Use cases · Physics
Simulations, observational data and theory worked through carefully, with error bars, finite-size checks and the literature value beside every result.
Real runs
Each one is a complete run in production: the question as it was asked, every step Propab took, and everything it made.
Reproduce the 2D Ising model ferromagnetic phase transition from first principles. Run Monte Carlo (Metropolis, plus a Wolff cluster algorithm near criticality) on square lattices of several sizes, measure magnetisation, susceptibility, specific heat and the Binder cumulant, and estimate the critical temperature by finite-size scaling. Compare your estimate with Onsager's exact result and with values reported in the literature.
Ready today
Start from one of these, or ask in your own words. Propab combines them when your question needs more than one.
Astrophysics
Mass-radius and period-radius diagrams (e.g. the radius valley) from the NASA Exoplanet Archive, with the selection cuts stated.
Astrophysics
Redshift, line fluxes and a BPT classification for a galaxy sample, from SDSS line catalogues or the spectra themselves.
Astrophysics
H0 / Omega_m posterior from the Pantheon+SH0ES distance moduli with the full covariance matrix, with a corner plot.
Astrophysics
Mass and spin distribution of merging black holes by hierarchical inference over the GWTC posterior samples.
Astrophysics
Halo profiles, projections and power spectra from a simulation snapshot the researcher uploads.
Computational physics
Measured convergence order and energy/momentum drift of an integrator (symplectic vs Runge-Kutta) on a test problem.
Computational physics
MEGNO / Lyapunov map and survival time of a multi-planet system over millions of orbits.
Computational physics
Finite-difference solution of a heat/wave/Poisson problem with a grid-refinement study against the exact solution.
Computational physics
Monte Carlo integral or expectation with variance reduction and a convergence plot.
Computational physics
Power spectral density (Welch/multitaper), peaks and their significance for a signal the researcher supplies.
Computational physics
Lagrangian to equations of motion symbolically, then integrated and plotted (phase portraits, energy).
Computational physics
Differentiable simulation fitted to data by automatic differentiation.
Computational physics
Stiff kinetics or an index-reduced DAE solved with an implicit integrator, with a solver-tolerance study.
Condensed matter
Band structure and DOS of a lattice model, checked against the analytic dispersion.
Condensed matter
Chern number or Z2 invariant of a Hamiltonian, with the Berry-curvature or Wilson-loop plot.
Condensed matter
Energy, correlations and entanglement entropy of a spin or Hubbard chain with TeNPy or quimb.
Condensed matter
Spectrum and correlation functions of a Heisenberg or Hubbard cluster by Lanczos.
Condensed matter
Candidates ranked by band gap, stability or magnetism from open DFT databases.
Condensed matter
Ordering temperature and susceptibility of a Heisenberg/Ising magnet on a lattice.
Fluid and continuum mechanics
Lid-driven cavity or flow past a cylinder with drag, lift and Strouhal number against published reference values.
Fluid and continuum mechanics
Orr-Sommerfeld eigenvalues, neutral curve and critical Reynolds number.
Fluid and continuum mechanics
Stress and deflection of a beam/plate/solid against an analytic or NAFEMS benchmark value.
Fluid and continuum mechanics
Minimum-compliance layout at a volume fraction (SIMP), with a mesh-independence check.
Fluid and continuum mechanics
Bifurcation diagram, Lyapunov exponent and period-doubling constants.
Fluid and continuum mechanics
Sparse identification (SINDy) of a dynamical system from measured trajectories, with a noise-robustness test.
Nuclear physics
Activities, decay heat and gamma lines of a nuclide inventory over time.
Nuclear physics
AME2020 binding energies vs the semi-empirical mass formula, with shell-closure residuals.
Nuclear physics
EXFOR measurements plotted and compared against ENDF/B-VIII and JEFF evaluations for a reaction.
Nuclear physics
Energy generation and abundance flow for a burning stage from a REACLIB network.
Nuclear physics
Thermonuclear rate vs temperature from an S-factor or narrow resonances, with its uncertainty.
Nuclear physics
Peak fits, energy/efficiency calibration and nuclide identification for a detector spectrum.
Optics and electromagnetism
Extinction, scattering and backscatter efficiencies vs size parameter and wavelength.
