MODELING AND SIMULATION IN SCIENCE, ENGINEERING, AND ECONOMICS

Lecture notes for an advanced undergraduate course at the Courant Institute of Mathematical Sciences, New York University
Copyright, Charles S. Peskin, 2018 & 2019 & 2020


MECHANICS

Dynamics of Structures: Networks of Springs and Dashpots with Point Masses at the Nodes

Numerical Instability

Structural Dynamics with Stiff Links: The Backward-Euler Method

Interaction of Dynamic Structures with the Ground: Non-Penetration and Sliding Frictional Forces

Dynamics of Rigid Bodies

How the Gyrocompass Points North in a Locally Horizontal Plane

3D Gyrocompass that Aligns with the Earth's Axis

Structural Dynamics with Rigid Links


DETERMINISTIC AND STOCHASTIC CHEMICAL KINETICS

The Law of Mass Action

The Principle of Detailed Balance

Enzyme Kinetics

Monod J, Wyman J, and Changeux J-P: On the Nature of Allosteric Transitions: A Plausible Model
Journal of Molecular Biology 12: 88-118, 1965

Hemeoglobin

Wang G and Peskin CS: Entrainment of a Cellular Circadian Oscillator by Light in the Presence of Molecular Noise
Physical Review E 97, paper number 062416, 2018

Genetic Switch


TRAFFIC

Traffic Simulation on an Arbitrary Network of Roads with Lights at Intersections and Cars that Steer to Destinations

Velocity functions for use in traffic simulations:
v.m and vlag.m


ECONOMICS

Notes on Economic Growth and Price Equilibrium