σT vs iTurbo3D

σT is a precision tool for physics students and researchers who need to propagate measurement uncertainties through calculations. Enter your experimental data, and σT handles the error math automatically. **FIVE ERROR MODES** Configure uncertainties in your data to match your orignal measurement method: • Constant — for physical constants and exact values • Absolute — fixed ±error (ruler measurements, digital readouts) • Relative — percentage-based uncertainty • Combined — both absolute and relative components (many typical multimeters) • Per-Value — individual error for each measurement **AUTOMATIC PROPAGATION** Create derived values and watch uncertainties flow through the calculation chain. σT uses Gaussian error-propagation and pre-calculated derivative-based methods to compute propagated errors correctly when combining independently measured variables. Available operations: • Basic: add, subtract, multiply, divide, reciprocal • Functions: exp, ln, sin, cos, normalize • Statistical & Sample Statistics: mean with standard error, average step width • Advanced: weighted sums, weighted products, polynomials • Physics: Lorentz factor (relativistic gamma), Logit sigmoid (Fermi-Dirac statistics) **INTERACTIVE CHARTS** Visualize your data with proper error bars. Pinch to zoom, drag to pan, double-tap to auto-fit. Add mathematical function overlays to compare your measurements against theoretical predictions, identify eligible parameter ranges matching your measurements. **EXPORT YOUR WORK** • CSV and TSV export for spreadsheets and analysis tools • High-resolution PNG charts for lab reports • Complete project files for sharing with classmates or colleagues • Copy data to clipboard with a swipe and continue in Sheets or Excel with errors in place **DESIGNED FOR LAB WORK** σT adapts to your device: • iPhone: Full-featured portable lab companion • iPad: Side-by-side layout for efficient data entry • Mac: Native desktop experience via Catalyst **YOUR DATA, YOUR DEVICE** All measurements are stored locally. No account required, no cloud sync, no tracking. σT works completely offline.

iTurbo 3D brings interactive three-dimensional turbulence simulation to iPhone. A pseudo-spectral incompressible Navier-Stokes solver evolves the velocity field while a Metal volume ray marcher displays the flow as it develops. Explore the volume using touch controls: drag to orbit, pinch to zoom, and double-tap to restore the camera. Switch between vorticity, Q-criterion, kinetic energy, and helicity, with a selection of scientific colormaps and light or dark backgrounds. Configure Taylor-Green or random turbulence, choose a 32 cubed, 64 cubed, or 128 cubed grid, set the Reynolds number, and adjust forcing. Higher grid resolutions reveal finer structures while using progressively more memory and processing power. Pause, resume, advance one step, or reset the simulation from the bottom toolbar. Live status values show the time step, iteration, simulation time, step rate, energy, and enstrophy. Expand the diagnostics to inspect energy history and the energy spectrum. Whether you are teaching fluid mechanics, studying turbulence, or simply enjoy computational physics, iTurbo 3D turns the equations of motion into something you can see and explore directly on iPhone.