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 Van der Waals Equation01:26

The Van der Waals Equation

214
The ideal gas law is based on two simplifying assumptions: first, that there are no intermolecular attractions between gas molecules, and second, that the volume occupied by the molecules themselves is negligible compared with the volume of the container. However, these assumptions don't hold up under all conditions - specifically, at high pressures and low temperatures, as gas tends to deviate from ideal gas behavior.The van der Waals equation is an enhanced version of the ideal gas law,...
214
Chemical Equations03:10

Chemical Equations

66.9K
Chemical equations represent the identities and relative quantities of substances involved in a chemical reaction. The substances undergoing reaction are called reactants, and their formulas are placed on the left side of the equation. The substances generated by the reaction are called products, and their formulas are placed on the right side of the equation. Plus signs (+) separate individual reactant and product formulas, and an arrow (→) separates the reactant and product (left and...
66.9K
Van der Waals Equation01:10

Van der Waals Equation

4.7K
The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the...
4.7K
The Nernst Equation02:59

The Nernst Equation

33.3K
Nonstandard Reaction Conditions
The interconnection between standard cell potentials and various thermodynamic parameters such as the standard free energy change ΔG° and equilibrium constant K has been previously explored. For example, a redox reaction involving zinc(II) and tin(II) ions at 1 M concentration with Eºcell = +0.291 V and ΔG° = −56.2 kJ is spontaneous.
33.3K
Debye–Huckel–Onsager Conductance Equation01:28

Debye–Huckel–Onsager Conductance Equation

285
The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect.
285
Chemical Equilibria: Systematic Approach to Equilibrium Calculations01:21

Chemical Equilibria: Systematic Approach to Equilibrium Calculations

1.8K
Equilibrium calculations for systems involving multiple equilibria are often complex. For example, to calculate the solubility of a sparingly soluble salt in an aqueous solution in the presence of a common ion, one must consider all the equilibria in this solution. Calculations for these systems can be complicated and tedious, so a systematic approach with a series of steps is often helpful. The process is detailed below.
The first step is to identify all the chemical reactions involved, The...
1.8K

You might also read

Related Articles

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

Sort by
Same author

Scalable, fast and accurate differential gene expression testing from millions of cells of multiple patients.

Nature communications·2026
Same author

Model reduction, coherence, and information transfer in stochastic biochemical systems.

Physical review. E·2026
Same author

CRAK-Velo: chromatin accessibility kinetics integration improves RNA velocity estimation.

Genome biology·2026
Same author

Efficiency, accuracy and robustness of probability generating function based parameter inference method for stochastic biochemical reactions.

PLoS computational biology·2026
Same author

Extending differential gene expression testing to handle genome aneuploidy in cancer.

PLoS computational biology·2026
Same author

Interpretable learning of temporal cellular dynamics from single-cell data.

Cell reports methods·2026

Related Experiment Video

Updated: Apr 27, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

7.6K

The complex chemical Langevin equation.

David Schnoerr1, Guido Sanguinetti2, Ramon Grima1

  • 1School of Biological Sciences, University of Edinburgh, United Kingdom.

The Journal of Chemical Physics
|July 17, 2014
PubMed
Summary
This summary is machine-generated.

The chemical Langevin equation (CLE) can break down for small molecule numbers. Extending the CLE to complex space eliminates this issue and improves accuracy for chemical system simulations.

More Related Videos

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

6.0K
Ligand-Mediated Nucleation and Growth of Palladium Metal Nanoparticles
11:54

Ligand-Mediated Nucleation and Growth of Palladium Metal Nanoparticles

Published on: June 25, 2018

9.9K

Related Experiment Videos

Last Updated: Apr 27, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

7.6K
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

6.0K
Ligand-Mediated Nucleation and Growth of Palladium Metal Nanoparticles
11:54

Ligand-Mediated Nucleation and Growth of Palladium Metal Nanoparticles

Published on: June 25, 2018

9.9K

Area of Science:

  • Computational chemistry
  • Chemical kinetics
  • Biophysics

Background:

  • The chemical Langevin equation (CLE) is widely used for simulating chemical system dynamics.
  • A key limitation of the CLE is its tendency to break down in finite time when molecule numbers become small, due to issues with square roots of negative quantities.

Purpose of the Study:

  • To address the breakdown issue of the chemical Langevin equation.
  • To evaluate existing correction methods for the CLE and propose a novel solution.
  • To restore the accuracy of CLE simulations, particularly for unimolecular systems.

Main Methods:

  • Investigating the intrinsic nature of the CLE breakdown.
  • Analyzing the artifacts introduced by existing CLE correction methods.
  • Extending the domain of the CLE to complex space (Complex CLE).
  • Comparing simulation results with the chemical master equation and other approximations.

Main Results:

  • The breakdown of the CLE is an intrinsic problem, not solely a numerical integration issue.
  • Existing CLE correction methods introduce undesirable artifacts and lead to inaccurate predictions, especially for unimolecular systems.
  • The Complex CLE eliminates breakdown and accurately predicts mean concentrations and fluctuation variances for unimolecular systems.
  • The Complex CLE provides a more accurate approximation of the chemical master equation for biochemical circuits than other methods.

Conclusions:

  • Extending the CLE to complex space resolves its finite-time breakdown.
  • The Complex CLE offers a physically interpretable and more accurate simulation method for chemical and biochemical systems.
  • This approach improves upon existing CLE corrections, linear-noise approximation, and moment-closure approximations.