Related Experiment Video
Updated: Aug 15, 2026

Precise, High-throughput Analysis of Bacterial Growth
Published on: September 19, 2017
Preferential growth: exact solution of the time-dependent distributions
1Department of Theoretical Physics, Institute of Physics, Technical University of Budapest, Budafoki út 8, H-1111 Budapest, Hungary.
Abstract:
We consider a preferential growth model where particles are added one by one to the system consisting of clusters of particles. A new particle can either form a new cluster (with probability q) or join an already existing cluster with a probability proportional to the size thereof. We calculate exactly the probability Pi(k,t) that the size of the ith cluster at time t is k. We analyze the asymptotics, the scaling properties of the size distribution and of the mean size, as well as the relation of our system to recent network models.
Related Concept Videos
Population Growth
Parametric Survival Analysis: Weibull and Exponential Methods
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
Growth Models with Integration: Problem Solving
Exponential Equations with Logarithms: Problem Solving
Exponential Equations for Modeling Growth
Modeling with Differential Equations

