https://ironegg.com.cn/modeling/ModelingsHugoBlox Kit (https://hugoblox.com)en-ushttps://ironegg.com.cn/media/icon_hu_29d01506278977f5.pnghttps://ironegg.com.cn/modeling/https://ironegg.com.cn/modeling/mcm26/Mon, 01 Jan 0001 00:00:00 +0000https://ironegg.com.cn/modeling/mcm26/<p>I and my teammates participated in the 2026 Mathematical Contest in Modeling (MCM). We chose <strong>Problem A: Modeling Smartphone Battery Drain</strong> and received <strong>Honorable Mention (H)</strong>. Our paper, <em>Making Smartphones Smarter</em>, 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.</p> <h2 id="problem-statement">Problem statement</h2> <p> </p> <h2 id="our-model">Our Model</h2> <p>We developed the framework in three stages: <strong>Model I - Baseline discharge:</strong> Represent the battery by a simplified Thevenin equivalent circuit and smartphone activities by power loads. <strong>Model II - Changing battery characteristics:</strong> Allow capacity, internal resistance, and open-circuit voltage to depend on temperature, cycle aging, and SOC. <strong>Model III - Thermal-electrical coupling:</strong> 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.</p> <h2 id="my-reflection">My Reflection</h2> <p>Modeling battery drain connected everyday phenomena with physics, mathematics, extensive research, and optimization. Mathematical gaps required rapid learning and AI support. Next, I&rsquo;ll study uncertainty analysis, multivariable calculus, and physics more deeply.</p> <h2 id="paper-and-certificate">Paper and Certificate</h2> <style> .ie-document { box-sizing: border-box; display: flex; align-items: center; justify-content: space-between; gap: 20px; margin: 1rem 0; padding: 18px; border: 1px solid #c8d5e1; border-radius: 12px; background: linear-gradient(135deg, #f7fafc, #e8eff5); color: #334155; font-family: inherit; } .ie-document__body { min-width: 0; } .ie-document__kind { display: block; margin: 0 0 5px; color: #47667f; font-family: inherit; font-size: 12px; font-weight: 600; line-height: 1.4; } .ie-document__title { margin: 0; color: #1c3a50; font-family: inherit; font-size: 17px; font-weight: 700; line-height: 1.4; overflow-wrap: anywhere; } .ie-document__description { margin: 8px 0 0; color: inherit; font-family: inherit; font-size: 0.95rem; line-height: 1.6; overflow-wrap: anywhere; } .ie-document__actions { display: flex; flex-shrink: 0; flex-wrap: wrap; gap: 10px; margin-top: 0; } .ie-document__link { box-sizing: border-box; display: inline-flex; align-items: center; justify-content: center; min-width: 44px; min-height: 44px; padding: 10px 14px; border: 1px solid #b7cbdc; border-radius: 8px; background: #e3eef6; color: #203c51; font-family: inherit; font-size: 0.9rem; font-weight: 600; line-height: 1.3; text-align: center; text-decoration: none; } .ie-document__link--download { background: transparent; } .ie-document__link:focus-visible { outline: 2px solid #2b6cb0; outline-offset: 3px; } html.dark .ie-document { border-color: #435366; background: linear-gradient(135deg, #253647, #1c2b38); color: #dce5ec; } html.dark .ie-document__kind { color: #a9c7df; } html.dark .ie-document__title { color: #d4e7f6; } html.dark .ie-document__link { border-color: #5a7186; background: #2b4255; color: #deedf8; } html.dark .ie-document__link--download { background: transparent; } html.dark .ie-document__link:focus-visible { outline-color: #b9dbf5; } @media (max-width: 620px) { .ie-document { flex-direction: column; align-items: flex-start; gap: 0; } .ie-document__actions { margin-top: 12px; } } </style> <article class="ie-document" aria-label="Making Smartphones Smarter - MCM 2026 Competition Paper"> <div class="ie-document__body"> <span class="ie-document__kind"> No. 001 · <time datetime="2026-02-03">2026-02-03</time> · Notes </span> <h3 class="ie-document__title">Making Smartphones Smarter - MCM 2026 Competition Paper</h3> <p class="ie-document__description">smartphone battery drain; continuous-time modeling; equivalent circuit model; state of charge (SOC); battery aging; thermal-electrical coupling;</p> </div> <div class="ie-document__actions"> <a class="ie-document__link" href="https://ironegg.com.cn/modeling/mcm26/mcm-2026-2604636.pdf" target="_blank" rel="noopener" aria-label="Read PDF: Making Smartphones Smarter - MCM 2026 Competition Paper">Read PDF</a> </div> </article> <!