53 lines
5.4 KiB
Markdown
53 lines
5.4 KiB
Markdown
|
||
---
|
||
|
||
"Act as an 'MCM Problem A Outstanding Winner + Strict Thesis Writing Coach'. I have uploaded the following files (you can read them directly):
|
||
|
||
1. Official Problem PDF (2026 MCM Problem A)
|
||
2. Our modeling/paper draft (including continuous-time model, variable definitions, derivations)
|
||
3. Numerical Calculation & Verification: Prompts + Output Results (including TTE tables, scenario analysis, robustness/step-size checks, UQ/Monte Carlo, sensitivity, and all other numerical values)
|
||
4. Paper Structure 2 (may contain errors/omissions, serves only as a reference; you need to critically absorb and improve upon it)
|
||
|
||
【Your Task】
|
||
Generate only the complete paper content corresponding to the 'Original Problem Second Sub-question (Time-to-Empty predictions)' (this can be used as a major chapter/subsection group in the final paper, ready for insertion). You must fill in the values from the 'Numerical Calculation & Verification Output Results' one by one into the main text, tables, and comparative conclusions. Fabricating any values is strictly prohibited.
|
||
|
||
【Must-Meet Problem Requirements (Cover every point, no omissions)】
|
||
A. Use the model to calculate/approximate the time-to-empty (TTE) under different initial charge levels and different usage scenarios.
|
||
B. Compare predictions with 'observed or reasonable behavior': provide justifications/consistency explanations, and quantify uncertainty.
|
||
C. Explain differences in results: point out specific drivers for each type of 'rapid drain' (e.g., screen/CPU/network/signal/temperature/background, etc.) and explain the mechanism chain.
|
||
D. Answer: 'Which activities/conditions reduce battery life the most? Which have surprisingly little impact?' Use the values extracted from the output results to support this.
|
||
|
||
【Workflow (Please execute in order and reflect in the final output)】
|
||
Step 1 — Reading & Extraction
|
||
|
||
1. Pinpoint and restate the requirements of the second sub-question from the original PDF (restate in your own words).
|
||
2. Extract all values and conclusions directly related to the second question from the 'Numerical Calculation & Verification Output Results' (including at least but not limited to: TTE for different z0, termination reasons, t*, avg_P, max_I, peak temperature; scenario comparison table ΔTTE; driver ranking; mean/quantiles/CI/survival curve key points for UQ; whether robustness/step-size checks passed, etc.).
|
||
3. If a certain type of value cannot be found in the files: explicitly state in the corresponding place in the text 'This quantity is not provided in the numerical output file, therefore this paper does not report this value'. Do not fabricate.
|
||
|
||
Step 2 — Generate 'Second Question' Main Text (Ready for Insertion)
|
||
Please output the entire content of this part following 'academic paper standards'. It is recommended to include the following structure (you are allowed to optimize, but it must be complete and logically self-consistent):
|
||
2.1 TTE Definition and Termination Criteria (event function/cutoff condition/interpolation for t*, and explain why this definition is reasonable)
|
||
2.2 Prediction Setup and Scenario Description (Initial SOC set, usage scenarios/parameters, brief description of simulation step size and numerical method; cite model variable symbols where necessary)
|
||
2.3 Summary of Results: TTE vs. Initial Charge (Must provide a table, values from output results, including key columns like termination reason)
|
||
2.4 Result Comparison: TTE Changes under Different Usage Scenarios & Attribution of 'Rapid Drain' Drivers
|
||
|
||
* Use a table of 'Scenario—TTE—ΔTTE—Termination Reason'
|
||
* Provide mechanistic explanations for the worst/most extreme scenarios (via paths like power, CPL current feedback, Δ approaching 0, temperature/internal resistance changes, etc.)
|
||
2.5 Uncertainty Quantification (Must provide: mean, quantiles or CI; explain that 'unpredictability' comes from input fluctuations rather than pure randomness)
|
||
2.6 Model Strengths/Weaknesses (Where explanatory power is strong vs. where deviations might be large; provide reasons and directions for improvement)
|
||
2.7 Summary: Answer the specific question in one sentence (Max reduction vs. little impact) and support it with your reported values
|
||
|
||
Step 3 — Critical Handling of 'Paper Structure 2'
|
||
|
||
* Do not blindly copy Structure 2; if its logic/order/omissions would cause the second question to fail meeting the requirements, you must point out its deficiencies (1–3 points suffice) and fix them in your generated structure.
|
||
* Your final output should be 'fully responsive to the prompt and capable of scoring high marks even if Structure 2 is wrong'.
|
||
|
||
【Expression & Formatting Requirements】
|
||
|
||
1. Language: Primarily Chinese; English terms (TTE/SOC/CPL, etc.) are allowed where necessary, but symbols and variables must be consistent.
|
||
2. Mathematical Expression: Key definitions and formulas in LaTeX; do not repeat the whole model, only cite model quantities necessary for the second question (e.g., P_tot, V_term, Δ, mechanism of I).
|
||
3. Results must be 'numerically narrated': Every key conclusion must be bound to a number from the output results (e.g., TTE=XX h, ΔTTE=XX h, Termination Reason=XX).
|
||
4. Do not use vague expressions like 'based on common sense/usually/probably' to replace numerical evidence.
|
||
|
||
【Final Output】
|
||
Output only the complete main text for the 'Second Sub-question' (organized by paper paragraphs and subheadings), do not output your thought process, and do not output chapters unrelated to other sub-questions." |