Physics

⚛️ Physics

Multi-Source Wave Interference - 多源波干涉可视化

Interactive visualization of multi-source wave interference patterns - explore how 2 to 12 coherent sources create interference fringes evolving from double-slit to diffraction grating, with adjustable wavelength, spacing, circular/plane wave modes, real-time 2D pattern and 1D intensity cross-section, color schemes, animation, and quick presets

⚛️ Physics

Quantum Computing Basics - Interactive Visualization | 量子计算基础

Interactive visualization of quantum computing fundamentals - Explore qubits and Bloch sphere representation with polar angle θ (0-π) and azimuthal angle φ (0-2π), superposition states including Hadamard gate H|0⟩=(|0⟩+|1⟩)/√2, quantum measurement with probability collapse and cos²(θ/2), sin²(θ/2) distributions, EPR entanglement with Bell states (|Φ⁺⟩=(|00⟩+|11⟩)/√2, |Φ⁻⟩=(|00⟩-|11⟩)/√2, |Ψ⁺⟩=(|01⟩+|10⟩)/√2, |Ψ⁻⟩=(|01⟩-|10⟩)/√2), quantum circuit simulator with gates (H, X, Y, Z, CNOT, SWAP), and quantum algorithms including Grover's search O(√N) vs classical O(N), Shor's factoring exponential speedup, Deutsch-Jozsa constant/balanced O(1) vs classical O(2^(n-1)+1), and Simon's period finding O(n) vs classical O(2^(n-1)). Features interactive 3D Bloch sphere visualization with real-time state updates and preset states (|0⟩, |1⟩, |+⟩, |-⟩, |i⟩, |-i⟩), animated superposition gate demonstrations with rotation control, statistical measurement simulation with configurable sample sizes, entanglement correlation visualization with perfect anti/correlation, quantum circuit builder with single-qubit and two-qubit gates, algorithm complexity comparison showing classical vs quantum speedup, and comprehensive educational content covering quantum computing fundamentals (qubits vs classical bits, Dirac notation, quantum gates as unitary matrices), quantum algorithms and their applications (cryptography, drug discovery, optimization, machine learning), current challenges (decoherence, error correction overhead ~1000x, scalability, NISQ limitations), and quantum advantage explanations. Perfect for physics education, quantum computing understanding, STEM learning, and exploring the foundations of quantum information science including superposition, entanglement, measurement, and quantum algorithms.

⚛️ Physics

Colloid Stability - DLVO Theory | 胶体稳定性 - DLVO理论

Interactive visualization of colloid stability and DLVO theory - Explore potential energy curves, double layer repulsion, van der Waals attraction, Debye length, zeta potential, critical coagulation concentration (CCC), energy barrier, primary and secondary minima, particle interactions, and stabilization mechanisms with adjustable Hamaker constant, particle radius, ionic strength, temperature, pH, and electrolyte type. Features dynamic DLVO potential curves showing V_tot = V_att + V_rep vs separation distance, real-time energy barrier calculation and stability state determination, interactive particle visualization with Brownian motion and double layer structure, Schulze-Hardy rule demonstration for different electrolyte valencies, and preset colloid systems (stable gold sol, latex particles, silver iodide, critical state, coagulated system, polymer bridging). Adjustable parameters: Hamaker constant A (0.1-10 ×10⁻²⁰ J), particle radius R (10-500 nm), zeta potential ζ (0-100 mV), ionic strength I (0.1-100 mM), temperature T (273-373 K), dielectric constant ε_r (1-100), electrolyte type (NaCl, CaCl₂, AlCl₃), and pH level (1-14). Real-time value displays: surface distance H, total potential V_tot, attraction V_att, repulsion V_rep, energy barrier V_max, Debye length κ⁻¹, stability state (stable/metastable/unstable/coagulated), critical coagulation concentration CCC, primary minimum, and secondary minimum. Educational content covers DLVO theory fundamentals (Derjaguin-Landau-Verwey-Overbeek), van der Waals attraction V_att = -AR/(12H), electrical double layer repulsion V_rep = 64πRk_BTρ_∞·exp(-κH), Debye length κ⁻¹ = √(ε_rε_0k_BT/(2e²I)), potential energy curve features (energy barrier, secondary minimum, primary minimum), Schulze-Hardy rule (CCC ∝ 1/z⁶), critical coagulation concentration, stabilization mechanisms (electrostatic, steric, electrosteric), factors affecting colloid stability, and practical applications in nanoparticle synthesis, pharmaceuticals, paints and coatings, water treatment, biological systems, and materials science. Perfect for colloid chemistry education, understanding DLVO theory, and learning about surface chemistry and dispersion stability.

