Currents

Continuous, directed large-scale movements of seawater generated by wind stress, Coriolis force, temperature, salinity differences, and…

Geostrophic Ocean Flow: 2 Ω sin φ v_ocean = (1 / ρ) (dP / dx) Sv (Sverdrups = 10⁶ m³/s) or m/s
Electromagnetism & Electronics

Ohm's Law

An empirical relation stating that the electric current flowing through an ohmic conductor is directly proportional to the applied voltage…

V = I R, J = σ E V = A · Ω
Astrophysics, Cosmology & Relativity

Olbers' Paradox

The apparent paradox that if the universe were static, infinite, and uniformly populated with stars, the night sky should be uniformly…

Night sky brightness J = ∫ 4 π I r² dr / (4 π r²) → ∞ (in static infinite universe) Cosmological Paradox
Waves, Oscillations & Acoustics

Open Organ Pipes

A cylindrical acoustic pipe open at both ends, containing displacement antinodes at both openings.

f_n = n v / (2 L) (n = 1, 2, 3, ...) Hz
Electromagnetism & Electronics

Operational Amplifier (Op-Amp)

A high-gain DC-coupled electronic voltage amplifier with differential inputs and single-ended output.

V_out = A_OL (V_+ - V_-) V (Volts)
Optics

Optical Axis

The imaginary central straight line passing through the centers of curvature of all optical elements in a rotationally symmetric system.

N/A N/A
Optics

Optical Fiber

A flexible, transparent glass or plastic fiber that transmits light signals across long distances via total internal reflection.

NA = √(n_core² - n_cladding²) dB/km
Optics

Optical Power

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) Diopters (D, m⁻¹)
Biophysics & Medical Physics

Optical Tweezers

A biophysical instrument using a strongly focused laser beam to trap, manipulate, and exert piconewton forces on microscopic dielectric…

F_gradient = ½ α ∇(E²), Hooke's Law F = -k_trap x pN (Piconewton Forces ~0.1–100 pN)
Quantum & Atomic Physics

Orbital Angular Momentum

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 J·s (Angular Momentum Units)
Classical Mechanics

Orbital Velocity

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) m/s
Foundations of Physics

Order of Magnitude

An exponential estimate of the size of a quantity, expressed as the power of ten closest to the numerical value.

10^n Dimensionless
Biophysics & Medical Physics

Osmosis

The net passive diffusion of solvent molecules (water) across a selectively permeable membrane from lower solute concentration toward…

Π = i C R T (van 't Hoff Equation) Pa or kPa (Osmotic Pressure)
Waves, Oscillations & Acoustics

Overtones

Any resonant frequency higher than the fundamental frequency in a musical sound.

First Overtone = 2nd Harmonic (for strings) Hz
Condensed Matter & Materials Physics

P-type Semiconductor

An extrinsic semiconductor in which trivalent acceptor impurities create an excess concentration of positive holes as majority charge…

p ≈ N_A ≫ n, n p = n_i² cm⁻³ (Hole Concentration)
Geophysics & Environmental Physics

Paleoclimatology

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 Geologic Climate History
Geophysics & Environmental Physics

Paleomagnetism

The study of the historical record and orientation of Earth's magnetic field preserved in iron-bearing minerals in rocks, sediments, or…

Remanent Magnetization Vector (Declination & Inclination) Degrees (° Declination / Inclination)
Classical Mechanics

Parallel Axis Theorem

A theorem stating that the moment of inertia about any axis parallel to a centroidal axis equals the centroidal moment of inertia plus mass…

I = I_cm + M d² kg·m²
Electromagnetism & Electronics

Parallel Circuit

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 Ω (Ohms)
Mathematical & Computational Physics

Parallel Computing

A computational architecture where large physical calculations are divided into smaller sub-tasks executed simultaneously across multiple…

Amdahl's Law Speedup S(P) = 1 / ((1 - p) + p / P) Speedup Factor S(P)
Electromagnetism & Electronics

Paramagnetism

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) Dimensionless (χ_m > 0)