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Gauss's Law: Problem-Solving

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Gauss's law helps determine electric fields even though the law is not directly about electric fields but electric flux. In situations with certain symmetries (spherical, cylindrical, or planar) in the charge distribution, the electric field can be deduced based on the knowledge of the electric flux. In these systems, we can find a Gaussian surface S over which the electric field has a constant magnitude. Furthermore, suppose the electric field is parallel (or antiparallel) to the area vector...

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Updated: Jul 19, 2026

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

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

Published on: February 13, 2021

Generalized finite element solution to one-dimensional flux problems.

G P Todd¹, R H Haschemeyer

¹Department of Biochemistry, Cornell University Medical College, 1300 York Avenue, New York, NY 10021, USA.

Biophysical Chemistry

|June 1, 1983

Summary

A novel finite element numerical solution simplifies simulating one-dimensional flow techniques like chromatography and electrophoresis. This versatile method accommodates diverse physical models and boundary conditions for biological scientists.

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Area of Science:

Biophysics
Computational Biology
Biochemistry

Background:

One-dimensional flow phenomena are crucial in various biological separation techniques.
Existing numerical methods often lack generality and require rederivation for different models or boundary conditions.
Simulating complex solute interactions and transport parameters presents a significant challenge.

Purpose of the Study:

To develop a general and convenient finite element numerical solution for the one-dimensional flow equation.
To create a versatile framework applicable to diverse biological flow techniques.
To simplify the incorporation of various physical models and boundary conditions.

Main Methods:

Derivation of a finite element numerical solution for the general one-dimensional flow equation.
Formulation of the solution in matrix equations for broad applicability.
Development of a method to accommodate diverse column geometries, solute interactions, and transport parameter dependencies.

Main Results:

A generalized numerical solution adaptable to ultracentrifugation, electrophoresis, and chromatography.
The framework accommodates models with position, time, or concentration-dependent transport parameters.
A key advantage is the straightforward application of various boundary conditions without rederiving the core solution.

Conclusions:

The derived finite element solution offers a powerful and flexible tool for simulating one-dimensional flow in biological systems.
This approach significantly enhances the ease of modeling diverse experimental conditions and physical scenarios.
The matrix-based formulation facilitates the incorporation of specific models through simple parameter substitution.