Langevin Curve Fitting for Magnetization and Applied Field Relationship

In summary, the conversation discusses a problem with using a curve fitting algorithm on a given distribution W(x). The algorithm being used is 'Origin 7' and the person is looking for help in finding A for a problem of the type M_i=M(H_i,T_i) within MATLAB. They also mention needing to learn about 'Nonlinear least squares optimization' and suggest looking into the Levenberg-Marquardt method.
  • #1
mhill
189
1
hi, there my question is let's suppose we have the magnetization (M) versus the applied field (H) as

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

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 [tex] W(x_i) [/tex] 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.
 
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  • #2
What data do you have? Next, what does [tex]W(x_i ) (x_i )[/tex] mean? Could you give it analytical? Do you want to find A, and have a set of data like M_i=M(H_i,T_i) where _i is an index of your data points? Is x_i a random number or what?

I know how to find A for a problem of the type M_i=M(H_i,T_i) within MATLAB but that maby not help you, but the idea is based on non-linear least square minimization.
 
  • #3
thank you, if possible where could i learn 'Nonlinear least squares optimization' ??
 
  • #4
Levenberg-Marquardt method... try looking for that.
 

1. What is the Langevin curve fitting method?

The Langevin curve fitting method is a mathematical technique used to model the relationship between magnetization and applied field in magnetic materials. It is based on the Langevin function, which describes the magnetization of a material as a function of temperature and applied field.

2. How does the Langevin curve fitting method work?

The Langevin curve fitting method involves fitting a theoretical Langevin function to experimental data points of magnetization and applied field. This is done by adjusting the parameters of the Langevin function until it closely matches the experimental data. The resulting curve can then be used to predict the magnetization of the material at different applied fields.

3. What are the advantages of using the Langevin curve fitting method?

The Langevin curve fitting method allows for a more accurate and precise determination of the relationship between magnetization and applied field in magnetic materials. It also takes into account the effects of temperature and applied field on the magnetization, making it a more comprehensive approach compared to simpler linear regression methods.

4. What are the limitations of the Langevin curve fitting method?

One limitation of the Langevin curve fitting method is that it requires a large amount of experimental data points to accurately fit the curve. Additionally, it may not be suitable for materials with complex magnetic properties or those that exhibit non-Langevin behavior.

5. How is the accuracy of the Langevin curve fitting method evaluated?

The accuracy of the Langevin curve fitting method can be evaluated by comparing the predicted magnetization values from the fitted curve to experimental data not used in the fitting process. The closer the predicted values are to the actual experimental values, the higher the accuracy of the curve fitting.

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