SOLVER KERNEL ACTIVE • FLOAT64 REAL-TIME NUMERICAL RIGOR

LIVESIMULATORS • INTERACTIVE ENGINEERING SIMULATIONS Don't Just Read Engineering. See It Happen.

Free interactive engineering simulations and virtual laboratories. Don't just read engineering — see it happen with real-time physics in your browser across electrical, mechanical, civil, and control disciplines.

Engineering Disciplines

Electrical & Electronic Systems (EE-200)

Analog circuits, switching power topologies, RF transmission lines, 3-phase grid power, and semiconductor dynamics.

Core Formulation: v(t)=Ldidt+Ri(t)+1C∫i(t)dtv(t) = L\frac{di}{dt} + Ri(t) + \frac{1}{C}\int i(t)dtv(t)=Ldtdi​+Ri(t)+C1​∫i(t)dt

Active Simulators: 24 | Subfields: Power Electronics, RF & Transmission Lines, Analog Active Filters, 3-Phase AC Grids, Semiconductor Physics

Control Systems & Robotics (CS-300)

Closed-loop feedback stability, PID gain tuning, root locus analysis, state-space representations, and inverted pendulum dynamics.

Core Formulation: u(t)=Kpe(t)+Ki∫0te(τ)dτ+Kdde(t)dtu(t) = K_p e(t) + K_i \int_0^t e(\tau)d\tau + K_d \frac{de(t)}{dt}u(t)=Kp​e(t)+Ki​∫0t​e(τ)dτ+Kd​dtde(t)​

Active Simulators: 14 | Subfields: PID Controllers, Bode & Nyquist Plots, State-Space Feedback, Inverted Pendulum, Robotic Kinematics

Mechanical & Thermal Dynamics (ME-400)

Damped harmonic oscillators, multi-degree-of-freedom vibrations, thermodynamic Carnot cycles, and heat transfer convection.

Advanced Turbomachinery & Rotor Dynamics →

Core Formulation: mx¨+cx˙+kx=F0cos⁡(ωt)m\ddot{x} + c\dot{x} + kx = F_0 \cos(\omega t)mx¨+cx˙+kx=F0​cos(ωt)

Active Simulators: 18 | Subfields: Vibration & Resonance, Carnot & Rankine Cycles, Heat Exchanger Conduction, Gear Train Dynamics, Fluid Bernouilli Flow

Chemical & Process Engineering (CH-250)

Continuous Stirred Tank Reactors (CSTR), McCabe-Thiele distillation columns, TEMA shell-and-tube heat exchangers, and packed gas absorbers.

Core Formulation: dCAdt=FV(CA0−CA)−k0e−Ea/RTCA2\frac{dC_A}{dt} = \frac{F}{V}(C_{A0} - C_A) - k_0 e^{-E_a/RT} C_A^2dtdCA​​=VF​(CA0​−CA​)−k0​e−Ea​/RTCA2​

Active Simulators: 13 | Subfields: CSTR Chemical Kinetics, McCabe-Thiele Distillation, TEMA Shell & Tube Exchangers, Packed Gas Absorbers, Reaction Thermodynamics

Civil & Structural Mechanics (CE-320)

Truss axial stress distribution, Euler-Bernoulli beam deflection under uniform distributed loads, and seismic response spectra.

Core Formulation: EId4wdx4=q(x)EI \frac{d^4 w}{dx^4} = q(x)EIdx4d4w​=q(x)

Active Simulators: 12 | Subfields: Beam Bending & Shear, Warren & Pratt Trusses, Buckling Instability, Seismic Base Isolation, Soil Consolidation

Quantum & Semiconductor Physics (PH-500)

P-N junction energy band bending, SiC MOSFET switching dynamics, IGBT multi-layer thermal Foster networks, and BSIM4 inversion channels.

