Open Compilations

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📎 Attached — companion site for the AI papers I’m reading: kader-xai.github.io/LearningAIPapers

⚡ Physics

Compiled reference for the physics I keep needing to look up — sensor families across the EM spectrum and the mechanical domain, the laws those families sit under, the natural phenomena they detect, and the famous equations that compress all of it.

Mechanism: Photoelectric & photovoltaic effect

Item What it is
Photodiode Silicon p-n junction; absorbs a visible photon, generates an electron-hole pair, drives a reverse current. The cheapest workhorse for “is there light.”
CCD Charge-coupled device array; each pixel collects photo-generated charge, then shuttles it serially to a single readout amplifier. Low noise, slow.
CMOS Active-pixel sensor; each pixel has its own amplifier and addressable readout. Fast, cheap, dominates phone and consumer cameras.
Photoresistor (LDR) Cadmium-sulfide film; resistance drops with light intensity. Slow, analog, used in night lights.
Phototransistor BJT or FET with light-controlled base or gate; gives gain compared to a plain photodiode but is slower.
PMT Photomultiplier tube; photocathode emits electrons that cascade through dynodes for 106–108 gain. Single-photon counting in vacuum.

↓ visible-light.md

Mechanism: Thermal & near-IR photon detection

Item What it is
Thermopile Many thermocouples in series; IR heats a hot junction, voltage measures the temperature difference. The detector inside non-contact thermometers.
Pyroelectric (PIR) Polarisation in a crystal shifts with temperature change; AC-coupled output. The motion sensor in burglar alarms.
Bolometer Temperature-dependent resistor; absorbs IR, resistance changes. The original thermal-imaging primitive.
InGaAs photodiode Short-wave-IR (0.9–1.7 µm) semiconductor; standard for fibre-optic links and SWIR cameras.
Microbolometer array Uncooled thermal-imaging chip; each pixel is a tiny bolometer. The detector behind every modern thermal camera.

↓ infrared.md

Mechanism: High-energy photon detection

Item What it is
SiC photodiode Silicon carbide; wide-bandgap, solar-blind. Used for flame detection.
GaN photodiode Gallium nitride; deep-UV (200–365 nm) semiconductor detector.
UV PMT PMT with a solar-blind photocathode; single-photon UV counting.
Phototube Simple vacuum diode photocathode (no dynodes). Historical UV detector.

↓ ultraviolet.md

Mechanism: Ionizing photon interaction

Item What it is
Scintillator + PMT High-Z crystal (NaI, BGO, LYSO) converts γ to visible photons; a PMT reads. Backbone of nuclear medicine and security imaging.
HPGe detector High-purity germanium; the gold standard for γ-ray spectroscopy. Liquid-nitrogen cooled.
CdTe / CZT Room-temperature γ semiconductor. Compact imaging without cryogenics.
Geiger–Müller tube Gas-filled tube; ionising photon triggers an avalanche that is counted. No energy info.
Image intensifier Photocathode → MCP → phosphor. Converts low-light, UV, or X-ray into a viewable image.

↓ x-ray-gamma.md

Mechanism: Electromagnetic wave reception

Item What it is
Antenna + rectifier Antenna captures the field, a diode rectifier demodulates.
Crystal diode Point-contact diode demodulator. The original cat’s-whisker AM radio detector.
Microwave bolometer Thermal RF detector; absorbed power heats a sensitive resistor.
SIS junction Superconductor-insulator-superconductor tunnel junction; quantum mixer used in mm-wave radio astronomy (ALMA).
HEMT mixer High-electron-mobility transistor; low-noise mixing across microwave bands.

↓ radio-microwave-thz.md

Mechanism: Newton’s second law on a proof mass

Item What it is
MEMS capacitive Silicon proof mass on flexible tethers; displacement changes a capacitance gap. The accelerometer in every phone.
Piezoelectric Charge across a piezoelectric crystal under stress. AC-coupled; can’t measure DC acceleration.
Piezoresistive Resistance changes with strain. DC-capable but temperature-sensitive.
Servo / force-balance Closed-loop nulling; feedback coil pushes the proof mass back to rest. Highest-accuracy class.

