Physics Examples

Natural language prompts for physics simulations and calculations.

Classical Mechanics

Simulate a double pendulum and show the chaotic motion over 60 seconds

Calculate the trajectory of a projectile with air resistance (drag coefficient 0.5)

Model three bodies orbiting each other and find periodic solutions

Compute the normal modes of a coupled oscillator system with 5 masses

Simulate a spinning top with precession and nutation

Find the Lagrangian and equations of motion for a bead on a rotating hoop

Model elastic and inelastic collisions between billiard balls

Calculate the moment of inertia tensor for an arbitrary 3D shape

Simulate a driven damped harmonic oscillator near resonance

Model a Foucault pendulum at latitude 45°N

Electromagnetism

Visualize the electric field lines around a quadrupole configuration

Compute the magnetic field of a Helmholtz coil pair

Simulate electromagnetic wave propagation through a dielectric slab

Calculate the radiation pattern of a dipole antenna

Model eddy currents in a conducting plate with a moving magnet

Solve for the potential inside a grounded conducting sphere with a point charge nearby

Compute the Poynting vector for a plane wave hitting a perfect conductor

Simulate the skin effect in a wire at different frequencies

Model a waveguide and find the cutoff frequencies for TE and TM modes

Calculate the force between two current-carrying wires

Thermodynamics & Statistical Mechanics

Simulate an ideal gas in a box and verify the Maxwell-Boltzmann distribution

Model a Carnot engine cycle and compute the efficiency

Calculate the partition function for a quantum harmonic oscillator

Simulate the Ising model on a 2D lattice and find the critical temperature

Model heat conduction in a rod with fixed boundary temperatures

Compute the entropy of mixing for two ideal gases

Simulate Brownian motion and extract the diffusion coefficient

Model a van der Waals gas and find the critical point

Calculate the specific heat of a solid using the Debye model

Simulate an adiabatic expansion and verify PV^gamma = constant

Quantum Mechanics

Solve the infinite square well and visualize the first 5 eigenstates

Simulate quantum tunneling through a double barrier (resonant tunneling)

Compute the hydrogen atom spectrum and compare to the Rydberg formula

Model a quantum harmonic oscillator in a coherent state

Simulate the Stern-Gerlach experiment with sequential measurements

Calculate transition probabilities using time-dependent perturbation theory

Model a particle in a periodic potential and show the band structure

Simulate the quantum Zeno effect with frequent measurements

Compute the Berry phase for a spin-1/2 particle in a rotating magnetic field

Model entanglement between two qubits and compute the Bell inequality violation

Special Relativity

Compute the Lorentz transformation for a frame moving at 0.8c

Calculate time dilation for a muon traveling at 0.99c - does it reach the ground?

Show length contraction for a meter stick moving at various velocities

Compute the relativistic Doppler shift for a galaxy receding at 0.1c

Calculate the relativistic momentum and energy of a proton at the LHC

Model the twin paradox with specific acceleration phases

Compute the velocity addition for two rockets moving at 0.6c relative to Earth

Calculate the proper time along a worldline with given coordinate time

Show the relativistic beaming effect for a flashlight on a moving train

Compute the threshold energy for pair production (gamma -> e+ e-)

General Relativity

Derive the Schwarzschild radius for a black hole of 10 solar masses

Calculate gravitational time dilation at Earth's surface vs GPS satellite altitude

Solve the geodesic equation for a particle in circular orbit around a black hole

Compute the perihelion precession of Mercury

Model gravitational lensing by a point mass

Calculate the gravitational redshift for light escaping a neutron star

Compute the ISCO (innermost stable circular orbit) for Schwarzschild and Kerr black holes

Model frame dragging near a rotating black hole

Calculate the Hawking temperature for a solar mass black hole

Estimate gravitational wave strain from a binary black hole merger

Fluid Dynamics

Simulate laminar flow between two parallel plates (Poiseuille flow)

Model vortex shedding behind a cylinder at Re=100

Compute the lift and drag coefficients for an airfoil at various angles of attack

Simulate the Rayleigh-Taylor instability at a density interface

Model turbulent flow in a pipe using k-epsilon model

Calculate the pressure drop in a pipe network with branching

Simulate a hydraulic jump in a channel

Model the Kelvin-Helmholtz instability between two fluid layers

Compute the terminal velocity of a sphere falling in viscous fluid

Simulate convection in a heated cavity (Rayleigh-Benard)

Waves & Optics

Simulate single-slit diffraction and compute the intensity pattern

Model a Fabry-Perot interferometer and find the transmission spectrum

Calculate the dispersion relation for light in a plasma

Simulate total internal reflection and evanescent waves

Model a Michelson interferometer with misaligned mirrors

Compute the diffraction pattern from a circular aperture (Airy disk)

Simulate pulse propagation in a dispersive medium with group velocity dispersion

Model the Doppler shift of a moving source with a stationary observer

Calculate the Brewster angle for glass-air interface

Simulate holographic reconstruction from an interference pattern

Acoustics

Model standing waves in a pipe (open and closed ends)

Simulate the Doppler effect for a moving ambulance

Calculate the resonant frequencies of a rectangular room

Model sound propagation through layered media with impedance mismatch

Simulate acoustic focusing by a parabolic reflector

Compute the directivity pattern of a speaker array

Model the beat frequency between two slightly detuned sources

Simulate acoustic wave diffraction around a barrier

Calculate the transmission loss through a wall at different frequencies

Model the cochlea as a tapered transmission line

Nuclear & Particle Physics

Calculate binding energy per nucleon using the semi-empirical mass formula

Model radioactive decay chains (U-238 to Pb-206)

Compute the cross-section for Rutherford scattering

Simulate a particle shower in a calorimeter

Calculate the Q-value for various nuclear reactions

Model beta decay spectrum including neutrino kinematics

Compute the Bethe-Bloch energy loss for a muon in iron

Simulate pair production and annihilation

Calculate the lifetime of a muon including time dilation

Model nucleosynthesis in stellar interiors

Condensed Matter

Compute the band structure of a 1D crystal with a periodic potential

Model electron transport in a semiconductor using drift-diffusion

Calculate the density of states for a 2D electron gas

Simulate phonon dispersion in a diatomic chain

Model superconductivity using BCS theory - find the gap energy

Compute the Hall effect in a 2D electron gas

Simulate magnetic domains and hysteresis in a ferromagnet

Model the quantum Hall effect at various filling factors

Calculate the optical conductivity of graphene

Simulate Anderson localization in a disordered 1D system

Plasma Physics

Compute the Debye length for a plasma at given temperature and density

Model plasma oscillations and find the plasma frequency

Simulate particle motion in a magnetic mirror

Calculate the cyclotron and synchrotron radiation from a relativistic electron

Model magnetic reconnection in a current sheet

Compute the dielectric function of a plasma

Simulate Landau damping of an electrostatic wave

Model a tokamak equilibrium with given pressure profile

Calculate the Alfven wave speed in the solar corona

Simulate plasma instabilities (e.g., two-stream instability)

Astrophysics

Model stellar structure using polytropic equations of state

Calculate the Chandrasekhar mass limit for white dwarfs

Simulate the Jeans instability for gravitational collapse

Model accretion disk dynamics around a black hole

Compute the synchrotron spectrum from relativistic electrons

Simulate cosmic ray propagation in the galaxy

Model supernova light curves with radioactive decay heating

Calculate the temperature profile of a protoplanetary disk

Simulate gravitational N-body dynamics for a star cluster

Model pulsar spin-down and magnetic field evolution