$80–110/hr
The role in one line
A physicist with published expertise in stochastic autocatalytic systems solves or audits research-level physics problems in your specialty.
Written by Training Turk from the public listing; it may be incomplete or out of date. Read the full posting on Mercor.
What you would do
- Create novel research problems or solve existing ones in stochastic growth and reaction network dynamics
- Audit solutions submitted by other researchers, checking for mathematical consistency and physical correctness
- Write detailed, publication-ready explanations that allow verification by peers in your field
- Apply chemical master equation and branching process techniques to specialized systems
- Document work in LaTeX with supporting numerical verification in Python or SymPy
Who they are looking for
- Doctoral degree in physics, mathematics, or a related quantitative field
- Published first-author papers on stochastic growth or reaction-network phenomena
- Proficiency with LaTeX, Python, SymPy, Jupyter notebooks and VS Code extensions
- Familiarity with generating-function methods, moment hierarchies, or circulant matrix analysis
- Strong ability to articulate complex reasoning clearly in writing
What the interview is likely to probe
1.Setting up master equations
You must translate physical scenarios into mathematically precise stochastic systems that remain tractable to solve.
Expect something like: “A researcher's autocatalytic cycle model has master equation transition rates that ignore boundary conditions. How do you spot this error, and what does it imply for transient dynamics?”
2.Problem specification clarity
Ambiguous problem statements lead to solutions that satisfy the wrong question; your role requires catching these before they reach evaluation.
Expect something like: “You're asked to create a problem on 'branching processes relevant to oscillations.' What specific context, parameters, and boundary conditions must you specify so another specialist can reproduce your intended solution?”
3.Moment hierarchy closure
Closing the moment hierarchy is the crux of many reaction network problems; mishandled closures produce specious results.
Expect something like: “A solver claims to have integrated the moment equations for a 3-species network with cubic interactions and obtained a stable fixed point at infinite moment order. What closure assumption or error are you likely to investigate first?”
4.Numerical verification design
Symbolic analysis and numerical computation must align; a mismatch reveals either a coding error or a conceptual mistake in the model.
Expect something like: “Your audit finds that a solution's analytic expression for the circulant eigenvalues of a reaction matrix doesn't match the numerical spectrum computed in Python for a concrete parameter set. Where does the discrepancy likely live?”
5.Generating function methodology
Generating functions compress moment information and expose structure; misuse here is subtle but produces incorrect growth rates or stability predictions.
Expect something like: “A problem asks you to determine whether a branching process in your model exhibits exponential growth or sub-exponential growth using generating functions. How do you extract the Malthusian parameter, and what does its sign reveal?”
Exercise you may get
Write a problem on a two-species autocatalytic cycle including solution outline using moment hierarchy methods, then verify predictions numerically in SymPy.
How to prepare
- Review the CritPt benchmark paper to understand the exact scope and style of research problems they accept
- Gather and study 2-3 of your own published papers that best showcase your methods and clarity
- Prepare concrete examples from your research where you designed or validated a novel stochastic model
- Practice writing technical explanations that are accessible to a specialist outside your narrow subfield but rigorous enough for verification
Facts
- Pay
- $80–110/hr
- Commitment
- hourly
- Hours
- 10 per week
- Work arrangement
- remote · Remote
- Domain
- Life, Physical, and Social Science
- Posted
- 9/25/2026
- Open slots
- 3