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

The Swing Equation01:21

The Swing Equation

684
The Swing Equation is a fundamental tool in power system dynamics, especially for analyzing the behavior of generating units like three-phase synchronous generators. This equation emerges from applying Newton's second law to the rotor of a generator, encompassing factors such as inertia, angular acceleration, and the interplay between mechanical and electrical torques.
In a steady-state operation, the mechanical torque (Τm) supplied to the generator is balanced by the electrical torque...
684
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

125
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,...
125
Euler Equations of Motion01:19

Euler Equations of Motion

326
Imagine a rigid body that is rotating at an angular velocity of ω within an inertial frame of reference. Along with this, picture a second rotating frame that is attached to the body itself. This frame moves along with the body and possesses an angular velocity of Ω. The total moment about the center of mass is calculated by adding the rate of change of angular momentum about the center of mass in relation to the rotating frame and the cross-product of the body's angular velocity...
326
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

404
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...
404
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

101
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...
101
Euler's Equations of Motion01:28

Euler's Equations of Motion

567
In fluid mechanics, shear stresses arise from viscosity, which represents a fluid's internal resistance to deformation. For low-viscosity fluids, like water, these stresses are minimal, simplifying flow analysis by allowing the fluid to be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent, leaving only normal stresses, which act perpendicularly to fluid elements. Notably, pressure — defined as the negative of the normal stress — remains...
567

You might also read

Related Articles

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

Sort by
Same author

Fast and Accurate Numerical Integration of the Langevin Equation with Multiplicative Gaussian White Noise.

Entropy (Basel, Switzerland)·2024
Same author

Limit Efficiency of a Silicon Betavoltaic Battery with Tritium Source.

Micromachines·2023
See all related articles

Related Experiment Video

Updated: Sep 13, 2025

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

6.3K

Numerical Generation of Trajectories Statistically Consistent with Stochastic Differential Equations.

Mykhaylo Evstigneev1

  • 1Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John's, NL A1B 3X7, Canada.

Entropy (Basel, Switzerland)
|July 29, 2025
PubMed
Summary

A new numerical method accurately simulates systems described by stochastic differential equations (SDEs) without direct noise simulation. This approach enhances trajectory generation for complex systems by reproducing key statistical properties.

Keywords:
Fokker–Planck equationLangevin equationcomputational physicscumulantsmultiplicative noise

More Related Videos

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

8.0K
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

8.3K

Related Experiment Videos

Last Updated: Sep 13, 2025

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

6.3K
Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

8.0K
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

8.3K

Area of Science:

  • Computational Physics
  • Numerical Analysis
  • Stochastic Processes

Background:

  • Stochastic Differential Equations (SDEs) model complex systems with inherent randomness.
  • Accurate numerical methods are crucial for simulating SDEs, but often require direct noise realization.
  • Existing methods like the Milstein algorithm have limitations in accuracy and computational efficiency.

Purpose of the Study:

  • To develop a novel, weak second-order numerical method for SDE trajectory generation.
  • To bypass direct noise realization for improved computational efficiency.
  • To achieve high accuracy by reproducing cumulants of the state variable.

Main Methods:

  • A weak second-order numerical scheme is proposed, updating system states with independent Gaussian random variables.
  • The method reproduces the first three cumulants of the state variable to second order in time-step size.
  • The update rule is derived from the Fokker-Planck equation in arbitrary dimensions.

Main Results:

  • The developed method demonstrates high accuracy, outperforming the standard Milstein algorithm.
  • Accuracy is validated using Büttiker's ratchet as a test case.
  • The method's second-order accuracy in time-step size is confirmed.

Conclusions:

  • The proposed numerical method offers an accurate and efficient alternative for SDE trajectory generation.
  • It provides a foundation for extending to higher-order approximations of SDE solutions.
  • This approach has broad applicability in fields relying on stochastic modeling.