Two ways to solve inhomogeneous elasticity
Direct iterative perturbation and equivalent eigenstrain, with derivations, editable notebooks and independent checks.
Run and explore the solvers →Mesoscale Microstructure
Modeling.
Learn the physics. Understand the numerical method. Run a simulation and check its results.
Experiments, models and movies.
Download all Julia + NumPy examples ↓
Explore computed results, understand the equations and run the same model in Julia or NumPy.
Elastic Stress Effects Laboratory
Misfit, habit lines, elastic kernels, phase interactions and soft or hard plates. Change the inputs and compare the resulting stresses and elastic energies.
Open the laboratory →PINNs, explained simply
Adjust a curve, test its physics, then learn how diffusion profiles can reveal unknown properties.
Start the PINN lesson →JULIA + NUMPY · HIGH-RESOLUTION MOVIESMonte Carlo: spins and grain growth
256 × 256 Ising and Potts simulations from the course.
Open the Monte Carlo lab →LIVE INTERACTIVE SIMULATION · JULIA + NUMPY SOURCEThe ink-drop experiment
Change the molecule count and step length, follow one molecule, and compare spreading with the diffusion prediction.
Open the interactive experiment →JULIA + NUMPYDiffusion through Fourier modes
Watch short wavelengths disappear first.
Open worked example →JULIA + NUMPYChemical spinodal decomposition
See how small composition fluctuations grow during spinodal decomposition.
Open worked example →JULIA + NUMPYElasticity reshapes phase separation
Use the elastic energy kernel from my teaching notebook in a phase-field calculation.
Open worked example →A SUGGESTED LEARNING PATHStart with a question.
Start with a question.
End with a checked result.
- 1
Thermodynamics & fields
Understand free energy, chemical potential, conserved fields and nonconserved order parameters.
- 2
Equations & discretization
Connect the Cahn–Hilliard and Allen–Cahn equations to finite-difference and spectral methods.
- 3
Verification before interpretation
Check conservation, time-step sensitivity, grid convergence and the relevant energy balance.
- 4
Coupled physics & performance
Introduce elasticity or additional fields, then explore parallel CPU and GPU implementations.
CODES, GUIDES & LEARNING MATERIAL
25 resourcesExplore the library.
Python calculations developed in notebook cells
Build the complete Python examples in explained cells, inspect plots and diagnostics, and run the notebooks in Jupyter.
Explore the notebook lessons ↗Developing teaching codes in steps
Write and test a small part before continuing: cluster labeling, diffusion, random walks, phase separation, Monte Carlo and spatial correlations.
Open the code lessons ↗Ternary spinodal decomposition in NumPy
Develop my ternary phase-separation calculation in nine checked steps, then save composition fields for structure and correlation analysis.
Open the notebook lesson ↗Bicontinuity and connected phases
Inspect measured connectivity in 2D and 3D simulations and explore the routes and connected networks within each phase.
Open the tutorial ↗Topology and connectivity of microstructures
Animate cluster labeling and periodic winding, then compare connected components, loops and percolation in editable patterns.
Open the tutorial ↗My NRCM phase-field workshop examples
Work through my original C examples for spinodal decomposition and precipitate growth, with equations, input files and run instructions.
Open the tutorial ↗Elastic Stress Effects Laboratory
Explore elastic stability, misfit tensors, self- and cross-interaction kernels, interface conditions and inhomogeneous elastic fields.
Open the tutorial ↗Two ways to solve inhomogeneous elasticity
Corrected course notebook and two fully explained solvers, with stress maps, orientation sweeps and independent validation.
Run and explore the solvers ↗PINNs, explained simply
Interactive equation and boundary checks, a staged diffusion inverse problem, and the complete teaching notebook.
Explore the PINN lesson ↗Monte Carlo: Ising and Potts
256 × 256 course simulations with high-resolution movies, diagnostics, and Julia/NumPy source.
Open Monte Carlo lab ↗Elasticity reshapes phase separation
Compare chemical phase separation with homogeneous elasticity and examine how misfit and elastic constants change the calculated microstructure.
Work through the lesson ↗Chemical spinodal decomposition
Follow composition fluctuations as they develop into domains, and check conservation and free-energy changes in a Cahn–Hilliard simulation.
Work through the lesson ↗Diffusion through Fourier modes
Watch Fourier modes decay during diffusion and compare the numerical solution with an analytical benchmark.
Work through the lesson ↗The ink-drop experiment
Connect random molecular motion to spreading with an interactive ink-drop experiment and Julia and NumPy random-walk codes.
Work through the lesson ↗MicroSim: microstructure simulator
An open-source collection of phase-field solvers for CPU and GPU architectures. Start here for the full software stack.
Source code ↗MicroSim documentation
Installation and solver documentation for preparing, running and understanding a MicroSim calculation.
Read documentation ↗Binary spinodal decomposition
My repository for studying spinodal decomposition in binary systems using a spectral method.
Explore repository ↗A reproducible Cahn–Hilliard example
A small Python example with periodic boundaries, mean-composition checks and an energy diagnostic. Includes the source for this website’s illustrative images.
Work through the example ↗MicroSim example simulations
Example simulations supplied with the MicroSim repository. Follow the instructions for the chosen solver and record its version.
View examples ↗GPU phase-field: KKS-CuFFT
Explore the CUDA and FFT-based KKS solver module in MicroSim. Consult the repository requirements before compiling.
Explore module ↗Parallel GPU phase-field: KKS-FD-CUDA-MPI
The finite-difference CUDA/MPI module for parallel phase-field simulations in the MicroSim stack.
Explore module ↗MicroSim workshop videos
The MicroSim team’s channel for demonstrations, tutorials and workshop recordings.
Watch tutorials ↗MS5033: Mesoscale Microstructure Modeling
Course folder with Julia examples, computational notebooks, assignments and simulation videos. Topics include random walks, coarse graining, variational methods, Fourier methods and phase-field modeling. Classroom topics also include elastic stress effects on microstructural evolution. Access is subject to the folder’s Google Drive permissions.
Open course folder ↗3D connectivity explorer
Rotate the simulated interface and inspect connected networks and periodic routes in both phases.
Open the explorer ↗Lab 01: Thermodynamics
Use Gibbs energy-composition curves and equal chemical potentials to calculate equilibrium phase compositions and amounts.
Open Lab 01 ↗No resources match your search. Try another topic or choose “All resources”.
How the simulations are calculated.
I explain the governing equations and numerical methods used in these examples, together with the parameters, units and boundary conditions. I include numerical checks to help assess the results, such as whether a conserved quantity remains constant and whether reducing the grid spacing or time step changes the solution.
How I develop my codes.
I start with a small calculation, check its result and then add the next part. These lessons follow the same sequence, with explanations and checks at each stage. Open the worked Python, Julia and C lessons →