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Numerical integration of non-polynomial functions

Submitted by Stephane Bordas on

Hello colleagues,

 Would anybody know good references on numerical integration of non-polynomial functions? It would be enough for me to obtain one-dimensional rules. Of course, it could have impact for XFEM applications, but for another, improved XFEM method that we are developing.

Note  that I am not talking about integrating singularities, but non-polynomial functions. Examples:

sqrt(x)

cos(x)

sin(x)

product of these.

Thanks for any help,

 

Stephane

Any open source code to generate carbon nanotube cap?

Submitted by Damodara Reddy on

Generation of open ends carbon nanotubes coordinates (atomic positions) is easy and the generation of cap for these carbon nanotubes is extremely difficult. Some of the half-fullerenes (C60, C240, C540…) fit as a cap for the armchair and zigzag nanotubes. NanotubeModeler  (http://www.jcrystal.com/products/wincnt/index.htm) software generates the carbon nanotubes with cap but they are limited to few armchair and zigzag configurations.

Mechanics associated with grain-boundary diffusion and sliding in polycrystals and its application to nanocrystals

Submitted by Yujie Wei on

As stated by Richard Vinci and Oliver Kraft in the announcement of 2008 Gordon Research Conference on Thin Film and Small-Scale Mechanical Behavior, there is a compelling need to understand the critical roles of different deformation mechanisms in structures with small characteristic dimensions, like nanocrystals and thin films. We have recently studied deformation behaviors in nanostructured materials and thin films with deformation mechanisms including grain-boundary diffusion, grain-boundary sliding, and grain-interior plasticity. Some interesting mechanical phenomena associated with heterogeneous grain-boundary properties are found and summarized here.

A theory of coupled diffusion and large deformation in polymeric gels

Submitted by Wei Hong on

   A large quantity of small molecules may migrate into a network of long polymers, causing the network to swell, forming an aggregate known as a polymeric gel.  This paper formulates a theory of the coupled mass transport and large deformation.

Need help: Relation between polymer end-to-end distance and mechanical properties

Submitted by ashfaqadnan on

Hi,

I found in polymer books and some literatures that mechanical properties of polymer improve with the increase of their radius of gyration or end-to-end distance for a fixed molecular weight. I, however, could not find any experimental evidence or any physical explanation. 

It will be a great help to me if anyone refer me some literatures that explains the connection between these two parameters.

 Thanks,

Ashfaq Adnan