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

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

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

410
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...
410
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

424
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,...
424
The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

62.0K
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
62.0K
Electron Orbital Model01:18

Electron Orbital Model

77.3K
Orbitals are the areas outside of the atomic nucleus where electrons are most likely to reside. They are characterized by different energy levels, shapes, and three-dimensional orientations. The location of electrons is described most generally by a shell or principal energy level, then by a subshell within each shell, and finally, by individual orbitals found within the subshells.
The first shell is closest to the nucleus, and it has only one subshell with a single spherical orbital called the...
77.3K
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

447
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
447
Modeling with Differential Equations01:25

Modeling with Differential Equations

278
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...
278

You might also read

Related Articles

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

Sort by
Same author

Selective intraoperative cholangiography: A retrospective single-centre analysis compared with national data and implications for surgical training.

Langenbeck's archives of surgery·2026
Same author

[The robot in the operating room - Robotic surgery in modern healthcare].

MMW Fortschritte der Medizin·2026
Same author

Conversion Rate in Laparoscopic Cholecystectomy as a Critical Benchmark.

Journal of laparoendoscopic & advanced surgical techniques. Part A·2026
Same author

The ultrafast pixel array camera system and its applications in high energy density physics.

The Review of scientific instruments·2022
Same author

CT Fluoroscopy-Guided Drain Placement to Treat Infected Gastric Leakage after Sleeve Gastrectomy: Technical and Clinical Outcome of 31 Procedures.

RoFo : Fortschritte auf dem Gebiete der Rontgenstrahlen und der Nuklearmedizin·2019
Same author

Safety and applicability of a pre-stage public access ventilator for trained laypersons: a proof of principle study.

BMC emergency medicine·2017

Related Experiment Video

Updated: Apr 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

9.1K

Numerical modeling considerations for an applied nonlinear Schrödinger equation.

Todd A Pitts, Mark R Laine, Jens Schwarz

    Applied Optics
    |May 14, 2015
    PubMed
    Summary
    This summary is machine-generated.

    Numerical methods significantly impact high-intensity optical pulse propagation simulations. Careful consideration of discrete implementations and operator coefficient calculations is crucial for accurate results in computational physics.

    More Related Videos

    Setting Limits on Supersymmetry Using Simplified Models
    07:46

    Setting Limits on Supersymmetry Using Simplified Models

    Published on: November 15, 2013

    9.0K
    Generation and Coherent Control of Pulsed Quantum Frequency Combs
    06:42

    Generation and Coherent Control of Pulsed Quantum Frequency Combs

    Published on: June 8, 2018

    9.8K

    Related Experiment Videos

    Last Updated: Apr 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

    9.1K
    Setting Limits on Supersymmetry Using Simplified Models
    07:46

    Setting Limits on Supersymmetry Using Simplified Models

    Published on: November 15, 2013

    9.0K
    Generation and Coherent Control of Pulsed Quantum Frequency Combs
    06:42

    Generation and Coherent Control of Pulsed Quantum Frequency Combs

    Published on: June 8, 2018

    9.8K

    Area of Science:

    • Nonlinear optics
    • Computational physics
    • Numerical methods

    Background:

    • High-intensity optical pulse propagation involves complex physical phenomena.
    • Accurate simulation requires robust numerical frameworks to model these effects.

    Purpose of the Study:

    • To investigate the influence of numerical methods on nonlinear optical propagation models.
    • To highlight potential errors arising from discrete implementations and operator coefficient calculations.

    Main Methods:

    • A split-step numerical framework was employed for nonlinear optical propagation.
    • Variable stencil-size Crank-Nicolson finite-difference method for the linear step.
    • Two distinct nonlinear integration schemes were utilized for the nonlinear step.

    Main Results:

    • Numerical effects can introduce significant errors in simulations of optical pulse propagation.
    • Increased operator support size and sampling frequency do not always guarantee accuracy.
    • The method for obtaining finite-difference operator coefficients critically affects simulation outcomes.
    • Plausible but incorrect solutions can emerge due to numerical artifacts.

    Conclusions:

    • Precise descriptions of numerical methods are essential for interpreting computational physics results.
    • Ensuring proper interpretation and reproducibility requires full disclosure of simulation methodologies.
    • Awareness of numerical limitations is vital for advancing the field of nonlinear optics.