⚛️ Physics

Neutron Stars - 中子星

Interactive visualization of neutron stars - extreme matter objects including pulsars, magnetars, and binary systems. Features the fundamental equations: Degeneracy Pressure P ∝ ρ^(5/3) (neutron degeneracy pressure supporting star against collapse), TOV Limit M_max ≈ 2-3 M☉ (Tolman-Oppenheimer-Volkoff maximum mass), Radius R ~ 10 km (compact object size), Spin-down Rate Ṗ = 8π²R⁶B²sin²α/(3c³I P) (rotational energy loss), Luminosity L = Ṁc² (accretion power), GW Strain h ∝ M_chirp^(5/3) f^(2/3)/d (gravitational wave amplitude). Real-time visualization includes: (1) Structure View showing layered internal structure - crust (atomic nuclei lattice, ~1 km), outer core (superfluid neutrons, ~5 km), inner core (exotic matter, ~3 km) with density gradient visualization from surface to ~10¹⁸ kg/m³; (2) Magnetic Field View displaying dipole magnetic field lines, magnetic axis vs rotation axis misalignment (inclination angle α), field strength from normal pulsars (B ~ 10⁸ T) to magnetars (B ~ 10¹¹ T) with field line animation; (3) Pulsar Lighthouse Effect showing rotating beams sweeping across space, beam width, observer detection angle (ζ), pulse profile plot showing intensity vs rotation phase, lighthouse analogy with real-time pulse detection; (4) Binary System View displaying neutron star with companion star, accretion disk with matter stream, Roche lobe overflow, orbital motion, X-ray emission from accretion (L ~ 10³⁶ erg/s), orbital period calculation; (5) Gravitational Waves Merger View showing inspiraling binary neutron stars with decreasing separation, increasing frequency, gravitational wave ripples propagating outward, strain waveform h(t) showing characteristic chirp signal, frequency evolution from ~10 Hz to kHz; (6) TOV Mass Limit plotting mass-radius diagram with theoretical TOV curve, current mass-radius position, collapse threshold at ~2.17 M☉, comparison with observed massive pulsars; (7) Equation of State chart showing pressure vs density relation, neutron degeneracy pressure (P ∝ ρ^(5/3)) vs nuclear repulsion (soft vs stiff EoS), implications for maximum mass and radius; (8) Discovery Timeline showing key milestones: 1967 (first pulsar discovery by Jocelyn Bell), 1974 (binary pulsar confirming GW emission), 1982 (millisecond pulsar confirming recycling), 2017 (GW170817 multi-messenger detection). Real-time value displays: Mass (M☉), Radius (km), Magnetic field B (T, log scale), Rotation period P (ms), Pulse rate (Hz), Orbital period (hr), Accretion rate (M☉/yr), GW frequency (Hz), Strain h. Interactive parameters: Mass (0.5-3.0 M☉), Radius (8-15 km), Magnetic field strength (log₁₀ B: 4-15), Rotation period (0.5-10 ms), Inclination angle (0-90°), Observer angle (0-90°), Spin-down rate, Companion mass (0.1-2.0 M☉), Orbital separation (0.5-5.0 R☉), Accretion rate (0.001-0.1 M☉/yr), Animation speed. Display options: toggle magnetic field lines, accretion disk, pulse profile. Presets: Standard Pulsar (1.4 M☉, B=10⁸ T), Millisecond Pulsar (recycled, B=10⁵ T), Magnetar (extreme field B=10¹¹ T), X-ray Binary (accreting), Binary Merger (GW170817 parameters). Educational content covers Neutron star formation (core-collapse supernova of 8-30 M☉ stars), Internal structure (crust, superfluid outer core, mysterious inner core with possible exotic matter), Pulsar mechanism (magnetic axis misalignment, lighthouse effect, types: radio, X-ray, gamma-ray, millisecond), Magnetic fields (formation by flux conservation, magnetars with strongest fields in universe, field decay), Binary systems (LMXB, HMXB, accretion, millisecond pulsar recycling, double neutron stars), Gravitational waves (inspiral, merger, kilonova, r-process nucleosynthesis, GW170817 confirmation), TOV limit and EoS (maximum mass, pressure-density relation, observational constraints from massive pulsars and tidal deformability), Current research (NICER mission, LIGO/Virgo detections, future detectors, SKA pulsar surveys). Multi-language support (zh, en).

