Thursday, July 28, 2016

Real science props for Hollywood

There is an interesting blog post Yes the equations are correct about how the latest Ghostbusters movie used props from the MIT physics department.

The Big Bang Theory is also known for using real science and equations, as I have noted before. This week Anne McCoy, who is a Deputy Editor of the Journal of Physical Chemistry A, told me about another prop, shown below, a Festschrift issue for Sheldon Cooper.

The story of how this came about is described here. It is not totally accurate, because these Festschrifts are normally for people on their 60th birthday and Sheldon is a string theorist, at least until recently, not a Physical Chemist. 

Below are a couple of screen shots from the show where you can see the prop in the background in Sheldon's office.

Tuesday, July 26, 2016

Seattle talk on quantum H-bonds

I am on sabbatical this semester. The first week I visiting the Chemistry Department at the University of Washington. My host is Anne McCoy who has done a lot of nice work on the theory of the infrared spectroscopy of H-bonds. [Some of her work featured in this post a while back].

Here is the current version of slides for a seminar I am giving tomorrow.
It is largely based on this paper and this preprint.

Saturday, July 23, 2016

Real science education teaches skills not just facts

Science is a verb not just a noun.
This idea is expanded upon in detail in the introduction to Phil Nelson's beautiful new textbook Physical Models of Living Systems.
“Science is not just a pile of facts for you to memorize. Certainly you need to know many facts, and this book will supply some as background to the case studies. But you also need skills. Skills cannot be gained just by reading through this (or any) book. Instead you'll need to work through at least some of the exercises, both those at the ends of chapters and others sprinkled throughout the text. Specifically, this book emphasises  
Model construction skills: It's important to find an appropriate level of description and then write formulas that make sense at that level. (Is randomness likely to be an essential feature of this system? Does the proposed model check out at the level of dimensional analysis?) When reading others' work, too, it's important to be able to grasp what assumptions their model embodies, what approximations are being made, and so on. 
Interconnection skills: Physical models can bridge topics that are not normally discussed together, by uncovering a hidden similarity. Many big advances in science came about when someone found an analogy of this sort. 
Critical skills: Sometimes a beloved physical model turns out to be. . . wrong. Aristotle taught that the main function of the brain was to cool the blood. To evaluate more modern hypotheses, you generally need to understand how raw data can give us information, and then understanding.  
Computer skills: Especially when studying biological systems, it's usually necessary to run many trials, each of which will give slightly different results. The experimental data very quickly outstrip our abilities to handle them by using the analytical tools taught in math classes. Not very long ago, a book like this one would have to content itself with telling you things that faraway people had done; you couldn't do the actual analysis yourself, because it was too difficult to make computers do anything. Today you can do industrial-strength analysis on any personal computer.  
Communication skills: The biggest discovery is of little use until it makes it all the way into another person's brain. For this to happen reliably, you need to sharpen some communication skills. So when writing up your answers to the problems in this book, imagine that you are preparing a report for peer review by a skeptical reader. Can you take another few minutes to make it easier to figure out what you did and why? Can you label graph axes better, add comments to your code for readability, or justify a step? Can you anticipate objections?  
 You'll need skills like these for reading primary research literature, for interpreting your own data when you do experiments, and even for evaluating the many statistical and pseudostatistical claims you read in the newspapers.  
 One more skill deserves separate mention. Some of the book's problems may sound suspiciously vague, for example, ‘Comment on. . . .’ They are intentionally written to make you ask, ‘What is interesting and worthy of comment here?’ There are multiple ‘right’ answers, because there may be more than one interesting thing to say. In your own scientific research, nobody will tell you the questions. So it's good to get the habit of asking yourself such things.“
Unfortunately, most courses [including ones taught by me!] don't do the above.
I am slowly reading through the book. [Phil kindly sent me a free copy].
It confirms my earlier suggestion that this is a course that every science undergraduate should take.

