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A题/数值分析检验/Response/10.md

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+# FINAL_SUMMARY_v1
+
+### TECHNICAL_HIGHLIGHTS_v1
+*   **Signal Quality vs. Power Consumption:** The non-linear signal penalty mechanism $P_{net} \propto (\Psi + \epsilon)^{-\kappa}$ represents the most significant driver of rapid drain. In the "Poor Signal" scenario ($S_4$), the TTE dropped from 4.60h to 2.78h, a reduction of approximately 40%.
+*   **Thermal-Electrochemical Coupling:** Cold ambient conditions ($0^\circ\text{C}$) induce a dual penalty: internal resistance $R_0$ increases via Arrhenius kinetics while effective capacity $Q_{eff}$ is restricted. This shifted the termination reason from a gradual `SOC_ZERO` to a premature `V_CUTOFF` at 3.15h.
+*   **CPL-Induced Voltage Instability:** The Constant Power Load (CPL) requirement forces discharge current $I$ to rise as terminal voltage $V_{term}$ falls. This feedback loop accelerates depletion near the end-of-discharge and increases the risk of voltage collapse ($\Delta \le 0$).
+*   **Worst-Case Impact:** The transition from baseline usage to a sustained poor-signal environment ($S_4$) resulted in the maximum observed TTE reduction of **1.82 hours**.
+
+### MODEL_STRENGTHS_v1
+1.  **Algebraic-Differential Nesting:** By nesting the quadratic CPL current solver within the RK4 integration stages, the model maintains strict physical consistency between power demand and electrochemical state at every sub-step.
+2.  **Continuous Radio Tail Dynamics:** The inclusion of the state variable $w(t)$ with asymmetric time constants ($\tau_{up} \ll \tau_{down}$) allows the model to capture the "tail effect" of high-power network persistence without the numerical overhead of discrete state machines.
+3.  **Rigorous Uncertainty Quantification:** The methodology integrates Saltelli-sampled Sobol indices for parameter sensitivity and Ornstein-Uhlenbeck stochastic processes for usage variability, providing a probabilistic bound on battery life rather than a single point estimate.
+
+### EXECUTIVE_DATA_SNIPPET
+Our model predicts a baseline time-to-empty (TTE) of **4.60h** under standard usage at $25^\circ\text{C}$. Environmental stress testing reveals a **31.5% reduction** in TTE during extreme cold ($0^\circ\text{C}$), primarily driven by increased internal resistance and capacity contraction. Uncertainty Quantification (UQ) analysis, accounting for stochastic fluctuations in user behavior, confirms a **90% survival rate** (probability that the device remains powered) up to **4.53h**, demonstrating that while usage is "unpredictable," the battery behavior remains bounded by identifiable physical constraints.
+
+### FUTURE_WORK_v1
+1.  **Dynamic SOH Aging Laws:** Extend the current framework by implementing a diffusion-limited SEI-layer growth ODE to model long-term capacity fade and resistance growth over hundreds of cycles.
+2.  **Spatial Thermal Distribution:** Transition from a lumped-parameter thermal model to a multi-node spatial network to account for localized heat generation in the CPU and radio modules, enabling more accurate throttling predictions.