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Related Concept Videos

Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and Faraday.
Eulerian and Lagrangian Flow Descriptions01:22

Eulerian and Lagrangian Flow Descriptions

Fluid flow analysis is critical in many scientific and engineering disciplines, and two principal approaches are used to describe this flow: the Eulerian and Lagrangian methods. These methods offer different perspectives on monitoring and analyzing the motion of fluids, each with distinct advantages depending on the scenario.
The Eulerian method focuses on fixed points in space where fluid properties, such as velocity, pressure, and temperature, are observed as the fluid moves between these...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Differential Equations: Problem Solving01:21

Differential Equations: Problem Solving

When analyzing the motion of falling objects, it is essential to consider not only the force of gravity but also the opposing force of air resistance. A practical example involves releasing a heavy test weight during a safety check on a ship. As the weight falls from rest, gravity accelerates it downward while air resistance exerts an upward force that increases with velocity. This dynamic interplay of forces is well described by differential equations, which provide a mathematical framework...
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.
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...

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Related Experiment Video

Updated: Jun 4, 2026

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
06:37

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

Differential geometry based solvation model II: Lagrangian formulation.

Zhan Chen1, Nathan A Baker, G W Wei

  • 1Department of Mathematics, Michigan State University, Lansing, MI 48824, USA.

Journal of Mathematical Biology
|February 1, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces a new Lagrangian formulation for solvation models, enhancing biomolecular surface analysis and calculations. The model integrates nonpolar and polar solvation theories, providing accurate solvation free energies and binding affinities.

Related Experiment Videos

Last Updated: Jun 4, 2026

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
06:37

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

Area of Science:

  • Computational Chemistry
  • Biophysics
  • Theoretical Chemistry

Background:

  • Solvation is fundamental to chemical and biological processes.
  • Understanding solvation is crucial for analyzing biomolecular systems.
  • Existing implicit solvent theories often require artificial adjustments for surface representation.

Purpose of the Study:

  • To present a Lagrangian formulation of differential geometry-based solvation models.
  • To analyze the relationship between Eulerian and Lagrangian formalisms for solvation.
  • To develop a unified model combining nonpolar and polar solvation effects.

Main Methods:

  • Utilized differential geometry for describing solvent-solute interfaces.
  • Developed a model integrating scaled particle theory (nonpolar) and Poisson-Boltzmann (polar) theories.
  • Employed a potential-driven geometric flow coupled with Poisson-Boltzmann equations, solved iteratively.

Main Results:

  • Successfully computed solvation free energies and protein-protein binding affinities.
  • Validated the model against experimental data and other theoretical methods.
  • Demonstrated that mean curvature flow yields minimal molecular surfaces and variational procedures yield minimal free energy.

Conclusions:

  • The Lagrangian formulation offers advantages in biomolecular visualization and computational consistency.
  • The unified solvation model accurately predicts solvation properties and binding affinities.
  • The developed computational methods provide robust solutions for complex solvation problems.