Wednesday, February 28, 2018

Physicists are not the only ones with hubris!

Physicists are notorious for thinking they can revolutionise other fields. The results are often embarrassing. Previously, I considered how to (not) break into a new field. One of the basic points ito remember is that there is a lot of nuance, a lot of rich history, and a lot of very smart hard-working people associated with any worthwhile intellectual endeavour.

In 2015 Steven Weinberg published To Explain the World: The Discovery of Modern Science. In the book he belittles all the nuance that historians of science bring to the subject. One review was entitled, Why Scientists Shouldn’t Write History.

The Harvard cognitive scientist Steven Pinker has a new book out, Enlightenment Now: The Case for Reason, Science, Humanism, and Progress. The book spans cognitive science, history, philosophy, economics, and politics.... It is receiving a lot of attention in the popular press.
My UQ history colleague, Peter Harrison has a robust critique, The Enlightenment of Steven Pinker.  I learnt a lot about the subtleties of the "Enlightenment" from reading it.

Monday, February 26, 2018

What were the intellectual highlights of your undergraduate education?

I think one of the greatest moments of being a teacher or student is when the student understands or learns something that they find exciting, satisfying, or stimulating. In this "Ah hah!" or Wow! moment they will say "That is really cool!" or "That is beautiful!" or something similar.
These moments can be so significant that the student can years later even remember the exact time, location, or circumstance in which the event happened.

Did you have any such experiences when you were an undergraduate?

I reflected on my own experience. Even though it is almost 40 years ago I can remember what I learnt and sometimes the place, the book, the person, ...
Here is some of the things that immediately came to mind. They are listed in random order. It is interesting that many involve learning how one result follows from a more fundamental result with a simple mathematical proof. Often it meant there was a deeper reason for something we had previously been told was "just the way it is".
Most of these beautiful moments were in theoretical physics and pure mathematics. None were in chemistry. I think this was partly because of my own interests and orientation and partly because of the quality (or lack thereof) or approach to teaching of different subjects.

Ehrenfest's theorem
The equations of motion of classical mechanics are the average of the equations of motion for position and momentum operators.

Heisenberg's uncertainty relation follows from commutation relations.

The energy eigenvalues for the harmonic oscillator can be derived from the commutation relations of creation and annihilation operators.
No differential equations or Hermite polynomials were required!

Experimental test of time dilation from measurement of the lifetime of cosmic-ray mesons
I read about this in the textbook on Special Relativity by French. The experiments are described here.

van der Waals interaction from the Schrodinger equation
I learnt this derivation from reading my father's copy of Quantum Chemistry (1957) by Walter Kauzmann.

Electromagnetic radiation and the speed of light from Maxwell's equations

The ideal gas equation of state from the partition function

The logical structure of the laws of thermodynamics
I learnt this axiomatic approach from Hans Buchdahl, both from his book and his lectures.

Functional analysis and the equivalence of matrix and wave mechanics
This was in a pure mathematics class. It is really just an isomorphism of Hilbert spaces.

Evaluation of infinite series from residues in complex analysis
Cauchy's residue theorem can be used.

Dimensional analysis in fluid mechanics
It was amazing the physical insights one could gain simply from dimensional analysis.

Newtonian gravity from Einstein's gravitational field equations

What were some examples from your own undergraduate education?
How do we create such moments for students?

Friday, February 23, 2018

Spin ice in a nutshell

What is spin ice? What its definitive and experimental signatures?

A good place to start is the lucid discussion by Roderich Moessner and Art Ramirez in a 2006 article on Geometrical Frustration. They emphasise two organising principles: local constraints on neigbouring spins and the emergence of new entities such as gauge fields.

First, let's discuss the "ice" bit since this involves some beautiful chemistry, physics, statistical mechanics, and history. In the solid phase of water at atmospheric pressure (ice Ih) the water molecules form a hexagonal lattice, with the oxygen atoms located a the vertices of the lattice. The molecules interact with one another via hydrogen bonds.

Now the key point is that there are many different ways of orienting the water molecules (arranging the protons). The only constraint is that one has to have two protons covalently bonded to the oxygen and two protons on next-nearest neighbour water molecules hydrogen bonded to the oxygen. This is known as the ice rule. Suppose we assign an Ising spin variable (+1,-1)=(in, out)  = (covalent, Hbond) to each "bond" on the lattice. Then the ice rule is that on each tetrahedron the sum of the four "spins" must be zero.