-- Save your certificate beside index.md as mcm-2026-certificate.pdf. --> <style> .ie-document { box-sizing: border-box; display: flex; align-items: center; justify-content: space-between; gap: 20px; margin: 1rem 0; padding: 18px; border: 1px solid #c8d5e1; border-radius: 12px; background: linear-gradient(135deg, #f7fafc, #e8eff5); color: #334155; font-family: inherit; } .ie-document__body { min-width: 0; } .ie-document__kind { display: block; margin: 0 0 5px; color: #47667f; font-family: inherit; font-size: 12px; font-weight: 600; line-height: 1.4; } .ie-document__title { margin: 0; color: #1c3a50; font-family: inherit; font-size: 17px; font-weight: 700; line-height: 1.4; overflow-wrap: anywhere; } .ie-document__description { margin: 8px 0 0; color: inherit; font-family: inherit; font-size: 0.95rem; line-height: 1.6; overflow-wrap: anywhere; } .ie-document__actions { display: flex; flex-shrink: 0; flex-wrap: wrap; gap: 10px; margin-top: 0; } .ie-document__link { box-sizing: border-box; display: inline-flex; align-items: center; justify-content: center; min-width: 44px; min-height: 44px; padding: 10px 14px; border: 1px solid #b7cbdc; border-radius: 8px; background: #e3eef6; color: #203c51; font-family: inherit; font-size: 0.9rem; font-weight: 600; line-height: 1.3; text-align: center; text-decoration: none; } .ie-document__link--download { background: transparent; } .ie-document__link:focus-visible { outline: 2px solid #2b6cb0; outline-offset: 3px; } html.dark .ie-document { border-color: #435366; background: linear-gradient(135deg, #253647, #1c2b38); color: #dce5ec; } html.dark .ie-document__kind { color: #a9c7df; } html.dark .ie-document__title { color: #d4e7f6; } html.dark .ie-document__link { border-color: #5a7186; background: #2b4255; color: #deedf8; } html.dark .ie-document__link--download { background: transparent; } html.dark .ie-document__link:focus-visible { outline-color: #b9dbf5; } @media (max-width: 620px) { .ie-document { flex-direction: column; align-items: flex-start; gap: 0; } .ie-document__actions { margin-top: 12px; } } </style> <article class="ie-document" aria-label="MCM 2026 - Honorable Mention Certificate"> <div class="ie-document__body"> <span class="ie-document__kind"> No. 002 · <time datetime="2026-10-08">2026-10-08</time> · Notes </span> <h3 class="ie-document__title">MCM 2026 - Honorable Mention Certificate</h3> <p class="ie-document__description">Mathematical Contest in Modeling; Honorable Mention; smartphone battery modeling</p> </div> <div class="ie-document__actions"> <a class="ie-document__link" href="https://ironegg.com.cn/modeling/mcm26/mcm-2026-certificate.pdf" target="_blank" rel="noopener" aria-label="Read PDF: MCM 2026 - Honorable Mention Certificate">Read PDF</a> </div> </article>https://ironegg.com.cn/modeling/himcm24/Mon, 01 Jan 0001 00:00:00 +0000https://ironegg.com.cn/modeling/himcm24/<p>I follow MIT&rsquo;s open courses to explore key derivations. Starting with single-variable calculus and progressing toward multivariable calculus, I share my notes, worked examples, and reflections on the learning way.</p> <p><strong>Courses:</strong> . . </p>https://ironegg.com.cn/modeling/himcm25/Mon, 01 Jan 0001 00:00:00 +0000https://ironegg.com.cn/modeling/himcm25/<p>I follow MIT&rsquo;s open courses to explore key derivations. Starting with single-variable calculus and progressing toward multivariable calculus, I share my notes, worked examples, and reflections on the learning way.</p> <p><strong>Courses:</strong> . . </p>https://ironegg.com.cn/modeling/himcm26/Mon, 01 Jan 0001 00:00:00 +0000https://ironegg.com.cn/modeling/himcm26/<p>I follow MIT&rsquo;s open courses to explore key derivations. Starting with single-variable calculus and progressing toward multivariable calculus, I share my notes, worked examples, and reflections on the learning way.</p> <p><strong>Courses:</strong> . . </p>https://ironegg.com.cn/modeling/midmcm23/Mon, 01 Jan 0001 00:00:00 +0000https://ironegg.com.cn/modeling/midmcm23/<p>I follow MIT&rsquo;s open courses to explore key derivations. Starting with single-variable calculus and progressing toward multivariable calculus, I share my notes, worked examples, and reflections on the learning way.</p> <p><strong>Courses:</strong> . . </p>