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

Gaussian Elimination: Problem Solving01:30

Gaussian Elimination: Problem Solving

135
Systems of linear equations in several variables are pivotal in modeling complex scenarios involving multiple unknowns and constraints. Such systems are widely used in various fields to represent relationships where several conditions must be simultaneously satisfied. Each variable in the system corresponds to an unknown quantity, while each equation imposes a linear constraint, leading to a structured approach for analyzing and solving real-world problems.A system of three equations with three...
135
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

308
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,...
308
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

875
In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
875
Stability of Conjugated Dienes01:28

Stability of Conjugated Dienes

4.1K
Introduction
A comparison of the enthalpies of hydrogenation of dienes reveals that conjugated dienes release less heat on hydrogenation, rendering them more stable than their nonconjugated analogs.
4.1K
Partial Fractions01:28

Partial Fractions

163
A partial fraction is a component of a rational expression represented as the sum of simpler fractions. When a rational function is expressed as a ratio of two polynomials, it can often be decomposed into a sum of fractions whose denominators are simpler polynomials, typically linear or irreducible quadratic factors. This process is called partial fraction decomposition, and it is used to simplify complex expressions for integration, solving equations, or analysis.Partial fraction decomposition...
163
Routh-Hurwitz Criterion I01:15

Routh-Hurwitz Criterion I

494
Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
494

You might also read

Related Articles

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

Sort by
Same author

EMBEDDED NONLOCAL OPERATOR REGRESSION (ENOR): QUANTIFYING MODEL ERROR IN LEARNING NONLOCAL OPERATORS.

International journal for uncertainty quantification·2026
Same author

Benchmarking the UMA Foundation Interatomic Potential for Gas-Phase Chemical Kinetics.

The journal of physical chemistry. A·2026
Same author

An interpretable machine learning framework for prediction of adsorption energies and generative design of active sites on arbitrary catalysts.

Faraday discussions·2026
Same author

Vibrational Quantum-State-Controlled Reactivity in the O<sub>2</sub><sup>+</sup> + C<sub>3</sub>H<sub>4</sub> Reaction.

The journal of physical chemistry letters·2026
Same author

Methyl Rotor State-Dependent Quenching of OH Tunneling in 2,6-Dimethylphenol.

The journal of physical chemistry letters·2026
Same author

KinCat: Kinetic Monte Carlo Parallel Computations of Surface Kinetics in Heterogeneous Catalysis.

Journal of chemical theory and computation·2026

Related Experiment Video

Updated: Jan 5, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

43.5K

Accelerated Saddle Point Refinement through Full Exploitation of Partial Hessian Diagonalization.

Eric D Hermes1, Khachik Sargsyan1, Habib N Najm1

  • 1Combustion Research Facility , Sandia National Laboratories , Livermore , California 94551-0969 , United States.

Journal of Chemical Theory and Computation
|October 16, 2019
PubMed
Summary

This study introduces a new computational method to speed up the identification of transition states in chemical reactions. The approach accelerates first-order saddle point (FOSP) refinement, reducing computational costs for complex molecular systems.

More Related Videos

Quantifying Intermembrane Distances with Serial Image Dilations
07:45

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

6.7K
Digital Inline Holographic Microscopy DIHM of Weakly-scattering Subjects
10:16

Digital Inline Holographic Microscopy DIHM of Weakly-scattering Subjects

Published on: February 8, 2014

12.6K

Related Experiment Videos

Last Updated: Jan 5, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

43.5K
Quantifying Intermembrane Distances with Serial Image Dilations
07:45

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

6.7K
Digital Inline Holographic Microscopy DIHM of Weakly-scattering Subjects
10:16

Digital Inline Holographic Microscopy DIHM of Weakly-scattering Subjects

Published on: February 8, 2014

12.6K

Area of Science:

  • Computational Chemistry
  • Chemical Dynamics
  • Materials Science

Background:

  • Characterizing reaction pathways computationally is crucial for understanding chemical systems.
  • Identifying first-order saddle point (FOSP) structures on potential energy surfaces (PES) is a common computational bottleneck.
  • Current FOSP refinement methods struggle with large molecular systems due to computational expense.

Purpose of the Study:

  • To develop an accelerated method for FOSP refinement in large molecular systems.
  • To improve the efficiency of computational chemistry calculations for reaction pathway characterization.
  • To overcome the limitations of full Hessian matrix calculations in complex systems.

Main Methods:

  • Developed a novel method to construct an approximate Hessian matrix using iterative diagonalization information.
  • Incorporated this approximate Hessian into FOSP refinement strategies.
  • Evaluated the method's performance on two established FOSP refinement benchmarks.

Main Results:

  • The new method significantly reduces the number of gradient evaluations needed for FOSP convergence.
  • Achieved an average reduction of 50% for one benchmark and 25% for another.
  • Demonstrated improved computational efficiency for refining saddle point structures.

Conclusions:

  • The proposed method offers a computationally efficient alternative for FOSP refinement in large chemical systems.
  • This advancement can accelerate the study of reaction mechanisms, particularly in fields like heterogeneous catalysis.
  • The approach provides a practical solution to a long-standing computational bottleneck in chemical dynamics.