Orientation distribution function

[pathfinder]

Hi everybody,
i have a problem that i wanted to share with you
if we consider a polycrystal made of cylindrical fibers following a von mises-fisher distribution equation (17) in http://bit.do/vmisesfisher (called orientation distribution function of fibers) . i must change the probability density in equation (28) http://bit.do/e28 with the von mises-fisher than i must follow the steps listed in the article http://bit.do/effectivetensor1 , http://bit.do/effectivetensor2 , http://bit.do/effectivetensor3 so that by using orientation averaging, i find the effective (elasticity) tensor of the polycrystal
it s an optimization problem
arg min of the integral over rotation group of the von mises-fisher distribution multiplied by the distance between the effective tensor of the polycrystal (what we are looking for) and the one of a single cylindrical fiber (given).

if anyone could give ideas about how can i start solving this optimization problem to find the effective tensor of the polycrystal
.
thank you

 

[Stephen Tashi]

Your links produce warnings about a malicious web site. I suggest you give ordinary links instead of those from bit.do.

 

[pathfinder]

sorry Stephen i changed the links

i have a problem that i wanted to share with you
if we consider a polycrystal made of cylindrical fibers following a von mises-fisher distribution equation (17) in http://www.hostingpics.net/viewer.php?id=786125Photo005.jpg (called orientation distribution function of fibers) . i must change the probability density in equation (28) http://www.hostingpics.net/viewer.php?id=235923Photo.jpg with the von mises-fisher than i must follow the steps listed in the article http://www.hostingpics.net/viewer.php?id=555305Photo001.jpg , http://www.hostingpics.net/viewer.php?id=275307Photo002.jpg , http://www.hostingpics.net/viewer.php?id=664133Photo003.jpg so that by using orientation averaging, i find the effective (elasticity) tensor of the polycrystal
it s an optimization problem
arg min of the integral over rotation group of the von mises-fisher distribution multiplied by the distance between the effective tensor of the polycrystal (what we are looking for) and the one of a single cylindrical fiber (given).

if anyone could give ideas about how can i start solving this optimization problem to find the effective tensor of the polycrystal
.
thank you

 

[Stephen Tashi]

I know nothing about this complicated looking problem. I'd be glad to discuss it with you. That will keep the thread alive while you can explain it to me! - and perhaps someone who knows the answer will chime in.

A fundamental question is "What do you consider a solution?" Even before defining whether a solution is a number, a function, a set, animal, vegetable or mineral, we have the question of how specifically it needs to be expressed.

The general problem (I think) is to find argmin...of something. A completely theoretical solution is: argmin ...of the thing = some function or expression expressed abstractly in terms of the variables in the problem. A completely numerical solution is a computer algorithm that produces a big file of numbers. in between these extremes you could have a solution that says if we consider a family of functions defined by some parameters then the answer is approximated by solving a certain system of equations where these parameters are the unknowns - and maybe you have use a computer algorithm to solve the equations numerically.

 

[blue_raver22]

for sharing your problem with us. The orientation distribution function of a polycrystal is an important factor in understanding the mechanical properties of materials. It describes the distribution of orientations of the crystalline fibers in the polycrystal.

To solve the optimization problem you have described, you can start by breaking it down into smaller steps. First, you need to understand the von Mises-Fisher distribution and how it relates to the orientation distribution function. Then, you can use the steps listed in the articles you have mentioned to calculate the effective tensor of the polycrystal.

Next, you can use the optimization equation to find the minimum value of the integral over the rotation group. This can be done using numerical methods or by simplifying the equation to make it more manageable. You may also want to consult with other researchers or experts in the field for guidance and potential solutions.

It is also important to carefully consider the assumptions and limitations of your approach, as well as the accuracy and reliability of your results. Overall, solving this optimization problem will require a deep understanding of the underlying theories and methods, as well as careful calculations and analysis. Good luck in finding a solution!