MCM 2026

I and my teammates participated in the 2026 Mathematical Contest in Modeling (MCM). We chose Problem A: Modeling Smartphone Battery Drain and received Honorable Mention (H). Our paper, Making Smartphones Smarter, developed an energy assumption model for smartphone applications. The project brought together mathematical modeling, numerical simulation for physical phenomena, and scientific writing within only 4 days with intensive team efforts.

Problem statement

Read the official 2026 Problem A

Our Model

We developed the framework in three stages: Model I - Baseline discharge: Represent the battery by a simplified Thevenin equivalent circuit and smartphone activities by power loads. Model II - Changing battery characteristics: Allow capacity, internal resistance, and open-circuit voltage to depend on temperature, cycle aging, and SOC. Model III - Thermal-electrical coupling: Add a heat-balance equation so that discharge current produces self-heating, temperature changes battery parameters, and those changes feed back into the electrical response. We compared baseline runtime predictions with published benchmarks for the iPhone 16 Pro Max and Samsung Galaxy S25 Ultra.

My Reflection

Modeling battery drain connected everyday phenomena with physics, mathematics, extensive research, and optimization. Mathematical gaps required rapid learning and AI support. Next, I’ll study uncertainty analysis, multivariable calculus, and physics more deeply.

Paper and Certificate