↓ acceleration.md

Mechanism: Coriolis & Sagnac effects

Item What it is
MEMS gyroscope Vibrating proof mass plus Coriolis effect; the gyro in every phone.
Fibre-optic gyro Two laser beams in a fibre loop in opposite directions; rotation gives a phase shift (Sagnac).
Ring laser gyro Counter-propagating lasers in a closed ring; rotation changes the beat frequency.
Spinning-rotor gyro Gimballed spinning rotor preserves orientation. Legacy aerospace.

↓ angular-rate.md

Mechanism: Classical mechanics baseline

Item What it is
First law A body at rest stays at rest, a body in motion stays in uniform motion — unless acted upon by a net external force. Inertia.
Second law F = ma. The net force on a body equals its mass times its acceleration.
Third law Every action has an equal and opposite reaction. Forces come in pairs.

↓ newtons-laws.md

Mechanism: Symmetries → conserved quantities (Noether)

Item What it is
Energy Total energy of a closed system is constant. Cannot be created or destroyed — only transformed.
Linear momentum Total momentum of a closed system is constant. Translation symmetry.
Angular momentum Total angular momentum is constant in isolation. Rotational symmetry.
Electric charge Net electric charge cannot be created or destroyed.
Baryon / lepton number Approximate conservation laws in particle physics.

↓ conservation-laws.md

Mechanism: Energy and entropy in macroscopic systems

Item What it is
Zeroth law If A and B are each in thermal equilibrium with C, then A and B are in equilibrium. Defines temperature.
First law Energy is conserved: ΔU = Q − W. Heat in minus work out equals change in internal energy.
Second law Entropy of an isolated system never decreases. Defines an arrow of time.
Third law Entropy of a perfect crystal at absolute zero is zero. Absolute zero is unreachable in a finite number of steps.

↓ thermodynamics.md

Mechanism: Foundations of classical electromagnetism

Item What it is
Gauss’s law ∇·E = ρ/ε₀ — electric charge produces an electric field.
Gauss’s law for magnetism ∇·B = 0 — no magnetic monopoles; magnetic field lines form closed loops.
Faraday’s law ∇×E = −∂B/∂t — a changing magnetic field induces an electric field.
Ampère–Maxwell law ∇×B = μ₀J + μ₀ε₀ ∂E/∂t — currents and changing E-fields produce magnetic fields.

↓ maxwells-equations-overview.md

Mechanism: Symmetry of spacetime under transformations

Item What it is
SR postulate 1 The laws of physics are the same in all inertial frames.
SR postulate 2 The speed of light in vacuum, c, is the same for all observers regardless of motion.
Time dilation Moving clocks tick slower by a factor γ = 1/√(1 − v²/c²).
Mass-energy E² = (mc²)² + (pc)². For a body at rest: E = mc².
General relativity Gravity is the curvature of spacetime caused by mass-energy. G_µν = 8πG T_µν / c⁴.

↓ relativity.md

Mechanism: EM wave / photon dual behaviour

Item What it is
Reflection Angle of incidence equals angle of reflection.
Refraction Light bends when crossing a boundary between media. Snell’s law: n₁ sinθ₁ = n₂ sinθ₂.
Diffraction Light bends around obstacles and through narrow apertures.
Interference Two coherent light waves add or cancel. Demonstrated by the double-slit experiment.
Polarisation Light is a transverse wave; the E-field oscillates in a specific direction.
Photoelectric effect Photons above a threshold frequency eject electrons from a material. Nobel-winning evidence for quantisation.

