Entanglements do exist, despite what atheists say

By entanglement I mean some discreet event between two or more chains. Discreet means that I can say at what time the entanglement appeared, when did it disappear, which monomers of which chains have participated etc. This might be contrasted with the tube or mean field approach which assumes a more uniform and continuous entanglement field, created by many chains.

In order to see entanglement clearly in molecular dynamics (MD) simulations, we have to get rid of fast and rather chaotic motion on short time scales (below tau_e). One way to do this is by time and ensemble averaging. Here is the video of two chains selected from the melt, which are clearly entangled. The details of the simulations can be found in our paper, the chains are slightly semi-flexible (kb=3, N=100). What you see is not the chain position, but position of tube axis of each chain. The tube axis for each configuration is defined in the following way: I start m jobs (m=50 in this case) from the same initial configuration, run them for about tau_e, average position of each monomer over this time, and then average results over ensemble. The resulting tube axis is much much smoother then the chains themselves, and (hopefully) most of fast degrees of freedom are averaged out. This creates some very clear pictures - enjoy.


The green chain has its ends fixed, the purple is free. In the beginning the entanglement is very strong. At frame 19 it becomes weaker (look at the chain end), and at frame 53 they completely disentangle.

The disentanglement process is clearly illustrated by plotting the minimal distance between the tube axis of this pair of chains as a function of time. If the chains are entangled, it remains very small (of order one atom).

Surprisingly, this is not an exotic case. In this particular melt (with about 15-20 entanglements per chain according to usual definitions), almost each chain has such a strong or "double" entanglement. But of course they are not all the story - there are much more weaker entanglements.

The reasons for starting this blog

This blog was inspired by reading a book called Wikinomics - a very optimistic and up-bit praise of openness and sharing. One of the main ideas of the book is that these two do not necessarily contradict competition, even in business. For example, IBM spends now $100M a year to fund Linux development, and find that it saves money. Another example is human genome project, partially sponsored by big pharmaceutical companies, but all results are published in public domain. The companies benefit from sharing if several conditions are in place:

• they encourage a wide community to co-create new intellectual property (IP). This widens the number of enthusiastic consumers (who become prosumers using book's terminology), and also helps to advance the field as a whole.
  
• the shared part of IP is not their main area of profit-making. For example, IBM makes money on servers and network solutions, and they benefit from having a free stable operating system.
• Putting results in public domain prevents competitors from patenting the information crucial to the business.
  

If it works is business, can it also work in science, and, in particular, in our beloved field of entangled polymer dynamics? At the moment, we hold on to our ideas until they are published or presented at the conference. Some people do not present unpublished results at conferences, but majority do. Most of people are afraid that somebody will publish their ideas before they do, or will develop them further and better than they do. So can we really benefit from sharing and more openness?

This blog is an experiment designed to answer this question.

However, of course I have a bit of theory as well. This are the arguments why me and you might benefit from contributing to these pages and share your ideas with the community:

• you might have more ideas than you and your co-workers can test. In this case you can post some of them here. I can envision several possible positive outputs
1. somebody tried it already and rejected
2. somebody wants to try it and collaborate with you
   
3. somebody can criticize this idea in the comment and explain why it will not work


• you want to discuss a subject you feel passionate about and want to hear the comments from your colleagues across the world. You can do it here at leisurely pace rather than wait until the next conference and discuss it in a queue for coffee with each individual separately.
  
• You want to explain your ideas presented elsewhere in this informal forum, and to hear the feedback.

Of course I will not be able to judge whether the experiment agrees with the theory since I am a bit biased - I want it to succeed because I invested some time in it. But the potential benefits will be much bigger than that. The best possible result will be that we as a field advance faster and more effectively than other fields, and will be viewed from outside as the successful branch of science worth investing into. We might even solve the whole problem in our lifetime.