How to Apply Curve Fitting Algorithms for Magnetization Analysis in Origin 7?

[mhill]

hi, there my question is let's suppose we have the magnetization (M) versus the applied field (H) as

$$M(H,T)= \sum _{n=1}^{N} W(x_i ) (x_i ) Lang (H.A.x_{i}/T)$$

here 'A' is a constant 'T' is the temperature of system Lang(x) is the Langevin function coth(x)-1/x ,

My problem is how to use a curve fitting algorithm to solve the problem ,i am working under the assumption that $$W(x_i)$$ i=1,2,3,...,N is a log normal distribution depending only on the value x_i

my curve fitting program is just 'Origin 7' i need the algorithm to curve-fitting to a certain given distribution W(x) thanks.

P.D in case you see this post in another forum, sorry i made a mistake erase this post and keep only the one made in the 'programming' forum.

 

[lofgran]

Hello,

Thank you for your question. It seems like you are trying to fit a log normal distribution to a set of data points in order to determine the parameters of your model. There are a few different approaches you could take to solve this problem using a curve fitting algorithm.

One approach is to use a least squares fitting method, which involves minimizing the sum of the squared differences between your model and the data points. This can be done using a built-in function in Origin 7 or by writing your own code to perform the fitting.

Another approach is to use a maximum likelihood estimation (MLE) method, which involves finding the parameters that maximize the likelihood of the observed data. This can also be done using a built-in function or by writing your own code.

In either case, you will need to specify the log normal distribution function and the data points you are trying to fit. The algorithm will then calculate the best-fit parameters for the distribution.

I suggest consulting the Origin 7 user manual or seeking help from their support team for more specific instructions on how to perform curve fitting using their software. Additionally, there are many online resources and tutorials available for using curve fitting algorithms in general, so you may find it helpful to do some additional research on this topic.

I hope this helps. Best of luck with your research.

 

[quicknote]

Hi there,

Thank you for your question. Langevin curve fitting is a commonly used technique in data analysis to fit a theoretical curve to a set of experimental data points. In your case, you have magnetization (M) as a function of applied field (H) and temperature (T). The equation you have provided is a sum of Langevin functions with a weight function W(x_i) that follows a log normal distribution. Your goal is to use a curve fitting algorithm to determine the best fit parameters for A, T, and W(x_i).

To solve this problem, you can use a non-linear curve fitting algorithm such as the Levenberg-Marquardt algorithm. This algorithm is commonly used in software packages such as Origin 7 to fit a theoretical curve to experimental data. It works by iteratively adjusting the parameters of the theoretical curve until the sum of squared residuals between the curve and the data points is minimized.

To use this algorithm, you will need to provide initial estimates for the parameters A, T, and W(x_i). These can be based on your knowledge of the system or can be estimated by plotting the data and making an educated guess. Once you have provided these initial estimates, the algorithm will adjust the parameters to find the best fit curve.

In your case, the weight function W(x_i) follows a log normal distribution, which means that it can be described by two parameters: the mean and the standard deviation. To incorporate this into your curve fitting, you can define W(x_i) as W(x_i) = exp(-((x_i - mu)^2)/(2*sigma^2)), where mu and sigma are the mean and standard deviation, respectively. These parameters can also be adjusted by the curve fitting algorithm.

I hope this helps to answer your question and guide you in using the Levenberg-Marquardt algorithm for your curve fitting problem. Best of luck with your research!