8 "Applied Modeling and Simulation" Posts

Real-world problems explored through mathematics, modeling, simulation, and code. These posts use specific problems as a way to develop broader techniques for reasoning about complex systems.

Modeling Heat Capacity and Evaporation with Python: Why Water Warms Slowly but Cools Fast

Using thermodynamics and Python to explain why pools resist daytime warming but lose heat rapidly at night
 • Category:  Applied Modeling and Simulation  • Tags:  · ·
What You'll Learn
  • Why water’s high specific heat makes a swimming pool warm much more slowly than the surrounding air
  • Why evaporation can remove heat from water faster than sunlight replaces it
  • How convection, radiation, solar absorption, and evaporation combine in a surface energy balance
  • How to translate conservation of energy into a Python model of water temperature
  • Why covering a pool can dramatically reduce nighttime heat loss
  • How simulation can reveal the effects of weather, geometry, and surface conditions on water temperature

The Five-Second Rule Explored with Math & Python

Why germs transfer immediately, and how math reveals what really happens after food hits the floor
 • Category:  Applied Modeling and Simulation  • Tags:  · ·
What You'll Learn
  • Why germs begin transferring to food as soon as it touches a surface
  • How moisture, contact area, and surface texture affect contamination
  • Why germ transfer happens fastest during the first moments of contact
  • How an exponential curve can model contamination over time
  • How calculus reveals the changing rate of germ transfer
  • How Python can estimate when contamination crosses a chosen threshold

The Meeting Diet: An Optimization Approach to Your Calendar

How optimization can help you decide which meetings deserve your limited time and energy
 • Category:  Applied Modeling and Simulation  • Tags:  · · ·
What You'll Learn
  • How to turn meeting choices into a mathematical optimization problem
  • How time and mental energy can be modeled as separate constraints
  • How a 0/1 knapsack model chooses the most valuable combination of meetings
  • How Python and PuLP can solve a meeting schedule automatically
  • How AI can scaffold optimization code when you give it the right mathematical structure
  • How simulation and visualization can reveal which meetings are worth attending