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

Modeling with Differential Equations01:25

Modeling with Differential Equations

257
Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
257
Laminar and Turbulent Flow01:07

Laminar and Turbulent Flow

11.9K
Fluid dynamics is the study of fluids in motion. Velocity vectors are often used to illustrate fluid motion in applications like meteorology. For example, wind—the fluid motion of air in the atmosphere—can be represented by vectors indicating the speed and direction of the wind at any given point on a map. Another method for representing fluid motion is a streamline. A streamline represents the path of a small volume of fluid as it flows. When the flow pattern changes with time, the...
11.9K
Dynamic Equilibrium02:20

Dynamic Equilibrium

67.3K
A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
67.3K
Navier–Stokes Equations01:28

Navier–Stokes Equations

2.7K
For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
2.7K
Diffusion01:12

Diffusion

230.8K
Diffusion is the passive movement of substances down their concentration gradients—requiring no expenditure of cellular energy. Substances, such as molecules or ions, diffuse from an area of high concentration to an area of low concentration in the cytosol or across membranes. Eventually, the concentration will even out, with the substance moving randomly but causing no net change in concentration. Such a state is called dynamic equilibrium, which is essential for maintaining overall...
230.8K
Diffusion01:21

Diffusion

7.3K
Diffusion is a type of passive transport. In passive transport, a substance tends to move from an area of high concentration to an area of low concentration until the concentration is equal across the space. For example, take the diffusion of substances through the air. When someone opens a perfume bottle in a room filled with people, the perfume is at its highest concentration in the bottle and is at its lowest at the edges of the room. The perfume vapor will diffuse, or spread away, from the...
7.3K

You might also read

Related Articles

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

Sort by
Same author

Fick's law and phase transitions in the Lorentz circuit.

Physical review. E·2026
Same author

Exact Response Theory for Delay Equations.

Entropy (Basel, Switzerland)·2026
Same author

Computing nonequilibrium transport from short-time transients: From Lorentz gas to heat conduction in one-dimensional chains.

The Journal of chemical physics·2026
Same author

Diffusion in the inverted triangular soft Lorentz gas.

Physical review. E·2025
Same author

Anomalous Dynamics of Superparamagnetic Colloidal Microrobots with Tailored Statistics.

Small (Weinheim an der Bergstrasse, Germany)·2025
Same author

Anomalous transport models for fluid classification: insights from an experimentally driven approach.

Discover nano·2025
Same journal

Topological dependence of viral mutation spread in complex host-interaction networks.

Chaos (Woodbury, N.Y.)·2026
Same journal

Multifractal signatures of Hamiltonian chaos in Hyperion's rotational dynamics.

Chaos (Woodbury, N.Y.)·2026
Same journal

Exploring mechanisms for reversal of flow in tunicate hearts.

Chaos (Woodbury, N.Y.)·2026
Same journal

State estimation in spatiotemporal chaos via low-rank StatFEM.

Chaos (Woodbury, N.Y.)·2026
Same journal

Universal response functions in driven dissipative tunneling dynamics.

Chaos (Woodbury, N.Y.)·2026
Same journal

A network-based approach to characterize the dynamics of the coupling field of thermoacoustic oscillators in annular geometry.

Chaos (Woodbury, N.Y.)·2026
See all related articles

Related Experiment Video

Updated: Apr 6, 2026

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior
10:07

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior

Published on: January 31, 2020

6.8K

A simple non-chaotic map generating subdiffusive, diffusive, and superdiffusive dynamics.

Lucia Salari1, Lamberto Rondoni1, Claudio Giberti2

  • 1Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24 I-10129 Torino, Italy.

Chaos (Woodbury, N.Y.)
|August 3, 2015
PubMed
Summary
This summary is machine-generated.

Researchers developed a simple deterministic model, the slicer map, to study normal and anomalous diffusion. This model analytically shows transitions between subdiffusion, normal diffusion, and superdiffusion by varying a single parameter.

More Related Videos

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

9.2K
Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
10:20

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules

Published on: September 5, 2019

8.9K

Related Experiment Videos

Last Updated: Apr 6, 2026

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior
10:07

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior

Published on: January 31, 2020

6.8K
The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

9.2K
Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
10:20

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules

Published on: September 5, 2019

8.9K

Area of Science:

  • Physics
  • Mathematics
  • Dynamical Systems

Background:

  • Analytically tractable models for deterministic diffusion are scarce.
  • Polygonal billiards exhibit normal and anomalous diffusion but are complex to analyze.
  • Simplified models are crucial for understanding diffusion mechanisms.

Purpose of the Study:

  • Introduce a novel, simple, non-chaotic dynamical system (slicer map) to model diffusion.
  • Analyze the system's transport properties and parameter dependence.
  • Investigate the minimal ingredients required for different diffusion regimes.

Main Methods:

  • Developed a model based on an interval exchange transformation lifted to the real line.
  • Ensured distance preservation except at a countable set of points, mimicking non-chaotic billiards.
  • Analytically calculated position moments under parameter variation.

Main Results:

  • The slicer map exhibits a transition from subdiffusion to normal diffusion and then to superdiffusion.
  • Demonstrated analytical calculation of all position moments.
  • Showcased a clear dependence of diffusion type on a single control parameter.

Conclusions:

  • The slicer map provides a tractable model for studying deterministic diffusion regimes.
  • Results offer insights into the parameter sensitivity of diffusion in polygonal billiards.
  • The model's transport properties align with different stochastic processes, explaining matching difficulties.