Lowlights and misses
Webpages of a group tend to give the impression that the owners just dance smoothly from one highlight to the other. In practice, of course, science hardly ever proceeds that way - more often than not doing physics is a hard struggle with nature and with oneself. On this page, I want to give an example one of the hard points in my career, and of some stupid things I missed.
Solvability as a selection mechanism for interfacial patterns
One of the outstanding issues in the early eighties in the field of interfacial pattern formation was the question what determines the shape and size of a dendrite tip or of a viscous finger. Quite independently, several groups then came with the suggestion that the perturbation theories that had been used up to then were fundamentally flawed. These perturbation approaches were based on starting from the analytic solutions for dendrite and finger shapes in the absence of surface tension. The effects of surface tension were then included perturbatively. In the absence of surface tension effects, however, the moving interface equations for these problems allow for a family of shapes, and the question then arises as to what sets the "selection" of the appropriate zero surface tension finger or dendrite solution. The answer that several groups proposed in the early eighties was that this whole picture is basically wrong. They showed that in simple model equations the surface tension term acts as a singular perturbation, so that one can not do a simple perturbation expansion about the zero surface tension solutions: there are only a discrete set of dendrite or finger shapes for any nonzero surface tension, however small. This is what is sometimes refered to as the solvability theory, and is was argued that the same mechanism applies to the full problem. There is no doubt that this scenario is correct for the simple model equations for moving interfaces in two dimensions, but since the full moving boundary problems are governed by integro-differential equations, it was not so obvious to John Weeks and myself that this was true for the full problem as well. For a long time, too long, we worked hard on this with an open mind about what the final answer could be, but in the end we did not really contribute very much to the solution of the debate. Although I believe the questions that we posed were quite justified, it just gradually became clear that the solvability scenario is correct indeed.
On hindsight, John Weeks and I wasted too much time on this problem, and we should have discussed more actively than we did with proponents of the solvability scenario. One lesson that I've drawn from this period is that one should watch out, in science, not to spend too much time on criticizing others. Instead, it's better to make ones own positive contributions.
How I could have been five years ahead of everyone else in granular media
At an Aspen meeting in the eighties, Steve Lipson from the Technion in Haifa showed me a little demonstration: a cilindrical glass tube of about 15 centimeters long, filled with two types of grains of different size and color. He showed me that if one puts the tube horizontally and makes it turn with the handle that was attached to it, quite soon the grains start to separate into a striped or banded pattern! There was clearly a type of phase separation into bands of one type of grain and of the other. I found this most curious, and did think about it for a while when I was in Aspen, but then forgot about it. It was at least five years later that studies of this type started to appear and attract attention, and that I started to realize that I could have had a headstart in granular media, had I realized the importance of what Steve Lipson had showed me!
How Pierre Hohenberg and I missed the homoclinic solutions
As explained in more detail in my write-up about the Complex Ginzburg Landau equation, in the early nineties, Pierre Hohenberg and I made an extensive study of so-called coherent structures in the this equation. We studied many aspects of front, pulse, source, and sink type solutions. However, although I remember that we briefly discussed some of these on the blackboard, we did not pay attention to coherent structures which correspond to so-called homoclinic orbits in the phase space that describes the flow defined by the o.d.e.'s for the coherent structure solutions that we analyzed. Such a homoclinic orbit solution can be thought of as a localized structure sandwiched between two states on its left and right which are the same. Quite soon after he got his PhD with me in Leiden and had moved to the Niels Bohr Institute in Copenhagen, Martin van Hecke discovered that these homoclinic solutions are not only quite interesting structures, but that they also play an important role in various chaotic regimes of the cubic Complex Ginzburg Landau equation [Phys. Rev. Lett. 80, 1896 (1998)]! This was a great discovery, whose ramifications are still being explored today. So, while I am very happy for Martin and Martin Howard, with whom he explored the issue in depth [Phys. Rev. Lett. 86, 2018 (2001)], and while I feel the pride of a the thesis advisor who sees his former graduate students flourish, I can not help but feel that I was rather stupid myself to overlook the importance of this class of solutions!
But in the end, science is erratic, and I now profit daily from my stupidity at the time: the work on homoclinic solutions gave Martin's career quite a boost, and he is now a colleague of mine in Leiden!
Formation of bands in colloidal solutions
In 1979, someone from Exxon Laboratories discovered that when he left a colloidal solution in a glass cylinder, it would sometimes tend to form a vertically banded stucture. Within a band the density of the colloidal solution was found to be roughly constant, but the density in the successive bands was different. David Huse and I thought quite a bit about this, and actually wrote an article about this suggesting that this might possibly be due to the way the initial colloidal solution was prepared, and that the "shocks" between the bands could be understood in terms of the Burgers equation (see my publication 40 of 1990). This was an interesting suggestion, but it was later in 1996 found to be wrong by David Grier and coworkers from Chicago: they showed experimentally that small temperture gradients in the experimental room were sufficient to give these effects, and offered a convincing explanation for them [Phys. Rev. Lett 77, 578 (1996)]. This is a simple example of a case where I turned out to be wrong in a way that I do not feel ashamed for. Our ideas were interesting and not farfetched, but precise experiments showed that the real physics was different!
Wim van Saarloos
last update September 18 2002
[Pattern formation] [Wim van Saarloos] [Instituut-Lorentz]