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Extraction: Partition and Distribution Coefficients

Extraction: Partition and Distribution Coefficients

The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
For extracting a solute from an aqueous phase into an...

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Grid-based partitioning for comparing attractors.

T L Carroll¹, J M Byers¹

¹US Naval Research Lab, Washington, DC 20375, USA.

Physical Review. E

|May 14, 2016

Summary

This summary is machine-generated.

Researchers developed a new method to analyze dynamical systems by partitioning attractors. This technique reveals detailed information about system structure and detects subtle changes in chaotic attractors.

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Area of Science:

Dynamical Systems and Chaos Theory
Information Theory
Nonlinear Dynamics

Background:

Stationary dynamical systems possess characteristic invariant measures or densities.
Understanding attractor structure is crucial for characterizing these systems.
Existing methods may lack the sensitivity to detect subtle changes.

Purpose of the Study:

To develop a novel method for characterizing invariant densities of stationary dynamical systems.
To identify the smallest informative regions within an attractor's phase space.
To create a statistic for quantifying information gain from data partitioning.

Main Methods:

Partitioning attractors into minimal regions containing structural information.
Developing an information-theoretic statistic to assess data partitioning effectiveness.
Applying the method to experimental circuit data and numerically generated chaotic attractors.

Main Results:

The developed method successfully characterizes attractor densities.
Small changes in attractors from circuit experiments were detected.
A large set of numerically generated chaotic attractors were distinguished.

Conclusions:

The new partitioning method effectively characterizes dynamical system densities.
The technique is sensitive enough to detect subtle attractor changes and distinguish between different chaotic systems.
The approach is applicable to signals from any finite-dimensional dynamical system.