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

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...
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
Typical Model Studies01:30

Typical Model Studies

Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
Modeling with Differential Equations01:25

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
The Power Flow Problem and Solution01:26

The Power Flow Problem and Solution

Power flow problem analysis is fundamental for determining real and reactive power flows in network components, such as transmission lines, transformers, and loads. The power system's single-line diagram provides data on the bus, transmission line, and transformer. Each bus k in the system is characterized by four key variables: voltage magnitude Vk​, phase angle δk​, real power Pk​, and reactive power Qk​. Two of these four variables are inputs, while the power flow program computes the...

You might also read

Related Articles

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

Sort by
Same author

Lightweight dual-backbone network with attentional fusion for wound image classification.

Scientific reports·2026
Same author

Correlation of neutrophil- and high-density lipoprotein cholesterol-related inflammatory markers with sarcopenia: Insights from a cross-sectional study.

The Journal of international medical research·2026
Same author

The emerging role of cuproptosis in spinal cord injury.

Frontiers in immunology·2025
Same author

Topological cues of microparticles train stem cells for tissue repair via mechanotransduction.

Bioactive materials·2025
Same author

CO2 response screen in grass Brachypodium reveals the key role of a MAP kinase in CO2-triggered stomatal closure.

Plant physiology·2024
Same author

Integrated image and location analysis for wound classification: a deep learning approach.

Scientific reports·2024

Related Experiment Video

Updated: May 29, 2026

A Computational Modeling Approach to Investigate the Influence of Hyperthermia on the Tumor Microenvironment
10:23

A Computational Modeling Approach to Investigate the Influence of Hyperthermia on the Tumor Microenvironment

Published on: December 1, 2023

ADAPTIVE FINITE ELEMENT MODELING TECHNIQUES FOR THE POISSON-BOLTZMANN EQUATION.

Michael Holst1, James Andrew McCammon, Zeyun Yu

  • 1Department of Mathematics, University of California San Diego, La Jolla CA 92093, Department of Physics, University of California San Diego, La Jolla CA 92093, Department of Chemistry & Biochemistry, University of California San Diego, La Jolla CA 92093, Center for Theoretical Biological Physics (CTBP), University of California San Diego, La Jolla CA 92093, National Biomedical Computational Resource (NBCR), University of California San Diego, La Jolla CA 92093, Howard Hughes Medical Institute (HHMI), University of California San Diego, La Jolla CA 92093.

Communications in Computational Physics
|September 28, 2011
PubMed
Summary

This study introduces a stable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). The new approach enhances numerical stability for biomolecular modeling, ensuring accurate electrostatic potential calculations.

More Related Videos

Lumped-Parameter and Finite Element Modeling of Heart Failure with Preserved Ejection Fraction
09:20

Lumped-Parameter and Finite Element Modeling of Heart Failure with Preserved Ejection Fraction

Published on: February 13, 2021

Related Experiment Videos

Last Updated: May 29, 2026

A Computational Modeling Approach to Investigate the Influence of Hyperthermia on the Tumor Microenvironment
10:23

A Computational Modeling Approach to Investigate the Influence of Hyperthermia on the Tumor Microenvironment

Published on: December 1, 2023

Lumped-Parameter and Finite Element Modeling of Heart Failure with Preserved Ejection Fraction
09:20

Lumped-Parameter and Finite Element Modeling of Heart Failure with Preserved Ejection Fraction

Published on: February 13, 2021

Area of Science:

  • Computational physics
  • Biophysics
  • Numerical analysis

Background:

  • The nonlinear Poisson-Boltzmann equation (PBE) is crucial for modeling electrostatic interactions in biological systems.
  • Existing regularization techniques for PBE, while theoretically sound, suffer from numerical instability in practical applications.
  • Adaptive finite element methods (AFEM) offer a powerful framework for solving complex differential equations like the PBE.

Purpose of the Study:

  • To develop a numerically stable and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE).
  • To address the instability issues associated with previous regularization techniques for the PBE.
  • To provide a robust computational tool for accurate biomolecular modeling.

Main Methods:

  • A modified two-term regularization technique is proposed to improve numerical stability.
  • A priori estimates and Galerkin finite element approximations are established for the regularized problem.
  • A contraction result for the error is proven to demonstrate the accuracy and reliability of the AFEM scheme.
  • Feature-preserving adaptive mesh generation algorithms are developed for biomolecular structures.

Main Results:

  • The new regularization technique exhibits enhanced numerical stability compared to the original approach.
  • The developed AFEM scheme is proven to be accurate and reliable, with a contraction result for the error.
  • The method demonstrates convergence and accuracy in approximating the electrostatic solvation energy of a protein (insulin).
  • Implementation in the Finite Element Toolkit (FETK) validates the stability advantages.

Conclusions:

  • The proposed stable AFEM for the nonlinear PBE offers a reliable and accurate computational method for biomolecular simulations.
  • The modified regularization technique overcomes previous numerical instability issues, enabling practical applications.
  • The integration of feature-preserving mesh generation further enhances the utility of the method for complex biological structures.