CritPt is a public benchmark of research-level physics challenges, built to test whether frontier AI models can carry out genuine physics research reasoning rather than textbook problem solving. The benchmark paper is arXiv:2509.26574 and we recommend reading it before applying. It will tell you quickly whether this work interests you.

Depending on where your publication record fits, that can mean creating problems, solving them, reviewing completed work, or auditing it. We agree the specific assignment with you once you are matched to an area.

This is research-grade work rather than volume work. Whatever you produce has to be complete enough for another specialist in your subfield to follow and verify independently, so written reasoning is part of every assignment.

Research areas in this panel

Two areas, both on the linear stability of buoyancy-driven convection. We match narrowly: you need to have published on convection stability specifically, not on fluid dynamics broadly. Each area lists the methods it requires.

1. Rayleigh-Benard convection: linear stability with mixed boundary conditions: Rayleigh-Benard convection, Boussinesq approximation, linear stability analysis, normal-mode perturbation expansion, mixed mechanical and thermal boundary conditions, fixed-flux thermal forcing, marginal stability analysis, spectral eigenvalue methods.

2. Porous-medium (Rayleigh-Darcy) convection: linear stability: Darcy's law for porous-medium flow, Rayleigh-Darcy convection, Boussinesq buoyancy approximation, linear stability analysis, constant-flux and open boundary conditions, normal-mode perturbation expansion, marginal stability analysis, buoyancy-driven transport in saturated porous layers.

Methods we expect to find in your own publications

You should be able to point to your own papers demonstrating at least one of the following families:

• Boussinesq approximation and buoyancy-driven flow.
• Linear stability analysis and normal-mode perturbation expansion.
• Marginal stability analysis and critical Rayleigh number determination.
• Spectral eigenvalue methods.
• Darcy's law and porous-medium flow.

Working proficiency with LaTeX, Python and Jupyter. Some familiarity with an agentic coding extension in VS Code is useful. Gaps there are acceptable if you declare them honestly.

• You will be engaged as an independent contractor.
• Projects can be extended, shortened, or concluded early depending on needs and performance.
• Your work at Mercor will not involve access to confidential or proprietary information from any employer, client, or institution.

A PhD in fluid mechanics, applied mathematics, mechanical engineering or a closely related field. This is a hard requirement. Postdoctoral researchers, research scientists and junior faculty are the strongest fit. Senior PhD students with a strong first-author record are welcome to apply.

Published work on convection stability specifically. This is the single most common reason we decline otherwise excellent researchers. Command of the methods is not enough if you have not published on the phenomenon itself.

A verifiable publication record. Three to five representative papers with DOIs or arXiv IDs, ideally from the last five years. First author strongly preferred. A journal DOI is expected here, since much of this literature is not on arXiv. Every paper you list will be checked against the public record.

1. Apply and complete the attached form. Basic information, education, research experience, your method self-attestation, and the areas above that you are the best fit for. For each area you select, give a DOI or arXiv ID of your own paper as proof, with your author position and the methods it demonstrates. A selection without proof is not scored.
2. We verify your papers and authorship against the public record.
3. Then one of two things happens. Either we onboard you directly, or we invite you to a short live alignment call to agree the area and the assignment with you.
4. A brief 30 to 45 minute assessment may be added, but only where we need it. Most applicants will not see one.

Work arrangement: Fully remote

• Please note: We are unable to support H1-B or STEM OPT candidates at this time.

• $80 to $110 per hour, set by depth of subdomain match.
• Payments are weekly on Stripe or Wise based on services rendered.