In partial fulfillment of the requirements for the degree of 

Doctor of Philosophy in Physics

School of Physics Thesis Dissertation Defense

Aryaman Jha

Dr. Jorge Laval, School of Civil and Environmental Engineering, Georgia Institute of Technology (Advisor) 

Dr. Kurt Wiesenfeld, School of Physics, Georgia Institute of Technology (Co-advisor)

Space-time percolation methods for lattice models of vehicular traffic: theory and computation

Date: Thursday, March 5, 2026

Time: 11:00 a.m.

Location: Howey N110 

Virtual: https://gatech.zoom.us/j/99642305500?pwd=rKTDcg9DYpVomo2fAWwcVYC3N6fhyZ.1

Meeting ID: 996 4230 5500 / Passcode: 543200

Committee members:

Dr. Peter Yunker, School of Physics, Georgia Institute of Technology

Dr. Harold Kim, School of Physics, Georgia Institute of Technology

Dr. Predrag Cvitanović, School of Physics, Georgia Institute of Technology

Abstract:

Analysis of nonequilibrium systems lacks a general theory, thus it is useful to explore alternate approaches. Methods for analyzing empirical traffic developed in traffic-flow theory differ significantly from those used to study traffic models in statistical physics. These methods treat space and time on a more equal footing and analyze quantities such as total jam delay not typically studied in physics. This suggests traffic-flow methods may offer a useful perspective for analyzing transport models in physics.

Motivated by questions arising in traffic-flow theory, we study a simple traffic model, elementary cellular automaton rule 184 (ECA 184). Interpreting congestion in its space–time representation as a connected-cluster problem, we numerically analyze the finite-size statistics of jam structures and find scaling behavior consistent with a percolation transition. Key observables, including total delay, relaxation time, and jam lifetimes, exhibit consistent scaling. We also define structures called elementary jams, which greatly simplify the computation of observables and suggest an underlying space–time structure.

Motivated by this numerical evidence for a percolation-like transition in space–time jamming, we develop an analytic description of the transient dynamics of ECA 184. The problem is reformulated in terms of a height function constructed from the initial condition, where macroscopic observables such as total delay and relaxation time, along with microscopic jam statistics, can be expressed as geometric properties of the height function. Their scaling under specific transformations reproduces the numerical exponents and finite-size scaling forms. This approach also admits a renormalization-group interpretation.

Finally, we apply the same space–time clustering analysis to the two-dimensional Biham–Middleton–Levine (BML) model of city traffic, where preliminary results suggest a continuous phase transition not previously reported.