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

State Space Representation01:27

State Space Representation

216
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
216
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

2.6K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
2.6K
Reaction Quotient02:35

Reaction Quotient

48.6K
The status of a reversible reaction is conveniently assessed by evaluating its reaction quotient (Q). For a reversible reaction described by m A + n B ⇌ x C + y D, the reaction quotient is derived directly from the stoichiometry of the balanced equation as
48.6K
Coupled Reactions01:17

Coupled Reactions

7.7K
Cellular processes such as building and breaking down complex molecules occur through stepwise chemical reactions. Some of these chemical reactions are spontaneous and release energy, whereas others require energy to proceed. Cells often couple the energy-releasing reaction with the energy-requiring one to carry out important cell functions. 
Energy in adenosine triphosphate or ATP molecules is easily accessible to do work. ATP powers the majority of energy-requiring cellular reactions....
7.7K
Woodward–Hoffmann Selection Rules and Microscopic Reversibility01:34

Woodward–Hoffmann Selection Rules and Microscopic Reversibility

3.1K
Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
3.1K
Stability of Equilibrium Configuration01:23

Stability of Equilibrium Configuration

458
Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
458

You might also read

Related Articles

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

Sort by
Same author

Am80 (tamibarotene) and ATRA induce highly similar molecular responses and myeloid differentiation in non-APL AML, enhanced by LSD1/GCN5 inhibition and increased RARA expression.

BMC cancer·2026
Same author

Finding Pathways in Reaction Networks Guided by Energy Barriers Using Integer Linear Programing.

Molecular informatics·2026
Same author

Antifungal susceptibility and in vitro virulence characteristics of clinical Magnusiomyces/Saprochaete isolates: a multicenter study from Türkiye.

Scientific reports·2026
Same author

Molecular insights into the oxidative perturbation of VIM-2 metallo-β-lactamase: Active site remodeling restores imipenem susceptibility in Pseudomonas aeruginosa.

Microbial pathogenesis·2026
Same author

Delayed Signaling in Mitotic Checkpoints: Biological Mechanisms and Modeling Perspectives.

Biology·2026
Same author

Artificial intelligence in mitotic checkpoint modeling: transforming our understanding of cellular division through machine learning and predictive biology.

Briefings in bioinformatics·2026
Same journal

MT-MRI for detection of renal interstitial fibrosis in renovascular disease.

Scientific reports·2026
Same journal

Detection of underground objects from GPR data using a lightweight YOLO-based approach.

Scientific reports·2026
Same journal

Early systemic inflammatory-metabolic trajectory phenotypes are associated with survival outcomes in metastatic renal cell carcinoma treated with nivolumab.

Scientific reports·2026
Same journal

Water balance components in a dry-seeded rice-wheat system: Untangling the effects of tillage and mulching practices.

Scientific reports·2026
Same journal

Topological approaches to quantum tensor train compression via ZX-calculus and SVD.

Scientific reports·2026
Same journal

determinants of flood impacts and adaptive capacity among market vendors in Walukuba-Masese, Jinja city, Uganda.

Scientific reports·2026
See all related articles

Related Experiment Video

Updated: Jul 13, 2025

In Situ Monitoring of Diffusion of Guest Molecules in Porous Media Using Electron Paramagnetic Resonance Imaging
06:34

In Situ Monitoring of Diffusion of Guest Molecules in Porous Media Using Electron Paramagnetic Resonance Imaging

Published on: September 2, 2016

6.4K

Computing all persistent subspaces of a reaction-diffusion system.

Stephan Peter1, Linus Woitke2, Peter Dittrich3

  • 1Department of Basic Sciences, Ernst-Abbe University of Applied Sciences Jena, Carl-Zeiss-Promenade 2, 07745, Jena, Germany.

Scientific Reports
|October 11, 2023
PubMed
Summary
This summary is machine-generated.

A new algorithm identifies all potential persistent solutions for reaction-diffusion partial differential equations (PDEs) by analyzing distributed organizations (DOs). This method reveals a hierarchical structure of these solutions, offering insights into PDE complexity.

More Related Videos

Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy
12:15

Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy

Published on: April 9, 2019

8.8K
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

8.2K

Related Experiment Videos

Last Updated: Jul 13, 2025

In Situ Monitoring of Diffusion of Guest Molecules in Porous Media Using Electron Paramagnetic Resonance Imaging
06:34

In Situ Monitoring of Diffusion of Guest Molecules in Porous Media Using Electron Paramagnetic Resonance Imaging

Published on: September 2, 2016

6.4K
Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy
12:15

Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy

Published on: April 9, 2019

8.8K
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

8.2K

Area of Science:

  • Computational chemistry
  • Systems biology
  • Chemical kinetics

Background:

  • Reaction-diffusion partial differential equations (PDEs) model complex spatio-temporal processes.
  • Identifying persistent solutions is crucial for understanding system stability and behavior.
  • Distributed organizations (DOs) have been recently identified as necessary conditions for persistent subspaces.

Purpose of the Study:

  • To develop an algorithm for computing all possible subspaces that can sustain persistent solutions of reaction-diffusion PDEs.
  • To identify and analyze the hierarchy of distributed organizations (DOs) within reaction networks.
  • To provide insights into the complexity of solving reaction-diffusion PDEs.

Main Methods:

  • An algorithm is presented to compute a hierarchy of DOs using a linear programming approach with integer cuts.
  • The algorithm identifies sub-networks that function as DOs, ensuring local closedness and global self-maintenance.
  • It determines organizational reactions and minimal compartmentalization required for subspace persistence.

Main Results:

  • The algorithm computes a hierarchy of DOs, starting from the largest.
  • It identifies organizational reactions and minimal compartmentalization for each persistent subspace.
  • A lattice structure of organizational reactions is proven, encompassing all potentially persistent sets of reactions.

Conclusions:

  • The developed algorithm provides a hierarchical structure of all persistent subspaces for reaction-diffusion PDEs.
  • This framework offers a comprehensive understanding of persistent solutions concerning species and reactions.
  • The study provides practical implications for solving reaction-diffusion PDEs and insights into their computational complexity.