Analog circuits, switching power topologies, RF transmission lines, 3-phase grid power, and semiconductor dynamics.
Core Formulation: v(t) = L\frac{di}{dt} + Ri(t) + \frac{1}{C}\int i(t)dt
Active Simulators: 18 | Subfields: Power Electronics, RF & Transmission Lines, Analog Active Filters, 3-Phase AC Grids, Semiconductor Physics
Closed-loop feedback stability, PID gain tuning, root locus analysis, state-space representations, and inverted pendulum dynamics.
Core Formulation: u(t) = K_p e(t) + K_i \int_0^t e(\tau)d\tau + K_d \frac{de(t)}{dt}
Active Simulators: 12 | Subfields: PID Controllers, Bode & Nyquist Plots, State-Space Feedback, Inverted Pendulum, Robotic Kinematics
Damped harmonic oscillators, multi-degree-of-freedom vibrations, thermodynamic Carnot cycles, and heat transfer convection.
Core Formulation: m\ddot{x} + c\dot{x} + kx = F_0 \cos(\omega t)
Active Simulators: 14 | Subfields: Vibration & Resonance, Carnot & Rankine Cycles, Heat Exchanger Conduction, Gear Train Dynamics, Fluid Bernouilli Flow
Continuous Stirred Tank Reactors (CSTR), multi-component distillation, mass transfer diffusion, and non-isothermal kinetics.
Core Formulation: \frac{dC_A}{dt} = \frac{F}{V}(C_{A0} - C_A) - k_0 e^{-E_a/RT} C_A^2
Active Simulators: 9 | Subfields: CSTR Chemical Kinetics, Distillation Columns, Heat Transfer Exchangers, Diffusion & Mass Transfer, Batch Reaction Thermodynamics
Truss axial stress distribution, Euler-Bernoulli beam deflection under uniform distributed loads, and seismic response spectra.
Core Formulation: EI \frac{d^4 w}{dx^4} = q(x)
Active Simulators: 11 | Subfields: Beam Bending & Shear, Warren & Pratt Trusses, Buckling Instability, Seismic Base Isolation, Soil Consolidation
P-N junction energy band bending, carrier drift-diffusion, quantum potential well tunneling, and wave-particle dispersion.
Core Formulation: 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)
Active Simulators: 8 | Subfields: P-N Diode Band Diagram, MOSFET Inversion Channel, Quantum Well Tunneling, Hall Effect Transport, Bragg Lattice Diffraction