Thermodynamics

Psychrometric Chart

Moist-air HVAC chart: dry-bulb, RH, humidity ratio, dew point, wet-bulb approximation, enthalpy, and two-stream mixing.

Brayton Cycle (Gas Turbine)

PV: isentropic compress, isobaric heat in, isentropic expand, isobaric cool — jet/GT core cartoon.

Joule–Thomson Throttling

Isenthalpic expansion: ideal gas ΔT = 0; toy μ_JT inversion for real gases.

van der Waals Isotherms

Reduced (P_r,V_r,T_r) curves; critical point; subcritical wiggle vs Maxwell plateaus (qualitative).

Bénard Convection (Rayleigh)

Heated-from-below layer: Ra vs Ra_c ~1708; schematic hex/roll pattern.

Black Body: Planck Spectrum

B_λ(λ,T); Wien λ_max ∝ 1/T; Stefan–Boltzmann M = σT⁴ and numeric ∫πB_λ dλ.

Rankine Cycle (Steam)

T–s with vapor dome + schematic P–v: pump, boiler, turbine, condenser; x₄ and pressure sliders.

Refrigeration Cycle (Reverse Carnot)

PV loop like Carnot but reversed; COP_R & COP_HP; T_C/T_H in K; symbolic fridge sketch.

Vapor-Compression Refrigeration Cycle

Compressor, condenser, expansion valve, evaporator: COP, cooling capacity, pressure ratio, and p-h sketch with states 1-2-3-4.

Fin Heat Transfer

Straight rectangular fin with convection: temperature profile, mL, fin efficiency ηf, effectiveness, and heat rate vs geometry.

Lumped Capacitance Cooling

Newton cooling with Biot number, characteristic length, τ = ρVc/(hA), temperature curve, and validity check Bi < 0.1.

Pipe Friction & Moody Chart

Reynolds number, relative roughness, Swamee-Jain/Colebrook-style friction factor, and Darcy-Weisbach head loss.

Open-Channel Flow & Hydraulic Jump

Rectangular-channel Froude number, critical depth, conjugate depths, energy loss, and subcritical/supercritical regimes.

Multilayer Wall Conduction

Three layers in series: R″ = L/k, q″ and U; T(x) sketch and preset plaster/brick/wool.

Adiabatic Cloud Parcel

Lift moist air: dry Γ, LCL, toy moist lapse; RH and cartoon cloud vs height.

Engine Cycles Compared (P–V)

One canvas: Carnot, Otto, Diesel, Stirling, Rankine sketch — switch cycles, same formulas as standalone labs.

Diesel Cycle (PV)

Air-standard: adiabat compress, isobaric heat, adiabat expand, isochoric out; η(ρ_c, β).

Maxwell’s Demon (Toy)

2D billiards + gate: fast |v| crosses; ⟨|v|⟩ left/right + Landauer note.

Leidenfrost Effect (Toy)

T_plate vs ~200 °C threshold: vapor gap and lifetime curves — pedagogical, not measured boiling data.

Peltier & Seebeck (Schematic)

Current pumps heat across junction; ΔT drives toy mV — same couple, two modes.

Joule Expansion

Ideal gas into vacuum: Q = W = ΔU = 0; ΔS = nR ln 2 when volume doubles.

2D Ising Model

Square lattice Metropolis: kT/J vs |m| and E; T_c ≈ 2.27; optional field h.

Lorentz Gas (Billiard)

Point particle specularly reflected from fixed disks in a box: chaotic paths and MSD growth toward diffusion.

Site Percolation (2D)

Square lattice occupation p: clusters, left–right spanning, p_c ≈ 0.593; rough box-counting D̂ on the largest cluster.

Diffusion-Limited Aggregation (DLA)

Random walkers stick on first contact with a seed cluster on a square lattice; branched fractal growth with literature mass dimension D ≈ 1.71 in 2D and a rough box-counting D̂.

Forest Fire (Cellular Automaton)

Toroidal lattice: trees regrow with probability p, lightning ignites trees with probability f, fire spreads to four neighbors; explore intermittent bursts and SOC-like phenomenology.

Schelling Segregation Model

Two agent types on a toroidal lattice with vacancies: unhappy agents swap into random empty cells when fewer than a fraction τ of occupied Moore neighbors share their type—mild local rules, global clustering.

Kuramoto Oscillators

All-to-all coupled phases θ_i with intrinsic frequencies ω_i: order parameter r = |N⁻¹ Σ e^{iθ_i}| grows as coupling K crosses the synchronization window—classic mean-field rhythm transition.

Vicsek Model (Active Matter)

Self-propelled particles on a torus align headings with neighbors within radius R, add noise η, then drift at v₀; polarization V_a = |⟨e^{iθ}⟩| captures the flocking crossover with density ρ = N/L².

Wolfram Elementary Cellular Automata

1D binary CA with Wolfram code R∈[0,255]: space–time raster, periodic or null boundaries, single-cell or random IC, rule-bit strip, and informal class hints for textbook rules (e.g. 30, 90, 110, 184).

Eden Growth (Lattice)

Square-lattice Eden model: each step occupies a uniformly random empty von-Neumann neighbor of the cluster; compact growth with a rough interface—track perimeter P vs 2√(πN) as a roughness proxy.

Ising 2D: Wolff Cluster Updates

Ferromagnetic toroidal Ising (h = 0): Swendsen–Wang bond freezing with probability 1 − e^(−2βJ), build a same-spin cluster, flip it—fast mixing near T_c compared to single-spin Metropolis.

Hopfield Associative Memory

10×10 binary Hopfield network: Hebbian pattern storage, energy E = −½ Σ w_ij S_i S_j, and random asynchronous updates that flow downhill to fixed-point recall after noisy cues.