Tuesday, January 17, 2017

Good and bad reasons to explore the parameter space of effective Hamiltonians

Too often I encounter papers or people that describe some detailed study of a particular region of the parameter space of some effective model Hamiltonian (Hubbard, Holstein, Hofstadter, ...) and I am left wondering, "why are you doing this?"

The most cynical answers I sometimes fear are "well, it is there" [just like Mount Everest], "no one has done this before", and "I can get a paper out of this."

It is not hard to find regions of unexplored parameter space for most models. One can simply add next-nearest neighbour hopping terms, change the lattice (anisotropic, triangular, Kagome, honeycomb, ...) , or add more Coulomb or exchange interactions, or add a magnetic flux, ....
The list is almost endless.
But, so what?

Here are a few good reasons of why exploring a particular parameter regime may be worth doing. Only one of them is sufficient. Often only one may be true.

In this parameter regime:

A1. There is an actual material that is believed to be described by this Hamiltonian.

A2. Given the inevitable uncertainty in the actual parameters for a specific material it is worth knowing how much calculated properties change as the parameters are varied.

B. There may be a new phase of matter or at least qualitatively different behaviour.

C. One can gain physical insight into the model.

D. A particular analytical approximation or numerical method is known to be reliable.

E. Provides a good testing ground for the reliability of a new analytical approximation or numerical method.

I welcome comments.

Friday, January 13, 2017

We need a TV satire of universities

Today is the last day of my vacation and so on monday I will be back to serious (?!) blogging about science. In the mean time...

On a recent long flight I enjoyed watching many episodes of Silicon Valley, a TV sitcom (?) that is a satire of start up companies. I thought it was pretty funny. [But maybe that was the long flight...]
This clip is a good sample.

The show reminded me of Utopia, an Australian TV satire of government bureaucracy.
Both shows do well at pillorying the personalities who peddle management, marketing, money, and metrics (M^4! ) and have a disproportionate influence on the direction of things. Universities are fertile for similar satire.

A starting point for ideas could be The Department, a play written in 1975 by David Williamson, one of Australia's best-known playwrights. He had been a lecturer in mechanical engineering and social psychology for a number of years before writing the play.

Tuesday, January 10, 2017

The shape of nature

I watched the first episode of The Forces of Nature narrated by Brian Cox, The Universe in a Snowflake.
[Unfortunately, I don't think the whole episode is free online. It should be! I watched it streamed through my university library website].

The imagery and creativity are stunning.
The episode focuses on shapes that occur in nature: spherical planets, human towers in Spain, hexagonal snowflakes, honeycomb beeswax, and "spherical" manatees, animals with bilateral symmetry,  ...
Cox nicely discusses some of the underlying principles, including how complexity emerges from simple underlying laws.

How do bees "know" that a honeycomb structure is optimal? This relates to a simple example of symmetry breaking and the much more difficult honeycomb conjecture that was only solved in 1999.

Friday, January 6, 2017

Theoretical physics is much more than this

Via Peter Woit's blog I read an interesting article What Does Any of This Have To Do with Physics? Einstein and Feynman ushered me into grad school, reality ushered me out by Bob Henderson.
The facts it is quite long and that I read it all on a phone (something I virtually never do) on vacation shows how interesting I found it.

During his Ph.D Henderson worked on a theory of quantum gravity at the University of Rochester in the 1990s. He then left physics for Wall Street and is now a science writer.

Here are a few comments.

First, as often happens in discussions that come up related to Woit's blog, I take umbrage at the common assumption that "theoretical physics" is equated with  theories of elementary particles and string theory. The simplest argument against the narcissism of the proponents of this narrow view is that there are five Physical Review journals (A and E). Each contains (very roughly half) theory papers and only D is concerned with such topics.

Issues of emotional and mental health feature prominently; although, not as explicitly discussed as they could be.

Henderson struggles with working 15 hours a day, confirming my view that this is a big mistake.
The echo of “You can do whatever you want” still rang in my ears.
This is something that he learnt from his father and I consider is one of the three biggest lies that Western high school students are taught and need to recnounce as undergraduates.

The lack of direction and floundering in his research project on quantum gravity is unrepresentative of most Ph.D research in theoretical physics. It just suggests the field itself it at an impasse and is arguably unsuitable for Ph.D research.

Thursday, December 22, 2016

Are power laws good for anything?

It is rather amazing that many complex systems, ranging from proteins to stock markets to cities, exhibit power laws, sometimes over many decades.
A critical review is here, which contains the figure below.

