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 Nernst Equation02:59

The Nernst Equation

44.7K
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.
44.7K
Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

912
In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis.
912
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

3.0K
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.
3.0K
Equilibrium Conditions for a Particle01:23

Equilibrium Conditions for a Particle

1.9K
When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
1.9K
The Swing Equation01:21

The Swing Equation

941
The Swing Equation is a fundamental tool in power system dynamics, especially for analyzing the behavior of generating units like three-phase synchronous generators. This equation emerges from applying Newton's second law to the rotor of a generator, encompassing factors such as inertia, angular acceleration, and the interplay between mechanical and electrical torques.
In a steady-state operation, the mechanical torque (Τm) supplied to the generator is balanced by the electrical torque (Τe)...
941
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

528
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from...
528

You might also read

Related Articles

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

Sort by
Same author

Negative feedback and oscillations in a model for mRNA translation.

Journal of the Royal Society, Interface·2025
Same author

On the gain of entrainment in the <i>n</i>-dimensional ribosome flow model.

Journal of the Royal Society, Interface·2023
Same author

Translation in the cell under fierce competition for shared resources: a mathematical model.

Journal of the Royal Society, Interface·2022
Same author

Large-scale mRNA translation and the intricate effects of competition for the finite pool of ribosomes.

Journal of the Royal Society, Interface·2022
Same author

Maximizing average throughput in oscillatory biochemical synthesis systems: an optimal control approach.

Royal Society open science·2021
Same author

A deterministic model for one-dimensional excluded flow with local interactions.

PloS one·2017

Related Experiment Video

Updated: Jul 23, 2026

Optogenetic Entrainment of Hippocampal Theta Oscillations in Behaving Mice
07:33

Optogenetic Entrainment of Hippocampal Theta Oscillations in Behaving Mice

Published on: June 29, 2018

Entrainment in the master equation.

Michael Margaliot1, Lars Grüne2, Thomas Kriecherbauer2

  • 1School of Electrical Engineering and the Sagol School of Neuroscience, Tel-Aviv University, Tel-Aviv 69978, Israel.

Royal Society Open Science
|May 17, 2018
PubMed
Summary

The master equation, crucial in many fields, entrains to periodic excitations. Solutions converge to a periodic state matching the excitation

Keywords:
Metzler matrixasymmetric simple exclusion processcontractive systemscooperative dynamical systemsfirst integralstability

More Related Videos

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

A Method for Tracking the Time Evolution of Steady-State Evoked Potentials
12:03

A Method for Tracking the Time Evolution of Steady-State Evoked Potentials

Published on: May 25, 2019

Related Experiment Videos

Last Updated: Jul 23, 2026

Optogenetic Entrainment of Hippocampal Theta Oscillations in Behaving Mice
07:33

Optogenetic Entrainment of Hippocampal Theta Oscillations in Behaving Mice

Published on: June 29, 2018

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

A Method for Tracking the Time Evolution of Steady-State Evoked Potentials
12:03

A Method for Tracking the Time Evolution of Steady-State Evoked Potentials

Published on: May 25, 2019

Area of Science:

  • Mathematical Physics
  • Systems Biology
  • Statistical Mechanics

Background:

  • The master equation models dynamic systems across diverse scientific disciplines.
  • Periodic transition rates can arise from external periodic forces, such as daily cycles or traffic signals.

Purpose of the Study:

  • To analyze the behavior of master equations with periodic transition rates.
  • To demonstrate the phenomenon of entrainment or phase locking to periodic excitations.

Main Methods:

  • Application of systems and control theory.
  • Mathematical analysis of master equation solutions.

Main Results:

  • Convergence of all solutions to a periodic solution.
  • The period of the solution matches the period of the transition rates.
  • Demonstration of entrainment (phase locking) to periodic driving forces.

Conclusions:

  • Master equations with periodic rates exhibit predictable entrainment behavior.
  • Theoretical results have implications for statistical mechanics and epidemiology models.