{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"critpt","formal_name":"CritPt","introduction":"研究水準の物理問題で、科学的理解と多段階の推論・計算を評価するベンチマークです。公開データには70の課題があり、問題文とコード雛形を組み合わせて解答を構成します。\n\nCritPt evaluates scientific understanding and multi-step reasoning and computation on research-level physics problems. Its public dataset contains 70 challenges with problem descriptions and code templates.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://critpt.com/","indexing_mode":"noindex"},"task_id":"53634481-bef5-5a83-9be9-c3cffe4819f4","task_key":"train--Challenge~5f31~5fmain","task_revision_id":"1","upstream_id":"Challenge_31_main","short_description":"Consider flow between two parallel plates heated from below and cooled from…","config":"","split":"train","body":"{\"code_template\":\"def answer():\\n    r\\\"\\\"\\\"\\n    Return the value of critical Rayleigh number and associated critical horizontal wavenumber.\\n\\n    Inputs\\n    ----------\\n    None\\n\\n    Outputs\\n    ----------\\n    Ra_c: float, critical Rayleigh number\\n    kx: float, associated critical horizontal wavenumber\\n    \\\"\\\"\\\"\\n\\n    # ------------------ FILL IN YOUR RESULTS BELOW ------------------\\n    Ra_c = ...\\n    kx = ...\\n    # ---------------------------------------------------------------\\n\\n    return Ra_c, kx\",\"problem_description\":\"\\n\\n# Problem setup:\\nConsider flow between two parallel plates heated from below and cooled from above (i.e., Rayleigh-Benard convection) with Prandtl number $Pr=1$ and horizontally periodic boundary conditions. The boundary condition on the top wall is free-slip with fixed temperature, and the boundary condition on the bottom wall is no-slip with constant heat flux.\\n\\n\\n# Main problem:\\n What are the critical Rayleigh number (allowing $\\\\pm 0.5$ error) and associated critical horizontal wavenumber (allowing $\\\\pm 0.02$ error), where above this critical Rayleigh number, the conduction base state is linearly unstable?\\n\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://critpt.com/","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}