↓ light.md

Mechanism: Mechanical longitudinal wave in matter

Item What it is
Pressure wave Sound is a compression / rarefaction wave; needs a medium.
Speed ≈ 343 m/s in air at 20 °C; ≈ 1480 m/s in water; ≈ 5100 m/s in steel.
Frequency Pitch perception: 20 Hz → 20 kHz for humans.
Doppler effect Frequency shifts with relative motion between source and observer.
Standing waves Resonance in pipes, strings, rooms; basis of musical instruments.

↓ sound.md

Mechanism: Energy transfer from random molecular motion

Item What it is
Conduction Heat flows through a material by molecular collisions. Fourier’s law: q = −k ∇T.
Convection Heat carried by fluid motion (free or forced).
Radiation Heat emitted as EM waves. Stefan–Boltzmann: P = εσAT⁴.
Specific heat Energy required to raise 1 kg of a substance by 1 K. Q = mcΔT.
Phase change Latent heat absorbed without temperature change during melting / boiling.

↓ heat.md

Mechanism: Attractive force between masses (or curvature of spacetime)

Item What it is
Newton’s law F = G m₁m₂ / r². G ≈ 6.674 × 10⁻¹¹ N·m²/kg².
Surface gravity g ≈ 9.81 m/s² on Earth.
Orbital motion Closed orbit when KE + PE < 0. Kepler’s third: T² ∝ a³.
Tides Differential gravity of the Moon (and Sun) deforms ocean shape.
General relativity view Mass-energy curves spacetime; objects follow geodesics.

↓ gravity.md

Mechanism: Charge, current, and the EM field

Item What it is
Coulomb’s law F = k q₁q₂ / r². Charges of like sign repel, unlike attract.
Current I = dQ/dt. Conventional current direction is opposite to electron flow.
Ohm’s law V = IR. Holds for ohmic conductors.
Lorentz force F = q(E + v × B). Foundation of motors, generators, mass spectrometers.
Induction A changing magnetic flux through a loop induces an EMF. ε = −dΦ/dt.

↓ electricity-magnetism.md

Mechanism: Compact statements that capture huge ranges of behaviour

Item What it is
Newton’s second law F = ma — net force equals mass times acceleration.
Universal gravitation F = G m₁m₂ / r² — gravitational force between two point masses.
Mass-energy equivalence E = mc² — rest energy of a body of mass m.
Schrödinger equation iℏ ∂ψ/∂t = Ĥψ — time evolution of a quantum state.
Planck relation E = hν — energy of a photon of frequency ν.
de Broglie λ = h / p — wavelength associated with a particle of momentum p.
Boltzmann entropy S = k_B ln Ω — entropy from the number of microstates.
Stefan–Boltzmann P = εσAT⁴ — radiative power from a hot body.
Ideal gas PV = nRT — pressure, volume, temperature for an ideal gas.
Lorentz force F = q(E + v × B).
Maxwell’s equations ∇·E = ρ/ε₀ · ∇·B = 0 · ∇×E = −∂B/∂t · ∇×B = μ₀J + μ₀ε₀ ∂E/∂t.
Dirac equation (iγ^µ ∂_µ − m)ψ = 0 — relativistic quantum mechanics of fermions.
Navier–Stokes ρ(∂v/∂t + v·∇v) = −∇p + µ∇²v + f — fluid motion.
Einstein field eqn. G_µν = 8πG T_µν / c⁴ — spacetime curvature from mass-energy.

