Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Continuous Charge Distributions

Continuous Charge Distributions

Imagine a bucket of water. It contains many molecules, of the order of 1026 molecules. Thus, although it contains discrete elements (molecules) at the microscopic level, macroscopically, it can be considered continuous. Small volume elements of water, infinitesimal compared to the bulk of the bucket's volume, still contain many molecules. Under this framework, quantized matter is approximated as continuous for practical purposes.
The electric charge can also be subjected to an analogical...

The Electrical Double Layer

The Electrical Double Layer

In the region where two bulk phases meet, an intricate electric charge distribution arises due to charge transfer, ion adsorption, molecular orientation, and charge distortion. This complex distribution is commonly referred to as the electrical double layer.When a solid electrode interfaces with ions in an electrolyte solution, the speed of electron transfer dictates the rates of oxidation and reduction. The electrode acquires a charge through the escape of atoms into the solution as cations or...

Energy Associated With a Charge Distribution

Energy Associated With a Charge Distribution

The work done to bring a charge through a distance r is given by the potential difference between the initial and the final position. To assemble a collection of point charges, the total work done can be expressed in terms of the product of each pair of charges divided by their separation distance, defined with respect to a suitable origin. Solving this expression gives the energy stored in a point charge distribution.

Multicompartment Models: Overview

Multicompartment Models: Overview

Multicompartment models are mathematical constructs that depict how drugs are distributed and eliminated within the body. They segment the body into several compartments, symbolizing various physiological or anatomical areas connected through drug transfer processes such as absorption, metabolism, distribution, and elimination.
These models offer a more comprehensive representation of drug behavior in the body than one-compartment models. They accommodate the complexity of drug distribution,...

Calculations of Electric Potential II

Calculations of Electric Potential II

An electric dipole is a system of two equal but opposite charges, separated by a fixed distance. This system is used to model many real-world systems, including atomic and molecular interactions. One of these systems is the water molecule, but only under certain circumstances. These circumstances are met inside a microwave oven, where electric fields with alternating directions make the water molecules change orientation. This vibration is equivalent to heat at the molecular level.
Consider a...

Processes at Electrodes

Processes at Electrodes

The electrode interacts with ions in the electrolyte solution at its interface. The rate of oxidation and reduction depends on the speed at which electrons can transfer through this interface. As ions attach to or leave the electrode surface, the electrode acquires a charge, and an electrical potential forms across the interface, making the process more difficult to reach equilibrium. The charge on the electrode affects the local ion concentrations in the solution, though thermal motion...

You might also read

Related Articles

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

Sort by

Same author

Persistent sheaf Laplacian analysis of protein stability and solubility changes upon mutation.

Protein science : a publication of the Protein Society·2026

Same author

Cellular Senescence and the SASP in HFpEF: Pathogenic Mechanisms and Therapeutic Targeting.

International journal of molecular sciences·2026

Same author

Correlated clustering and projection for dimensionality reduction.

Machine learning: science and technology·2026

Same author

Physical Activity interventions on health-related quality of life (HR-QoL) in major depressive disorder (MDD): a systematic review and meta-analysis of randomized controlled trials.

Frontiers in psychiatry·2026

Same author

Value of dual-energy CT parameters DER and DEI in predicting calcium-containing urinary stones and differentiating pure calcium oxalate monohydrate.

American journal of translational research·2026

Same author

A meta-analysis of the incidence proportion of obesity and associated risk factors in patients with schizophrenia.

Frontiers in psychiatry·2026

Search research articles

Related Experiment Video

Updated: May 16, 2026

Finite Element Modelling of a Cellular Electric Microenvironment

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

Variational multiscale models for charge transport.

Guo-Wei Wei¹, Qiong Zheng, Zhan Chen

¹Department of Mathematics Michigan State University, MI 48824, USA ; Department of Electrical and Computer Engineering Michigan State University, MI 48824, USA.

SIAM Review. Society for Industrial and Applied Mathematics

|November 23, 2012

Summary

This summary is machine-generated.

This study introduces variational multiscale models for charge transport in biological and engineering systems. The models use differential geometry and energy functionals to accurately predict electrostatic potential and charge densities, validated with ion channel experiments.

More Related Videos

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Rapid in-silico Battery Electrolyte Electrochemical Reaction Generation using 3T-VASP Multi-Scale Energy Minimization

Rapid in-silico Battery Electrolyte Electrochemical Reaction Generation using 3T-VASP Multi-Scale Energy Minimization

Published on: August 22, 2025

Related Experiment Videos

Last Updated: May 16, 2026

Finite Element Modelling of a Cellular Electric Microenvironment

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Rapid in-silico Battery Electrolyte Electrochemical Reaction Generation using 3T-VASP Multi-Scale Energy Minimization

Rapid in-silico Battery Electrolyte Electrochemical Reaction Generation using 3T-VASP Multi-Scale Energy Minimization

Published on: August 22, 2025

Area of Science:

Multiscale modeling
Computational physics
Mathematical biology

Background:

Charge transport is crucial in diverse systems, from biological ion channels to engineered devices like fuel cells and transistors.
Existing models often struggle with the complexity of heterogeneous systems and the interplay between different physical domains.
A unified approach is needed to accurately describe charge dynamics across various scales.

Purpose of the Study:

To develop novel variational multiscale models for charge transport.
To incorporate differential geometry for geometric separation of macroscopic and microscopic domains.
To couple continuum and discrete descriptions dynamically.

Main Methods:

Constructing a total energy functional including solvation and chemical potential energies.
Deriving coupled Laplace-Beltrami and Poisson-Nernst-Planck (LB-PNP) equations via Euler-Lagrange variation.
Utilizing Boltzmann distribution for computational efficiency, leading to Laplace-Beltrami and Poisson-Boltzmann-Nernst-Planck (LB-PBNP) equations.
Extending models to include fluid dynamics via coupled Navier-Stokes equations.

Main Results:

The derived LB-PNP and LB-PBNP equations accurately predict electrostatic potential and charge species densities.
The LB-PBNP model demonstrates consistency with equilibrium LB-PB theory and recovers LB-PNP predictions at non-equilibrium.
Models were validated using protein molecules and the Gramicidin A ion channel, showing good agreement with experimental current-voltage data.

Conclusions:

The proposed variational multiscale models offer a robust framework for simulating charge transport in complex systems.
The integration of differential geometry and energy minimization provides a powerful tool for understanding electrostatics and ion transport.
The models are computationally efficient and experimentally validated, paving the way for applications in nanotechnology and biophysics.