⚛️ Physics

Universe Expansion - 宇宙膨胀

Interactive visualization of universe expansion with Hubble's law and cosmic evolution. Features the fundamental equations: Hubble's Law v = H₀·d (recessional velocity proportional to distance), Redshift z = (λ_obs - λ_emit)/λ_emit ≈ v/c (light wavelength stretches as space expands), Scale Factor a(t) = R(t)/R₀ (universe size relative to today), Hubble Parameter H(t) = ȧ(t)/a(t) (expansion rate), Friedmann Equation H² = H₀²[Ω_r/a⁴ + Ω_m/a³ + Ω_k/a² + Ω_Λ] (evolution of expansion). Real-time visualization includes: (1) Scale Factor Chart plotting a(t) vs time from Big Bang (t = -13.8 Gyr) to future (t = +20 Gyr), showing inflation, radiation-dominated, matter-dominated, and dark energy-dominated eras with current time marker; (2) Hubble Law View displaying galaxy recession with distance vs velocity linear relationship (Hubble diagram), individual galaxies with color-coded velocities, proportional expansion visualization; (3) Balloon Analogy showing 2D expansion analogy with galaxies on expanding surface, velocity vectors indicating recession, radius scaling with a(t); (4) Redshift Observation demonstrating spectral line shift from rest frame to observed frame, color spectrum showing redshift effect, emission/absorption lines with calculated z values; (5) Hubble Diagram plotting observational data (distance vs velocity) with best-fit line, galaxy distribution showing linear Hubble relationship; (6) Universe Composition pie chart displaying current cosmological parameters: Dark Energy Ω_Λ (~68%), Dark Matter Ω_m (~27%), Ordinary Matter (~5%) with dynamic updates based on user parameters; (7) Expansion Stages timeline showing cosmic evolution phases: Inflation (10⁻³⁶ to 10⁻³² s), Radiation Era (to 47,000 years), Matter Era (to ~9 Gyr), Dark Energy Era (~9 Gyr to present) with animated progression; (8) Future Fate visualization showing three scenarios: Big Freeze (heat death - eternal expansion, galaxies drift apart, cold empty universe), Big Rip (phantom energy tears apart spacetime), Big Crunch (matter-dominated collapse). Real-time value displays: Current time (Gyr), Scale factor a(t), Hubble constant H₀ (km/s/Mpc), Recession velocity (km/s), Redshift z, Velocity/c ratio, Distance (Mpc). Interactive parameters: Hubble constant H₀ (50-100 km/s/Mpc), Matter density Ω_m (0.1-1.0), Dark energy density Ω_Λ (0.0-1.0), Radiation density Ω_r (0.00001-0.01), Time scale (0.1-5x), Animation speed (0.1-3x), Galaxy count (10-100). Display options: toggle grid, galaxy trajectories. Presets: Standard Model (ΛCDM), Matter-Only Universe, Empty Universe, Accelerating Expansion, Decelerating Expansion. Educational content covers Universe expansion definition (metric expansion of space, galaxies recede, more distant galaxies recede faster, no center to expansion), Hubble's law explanation (linear relationship discovered by Edwin Hubble in 1929, measured using standard candles, redshift increases with distance), Scale factor and redshift (a=1 today, a<1 in past, a>1 in future, 1+z = 1/a relation), Universe composition (dark energy causing accelerated expansion discovered 1998, dark matter affecting structure formation, ordinary matter only 5%), Cosmic timeline (Big Bang, Inflation, nucleosynthesis, recombination, dark ages, first stars, galaxy formation, dark energy era), Future scenarios (Big Freeze most likely, Big Rip if phantom energy, Big Crunch if matter dominates). Multi-language support (zh, en, de, fr, es, pt, ru).

⚛️ Physics

Gravitational Waves - 引力波

Interactive visualization of gravitational waves from binary black hole mergers with LIGO detector simulation. Features the fundamental equations: Strain h = ΔL/L ≈ 10⁻²¹ (LIGO detection sensitivity), Gravitational wave frequency f_GW = 2·f_orb (twice the orbital frequency), Chirp mass M_chirp = (m₁m₍₂₎)^(3/5)/(m₁+m₂)^(1/5) (determines inspiral rate), Waveform h(t) ~ A(t)·cos(Φ(t)) (amplitude and phase evolution), plus (+) and cross (×) polarizations h₊ = h₀(1+cos²ι)cos(2ϕ), hₓ = 2h₀cosι sin(2ϕ). Real-time visualization includes: (1) Spacetime Grid View showing 3D grid distortion from passing gravitational waves with wave propagation animation, strain amplitude visualization (10⁻²¹ scale), grid point displacement based on wave phase, exponential decay with distance from source; (2) Binary System View displaying two black holes (m₁ and m₂) with Schwarzschild radii proportional to mass, orbital trails showing inspiral trajectory, velocity vectors indicating orbital speed, separation distance decreasing over time, real-time mass and position labels; (3) LIGO Detector View showing Michelson interferometer with 4km arms, laser source, beam splitter, end mirrors, detector, phase shift from passing gravitational waves ΔL/L = h, real-time strain measurement display, detector readout; (4) Waveform Chart plotting h(t) with both plus (+) and cross (×) polarizations showing characteristic chirp (increasing frequency and amplitude), merger peak, and ringdown exponential decay; (5) Frequency Evolution Chart displaying f_GW vs time showing the frequency chirp from ~10Hz to ~100Hz for stellar-mass black holes, merger frequency spike; (6) Strain Amplitude Chart showing |h| vs time demonstrating amplitude increase during inspiral, peak at merger, exponential decay during ringdown. Real-time value displays: Strain h (×10⁻²¹), GW frequency (Hz), Orbital separation (km), Orbital velocity (fraction of c), Current phase (inspiral/merger/ringdown) with progress bar. Interactive parameters: Black hole masses m₁, m₂ (5-50 M☉ each), Distance to source (10-1000 Mpc), Inclination angle ι (0-90°), Initial separation (500-2000 km), Simulation speed (0.1-3x). Display options: toggle spacetime grid, wave propagation visualization, orbital velocity vectors. Event presets: GW150914 (first LIGO detection, m₁=36 M☉, m₂=29 M☉, D=410 Mpc), GW170817 (binary neutron star merger, m₁=1.46 M☉, m₂=1.27 M☉, D=40 Mpc), Generic Binary (custom parameters). Educational content covers Gravitational waves definition (ripples in spacetime predicted by Einstein's 1916 general relativity, propagate at speed of light, produced by accelerating masses, quadrupole radiation), Binary evolution phases (inspiral - black holes spiral inward losing energy to GW emission over millions of years, merger - violent collision releasing enormous energy in milliseconds, ringdown - distorted final black hole settles to stable Kerr state), LIGO detection principle (Michelson interferometer measures arm length difference ΔL ~ 10⁻¹⁸ m, laser interference pattern shift, two detectors for coincidence, Hanford and Livingston), Waveform characteristics (chirp signal - frequency and amplitude increase, merger peak - maximum amplitude, ringdown - quasi-normal mode decay, different mass ratios produce different waveforms), Astrophysical sources (binary neutron stars - inspiral detected minutes before merger, binary black holes - no electromagnetic counterpart, supernovae - asymmetric collapse, pulsars - continuous waves, stochastic background - unresolved superposition), Strain sensitivity (h ~ 10⁻²¹ for LIGO, corresponds to ΔL/L for 4km arms, Advanced LIGO design, future detectors Einstein Telescope, Cosmic Explorer, LISA for space-based low-frequency GW). Multi-language support (zh, en, de, fr, es, pt, ru).

