{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"frontierscience","formal_name":"FrontierScience","introduction":"専門的な科学課題を解く能力を評価するベンチマークです。公開データはolympiadとresearchに分かれ、競技問題と研究課題を区別して扱います。\n\nFrontierScience evaluates the ability to solve expert-level scientific tasks. Its public data separates olympiad and research problems so that competition and research tasks can be examined independently.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/openai/frontierscience","indexing_mode":"noindex"},"task_id":"2a0ed85d-7163-5317-bd65-d1f01ef421db","task_key":"olympiad--test--69bd11e8~2d5f96~2d45dc~2d8123~2db9d800101430","task_revision_id":"1","upstream_id":"69bd11e8-5f96-45dc-8123-b9d800101430","short_description":"Domain Wall 2**","config":"olympiad","split":"test","body":"{\"problem\":\"**Domain Wall 2**\\n\\nConsider a one-dimensional model where the magnetization as a function of the `\\\\(x\\\\)`-coordinate is denoted by `\\\\(M(x)\\\\)`. The energy of the system is\\n\\n`\\\\(E=\\\\int_{-\\\\infty}^{\\\\infty}dx{\\\\left[\\\\frac\\\\rho2{\\\\left(\\\\frac{dM}{dx}\\\\right)}^2+\\\\frac\\\\kappa4{\\\\left(M^2-M_0^2\\\\right)}^2\\\\right]}\\\\)`\\n\\nHere, `\\\\(\\\\rho>0\\\\)`, `\\\\(\\\\kappa>0\\\\)`, and `\\\\(M_0\\\\)` are constants related to the kinetic term and the shapes of the potential respectively.\\n\\nSuppose that the boundary condition is\\n\\n`\\\\(M(\\\\infty)=-M(-\\\\infty)=M_0\\\\)`\\n\\nwhich means the magnetization should gradually change from `\\\\(-M_0\\\\)` to `\\\\(M_0\\\\)` somewhere in space.\\nAt the temperature `\\\\(T=0K\\\\)`,  Determine the expectation value of the energy `\\\\(\\\\langle E\\\\rangle\\\\)` in terms of the parameters of the model.\\n\\nThink step by step and solve the problem below. At the end of your response, write your final answer on a new line starting with “FINAL ANSWER”. It should be an answer to the question such as providing a number, mathematical expression, formula, or entity name, without any extra commentary or providing multiple answer attempts.\",\"subject\":\"physics\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/openai/frontierscience","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}