How much degeneracy is there?
There are 2^4= 16 possible spin states on a tetrahedron. But, only six (a fraction of 3/8) satisfy the ice rule. To see this, put +1 on site one, then one must put +1 on one of the other three sites, and -1 on the other two. This gives 6 = 2 x 3 options.
If one neglects the interaction between vertices, the thermodynamic entropy per tetrahedron (water molecule) is

S = k ln (3/2)

Historical asides.
This "residual" entropy in ice was observed experimentally by William Giauque in the chemistry department at Berkeley in the 1930s.
Linus Pauling explained this in 1935, even arguing it as evidence for a specific crystal structure of ice.
Pauling's picture led to the ice-type models that are very important  (from a mathematical and conceptual point of view) in classical statistical mechanics as they are exactly soluble in two dimensions.
In 1956 Phil Anderson (who else!) noted that Pauling's problem was equivalent to that of Ising spins on a pyrochlore lattice.
It was not until four decades later than an experimental realisation was observed in a magnetic material. The experimental data is shown below.

But there is much more to spin ice. The local constraints lead naturally to an emergent gauge field (a pseudo-magnetic field), analogues of "magnetic monopoles", and unusual spin correlations (algebraic correlations without criticality). I now discuss the latter as they can be viewed as a "smoking gun" of spin ice.

The "magnetic field" B satisfies the constraint Div B =0. As a result the spin correlations have a dipolar form, i.e. they have a distance and directional dependence similar to the magnetic field associated with a magnetic dipole. This means the spin correlations fall off algebraically. This is in contrast to conventional magnets where spin correlations decay exponentially, except at a critical point. Furthermore, if one plots or measures the static spin structure factor S(q) one finds "pinch points" occur in high symmetry planes. The figure below shows an experimental measurement for Holonium Titanate, taken from here.

Wednesday, February 21, 2018

What makes a good theory or modelling paper?

There is an excellent editorial in the journal Langmuir
Writing Theory and Modeling Papers for Langmuir: The Good, the Bad, and the Ugly
Han Zuilhof, Shu-Hong Yu, David S. Sholl

The article is written in the context of a specific journal, that has a focus on surface and colloid chemistry, and predominantly experimental papers and readers.
The article is structured around the five questions below, that should actually be asked about any theory or computational paper.

Who is the intended audience?
Specifically, will the paper have an influence on the experimental community?

Are approximations and limitations clearly described? 

What physical insight is gained? 

Where does theory touch reality? 
Specifically, how does the work relate to experiment? Does it suggest new experiments to test the theory?

How can calculations be made reproducible? 

This is helpful advice and good for anyone to reflect on. On the other hand, this is so basic that the need for such an editorial reflects how bad science, and particularly computational modelling, has gotten. It is just too easy to download some software, run it for some complex chemical system that is fashionable, produce some pretty graphs, and write a paper....

Monday, February 19, 2018

The value of vacations (again).

This is almost the same post I wrote a year ago. 
This is the first week of classes for the beginning of the academic year in Australia.

In preparation for a busy semester, I took last week off work and visited my son in Canberra (where I grew up) and spent some time hiking in one of my favourite places, Kosciusko National Park. This reminded me of the importance of vacations and down time, of the therapeutic value of the nature drug, and of turning off your email occasionally.

One thing I am very thankful for is that my mental health is so much better than it was a year ago, arguably because of being pro-active.

Below is a picture of our campsite near Mount Tate. My son pointed out that it is possible that night we were the highest people in Australia since we did not see anyone else for 24 hours and you are not allowed to camp near some of the higher peaks, such as Mt. Kosciusko.

Sunday, February 11, 2018

Rethinking On-Line courses

About five years ago Massive On-Line Courses (MOOCs) were all the rage among politicians and university managers. Like most hyped up fashions, they have lost their gloss as reality has set in. There are no simple panaceas, particularly technological ones, for the complexities of tertiary education. I have previously expressed skepticism and concern about MOOCs, but recently I have rethought some of my views.