Core Formulation: iℏ∂∂tΨ(r,t)=[−ℏ22m∇2+V(r)]Ψ(r,t)i\hbar \frac{\partial}{\partial t} \Psi(\mathbf{r},t) = \left[ -\frac{\hbar^2}{2m}\nabla^2 + V(\mathbf{r}) \right] \Psi(\mathbf{r},t)iℏ∂t∂​Ψ(r,t)=[−2mℏ2​∇2+V(r)]Ψ(r,t)

Active Simulators: 12 | Subfields: P-N Diode Band Diagram, SiC MOSFET Double-Pulse, IGBT Thermal Foster Model, MOSFET Inversion Channel, Quantum Well Tunneling

Complete Interactive Simulation Library

Explore our comprehensive collection of first-principles client-side solvers:

RLC Resonant Circuit & Damping Transient — Observe underdamped ringing, critical damping, and impedance resonance in real time.
3-Phase AC Synchronous Motor & Rotating Field — Track how three balanced 120° sinusoidal currents generate a continuous rotating stator flux vector.
Buck-Boost DC-DC Switching Regulator — Explore inductor energy storage, Continuous vs Discontinuous mode, and voltage inversion.
2nd-Order Sallen-Key Active Low-Pass Filter — Tweak component values to shape Butterworth, Chebyshev, or Bessel frequency responses.
RF Transmission Line & Reflection Coefficient — See incident and reflected TEM voltage waves collide to form standing wave envelopes.
Fourier Series Harmonic Decomposition & THD — Sum discrete sinusoidal harmonics to assemble square, triangle, and pulse waveforms.
Operational Amplifier (Op-Amp) Linear & Filter Topologies — Explore inverting, non-inverting, integrator, and differentiator op-amp circuits with supply rail saturation clipping.
RC & RL Circuit Transients & Exponential Time Constants — Track charge accumulation, inductive kick, time constant τ, and 5τ settling response.
Single-Phase Transformer OC & SC Tests (Equivalent Circuit) — Extract core losses (Rc, Xm) and winding impedance (Req, Xeq) to calculate full-load efficiency and regulation.
DC Shunt & Separately Excited Motor Speed Control — Master armature voltage regulation, field flux weakening, Ward-Leonard control, and speed-torque droop.
3-Phase Induction Motor Torque-Slip & Breakdown Speed — Explore stator R-X parameters, starting torque, pull-out breakdown T_max, and rotor resistance effects.
Solar PV Cell Single-Diode Model & MPPT Tracking — Simulate single-diode I-V & P-V curves, irradiance/temperature impacts, and P&O Maximum Power Point Tracking.
Planar 4-Bar Grashof Kinematics & Coupler Curves — Synthesize crank-rocker vs double-crank inversions and trace continuous coupler point trajectories.
Thermodynamic Rankine Steam Power Cycle — Track steam expansion through high-pressure boilers, turbines, condensers, and feed pumps on a T-s diagram.
Damped Forced Harmonic Oscillator & Resonance Peak — Visualize mass-spring-damper resonance, phase lag φ(ω), and displacement amplification M(ω).
Involute Spur Gear Mesh Dynamics & Backlash — Track tooth contact along the line of action, verify contact ratio CR ≥ 1.4, and check sliding velocity.
Otto & Diesel Internal Combustion Thermodynamic Cycles — Analyze 4-stroke spark-ignition and compression-ignition P-V diagrams with moving piston kinematics.
Projectile Motion & Ballistics with Aerodynamic Drag — Compare ideal vacuum parabolic trajectory against realistic quadratic atmospheric air drag.
Centrifugal Pump & System Hydraulic Operating Point — Find the duty point (Q_duty, H_duty), evaluate affinity laws, hydraulic efficiency, and NPSHr margin.
Vapor-Compression Refrigeration & Heat Pump Cycle — Plot the P-h diagram, evaluate evaporator subcooling/superheat, compressor isentropic efficiency, and COP.
Industrial Closed-Loop PID Tuning & Anti-Windup — Tune proportional, integral, and derivative gains with integrator anti-windup clamping.
