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

Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

85
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
85
Navier–Stokes Equations01:28

Navier–Stokes Equations

526
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...
526
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

316
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured...
316
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

62
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
62
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

3.0K
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
3.0K
Second Order systems II01:18

Second Order systems II

115
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
115

You might also read

Related Articles

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

Sort by
Same author

Divergent protein kinase A contributes to the regulation of flagellar waveforms in Leishmania mexicana.

Journal of cell science·2026
Same author

A shear-induced limit on bacterial surface adhesion in fluid flow.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same author

Axonemal dynein contributions to flagellar beat types and waveforms.

bioRxiv : the preprint server for biology·2025
Same author

Designing reaction-cross-diffusion systems with Turing and wave instabilities.

Journal of mathematical biology·2025
Same author

Pattern Formation as a Resilience Mechanism in Cancer Immunotherapy.

Bulletin of mathematical biology·2025
Same author

Pattern formation along signaling gradients driven by active droplet behavior of cell swarms.

Proceedings of the National Academy of Sciences of the United States of America·2025
Same journal

Effects of Seasonal Births and Predation on Disease Spread.

Bulletin of mathematical biology·2026
Same journal

Identifiability, Sensitivity, and Genetic Algorithms in Bacterial Biofilm Selection Models.

Bulletin of mathematical biology·2026
Same journal

Slow Evolution Towards Generalism in a Model of Variable Dietary Range.

Bulletin of mathematical biology·2026
Same journal

CBINN: Cancer Biology-Informed Neural Network for Unknown Parameter Estimation and Missing Physics Identification.

Bulletin of mathematical biology·2026
Same journal

A Cost-Sensitive Behavioral Modeling Analysis of the Early Identification and Control of Infectious Diseases.

Bulletin of mathematical biology·2026
Same journal

Tracking Dynamics of Superspreading Through Contacts, Exposures, and Transmissions in Edge-Based Network Epidemics.

Bulletin of mathematical biology·2026
See all related articles

Related Experiment Video

Updated: Jul 13, 2025

Author Spotlight: Advancing Cell Membrane Biophysics - Exploring Interactions and Challenges Through Experimental and Computational Approaches
07:31

Author Spotlight: Advancing Cell Membrane Biophysics - Exploring Interactions and Challenges Through Experimental and Computational Approaches

Published on: September 1, 2023

2.3K

VisualPDE: Rapid Interactive Simulations of Partial Differential Equations.

Benjamin J Walker1,2, Adam K Townsend3, Alexander K Chudasama3

  • 1Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK.

Bulletin of Mathematical Biology
|October 12, 2023
PubMed
Summary
This summary is machine-generated.

VisualPDE is a new online tool that makes complex nonlinear systems easier to understand through interactive exploration. This open-source solver for partial differential equations enhances education and research by allowing immediate manipulation of models.

Keywords:
Interactive mathematicsSpatial modellingTime-dependent partial differential equationsWeb-based visualisation

More Related Videos

A Modeling and Simulation Method for Preliminary Design of an Electro-Variable Displacement Pump
09:04

A Modeling and Simulation Method for Preliminary Design of an Electro-Variable Displacement Pump

Published on: June 1, 2022

3.1K
Precise Electrochemical Sizing of Individual Electro-Inactive Particles
05:03

Precise Electrochemical Sizing of Individual Electro-Inactive Particles

Published on: August 4, 2023

1.3K

Related Experiment Videos

Last Updated: Jul 13, 2025

Author Spotlight: Advancing Cell Membrane Biophysics - Exploring Interactions and Challenges Through Experimental and Computational Approaches
07:31

Author Spotlight: Advancing Cell Membrane Biophysics - Exploring Interactions and Challenges Through Experimental and Computational Approaches

Published on: September 1, 2023

2.3K
A Modeling and Simulation Method for Preliminary Design of an Electro-Variable Displacement Pump
09:04

A Modeling and Simulation Method for Preliminary Design of an Electro-Variable Displacement Pump

Published on: June 1, 2022

3.1K
Precise Electrochemical Sizing of Individual Electro-Inactive Particles
05:03

Precise Electrochemical Sizing of Individual Electro-Inactive Particles

Published on: August 4, 2023

1.3K

Area of Science:

  • Computational Science
  • Applied Mathematics
  • Nonlinear Dynamics

Background:

  • Computing has transformed the study of complex nonlinear systems, enabling solutions to intractable models and novel visualization techniques.
  • Interactive exploration via ubiquitous computing infrastructure offers a powerful method for understanding complex models.
  • Existing tools often lack the instantaneous and interactive capabilities needed for intuitive exploration of dynamical systems.

Purpose of the Study:

  • To introduce VisualPDE, an online, interactive solver for partial differential equations (PDEs).
  • To facilitate intuitive understanding of abstract dynamical systems concepts through hands-on exploration.
  • To provide a freely available, open-source, and customizable tool for education, research, and knowledge exchange.

Main Methods:

  • Development of an online, interactive solver for 1D and 2D partial differential equation systems.
  • Implementation of features allowing users to explore system responses to changes in parameters, initial conditions, boundary conditions, and spatiotemporal forcing.
  • Design for high customizability and ease of sharing simulations via URLs.

Main Results:

  • VisualPDE enables intuitive understanding of concepts like symmetry-breaking instabilities and bifurcations.
  • The tool allows immediate investigation of how models respond to various dynamic changes.
  • Freely available and open-source, VisualPDE is highly customizable for diverse applications.

Conclusions:

  • VisualPDE offers a powerful, interactive platform for exploring complex nonlinear systems and PDEs.
  • It has significant potential for enhancing teaching, research, and knowledge exchange in mathematical biology and related fields.
  • The tool aims to promote more interactive and accessible mathematical exploration.