↓ famous-physics-equations.md

Constants

Symbol / quantity Value
Speed of light in vacuum c = 299,792,458 m/s (exact, defines the metre)
Gravitational constant G ≈ 6.674 × 10⁻¹¹ N·m²/kg²
Planck constant h ≈ 6.626 × 10⁻³⁴ J·s
Reduced Planck constant ℏ = h/2π ≈ 1.055 × 10⁻³⁴ J·s
Fine-structure constant α ≈ 1/137.036
Symbol / quantity Value
Elementary charge e ≈ 1.602 × 10⁻¹⁹ C
Vacuum permittivity ε₀ ≈ 8.854 × 10⁻¹² F/m
Vacuum permeability µ₀ ≈ 1.257 × 10⁻⁶ N/A²
Coulomb constant k_e = 1/(4πε₀) ≈ 8.988 × 10⁹ N·m²/C²
Impedance of free space Z₀ = µ₀c ≈ 376.73 Ω
Symbol / quantity Value
Boltzmann constant k_B ≈ 1.381 × 10⁻²³ J/K
Avogadro number N_A ≈ 6.022 × 10²³ /mol
Ideal-gas constant R = N_A k_B ≈ 8.314 J/(mol·K)
Stefan–Boltzmann constant σ ≈ 5.670 × 10⁻⁸ W/(m²·K⁴)
Wien displacement constant b ≈ 2.898 × 10⁻³ m·K
Rydberg constant R_∞ ≈ 1.097 × 10⁷ /m
Bohr radius a₀ ≈ 5.292 × 10⁻¹¹ m
Symbol / quantity Value
Electron mass m_e ≈ 9.109 × 10⁻³¹ kg ≈ 0.511 MeV/c²
Proton mass m_p ≈ 1.673 × 10⁻²⁷ kg ≈ 938.3 MeV/c²
Neutron mass m_n ≈ 1.675 × 10⁻²⁷ kg ≈ 939.6 MeV/c²
Atomic mass unit u ≈ 1.661 × 10⁻²⁷ kg
Symbol / quantity Value
Astronomical unit AU = 1.496 × 10¹¹ m
Light-year ly ≈ 9.461 × 10¹⁵ m
Parsec pc ≈ 3.086 × 10¹⁶ m ≈ 3.262 ly
Solar mass M_☉ ≈ 1.989 × 10³⁰ kg
Solar luminosity L_☉ ≈ 3.828 × 10²⁶ W
Earth mass M_⊕ ≈ 5.972 × 10²⁴ kg
Earth radius (equatorial) R_⊕ ≈ 6.378 × 10⁶ m
Standard gravity g₀ = 9.806 65 m/s² (exact, by definition)
Hubble constant (current best) H₀ ≈ 67–73 km/s/Mpc (tension between methods)

↓ physics-constants.md

∑ Mathematics

The mathematics that shows up underneath everything else on this page — arithmetic, algebra, linear algebra, calculus, and the small set of equations worth memorising.

Mechanism: The four operations and what they preserve

Item What it is
Addition / subtraction Combine or remove quantities. Identity: 0. Inverse: negation.
Multiplication / division Scale or split. Identity: 1. Inverse: reciprocal.
Exponents a^n = a · a · … · a (n times). a^0 = 1, a^{−n} = 1/a^n.
Roots ⁿ√a is the inverse of a^n. √a means n = 2.
Order of operations PEMDAS / BODMAS — parentheses, exponents, multiplication, addition.
Fractions & percentages a/b, percentage = (part / whole) × 100.

↓ arithmetic.md

Mechanism: Symbolic manipulation of unknowns

Item What it is
Variables Letters standing for unknown or general numbers.
Linear eq. ax + b = 0 → x = −b/a.
Quadratic eq. ax² + bx + c = 0 → x = (−b ± √(b² − 4ac)) / 2a.
Polynomial Sum of terms aₙxⁿ. Degree = highest n.
Factoring Rewriting an expression as a product. e.g. x² − 9 = (x − 3)(x + 3).
Functions f : X → Y maps each input to one output.

↓ algebra-basics.md

Mechanism: Vectors, matrices, and linear maps

Item What it is
Vector An ordered list of numbers; an arrow with magnitude and direction.
Vector space Set closed under addition and scalar multiplication.
Inner product ⟨u, v⟩ = Σ uᵢvᵢ. Defines length and angle.
Matrix Rectangular array; a representation of a linear map.
Matrix product (AB)ᵢⱼ = Σ AᵢₖBₖⱼ. Composition of linear maps.
Determinant det(A) — scaling factor of A’s linear map. Zero ⇔ singular.
Eigenvalue / eigenvector Av = λv. Directions A only stretches, factor λ.
Rank Dimension of the column space; how many independent directions A spans.
SVD A = UΣVᵀ. Decomposes any matrix into rotation–scaling–rotation.
Norm ‖v‖ — vector length. ℓ² = √Σ vᵢ².