⚛️ Physics

Angular Momentum Conservation - 角动量守恒

Interactive visualization of angular momentum conservation with rotating platform experiment, figure skating analogy, and diver demonstration. Features the fundamental equations: Angular momentum L = I·ω (product of moment of inertia and angular velocity), Moment of inertia I = Σmr² (sum of mass times distance squared from axis), Conservation law I₁ω₁ = I₂ω₂ (when external torque τ_ext = 0, angular momentum remains constant), Torque τ = dL/dt (rate of change of angular momentum), Rotational kinetic energy E = ½Iω² = L²/(2I) (energy increases when I decreases, work done by internal forces). Real-time visualization includes: (1) Main Animation canvas with three scenarios - Rotating Platform (person with dumbbells on spinning platform, arm position r adjustable from 0.2-1.5m, platform radius 0.5-2.0m), Figure Skater (cylindrical body model with arm extension, body radius 0.15-0.6m, arm extension 0.0-1.0m), Diver (spherical body model for tucked/extended positions, body radius 0.2-1.0m). Each scenario shows 2D rotation with angular velocity ω display, person representation with body and arms, rotation axis visualization, motion trail showing path; (2) Angular Velocity Chart plotting ω vs time showing dramatic increase when arms contract, instantaneous ω values, comparison of different arm positions; (3) Moment of Inertia Chart plotting I vs time demonstrating I = mr² relationship, inverse correlation with angular velocity; (4) Angular Momentum Chart showing L = Iω = constant (horizontal line) proving conservation principle. Real-time value displays: Moment of Inertia I (kg·m²), Angular Velocity ω (rad/s), Angular Momentum L (kg·m²/s), Rotational Energy E (J). Interactive parameters: Mass m (30-120 kg), Initial angular velocity ω₀ (0.5-5.0 rad/s), Arm position r (0.2-1.5 m for platform), Body radius (0.15-0.6 m for skater), Arm extension (0.0-1.0 m for skater), Tuck position (0.2-1.0 m for diver), Platform radius (0.5-2.0 m), Animation speed (0.1-3x). Control buttons: Start, Pause, Reset, Contract Arms (r→0.2m), Extend Arms (r→1.5m), Auto Animate Arms (sinusoidal motion). Display options: toggle angular velocity vector visualization, motion trail, automatic arm animation. Educational content covers Angular momentum definition and conservation (L = Iω, vector quantity with direction along rotation axis, conserved when no external torque, fundamental law of physics), Moment of inertia concepts (I = Σmr² for discrete masses, I = ∫r²dm for continuous bodies, depends on mass distribution, farther mass = larger I), Rotating platform experiment (person with dumbbells, arms extended → large I → slow ω, arms contracted → small I → fast ω, dramatic speed-up clearly visible, L = Iω stays constant), Figure skating applications (skaters pull arms tight to spin faster, starting with extended arms for slow rotation, then rapid spin for jumps and camel spins, kinetic energy increase from muscle work, conservation in aerial maneuvers), Diver mechanics (tucked position reduces I for faster rotation, extended position slows rotation for water entry, angular momentum set at takeoff, cannot change in air, somersault and twist control), Everyday examples (playground merry-go-round, spinning chair with weights, cat's righting reflex, astronaut maneuvering, bicycle wheel demonstrations), Advanced applications (spacecraft attitude control with reaction wheels, neutron star spin-up during collapse, pulsar formation, planetary formation and angular momentum, helicopter rotor tail compensation). Multi-language support (zh, en, de, fr, es, pt, ru).

