Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Exponential Equations for Modeling Growth02:33

Exponential Equations for Modeling Growth

135
Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is...
135
Population Growth00:57

Population Growth

27.7K
Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.
27.7K
Exponential Equations with Logarithms: Problem Solving01:29

Exponential Equations with Logarithms: Problem Solving

111
In ecological studies, exponential models are often used to predict how populations grow over time under favorable conditions. These models assume that the growth rate is proportional to the current population, leading to continuous and compounding increases.The model expresses the population as a function of time, combining the initial population with a growth factor raised to an exponent involving the growth rate and time. To estimate how long it takes for a population to reach a specific...
111
Generation Time01:22

Generation Time

1.2K
Bacterial generation time, the period required for a bacterial population to double during its exponential growth phase, serves as a critical measure of microbial growth dynamics under optimal conditions. This parameter varies significantly across bacterial species and can be influenced by factors such as temperature, pH, and the availability of nutrients. For example, Escherichia coli can achieve a generation time of approximately 20 minutes, while Mycobacterium tuberculosis exhibits a much...
1.2K
Genetic Drift03:33

Genetic Drift

42.7K
Natural selection—probably the most well-known evolutionary mechanism—increases the prevalence of traits that enhance survival and reproduction. However, evolution does not merely propagate favorable traits, nor does it always benefit populations.
42.7K
Mutation, Gene Flow, and Genetic Drift01:09

Mutation, Gene Flow, and Genetic Drift

61.5K
In a population that is not at Hardy-Weinberg equilibrium, the frequency of alleles changes over time. Therefore, any deviations from the five conditions of Hardy-Weinberg equilibrium can alter the genetic variation of a given population. Conditions that change the genetic variability of a population include mutations, natural selection, non-random mating, gene flow, and genetic drift (small population size).
61.5K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Uncertainty in AI-driven Monte Carlo simulations.

Physical review. E·2026
Same author

Ground State Energy Fluctuations of Pinned Elastic Manifolds.

Journal of statistical physics·2026
Same author

Anomalous Critical Behavior of Driven Disordered Systems Beyond the Overdamped Limit.

Physical review letters·2026
Same author

Mean-field theory for heterogeneous random growth with redistribution.

Physical review. E·2026
Same author

Discontinuity in the distribution of field increments between avalanches in the non-Abelian random field Blume-Emery-Griffiths model with no passing violation.

Physical review. E·2026
Same author

Nonuniqueness of the steady state for run-and-tumble particles with a double-well interaction potential.

Physical review. E·2026
Same journal

Erratum: Low-dimensional model for adaptive networks of spiking neurons [Phys. Rev. E 111, 014422 (2025)].

Physical review. E·2026
Same journal

Disentangling the effects of many-body forces on depletion interactions.

Physical review. E·2026
Same journal

Charge transport and mode transition in dual-energy electron beam diodes.

Physical review. E·2026
Same journal

Optimization of multisite reactions in complex compartmentalized media.

Physical review. E·2026
Same journal

Origin of geometric cohesion in nonconvex granular materials: Interplay between interdigitation and rotational constraints enhancing frictional stability.

Physical review. E·2026
Same journal

Interaction of walkers with a standing Faraday wave.

Physical review. E·2026
See all related articles

Related Experiment Video

Updated: Dec 21, 2025

Precise, High-throughput Analysis of Bacterial Growth
09:00

Precise, High-throughput Analysis of Bacterial Growth

Published on: September 19, 2017

24.7K

Stochastic growth in time-dependent environments.

Guillaume Barraquand1, Pierre Le Doussal1, Alberto Rosso2

  • 1Laboratoire de Physique de l'École Normale Supérieure, ENS, CNRS, Université PSL, Sorbonne Université, Université de Paris, 24 rue Lhomond, 75231 Paris, France.

Physical Review. E
|May 20, 2020
PubMed
Summary
This summary is machine-generated.

This study explores the Kardar-Parisi-Zhang (KPZ) growth equation with time-dependent noise. A critical transition at α=1/2 dictates whether solutions saturate or exhibit scaling behavior, impacting surface growth dynamics.

More Related Videos

High-Throughput Live Imaging of Microcolonies to Measure Heterogeneity in Growth and Gene Expression
12:52

High-Throughput Live Imaging of Microcolonies to Measure Heterogeneity in Growth and Gene Expression

Published on: April 18, 2021

5.3K
Continuous Measurement of Biological Noise in Escherichia Coli Using Time-lapse Microscopy
08:25

Continuous Measurement of Biological Noise in Escherichia Coli Using Time-lapse Microscopy

Published on: April 27, 2021

4.0K

Related Experiment Videos

Last Updated: Dec 21, 2025

Precise, High-throughput Analysis of Bacterial Growth
09:00

Precise, High-throughput Analysis of Bacterial Growth

Published on: September 19, 2017

24.7K
High-Throughput Live Imaging of Microcolonies to Measure Heterogeneity in Growth and Gene Expression
12:52

High-Throughput Live Imaging of Microcolonies to Measure Heterogeneity in Growth and Gene Expression

Published on: April 18, 2021

5.3K
Continuous Measurement of Biological Noise in Escherichia Coli Using Time-lapse Microscopy
08:25

Continuous Measurement of Biological Noise in Escherichia Coli Using Time-lapse Microscopy

Published on: April 27, 2021

4.0K

Area of Science:

  • Statistical Physics
  • Nonlinear Dynamics
  • Surface Growth Phenomena

Background:

  • The Kardar-Parisi-Zhang (KPZ) equation models random surface growth.
  • Understanding the effect of time-dependent noise on KPZ universality classes is crucial.

Purpose of the Study:

  • Investigate the one-dimensional KPZ equation with time-dependent noise variance, c(t) ∝ t^{-α}.
  • Identify critical exponents and scaling behavior for different values of α.

Main Methods:

  • Analytical techniques involving variable transformations to map to constant noise KPZ variants.
  • Exact solution of a discretized log-gamma polymer model.
  • Computational verification through numerical simulations.

Main Results:

  • A phase transition occurs at α=1/2.
  • For α > 1/2, the system saturates to a nonuniversal distribution at large times.
  • For α < 1/2, scaling exponents depend on α, with limiting statistics resembling constant noise cases.

Conclusions:

  • The time-dependence of noise variance significantly alters KPZ universality.
  • The α=1/2 transition point separates distinct large-time behaviors.
  • The findings provide insights into driven systems and non-equilibrium statistical mechanics.