↓ linear-algebra.md

Mechanism: Limits, derivatives, integrals

Item What it is
Limit limₓ→a f(x) = L — what f approaches as x approaches a.
Derivative f’(x) = limₕ→0 (f(x+h) − f(x)) / h — instantaneous rate of change.
Power rule d/dx (xⁿ) = n x^{n−1}.
Product / chain rule (fg)’ = f’g + fg’. (f(g(x)))’ = f’(g(x)) · g’(x).
Indefinite integral ∫ f(x) dx — antiderivative. d/dx (∫ f dx) = f.
Definite integral ∫ₐᵇ f(x) dx — signed area under f from a to b.
Fundamental theorem If F’(x) = f(x), then ∫ₐᵇ f dx = F(b) − F(a).
Partial derivative ∂f/∂xᵢ — derivative with respect to one variable, others fixed.
Gradient ∇f — vector of partial derivatives; points in direction of steepest ascent.
ODE / PDE Equations involving derivatives. Ordinary: one variable. Partial: many.

↓ calculus-basics.md

Mechanism: Compact statements that anchor whole subjects

Item What it is
Pythagorean theorem a² + b² = c² — right triangle side lengths.
Euler’s identity e^{iπ} + 1 = 0 — five constants, three operations, no equals signs to spare.
Quadratic formula x = (−b ± √(b² − 4ac)) / 2a.
Binomial coefficient C(n, k) = n! / (k!(n−k)!) — count of k-subsets of an n-set.
Binomial theorem (x + y)^n = Σ_{k=0}^{n} C(n, k) x^{n−k} y^k.
Cauchy–Schwarz
Fourier transform F(ω) = ∫ f(t) e^{−iωt} dt — decompose a signal into frequencies.
Bayes’ rule P(A
Normal distribution p(x) = (1/√(2πσ²)) exp(−(x − µ)² / 2σ²).
Geometric series Σ_{n=0}^∞ rⁿ = 1 / (1 − r) for
Basel problem Σ_{n=1}^∞ 1/n² = π²/6.
Gauss integral ∫_{−∞}^{∞} e^{−x²} dx = √π.
Power rule (calculus) d/dx (xⁿ) = n x^{n−1}.
Fundamental theorem of calculus ∫ₐᵇ f dx = F(b) − F(a) where F’ = f.

↓ famous-math-equations.md

Constants

Constant Value & note
π (pi) ≈ 3.141 592 653 589 793 … Ratio of a circle’s circumference to its diameter. Transcendental.
e (Euler’s number) ≈ 2.718 281 828 459 045 … Base of the natural exponential; e = lim (1+1/n)^n.
φ (golden ratio) ≈ 1.618 033 988 749 894 … (1+√5)/2. Limit of consecutive Fibonacci ratios.
γ (Euler–Mascheroni) ≈ 0.577 215 664 901 532 … γ = lim (Hₙ − ln n). Irrationality unknown.
√2 ≈ 1.414 213 562 373 095 … Diagonal of the unit square.
√3 ≈ 1.732 050 807 568 877 … Height of an equilateral triangle with side 2.
ln 2 ≈ 0.693 147 180 559 945 … Natural logarithm of two.
ln 10 ≈ 2.302 585 092 994 045 … Bridge between natural and common logs.
log₂ e ≈ 1.442 695 040 888 963 …
π/180 (degree → rad) ≈ 0.017 453 292 519 943 …
Catalan constant G ≈ 0.915 965 594 177 219 … Σ (−1)ⁿ / (2n+1)².
Apéry’s constant ζ(3) ≈ 1.202 056 903 159 594 … Irrational (Apéry 1978).
Khinchin constant K ≈ 2.685 452 001 … Geometric mean of partial quotients of almost every real.
Twin-prime constant C₂ ≈ 0.660 161 815 8 … Density coefficient for twin primes.
Meissel–Mertens constant M ≈ 0.261 497 … Difference between harmonic prime sum and ln ln n.