⚛️ Physics

Center of Mass Motion - 质心运动

Interactive visualization of center of mass motion in multi-particle systems with projectile motion, explosion dynamics, and momentum conservation. Features the fundamental equations: Center of mass position r_cm = (Σmᵢrᵢ)/(Σmᵢ) (weighted average position of all mass), COM velocity v_cm = (Σmᵢvᵢ)/(Σmᵢ) (mass-weighted average velocity), Total momentum P = M·v_cm = Σmᵢvᵢ (system momentum equals total mass times COM velocity), External force F_ext = M·a_cm (only external forces affect COM motion), Internal forces ΣF_int = 0 (internal forces cancel out, no effect on COM), Motion decomposition rᵢ = r_cm + r'_i (any particle's motion equals COM motion plus motion relative to COM). Real-time visualization includes: (1) System Display canvas showing 3 particles with different masses (m₁, m₂, m₃) and sizes proportional to mass, color-coded particles (red=m₁, blue=m₂, green=m₃), real-time COM marker (× symbol) showing weighted center position, velocity vectors on each particle showing direction and magnitude, particle trails showing individual trajectories, ground plane with gravitational field, time indicator and scenario label; (2) COM Trajectory canvas plotting the parabolic path of the center of mass regardless of internal motions, coordinate axes with distance (x) and height (y) scales, trajectory trace showing historical COM positions, current position marker, comparison with individual particle paths; (3) Momentum Analysis displaying individual particle momentum vectors (P₁, P₂, P₃) with magnitude proportional to mass×velocity, total momentum vector P (COM motion) showing conservation principle, vector addition demonstration, real-time momentum values (Total Momentum P, COM Velocity v_cm, Total Mass M), momentum conservation verification during explosions; (4) Position Coordinates showing bar charts of individual particle x-positions (x₁, x₂, x₃), COM x-position (x_cm) for comparison, real-time position updates, relative positions demonstrating motion decomposition. Interactive scenarios: (a) Projectile Motion - standard projectile launch where COM follows parabolic trajectory while particles may rotate or move internally; (b) System Explosion - explosive forces push particles apart symmetrically while COM continues on original trajectory, demonstrating internal forces don't affect COM motion, explosion parameters (force magnitude, timing, duration); (c) Sand Pendulum - leaking pendulum showing mass redistribution effects, sand stream visualization, COM motion with changing mass; (d) Motion Decomposition - visualization separating COM motion from relative motion, showing how complex motion breaks into simple translation plus rotation/vibration. Interactive parameters: Particle masses m₁, m₂, m₃ (0.5-10 kg each), Initial velocity v₀ (5-30 m/s), Launch angle θ (10-80°), Initial height h₀ (0-20 m), Explosion force (10-200 N), Explosion time (0.2-3 s), Explosion duration (0.05-0.5 s), Gravity g (1.6-20 m/s²), Air resistance k (0-0.5), Animation speed (0.1-3x). Display options: toggle particle trails, COM marker, motion decomposition view, velocity vectors. Quick presets: Cannonball (m=[5,3,2]kg, v₀=20m/s, standard projectile), Firework Explosion (m=[0.5,0.3,0.2]kg, symmetric explosion at peak), Shrapnel (high explosion force, air resistance), Space Debris (low gravity g=1.6m/s²). Educational content covers COM definition and calculation (weighted average position, balance point concept, for discrete particles and continuous objects), COM velocity and momentum (mass-weighted velocity, total momentum equals M×v_cm, conservation principles), Projectile motion of systems (COM always parabolic regardless of internal complexity, tumbling objects, rotating systems, why athletes can rotate while COM follows predictable path), Explosions and internal forces (momentum conservation during explosion, symmetric fragment distribution, COM trajectory unchanged, firework physics examples, space applications), Sand pendulum demonstration (leaking pendulum with changing mass, period independence from mass for slow leaks, COM of pendulum plus fallen sand), Motion decomposition (separating COM translation from internal motion, kinetic energy K = K_cm + K_internal, applications in molecular physics and biomechanics), Real-world applications (Sports: gymnastics, diving, throwing events; Ballistics: bullet trajectories, fragmenting projectiles; Robotics: spacecraft attitude control, robot stability; Vehicle dynamics: COM height affects stability, rollover prevention; Structural engineering: building oscillations, earthquake response), Historical context (Archimedes' center of gravity concept 3rd century BCE, Lagrange's 1788 analytical mechanics formalization, development in 18th-19th century mechanics, modern applications in quantum mechanics and astrophysics). Multi-language support (zh, en, de, fr, es, pt, ru).

