A refreshing review of our new paper on a model of self healing

There are times when one of my less stellar papers, in my opinion, gets accepted for publication without trouble; and, at other times, what I think are very significant papers have lots of trouble.  Perhaps this is a matter of taste, or perhaps papers that are outside the norm are misunderstood and therefore rejected.

As a case in point, I was invited to submit a paper to a special issue of a journal dedicated to self-healing polymers.  The focus of this special issue is on polymers that are made to self heal after mechanical cracking by incorporating tiny reserves of monomer that runs into cracks as they form, thus filling them and repairing the material.

Our work is very different, so I thought that our invitation was an effort by the editors to broaden the scope of the journal.  However, we were shocked to find that our paper was rejected without review based on the assessment that the work was "incremental."  We responded to the editors, reminding them that we were invited to write the paper.  The next email informed us that the editors had made an error,and that the paper would go out for review.

Two reviewers responded and one of them recommended that our paper be rejected on the grounds that the work was incremental.  However, the editor gave us the opportunity to respond.

In the meantime, we had found data at the extremes that were inconsistent with our model.  We fixed the model with one simple change in the underlying assumptions, and the new model fit all of our data. (This in itself is a very interesting story which I will report on later.) We revised the manuscript to include the new data and resubmitted it.

The editors sought an opinion from a forth reviewer.  An excerpt from his/her comments, follow,"One of the reviewers evidently commented that this work is incremental. However, I don’t agree. The authors are clearly refining their model, and this is an entirely new set of data and observations. The authors search for a better physical understanding will naturally require a significant amount of investigation, and it is helpful to the community to see the work as it unfolds, not wait 25 years for a definitive explain‐all paper that may never appear."

We, of course, agree with this reviewer, and are glad that this paper came to a happy ending, especially in light of the fact that I believe that our new results provide important insights that are taking us a step closer to understanding a new phenomena. 

The new version was accepted with minor revisions suggested, which we made.  The paper was then accepted and the page proofs arrived a couple weeks ago.  We fixed minor typos and now the paper is in the queue for publication in the early summer.  I ust learned today that the electronic version is already available online.  It's ironic that we were even invited to provide an artistic rendition of a figure that might be used as a cover photo.  What a difference a revision makes!  From incremental to cover story material with the change of one variable!

For the interested reader, below is the introductory paragraph, which describes our work and how it differs from the norm, "Structural damage and degradation of a polymer is usually associated with cracking. Mitigating damage or developing methods to promote healing in polymeric materials after cracking is an active area of research motivated by its practical utility. White and coworkers reported on a structural polymeric material with the ability to autonomically self-repair cracks. Such polymers incorporate a microencapsulated healing agent that is released in the cracking process with polymerization being triggered by contact of a catalyst with the healing agent, thus bonding the crack faces. White observed as much as 75% recovery in toughness. 

"Our work presented here is different in two regards. First, the sample is a dye-doped polymer rather than a neat polymer and the degradation process is through optically induced burning, so chemical changes are induced rather than solely mechanical/structural damage – though cracking can accompany burning. The dopant molecules thus mediate the phenomena. The degree of damage is observed using optical techniques, the simplest of which is the detection of a color change. Secondly, the healing process is a microscopic one, originating at a molecular level that we believe involves a cooperative process of aggregates of molecules. The polymers of interest to our work have applications as optical materials where photodegradation is a common cause of optical and optoelectronic device failures, either as catastrophic failure or a slow deterioration of performance."

The final paragraph in the conclusion succinctly states what we believe is cool about our work, as follows, "The concept that a material would exhibit such complex behavior without intentional design by the experimenter is an interesting one. Though self-healing is a process with great practical utility, it is intriguing that nature has been kind enough to provide an inherently smart material system that appears to behave in a way contrary to most others; it mediates recovery in a world in which irreversible damage is the norm. Further advances in understanding the physics underlying this phenomena will surely enable new applications that require materials to withstand high light intensities; and, may lead to new physics.

Now the next battle...

Monopoles, electric dipoles, and the inverse square potential

Research is a fulfilling enterprise, especially when it takes us on an unexpected path that leads to new insights even when others may have crossed the same path.

A couple years ago on Christmas eve, I was toying with a calculation based on my realization that a potential of the form V(x) = x^q captures all of the interesting toy models of quantum mechanics such as the harmonic oscillator (q=2), the particle in a box (q = ∞), and the hydrogen atom (q= -1). I wanted to derive a general analytical expression for the energy spectrum as a function of q so that I could analyze the nonlinear-optical properties of all such systems. To my delight, I was able to get such an expression using a mathematical trick. I was am certain that I was not the first to do so, but I nevertheless felt satisfied.

A plot of my results showed a removable singularity at q=0, which corresponds to a free particle that has no bound states (bound states are needed for my calculation of the nonlinear-optical properties), and a divergence at q = -2. I dutifully wrote up the results and left them sitting on my computer for a couple years. The work was given new life when I handed it over to new graduate student.

