{"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":"86c86e08-b464-5459-b5b9-23141c16de50","task_key":"train--Challenge~5f59~5fmain","task_revision_id":"1","upstream_id":"Challenge_59_main","short_description":"Consider a simple cubic crystal with a static periodic strain field of long…","config":"","split":"train","body":"{\"code_template\":\"import sympy as sp\\n\\nM = sp.symbols('M')\\nepsilon = sp.symbols('epsilon')\\na = sp.symbols('a')\\n\\ndef answer(M, epsilon, a):\\n    r\\\"\\\"\\\"\\n    Return the expressions of the $n_x$ criteria for structural factor to be nonvanishing\\n    and the corresponding structure factors in Sympy format.\\n\\n    Inputs\\n    ----------\\n    M         : sympy.Symbol\\n        Large integer relating the strain wavelength to the lattice spacing.\\n    epsilon   : sympy.Symbol\\n        Amplitude of the static periodic strain.\\n    a         : sympy.Symbol\\n        Lattice spacing of the simple-cubic crystal.\\n\\n    Outputs\\n    ----------\\n    allowed : set[(sympy.Expr, sympy.Expr)], Set of nonvanishing $n_x$ criteria with corresponding structure factor, {(nx, S)}\\n        nx: sympy.Expr, $n_x$ component of the reciprocal space vector in the lowest possible order Brillouin Zone\\n          for which the structure factor is nonvanishing (besides $n_x = M$).\\n        S: sympy.Expr, corresponding structure factor to the first order in $\\\\varepsilon$\\n    \\\"\\\"\\\"\\n\\n    # ------------------ FILL IN YOUR RESULTS BELOW ------------------\\n    allowed = ...\\n    # ---------------------------------------------------------------\\n\\n    return allowed\",\"problem_description\":\"# Problem setup:\\n\\nConsider a simple cubic crystal with a static periodic strain field of long wavelength described by a displacement vector $\\\\vec{u}=\\\\vec{\\\\varepsilon}\\\\sin(\\\\vec{Q}\\\\cdot\\\\vec{r})$, where $\\\\vec{u}(\\\\vec{r})$ is the vector displacement from the perfect-crystal position for the atom at lattice site $\\\\vec{r}$, and $\\\\vec{Q}$ denotes the wave vector of the displacement wave (not a scattering wave vector).\\n\\nYou may assume that the lattice-wave period is a large integer ($M$) multiple of the lattice spacing $a$ and that all displacements are much smaller than the lattice spacing.\\n\\n\\n\\n# Main problem:\\n\\nCalculate the structure factor to first order in $\\\\varepsilon$ for diffraction peaks at reciprocal space vector $(n_x, n_y, x_z)$ for $\\\\vec{\\\\varepsilon} \\\\parallel [100]$, $\\\\vec{Q} \\\\parallel [100]$. Write down the criteria for the structural factor to be nonvanishing (besides $n_x = M$) in the lowest-possible-order Brillouin Zone and the corresponding structural factor.\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://critpt.com/","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}