# Orientation distribution function

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1. Dec 4, 2014

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

2. Dec 5, 2014

3. Dec 5, 2014

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

4. Dec 6, 2014

### 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.