⚛️ Physics

Thermoelectric Effect - 热电效应

Interactive visualization of thermoelectric effects including Seebeck, Peltier, and Thomson effects with voltage generation, heat absorption, and material properties. Features the fundamental equations: Seebeck effect V = S(T₂ - T₁) (voltage generated from temperature difference where S is Seebeck coefficient in µV/K), Peltier effect Q = Π·I = S·T·I (heat absorbed/released at junction due to current flow where Π is Peltier coefficient), Thomson effect Q = τ·I·ΔT (heat absorption/release in temperature gradient where τ is Thomson coefficient), Thomson coefficient τ = T·dS/dT (relating Thomson to Seebeck coefficient temperature dependence), Figure of merit ZT = S²σT/κ (dimensionless performance parameter combining electrical conductivity σ and thermal conductivity κ), Efficiency η = (T_h - T_c)/T_h · (√(1+ZT) - 1)/(√(1+ZT) + T_c/T_h) (conversion efficiency for thermoelectric generators). Real-time visualization includes: (1) Thermocouple Display showing two dissimilar materials (A and B) joined at hot and cold junctions, temperature gradient visualization with color-coded regions (blue=cold T₁, red=hot T₂), animated electron flow showing charge carrier diffusion from hot to cold (Seebeck) or current-driven flow (Peltier), junction point with temperature indicator, material labels (Cu, Bi₂Te₃, PbTe, SiGe, Constantan, Sb₂Te₃); (2) Temperature Distribution canvas plotting temperature vs position along the thermocouple length, linear gradient profile in each material, temperature drop at junctions, material regions labeled (A and B), temperature scale from 200-550 K, animated heat flow visualization; (3) Electrical Measurements displaying voltage meter (Seebeck voltage in mV), current meter (Peltier current in A), power calculation (P = V×I in W), efficiency percentage for generators, analog meter dials with animated needles, color-coded displays (red for voltage, blue for current, green for power); (4) Heat Flow Diagram showing hot reservoir (T₂) and cold reservoir (T₁), central thermoelectric (TE) device, animated energy flow arrows (Q_h from/to hot, Q_c to/from cold, W_e electrical power), reversible flow direction based on effect type, intensity modulation on arrows, real-time heat values displayed (Q_h, Q_c, Thomson heat τQ). Interactive parameters: Hot junction temperature T₂ (300-500 K), Cold junction temperature T₁ (200-400 K), Current I (0-10 A for Peltier), Seebeck coefficient S (10-200 µV/K), Resistance R (0.1-10 Ω), Thermal conductivity κ (0.5-5 W/(m·K)), Material selection (Material A: Cu, Bi₂Te₃, PbTe, SiGe; Material B: Constantan, Bi₂Te₃, PbTe, Sb₂Te₃), Animation speed (0.1-3x). Quick presets: Thermocouple Sensor (Seebeck mode, Th=350K, Tc=300K for temperature measurement), Peltier Cooler (Peltier mode, Th=320K, Tc=280K, I=5A for solid-state refrigeration), Thermoelectric Generator (Seebeck mode, Th=500K, Tc=300K for waste heat recovery), Waste Heat Recovery (Th=450K, Tc=320K for industrial applications). Display options: toggle electron flow visualization, heat flow animation, voltage display. Educational content covers Seebeck effect principle (charge carrier diffusion due to temperature gradient creating voltage, thermocouple operation for temperature sensing, voltage proportional to ΔT, different thermocouple types K/J/T for various ranges), Peltier effect applications (solid-state cooling without moving parts, reversible heating/cooling with current direction, cascaded devices for larger ΔT, CPU cooling, laser diode temperature stabilization, portable refrigerators, coefficient of performance COP), Thomson effect fundamentals (heat in temperature gradients due to current, relationship between Seebeck and Thomson coefficients via Kelvin relations, contribution to device efficiency), thermoelectric materials (figure of merit ZT optimization, high power factor S²σ and low thermal conductivity κ, Bi₂Te₃ for room temperature ZT~1, PbTe for mid-temperature 500-900K ZT~1.5, SiGe for high-temperature 900-1200K ZT~0.6, nanostructuring for phonon scattering), real-world applications (thermocouple temperature sensors in industrial processes and HVAC, Peltier coolers for electronics and medical devices, thermoelectric generators for automotive exhaust recovery, radioisotope thermoelectric generators RTGs for space missions like Curiosity rover, body heat harvesting for wearable electronics), historical context (Seebeck's 1821 discovery of thermoelectricity, Peltier's 1834 finding of current-driven heating/cooling, Thomson's 1851 theoretical framework and Kelvin relations, 20th century semiconductor advances enabling practical devices, modern nanostructured materials research). Multi-language support (zh, en, de, fr, es, pt, ru).

