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

Reaction Mechanisms: Rate-limiting Step Approximation01:29

Reaction Mechanisms: Rate-limiting Step Approximation

The rate-determining step, or RDS, in a chemical reaction is the slowest step that determines the overall reaction rate. It is identified by using the observed rate law and typically involves approximation methods like the RDS approximation or the steady-state approximation.In the RDS approximation, also known as the rate-limiting-step or equilibrium approximation, the reaction mechanism consists of one or more reversible reactions near equilibrium, followed by a slower RDS, and then one or...
Reaction Mechanisms: The Steady-State Approximation01:26

Reaction Mechanisms: The Steady-State Approximation

The steady-state approximation, also referred to as the quasi-steady-state approximation to differentiate it from a true steady state, is a widely used method for simplifying calculations in complex reaction mechanisms. This approach is particularly useful when dealing with multi-step reactions that involve reverse reactions or several steps, which can significantly increase mathematical complexity and make the reactions nearly unsolvable analytically.The steady-state approximation operates on...
Linearization and Approximation01:26

Linearization and Approximation

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...
Approximate Integration01:24

Approximate Integration

In many practical and theoretical contexts, the exact value of a definite integral may be inaccessible. This limitation typically arises when the antiderivative of a function is either unknown or cannot be expressed in a closed mathematical form. Alternatively, it can occur when a function is defined not by a formula but by a finite set of empirical data points, such as those collected during experiments. In these cases, approximate integration techniques provide a valuable solution.One of the...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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...
The Small x Assumption02:20

The Small x Assumption

If a reaction has a small equilibrium constant, the equilibrium position favors the reactants. In such reactions, a negligible change in concentration may occur if the initial concentrations of reactants are high and the Kc value is small. In such circumstances, the equilibrium concentration is approximately equal to its initial concentration. This estimation can be used to simplify the equilibrium calculations by assuming that some equilibrium concentrations are equal to the initial...

You might also read

Related Articles

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

Sort by
Same author

Dynamics of an outlier in the Gaussian unitary ensemble.

Physical review. E·2026
Same author

From nullomers to abundant motifs: Fractals, CpG Bias, and Chargaff's rules in genomic sequences.

Bio Systems·2025
Same author

Machine learning approach to fast thermal equilibration.

Physical review. E·2025
Same author

Self-organized critical dynamic on the Sierpinski carpet.

Physical review. E·2025
Same author

Analytical results and universal behavior in fast thermal equilibration protocols.

Physical review. E·2024
Same author

Information, Coding, and Biological Function: The Dynamics of Life.

Artificial life·2024

Related Experiment Video

Updated: May 10, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Interacting steps with finite-range interactions: analytical approximation and numerical results.

Diego Felipe Jaramillo1, Gabriel Téllez, Diego Luis González

  • 1Departamento de Física, Universidad de Los Andes, A.A. 4976 Bogotá, Colombia. df.jaramillo326@uniandes.edu.co

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 18, 2013
PubMed
Summary
This summary is machine-generated.

We derived an analytical model for terrace-width distribution in interacting step systems. Including next-nearest neighbor interactions causes modest changes, with distant interactions having negligible effects on surface structure.

More Related Videos

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
10:52

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Published on: April 12, 2019

Related Experiment Videos

Last Updated: May 10, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
10:52

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Published on: April 12, 2019

Area of Science:

  • Surface science and condensed matter physics.
  • Statistical mechanics of interacting systems.

Background:

  • Understanding surface morphology is crucial for catalysis and thin-film growth.
  • Step-edge interactions significantly influence surface structure and properties.

Purpose of the Study:

  • To develop an analytical expression for the terrace-width distribution P(s) in interacting step systems.
  • To investigate the impact of interaction range (q) on surface properties.
  • To provide methods for extracting potential parameters from experimental data.

Main Methods:

  • Analytical calculation of terrace-width distribution.
  • Mapping the step system to an equivalent one-dimensional classical particle system.
  • Validation through numerical simulations and comparison with experimental results.

Main Results:

  • An analytical expression for P(s) was derived, considering nearest- and next-nearest-neighbor interactions.
  • Modest changes in P(s) and correlation functions were observed with next-nearest-neighbor interactions.
  • Distant interactions (q > 2) showed negligible effects on the terrace-width distribution.

Conclusions:

  • The analytical model accurately describes terrace-width distributions for interacting step systems.
  • Next-nearest-neighbor interactions play a minor role in surface morphology for typical conditions.
  • The study offers a framework for analyzing surface structure and potential parameters from experimental data.