Last year I was visiting some friends in a small Majority World college and I noticed that one of the administrators had a copy of the book Poor Economics on his desk. I told him how much I liked it and he said that he had really enjoyed and benefited from taking the associated on-line course at MIT. Then he said, "But the online course I really like is the Oxford one, From Poverty to Prosperity, by Paul Collier.'' Wow!

To me, this represents the best of on-line courses; when they provide access to educational opportunities that were inconceivable a decade ago.

I have also been helping another friend with an on-line Masters course. A positive here is that it is not a substitute for regular classes for traditional students in physical classrooms but a course for students who are in life situations (family, jobs, location, ...) that do not afford them the luxury of full-time study in a traditional setting. I think a big positive is having an excellent on-line tutor who actively engages with the students.

Overall, I think the key issue here is that On-line courses are not a desirable substitute for traditional courses, but rather can complement them. Similarly, I think within traditional contexts (i.e. students on physical campuses) "blended courses" (i.e. ones with a mixture of face-to-face and on-line interaction) can be superior to traditional ones. For example, I have found that an on-line quiz about pre-lecture reading seems to increase the quality of the experience for students who then come to the lecture.

However, I want to emphasize a basic claim: the ideal educational environment and strategy for most students (particularly young undergraduates) is one where you have a group of students and a teacher in a physical classroom interacting with each other. People are relational and learning best happens in the context of relationships.

I welcome comments.

Postscript (Feb. 13).
I forgot to link to this excellent NYT article.
Online Courses Are Harming the Students Who Need the Most Help Economic View, by Susan Dynarski

Saturday, February 3, 2018

Seth Olsen (1975-2018): theoretical chemist

I was very sad to learn last week of the tragic death of Seth Olsen in an accident. He was a former collaborator and colleague at UQ.

Seth was an outstanding and energetic scientist who easily crossed discipline boundaries, especially between chemistry, physics, and molecular biology.

Much of what I know about computational quantum chemistry, fluorescent proteins, conical intersections, and diabatic states, I learnt from Seth. He played a significant role in this blog. A search revealed that his name is mentioned in more than 70 posts. Many posts were stimulated by his work, his questions, or his suggestions. He often wrote comments, covering a wide range of topics. I found his interest helpful and stimulating.

Seth grew up in the USA. He was a physics major at the College of William and Mary. In 2004 he completed a Ph.D in in Biophysics and Computational Biology at The University of Illinois at Urbana-Champaign. His thesis was entitled, ` Electronic Excited States of Green Fluorescent Protein Chromophore Models,'' and his advisor was Todd Martínez, now at Stanford.

I first met Seth in 2005 when he was a postdoc with Sean Smith at the Centre for Computational Molecular Science at University of Queensland. During that time he met Louise Kettle, a Ph.D student in chemistry, who he later married.

I was very happy when in 2008 I was able to persuade Seth to join my group as a Research Fellow. He helped my group expand from condensed matter into chemical physics.  In 2010 I was pleased when Seth was awarded a 5-year Australian Research Fellowship. We continued to collaborate, although in many ways I was the junior author.

A significant contribution of Seth was to use high-level quantum chemistry calculations to show that the low-lying excited electronic states of the chromophore molecule in the green fluorescent protein has a natural description in terms of the resonant colour theory of organic dyes developed in the middle of the twentieth century by Brooker, Platt, and Moffitt. In different words, he used quantum chemistry to justify and parametrise a simple effective Hamiltonian for a complex system. Furthermore, he provided a rigorous quantum chemical justification for the colour theory description of a very wide class of organic dyes based on the methine motif. These results provide chemical and physical insight, an understanding of trends, elucidate design principles, and make modeling in condensed environments such as proteins, solvents, and glasses much more feasible.

I had great respect for Seth's integrity, both personal and scientific. He carefully checked calculations and arguments, would not rush to publish, and would not indulge in hype. Much of my skepticism and caution about computational materials science I gained from Seth's critiques.

Seth had his priorities right, putting family first.
My kids thought Seth was pretty cool, particularly when he came to a group social at our house with a backpack that contained a home brew beer set up!

My sincere condolences to Louise and their three young children.

Don't know what else to say. This is the saddest blog post I have had to write.