Complexity theory makes much of these power laws.

But, sometimes I wonder what the power laws really tell us, and particularly whether for social and economic issues they are good for anything.
Recently, I learnt of a fascinating case. Admittedly, it does not rely on the exact mathematical details (e.g. the value of the power law exponent!).

The case is described in an article by Dudley Herschbach,
Understanding the outstanding: Zipf's law and positive deviance
and in the book Aid at the Edge of Chaos, by Ben Ramalingam.

Here is the basic idea. Suppose that you have a system of many weakly interacting (random) components. Based on the central limit theorem one would expect that a particular random variable would obey a normal (Gaussian) distribution. This means that large deviations from the mean are extremely unlikely. However, now suppose that the system is "complex" and the components are strongly interacting. Then the probability distribution of the variable may obey a power law. In particular, this means that large deviations from the mean can have a probability that is orders of magnitude larger than they would be if the distribution was "normal".

Now, lets make this concrete. Suppose one goes to a poor country and looks at the weight of young children. One will find that the average weight is significantly smaller than in an affluent country, and most importantly the average less than is healthy for brain and physical development. These low weights arise from a complex range of factors related to poverty: limited money to buy food, lack of diversity of diet, ignorance about healthy diet and nutrition, famines, giving more food to working members of the family, ...
However, if the weights of children obeys a power law, rather than a normal, distribution one might be hopeful that one could find some children who have a healthy weight and investigate what factors contribute to that. This leads to the following.
Positive Deviance (PD) is based on the observation that in every community there are certain individuals or groups (the positive deviants), whose uncommon but successful behaviors or strategies enable them to find better solutions to a problem than their peers. These individuals or groups have access to exactly the same resources and face the same challenges and obstacles as their peers. 
The PD approach is a strength-based, problem-solving approach for behavior and social change. The approach enables the community to discover existing solutions to complex problems within the community. 
The PD approach thus differs from traditional "needs based" or problem-solving approaches in that it does not focus primarily on identification of needs and the external inputs necessary to meet those needs or solve problems. A unique process invites the community to identify and optimize existing, sustainable solutions from within the community, which speeds up innovation. 
The PD approach has been used to address issues as diverse as childhood malnutrition, neo-natal mortality, girl trafficking, school drop-out, female genital cutting (FGC), hospital acquired infections (HAI) and HIV/AIDS.

Tuesday, December 20, 2016

More subtleties in protein structure and function

Almost three years ago I posted about the controversy concerning whether the photoactive yellow protein has low-barrier hydrogen bonds [for these the energy barrier for proton transfer is comparable to the zero-point energy]. I highlighted just how difficult it is going to be, both experimentally and theoretically to definitively resolve the issue, just as for an enzyme I recently discussed.
A key issue concerns how to interpret large proton NMR chemical shifts.

Two recent papers weigh in on the issue

The Low Barrier Hydrogen Bond in the Photoactive Yellow Protein: A Vacuum Artifact Absent in the Crystal and Solution 
Timo Graen, Ludger Inhester, Maike Clemens, Helmut Grubm├╝ller, and Gerrit Groenhof

A Dynamic Equilibrium of Three Hydrogen-Bond Conformers Explains the NMR Spectrum of the Active Site of Photoactive Yellow Protein 
Phillip Johannes Taenzler, Keyarash Sadeghian, and Christian Ochsenfeld

I think the caveats I have offered before need to kept in mind.
As with understanding the active sites of most proteins the problem is that we don't have very direct experimental probes, but have to use indirect probes which produce experimental results that require significant modelling and interpretation.

I thank Steve Boxer for bringing one of these papers to my attention.

Sunday, December 18, 2016

A possible Christmas gift for thoughtful non-scientists?

Are you looking for Christmas gifts?

I think that scientists should be writing popular books for the general public. However, I am disappointed by most I look at. Too many seem to be characterised by hype, self-promotion, over-simplification, or promoting a particular narrow philosophical agenda. The books lack balance and nuance. We should not be just explaining about scientific knowledge but also give an accurate picture of what science is, and what it can and can't do.
(Aside: Some of the problems of the genre, particularly its almost quasi-religious agenda, is discussed in a paper by my UQ history colleague, Ian Hesketh.)

There is one book I that I do often hear non-scientists enthusiastically talk about.
A Short History of Nearly Everything by the famous travel (!) writer Bill Bryson.
There is a nice illustrated edition.

I welcome comments from people who have read the book or given it to non-scientists.