Levenberg-Marquardt Fitting of Nuclear Decay Model

written by
Larry Engelhardt

The Levenberg-Marquardt Fitting of Nuclear Decay Model demonstrates how EJS can be used to fit experimental data. In this simulation, nuclear decay data are used to provide a simple example, but this same process can be applied to any type of data. The sum of squared deviations is minimized but this can be modified to instead minimize the value of the chi-squared or reduced chi-squared deviation but if your data has uncertainty estimates. The Levenberg-Marquardt algorithm is used to carry out the minimization, and you can choose whether you want your theory data to be generated using the analytical function for nuclear activity, A(t) = Ai exp(-λt), or by numerically solving the ODE, dN/dt = -λN, where N represents the number of radioactive nuclei at time t, and using the relation A = Nλ. Note that this ODE could be replaced with a system of several coupled ODEs to simulate more complicated theoretical data.

The Levenberg-Marquardt Fitting of Nuclear Decay Model was created using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_fmu_Fitting_LeastSquares_LevenbergMarquardt.jar file will run the program if Java is installed. You can modify this simulation if you have EJS installed by right-clicking within the plot and selecting "Open Ejs Model" from the pop-up menu item.

Please note that this resource requires
at least version 1.5 of
Java.

Levenberg-Marquardt Fitting of Nuclear Decay Source Code
The source code zip archive contains an EJS-XML representation of the Levenberg-Marquardt Fitting of Nuclear Decay Model. Unzip this archive in your EJS workspace to compile and run this model using EJS. download 11kb .zip
Last Modified: June 10, 2014
previous versions

L. Engelhardt, Computer Program LEVENBERG-MARQUARDT FITTING OF NUCLEAR DECAY MODEL, Version 1.0 (2011), WWW Document, (http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11537&DocID=2457).

L. Engelhardt, Computer Program LEVENBERG-MARQUARDT FITTING OF NUCLEAR DECAY MODEL, Version 1.0 (2011), <http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11537&DocID=2457>.

Engelhardt, L. (2011). Levenberg-Marquardt Fitting of Nuclear Decay Model (Version 1.0) [Computer software]. Retrieved January 16, 2017, from http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11537&DocID=2457

Engelhardt, Larry. "Levenberg-Marquardt Fitting of Nuclear Decay Model." Version 1.0. http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11537&DocID=2457 (accessed 16 January 2017).

%A Larry Engelhardt %T Levenberg-Marquardt Fitting of Nuclear Decay Model %D November 12, 2011 %U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11537&DocID=2457 %O 1.0 %O application/java

%0 Computer Program %A Engelhardt, Larry %D November 12, 2011 %T Levenberg-Marquardt Fitting of Nuclear Decay Model %7 1.0 %8 November 12, 2011 %U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11537&DocID=2457

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The Easy Java Simulations Modeling and Authoring Tool is needed to explore the computational model used in the Levenberg-Marquardt Fitting of Nuclear Decay Model.