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

289
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...
289
Relation between Mathematical Equations and Block Diagrams01:20

Relation between Mathematical Equations and Block Diagrams

3.9K
In a spring-mass-damper system, the second-order differential equation describes the dynamic behavior of the system. When transformed into the Laplace domain under zero initial conditions, this equation can be effectively analyzed and manipulated. The transformation into the Laplace domain converts differential equations into algebraic equations, simplifying the process of isolating the output.
3.9K
Pharmacodynamic Models: Link Model and Systems Pharmacodynamic Model01:14

Pharmacodynamic Models: Link Model and Systems Pharmacodynamic Model

128
The link model is a fundamental pharmacokinetic-pharmacodynamic (PK–PD) approach to account for delayed drug responses when the observed effect does not immediately correlate with the drug's plasma concentration peak. This delay is mathematically addressed by introducing an effect compartment concentration, Ce, which is kinetically linked to the plasma concentration, Cp, via a first-order rate constant, ke0. The linkage allows for a more accurate prediction of drug effects over time. A...
128
Kinematic Equations - III01:18

Kinematic Equations - III

12.6K
The first two kinematic equations have time as a variable, but the third kinematic equation is independent of time. This equation expresses final velocity as a function of the acceleration and distance over which it acts. The fourth kinematic equation does not have an acceleration term and provides the final position of the object at time t in terms of the initial and final velocities. This equation is useful when the value of the constant acceleration is unknown.
Using the kinematic equations,...
12.6K
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

427
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,...
427
Introduction to Differential Equations01:20

Introduction to Differential Equations

461
A differential equation is a mathematical expression that establishes a relationship between a function and its derivatives. These equations are fundamental in modeling dynamic systems across various fields of science and engineering. The order of a differential equation is defined by the highest order derivative present in the equation. A first-order differential equation includes only the first derivative, while a second-order differential equation includes up to the second derivative of the...
461

You might also read

Related Articles

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

Sort by
Same author

Practical phylogenetic usage of theoretical advances in distance-based tree learning.

BMC bioinformatics·2026
Same author

Inference in spreading processes with neural-network priors.

Physical review. E·2026
Same author

Dynamical cavity method for hypergraphs and its application to quenches in the k-XOR-SAT problem.

Physical review. E·2025
Same author

Integer traffic assignment problem: Algorithms and insights on random graphs.

Physical review. E·2025
Same author

Learning of networked spreading models from noisy and incomplete data.

Physical review. E·2024
Same author

Dynamical regimes of diffusion models.

Nature communications·2024
Same journal

Tension on dsDNA bound to ssDNA-RecA filaments may play an important role in driving efficient and accurate homology recognition and strand exchange.

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Amplitude-phase coupling drives chimera states in globally coupled laser networks [Phys. Rev. E 91, 040901(R) (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Shapes of sedimenting soft elastic capsules in a viscous fluid [Phys. Rev. E 92, 033003 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Attenuation of excitation decay rate due to collective effect [Phys. Rev. E 90, 022142 (2014)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Role of connectivity and fluctuations in the nucleation of calcium waves in cardiac cells [Phys. Rev. E 92, 052715 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Lattice Boltzmann approach for complex nonequilibrium flows [Phys. Rev. E 92, 043308 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
See all related articles

Related Experiment Video

Updated: Apr 17, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

9.1K

Dynamic message-passing equations for models with unidirectional dynamics.

Andrey Y Lokhov1, Marc Mézard2, Lenka Zdeborová3

  • 1Université Paris-Sud/CNRS, LPTMS, UMR8626, Bât. 100, 91405 Orsay, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 14, 2015
PubMed
Summary
This summary is machine-generated.

Researchers developed a general method using the dynamic cavity method to solve complex disordered out-of-equilibrium models. This approach, applicable to unidirectional dynamics, offers accurate approximations for real-world network dynamics.

More Related Videos

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
06:37

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

4.3K
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

3.5K

Related Experiment Videos

Last Updated: Apr 17, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

9.1K
Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
06:37

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

4.3K
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

3.5K

Area of Science:

  • Statistical physics
  • Complex systems dynamics
  • Computational modeling

Background:

  • Disordered out-of-equilibrium models are crucial across scientific disciplines.
  • Quantifying their dynamics presents significant challenges.
  • Existing methods often lack generality or applicability to complex networks.

Purpose of the Study:

  • To develop a general procedure for deriving dynamic message-passing equations.
  • To provide a solvable framework for a broad class of unidirectional dynamical models.
  • To offer accurate analytical approximations for dynamics on real-world networks.

Main Methods:

  • Utilized the dynamic cavity method applied to time trajectories.
  • Constructed general dynamic message-passing equations.
  • Focused on models exhibiting unidirectional dynamics.

Main Results:

  • Established a general procedure for deriving dynamic message-passing equations.
  • Demonstrated that unidirectionality is key to solvability.
  • Showed asymptotic exactness on locally treelike graphs.
  • Confirmed good analytical approximations for real-world network dynamics.

Conclusions:

  • The dynamic cavity method provides a powerful tool for analyzing disordered out-of-equilibrium systems.
  • Unidirectional dynamics simplify complex systems, enabling analytical solutions.
  • The derived equations offer a valuable approximation for real-world network behavior.