After working on the problem for a summer and part of a semester, he found a huge literature on the x^-2 potential, the location of the divergence in my plot. It turns out that this potential has all sorts of interesting mathematical problems. It has a continuum of bound states -- very unusual and in fact an impossibility; and, the wave functions and their duals do not span the same space -- a peculiar state of affairs. The known fix, as the student found in the literature, is to exclude a small region near x = 0 and then solve the problem in the limit as this small region tends to zero. Doing so fixes the problems by essentially removing the point-like properties of the dipole. 

The x^-2 potential describes the influence of an electric dipole moment on a point charge. Certainly nature must reconcile these funny mathematical difficulties given that dipoles and point charges exist. But how?

Nature is very clever by not allowing true point electric dipoles to exist.  Instead, all dipoles are extended dipoles where the potential deviates from x^-2 at close range, thus removing the pathological behavior. In fact, this may be the reason why an ideal point dipole is not observed in any particle. If it existed, serious paradoxes would ensue.

The electron has a very tiny electric dipole moment beyond the limits of measurability with today's technology, and arises from the CP-violating part of the CKM matrix in the standard model. The moment is tiny because CP violation involves quarks that are created as virtual particles, interact with the electron, and then are annihilated. As a result, the dipole moment is not a point dipole but is due to a sea of virtual quarks. All elementary particles have only small electric dipole moments with an extended charged cloud, so nature avoids potential pathologies by forbidding point dipoles.

Magnetic dipoles, which are a consequence of moving charges through spin and orbital angular momentum, are a different story. Spin angular momentum does not originate from spread out charge that spins in physical space.The spin anguar momentum lives in its own space so the associated magnetic dipole moment is pointlike, and will lead to pathologies when interacting with a magnetic monopole. Nature has apparently avoided such problems by forbidding the existence of magnetic monopoles. While there are theories that allow for magnetic monopoles, searches for them have come up short and I don't think they will be found.

In summary, the interaction of a point dipole that interacts with a point charge leads to all kinds of pathologies that can only be resolved by demanding that the dipole be an extended object that avoids being a true x^-2 potential. Nature seems to have solved the problem by allowing point electric charges but no point electric dipoles. Magnetic point dipoles, on the other hand exist; but, there are no magnetic monopoles with which they can interact.  The symmetry between the electric and magnetic parts of Maxwell's equations is broken to avoid unphysical behavior.

I cannot claim to be the first person to have this idea and wouldn't be surprised if this argument is common knowledge. Or, my argument may be faulty.  This does not make my musings any less exciting to me. I continue to be in awe of the power of physics, which allows us to ponder domains that are far removed from our daily experiences. My job not only allows me to think of such things, but encourages it; it is indeed a wonderful life

In studying the complex ramifications of the simple x^-2 potential when applied to nonlinear optics leads to insights into why point electric dipoles and magnetic monopoles can't exist.  How can I sleep tonight!

Ambien Rambling II - Your face contains an impressive geography of regions.

I previously posted one of my Ambien-induced ramblings as recorded by my wife.  A much more interesting and complex example of an Ambien rambling took place a few years ago while I was reading in bed.  My wife was apparently falling asleep after taking an Ambien when quite unexpectedly, she sat up and stretched her neck in my direction, placing her head between me and my book.  Her head swaying like a newborn's, she playfully inspected my face, tracing out its contours with her index finger.  "Your face contains an impressive geography of regions," she  informed me.  As if overcome by a stroke of genius, she rolled over and comandeered a notebook and a red pen that she often used for grading.

She proceeded with her narrative, carefully recording each word as she spoke.  When done, she rolled over and fell asleep.  As time passed, my wife used the notebook to jot down ideas, ripping out pages for shopping lists, etc.  While the notebook remained in the bedroom, over time, it thinned out and got used up.  Sadly, the Ambien rambling eventually got separated from the notebook and was lost.

For years, I searched for it.

This past week, we visited out family in Philadelphia, and once again we used Ambien to fight the jet lag.  Our last night in Philadelphia, we took an Ambien at 9:15 pm so that we could get some sleep before getting up at 4:00 am for the early flight.  When we woke up to our phone alarm, Pat was horrified to find that she had sent a text message to our friend,

"Change dinner time on Monday to 7 pm please."

She had no memory of sending the text, but was understandably embarrassed.  She quickly sent an apologetic text message explaining the circumstances.

This incident once again reminded me of the poetic rambling from years past.  Just this morning, my wife was reorganizing a dresser.  As she removed a drawer stuffed with clothing, a piece of paper floated to the floor.  It was the infamous Ambien rambling.  It is reproduced verbatim below. Even under the influence of Ambien, my wife's penmanship is perfect.

"Your face contains an impressive geography of regions. The central nasal range dominates the visual landscape.

"As you speak, the little creatures in your eyes listen and they respond by speaking back. It’s surprising, but they’ve been exposed to the whole vocabulary, just as you. 

"She’s a tender little creature like a small colorful caterpillar – fluffy, but strong enough to stand up with ease. When you would talk she would stand in your eye socket (careful not to get her feet wet in tearducts) and talk back to you. She was your very own, mythical whispering eye."