↓ math-constants.md

🧪 Chemistry

Atoms, bonds, reactions, and the periodic table — the structural picture that everything chemical builds on.

Mechanism: Electron sharing & transfer between nuclei

Item What it is
Atom Nucleus (protons + neutrons) surrounded by electrons. Atomic number = proton count.
Isotope Same Z, different N. Same chemistry, different mass.
Electron shell Energy levels around the nucleus. Outer shell electrons drive chemistry.
Ionic bond Full transfer of electrons; opposite ions attract (NaCl).
Covalent bond Shared electron pair between atoms (H₂O, CO₂).
Metallic bond Delocalised “sea” of electrons; explains conductivity and ductility.
Hydrogen bond Weak electrostatic attraction; gives water its high boiling point.

↓ atoms-bonding.md

Mechanism: Rearrangement of atoms; mass conserved

Item What it is
Balancing Atoms in = atoms out for every element. Coefficients balance the equation.
Synthesis A + B → AB.
Decomposition AB → A + B.
Single replacement A + BC → AC + B.
Double replacement AB + CD → AD + CB.
Combustion Fuel + O₂ → CO₂ + H₂O + energy.
Acid / base Brønsted: proton transfer. pH = −log[H⁺].
Redox Electron transfer; oxidation = loss, reduction = gain (OIL RIG).

↓ reactions.md

Mechanism: Periodic recurrence of properties with atomic number

Item What it is
Group Column — atoms with similar outer-shell electron count and chemistry.
Period Row — atoms with the same number of electron shells.
Alkali metals Group 1; one outer electron; reactive, soft.
Halogens Group 17; one electron short of full outer shell; very reactive.
Noble gases Group 18; full outer shell; chemically inert.
Transition metals d-block; variable oxidation states; coloured compounds.
Lanthanides / actinides f-block; rare-earth and heavy radioactive elements.

↓ periodic-table.md

🔧 Sensors

A cross-modality reference for which transducer to reach for given a physical quantity. Sits next to the physics sensor pages but indexed by what you want to measure rather than what physics it uses.

Mechanism: Which transducer for which physical quantity

Item What it is
Temperature Thermistor · RTD · thermocouple · IR pyrometer · semiconductor (LM35, TMP117).
Pressure Piezoresistive bridge · capacitive diaphragm · piezoelectric · MEMS.
Flow Differential pressure (orifice / venturi) · turbine · ultrasonic · thermal mass flow · Coriolis.
Position Encoder (optical / magnetic) · LVDT · potentiometer · capacitive · Hall-effect.
Motion Accelerometer (MEMS) · gyroscope (MEMS / FOG) · magnetometer · IMU.
Light Photodiode · CCD · CMOS · LDR · phototransistor · PMT.
Magnetic field Hall-effect · fluxgate · SQUID · magnetoresistive (AMR / GMR / TMR).
Chemical pH electrode · ion-selective electrode · electrochemical gas · MOS / e-nose.
Humidity Capacitive polymer film · resistive · psychrometer.
Sound Condenser microphone · MEMS mic · piezo · hydrophone · geophone.
Radiation Geiger–Müller · scintillator + PMT · semiconductor (CZT, HPGe).
Distance Ultrasonic · LIDAR · ToF camera · stereo vision · radar.
Vibration Accelerometer · velocity transducer · proximity probe.
Strain Foil strain gauge · semiconductor gauge · fibre Bragg grating.
Gas concentration NDIR (CO₂) · electrochemical (CO, O₂) · MOS · catalytic bead · PID.

↓ sensors-by-modality.md