Pneumatic Control Valve Flow Cv & Cavitation — Compare Linear, Equal-Percentage, and Quick-Opening trims under varying differential pressures.
4-20mA Current Loop Transmitter & Line Resistance — Simulate 2-wire smart transmitters, cable loop resistance drops, and NAMUR fault alarms.
Differential Pressure Orifice Plate Flowmeter — Calculate volumetric flow through concentric thin-plate square-edge orifices and tap dP.
Bode Plot & Nyquist Diagram Frequency Stability — Evaluate Gain Margin, Phase Margin, crossover frequencies, and Cauchy stability encirclements.
Root Locus Plotter & Closed-Loop Stability Analysis — Trace closed-loop pole trajectories across the complex s-plane as feedback gain K varies from 0 to ∞.
Euler-Bernoulli Beam Deflection, Shear & Moment — Calculate Shear Force Diagrams (SFD), Bending Moments (BMD), and elastic deflection profiles.
Warren & Pratt Truss Bridge Analysis — Solve Method of Joints 2D nodal equilibrium under moving deck truck live loads and check Euler buckling.
Seismic Base Isolation & Dynamic Multi-Story Response — Compare conventional fixed-base vs elastomeric Lead-Rubber Bearing (LRB) building lateral drift.
Mohr’s Circle of Stress & Soil Shear Slip Failure — Transform 2D normal and shear stresses to principal axes (σ₁, σ₂) and evaluate Coulomb failure envelopes.
Reinforced Concrete Beam Flexural Design & Whitney Stress Block — Calculate nominal moment capacity Mn, Whitney block depth a, rebar strain εt, and tension-controlled safety.
Non-Isothermal CSTR & Thermal Runaway Dynamics — Simulate continuous reaction kinetics, cooling jacket heat transfer, and thermal runaway thresholds.
Binary Distillation Column & McCabe-Thiele Stages — Step through McCabe-Thiele theoretical equilibrium trays, adjust reflux ratio, and evaluate minimum reflux R_min.
Shell-and-Tube Heat Exchanger & ε-NTU Rating — Evaluate countercurrent thermal gradients, logarithmic mean temperature difference (LMTD), and ε-NTU effectiveness.
Packed Gas Absorption Tower & Flooding Hydraulics — Simulate countercurrent solvent scrubbing, calculate packing height Z via HTU-NTU, and detect Sherwood flooding limits.
Batch Reactor & Plug Flow Reactor (PFR) Kinetics — Compare 1st vs 2nd order kinetics, Arrhenius temperature sensitivity, Damköhler number Da, and conversion X_A.
P-N Junction Diode Band Bending & Carrier Transport — Visualize energy band bending (Ec, Ev, Ef), space-charge depletion width, and carrier drift-diffusion.
Silicon Carbide (SiC) MOSFET Double-Pulse Switching & Slew Rates — Capture ultra-fast dv/dt (up to 100 V/ns), Miller plateau dynamics, inductive ringing, and switching energy losses E_on / E_off.
IGBT Module Multi-Layer Thermal Foster Network & SOA — Model multi-layer conduction from Silicon Die through DBC ceramic and baseplate to heatsink, tracking T_j ripple.
MOSFET Inversion Channel, Band Bending & 2D Electron Gas — Solve surface potential band bending, visualize 2D electron sheet accumulation, and observe channel pinch-off.
Photoelectric Effect & Einstein Quantum Work Function — Verify quantum photon particle theory, metal work functions Φ, and stopping potential V_stop.

Platform Architecture & Numerical Integrity

Every simulation executes directly inside the user's browser using 4th-Order Runge-Kutta (RK4) integration algorithms. Discrete parameter adjustments trigger continuous differential solutions evaluated at 60 frames per second without network lag.

            STANDARDS: IEEE Std 1459, ASME MFC-3M, ISO 5167, IEC 60076, AISC 360, SI-CODATA 2022
          