Optics and electromagnetism
Reflectance/transmittance spectra of a multilayer coating from real dispersion data.
Optics and electromagnetism
Fraunhofer/Fresnel propagation of an aperture and the PSF with aberrations.
Optics and electromagnetism
Cavity resonances, Q factors and transmission of a 2D photonic structure.
Optics and electromagnetism
Band diagram and band gaps of a photonic crystal slab.
Optics and electromagnetism
Diffraction efficiencies of a periodic grating vs wavelength and angle.
Optics and electromagnetism
Sequential ray trace of a lens with real glasses: spot diagrams, aberrations and a tolerance check.
Optics and electromagnetism
Touchstone network data de-embedded, fitted and plotted (Smith chart, return loss).
Particle physics
Dimuon invariant-mass spectrum from CMS open data with fitted resonance masses and widths.
Particle physics
Search for a resonance in a mass spectrum with a look-elsewhere-corrected significance.
Particle physics
95% CL CLs limits on a signal from binned templates.
Particle physics
Anti-kt jets and substructure observables of boosted objects on open data or supplied events.
Particle physics
Literature synthesis of a precision observable (e.g. muon g-2): each value, source and tension in sigma.
Particle physics
Reconstruction/ID efficiency vs pT/eta in data and simulation, and their ratio.
Plasma physics
Debye length, plasma frequency, beta, collisionality and the regime they imply, for stated conditions.
Plasma physics
Roots of the plasma dispersion function (Landau damping, ion-acoustic waves) against analytic limits.
Plasma physics
Two-stream instability growth rate from a PIC run against linear theory.
Plasma physics
OMNI solar-wind coupling functions against Dst/AE over a storm set, with lag correlations.
Plasma physics
Spectral index and break frequency of solar-wind or magnetosheath turbulence (Wind, MMS).
Plasma physics
Grad-Shafranov equilibrium and the coil currents that produce a target shape.
Plasma physics
Brio-Wu shock tube or Orszag-Tang vortex with a finite-volume MHD solver, checked against reference solutions and div B.
Plasma physics
Electron temperature, density and floating/plasma potential from an I-V characteristic.
Quantum physics
T1/T2 and Rabi dynamics from a Lindblad master equation.
Quantum physics
VQE or QAOA with gradients, converged energy and comparison with exact diagonalisation.
Quantum physics
Circuits under a device noise model, up to the memory limit of a statevector/density matrix.
Quantum physics
Logical error rate vs physical error rate across code distances, and the crossing point.
Quantum physics
State/process tomography and RB decay on a simulated device.
Quantum physics
NPA-hierarchy bound on a Bell expression with the SDP certificate.
Quantum physics
MPS/tensor-network simulation of a low-entanglement circuit beyond statevector size.
Quantum physics
Qubit Hamiltonian of a small molecule and a VQE energy against full CI.
Quantum physics
GRAPE/CRAB pulse that implements a gate at target fidelity under constraints.
Relativity and mathematical physics
Christoffel, Riemann, Ricci and Einstein tensors, and whether the metric solves the field equations.
Relativity and mathematical physics
Orbits, perihelion precession, light bending or a black-hole shadow by geodesic integration.
Relativity and mathematical physics
Level-spacing distribution and spectral form factor against GOE/GUE predictions.
Relativity and mathematical physics
Series/asymptotic forms derived symbolically and checked numerically to high precision.
Relativity and mathematical physics
Pure-gauge U(1)/SU(2) Monte Carlo with Wilson loops and the string tension.
Relativity and mathematical physics
Bethe-ansatz energies of an integrable chain checked against exact diagonalisation.
Statistical mechanics
Critical temperature and an order-parameter exponent with statistical and systematic errors separated.
Statistical mechanics
Wolff/Swendsen-Wang updates with measured autocorrelation times vs Metropolis.
Statistical mechanics
g(E) of a lattice model and thermodynamics at any temperature from one run.
Statistical mechanics
Integrated autocorrelation time and binning/blocking error for a Monte Carlo series.
Statistical mechanics
p_c and cluster-size exponents by finite-size scaling.
Statistical mechanics
Energy and pressure of LJ configurations compared with the NIST Standard Reference Simulation values.
Statistical mechanics
Exclusion processes, kinetic Monte Carlo or Gillespie simulations with scaling exponents.