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

388
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,...
388
Application of Linearization and Approximation01:29

Application of Linearization and Approximation

127
A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
127
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

377
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...
377
Linearization and Approximation01:26

Linearization and Approximation

124
Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
124
Separable Differential Equations01:20

Separable Differential Equations

186
A separable differential equation is a type of first-order differential equation where the derivative dy/dx can be expressed as a product of two functions: one that depends only on x and another that depends only on y. This allows for the rearrangement of the equation so that all terms involving y are on one side, and all terms involving x are on the other. This process, known as the separation of variables, simplifies the process of solving the equation by enabling the integration of both...
186
Linear time-invariant Systems01:23

Linear time-invariant Systems

1.0K
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
1.0K

You might also read

Related Articles

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

Sort by
Same author

TR2-D2: Tree Search Guided Trajectory-Aware Fine-Tuning for Discrete Diffusion.

ArXiv·2025
Same author

SODA: Spectral Orthogonal Decomposition Adaptation for Diffusion Models.

IEEE Winter Conference on Applications of Computer Vision. IEEE Winter Conference on Applications of Computer Vision·2025
Same author

Can specific THz fields induce collective base-flipping in DNA? A stochastic averaging and resonant enhancement investigation based on a new mesoscopic model.

Chaos (Woodbury, N.Y.)·2024
Same author

Dynamic mode decomposition for multiscale nonlinear physics.

Physical review. E·2019
Same author

Analysis and Design of Capacitive Parametric Ultrasonic Transducers for Efficient Ultrasonic Power Transfer Based on a 1-D Lumped Model.

IEEE transactions on ultrasonics, ferroelectrics, and frequency control·2018
Same author

An improved wave-vector frequency-domain method for nonlinear wave modeling.

IEEE transactions on ultrasonics, ferroelectrics, and frequency control·2014

Related Experiment Video

Updated: Mar 12, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

9.0K

Explicit symplectic approximation of nonseparable Hamiltonians: Algorithm and long time performance.

Molei Tao1

  • 1Georgia Institute of Technology, Atlanta, Georgia 30332, USA.

Physical Review. E
|November 15, 2016
PubMed
Summary

This study introduces new explicit symplectic integrators for arbitrary Hamiltonians, offering accurate long-term simulations for mechanical systems. These integrators demonstrate pleasant long-time properties and improved error bounds for integrable systems.

More Related Videos

Robotic Mirror Therapy System for Functional Recovery of Hemiplegic Arms
10:32

Robotic Mirror Therapy System for Functional Recovery of Hemiplegic Arms

Published on: August 15, 2016

16.1K

Related Experiment Videos

Last Updated: Mar 12, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

9.0K
Robotic Mirror Therapy System for Functional Recovery of Hemiplegic Arms
10:32

Robotic Mirror Therapy System for Functional Recovery of Hemiplegic Arms

Published on: August 15, 2016

16.1K

Area of Science:

  • Computational Physics
  • Numerical Analysis
  • Mechanical Systems

Background:

  • Explicit symplectic integrators are crucial for accurate approximations of mechanical systems with separable Hamiltonians.
  • Existing methods face limitations with arbitrary Hamiltonians.

Purpose of the Study:

  • To propose novel explicit integrators for arbitrary Hamiltonians.
  • To ensure symplectic properties in an extended phase space and achieve favorable long-time behavior.

Main Methods:

  • Development of integrators based on a mechanical restraint binding two copies of phase space.
  • Application of backward error analysis, Kolmogorov-Arnold-Moser theory, and multiscale analysis.

Main Results:

  • An error bound of O(Tδ^{l}ω) is established for integrable systems.
  • Satisfactory statistical behaviors were observed for nonintegrable systems, including a nonlinear Schrödinger equation.

Conclusions:

  • The proposed integrators offer a promising approach for accurate and efficient long-term simulations of mechanical systems.
  • These methods extend the applicability of symplectic integration to a broader class of Hamiltonians.