⚛️ Physics

Heat Engine & Refrigerator - 热机与制冷机

Interactive visualization of heat engines and refrigerators demonstrating thermodynamic cycles, efficiency analysis, and energy flow. Features the fundamental equations: Thermal efficiency η = W/Q_h = 1 - Q_c/Q_h showing energy conversion from heat to work, COP_cooling = Q_c/W for refrigerators (heat removed per work input), COP_Heating = Q_h/W for heat pumps (heat delivered per work input), Carnot efficiency η_Carnot = 1 - T_c/T_h representing theoretical maximum efficiency, First Law of Thermodynamics ΔU = Q - W (energy conservation), Ideal Gas Law PV = nRT. Real-time visualization includes: (1) P-V Diagram canvas showing thermodynamic cycles with pressure-volume plots, multiple cycle types (Carnot, Otto, Diesel cycles), animated current state marker moving along cycle path, color-coded processes (compression in red, expansion in blue, isothermal in green), area under curve representing work done, cycle direction arrows (clockwise for heat engines, counter-clockwise for refrigerators), dynamic scale adjustment based on pressure/volume parameters; (2) Piston Animation showing realistic cylinder-piston-crankshaft mechanism with connecting rod, combustion chamber with color-coded temperature (blue=cold, red=hot), piston rings detail, four-stroke cycle visualization (intake, compression, power, exhaust), crankshaft rotation synchronized with cycle phase, gas color changes during combustion, temperature indicator showing current gas temperature; (3) Energy Flow Diagram displaying hot reservoir (T_h) and cold reservoir (T_c) as thermal sources, central engine/refrigerator unit, animated energy flow arrows with intensity modulation, Q_h arrow (heat from/to hot reservoir), Q_c arrow (heat to/from cold reservoir), W arrow (work output/input), real-time energy balance display, COP values for refrigeration mode; (4) Four-Stroke Display showing circular stroke sequence with numbered positions (1: Intake, 2: Compression, 3: Power/Combustion, 4: Exhaust), animated indicator tracking current stroke position, color-coded active stroke highlighting, stroke labels in multiple languages, cycle phase synchronization with piston animation. Interactive parameters: Hot reservoir temperature T_h (300-1000 K), Cold reservoir temperature T_c (100-500 K), Compression ratio (4-20:1), Maximum pressure (10-100 bar), Animation speed control (0.1-5x), Cycle type selection (Heat Engine, Refrigerator, Carnot, Otto, Diesel). Quick presets: Gasoline Engine (Otto cycle, Th=2300K, r=10:1), Diesel Engine (Diesel cycle, Th=2200K, r=18:1), Home Refrigerator (Th=320K, Tc=260K), Heat Pump (Th=340K, Tc=280K). Display options: toggle P-V path overlay, energy flow animation, temperature display. Educational content covers heat engine operation (converting thermal energy to mechanical work through thermodynamic cycles, efficiency limits from Second Law, irreversibilities reducing real efficiency, practical applications in power generation and transportation), refrigerator and heat pump principles (reverse cycle requiring work input to transfer heat against natural gradient, COP can exceed 1 unlike efficiency, vapor compression refrigeration cycle, applications in air conditioning and food preservation), Carnot cycle analysis (ideal reversible cycle with maximum efficiency, two isothermal and two adiabatic processes, temperature-dependent efficiency formula, practical impossibility due to finite-time constraints and irreversibilities), Otto vs Diesel cycles (spark ignition vs compression ignition, different combustion processes, compression ratio effects on efficiency, modern engine improvements with turbocharging and direct injection), real-world applications (automotive engines comparing gasoline vs diesel, steam turbines in power plants, Rankine cycle for steam power, refrigeration technologies, heat pumps for efficient heating), historical context (James Watt's steam engine improvements 1769, Sadi Carnot's 1824 theoretical foundation, Rudolf Diesel's 1890s invention, modern developments in hybrid systems and alternative fuels). Multi-language support (zh, en, de, fr, es, pt, ru).

⚛️ Physics

Bernoulli's Equation - 伯努利方程

Interactive visualization of Bernoulli's equation demonstrating fluid dynamics, pressure-velocity relationship, and Venturi effect. Features the fundamental equations: P + ½ρv² + ρgh = constant (Bernoulli equation showing energy conservation per unit volume), A₁v₁ = A₂v₂ (continuity equation for incompressible flow), v₂ = (A₁/A₂)v₁ = (D₁/D₂)²v₁ (velocity relation from continuity), P₂ = P₁ + ½ρ(v₁² - v₂²) (pressure relation from Bernoulli), Q = A₁v₁ (volume flow rate), ṁ = ρA₁v₁ (mass flow rate). Real-time visualization includes: (1) Venturi tube animation showing pipe constriction (inlet → throat → outlet) with smooth radius transitions, animated flow particles with velocity-dependent speed (faster in throat section), color-coded particles (blue=slow, red=fast), pressure gradient visualization showing high pressure (red) at inlet, low pressure (blue) at throat, pressure recovery at outlet; (2) Manometer tubes displaying liquid heights proportional to local pressure, real-time pressure readings P₁, P₂, P₃ with proper units (Pa), dynamic liquid level changes responding to parameter adjustments; (3) Streamline visualization showing smooth flow paths through varying cross-section, velocity vectors with magnitude indication, laminar flow patterns with particle tracking; (4) Pressure distribution chart P(x) showing pressure drop in constriction and recovery, velocity distribution chart v(x) showing velocity increase in throat, both with real-time updates and key point markers. Interactive parameters: fluid type (water ρ=1000 kg/m³, air ρ=1.225 kg/m³, oil ρ=900 kg/m³, gasoline ρ=720 kg/m³), inlet velocity v₁ (1-20 m/s), inlet pressure P₁ (50,000-200,000 Pa), inlet diameter D₁ (5-20 cm), throat diameter D₂ (2-15 cm), tube length (50-200 cm). Display options: show/hide flow particles, streamlines, pressure gradient color map, velocity vectors, manometer tubes. Presets include: Water Flow (standard water parameters), Air Flow (low density, high velocity), High Velocity (enhanced visualization), Extreme Contraction (maximum pressure drop). Educational content covers Bernoulli equation derivation (energy conservation along streamline, work-energy principle for fluids), key concepts (pressure energy P, kinetic energy ½ρv², potential energy ρgh, speed-pressure trade-off), Venturi effect physics (constriction accelerates flow, pressure drops in throat, applications in flow measurement), real-world applications (airplane wings lift, carburetors, perfume atomizers, chimney draft, sailing), limitations (inviscid assumption, incompressible flow, steady flow, laminar vs turbulent), and historical context (Daniel Bernoulli 1738, Euler refinement, Venturi's 1797 work on pipe flow). Multi-language support (zh, en, de, fr, es, pt, ru).

⚛️ Physics

Black Hole Hawking Radiation - 黑洞霍金辐射

Interactive visualization of black hole Hawking radiation demonstrating quantum effects near event horizons, black hole evaporation, and thermodynamics. Features the fundamental equations: Hawking temperature T = ħc³/(8πGMk_B) showing temperature inversely proportional to mass - solar mass black hole has T ~ 60 nK while 10¹² kg black hole has T ~ 10¹² K; Schwarzschild radius R_s = 2GM/c² defining the event horizon boundary; evaporation rate dM/dt = -ħc⁴/(15360πG²M²) with power output P ∝ 1/M²; black hole lifetime τ = 5120πG²M³/(ħc⁴) ~ 10⁶⁷ years for stellar mass; black hole entropy S = A/4 = 4πGM²/(ħc) proportional to surface area supporting holographic principle. Real-time visualization includes: (1) Black hole view canvas showing event horizon with relativistic effects, accretion disk with Doppler beaming, relativistic jets, photon sphere at 1.5 R_s, animated Hawking radiation particles escaping from near horizon, dynamic size changes as mass decreases through evaporation; (2) Hawking radiation visualization showing virtual particle pairs creation near event horizon with one particle falling in (negative energy) and one escaping (positive energy), temperature-based color coding (red for hot small black holes, blue for cold large ones), radiation intensity proportional to temperature; (3) Mass vs time chart showing evaporation curve M(t) with accelerating mass loss as black hole shrinks, real-time plotting of current state; (4) Temperature vs mass chart showing T ∝ 1/M relationship on log-log scale with current temperature marker; (5) Power vs mass chart showing P ∝ 1/M² relationship demonstrating dramatic power increase near end of evaporation. Interactive parameters: initial black hole mass (0.1-100 M☉ for stellar, 10¹² kg for primordial, 10⁶ M☉ for supermassive), black hole type presets (stellar, supermassive, primordial, micro, intermediate), time speed control (0.1-100x for accelerated visualization), mass scale display (linear/logarithmic), radiation intensity (10-100%). Display options: show/hide accretion disk, relativistic jets, virtual particle pairs, event horizon, photon sphere, information paradox indicator tracking quantum information loss. Presets include: Stellar Black Hole (10 M☉, T ~ 10⁻⁸ K, τ ~ 10⁶⁷ years - effectively stable), Primordial Black Hole (10¹² kg, T ~ 10¹² K, evaporating now), Micro Black Hole (10¹² kg, extremely short-lived), Final Explosion Phase (demonstrating last moments of evaporation with dramatic temperature/power increase). Educational content covers physical mechanism (quantum field theory in curved spacetime, virtual particle pairs, negative energy infalling particles, thermal radiation spectrum), key properties (mass-temperature relation T ∝ 1/M, lifetime τ ∝ M³, power P ∝ 1/M², entropy S ∝ A), types of black holes (stellar 3-100 M☉ from collapsed stars, supermassive 10⁶-10⁹ M☉ in galactic centers, primordial 10¹²-10²⁰ kg from early universe, micro <10¹² kg extremely short-lived), scientific significance (quantum gravity prediction, black hole thermodynamics, information paradox, cosmological implications, holographic principle support), and historical context (Stephen Hawking's 1974 discovery, revolution in understanding black holes, first concrete link between gravity and quantum theory, holographic principle and AdS/CFT correspondence, remains unobserved experimentally but crucial for theoretical physics). Multi-language support (zh, en, de, fr, es, pt, ru).