Thursday, July 21, 2016

Bad metals and the unitary limit

In clean elemental metals the mean free path is much larger than the lattice constant and the Fermi wavelength. This means that an electron (or quasi-particle) has a well defined wavelength and momentum (wave vector) between collisions which change its momentum.
Thus, quasi-particles are a well defined entity.
However, consider that limit where the scattering becomes so strong that the mean-free path becomes comparable to the Fermi wavelength (or lattice constant).
Then clearly the idea of a quasi-particle with a well define wave vector and a mean free path does not make sense.

The resistivity (in a Boltzmann-Bloch) picture is inversely proportional to kF l.
Waving ones hands one can argue that in a metal there is a maximum value for the resistivity.
This is known as the Mott-Ioffe-Regel (MIR) limit.
Waving one hands  some more, one might argue that as the temperature increases (and inelastic scattering increases) towards the MIR limit the resistivity might saturate or even decrease because the material becomes an insulator.
Some people also debate whether the minimum value of kF l is 1, pi or 2 pi.

In reality, it is not clear whether the MIR limit exists in any known material.
Bad metals, by definition, violate it.

So what about the above argument? Obviously, there is significant hand waving.
The argument basically extrapolates results for weak scattering to the strong scattering limit.
Is there any way one can make some of the argument more rigorous?

One case where one can do better is for the specific case of elastic scattering due to impurities. Large scattering corresponds to what is known as the unitary limit.
[I often find the terminology obscure. I think it may relate to the optical theorem and the scattering S- matrix having the maximum possible value (unit = -1). I welcome clarification].

This post was stimulated by discussions with my colleagues who wrote the following paper, which has a brief discussion of some of the issues in Section II.

Breakdown of the universality of the Kadowaki-Woods Ratio in multi-band metals
D C Cavanagh, A C Jacko, and B J Powell

Here is my version of the argument, drawing on results found in Hewson’s wonderful book on The Kondo Problem.

Consider an electron scattering off a single impurity potential.
In the weak scattering limit the scattering cross section and mean-free path can be calculated in the Born approximation. However, the strong scattering limit can also be solved using a T-matrix which
sums all of the relevant Feynman diagrams.
Results can be expressed in terms of the scattering phase shifts.
In the limit of an infinite s-wave potential, the relevant phase shift becomes pi/2.
The scattering cross section is proportional to 1/k^2 which is must on dimensional grounds since there is no other well-defined length scale when the scattering length associated with the potential becomes infinite.

The scattering rate for the electrons is written in terms of phase shifts eta_l

If the only non-zero phase shift is the s-wave one and it equals pi/2, one sees that the scattering rate scales as 1/kF.
Note: this is what determines the resistivity in the Kondo problem at very low temperatures.
This (unitary limit) is similar to what one would get from a hand waving argument that takes the weak coupling result and sets kF l = 1.

So how does this relate to bad metals?
Well it should be stressed that the above argument is for elastic scattering and so does not necessarily carry over to inelastic scattering, which is actually what is relevant to bad metals.

I welcome clarifications on any of this.

Wednesday, July 20, 2016

Deconstructing the bad science job market

The New York Times has a good article So Many Research Scientists, So Few Openings as Professors.

I am happy these issues are getting more attention in the media.
However, I feel that it fits with a common unquestioned narrative:
“The purpose of science Ph.Ds is to train people to be faculty members at research universities.
However, it turns out the Ph.D production rate is vastly greater (an order of magnitude or more?) than the job vacancy rate.
Therefore, Ph.D production rates should be reduced.”

My perspective is somewhat different. I think having a lot of science Ph.Ds is arguably good for society. Here is what needs to change in the three relevant communities.

Politicians, funding agencies, and university administrators and marketers.
Stop lying or being deluded.
There is no shortage of science Ph.Ds.
Tenured jobs in academia are very limited. Most Ph.Ds have very little chance of getting one.
The job market is pretty much like it has been for the past 40 years.
Don't tell prospective students otherwise.

Faculty at research universities.
Give your students accurate job advice. The chance of most of your students being a clone of you is close to zero.
Don’t use them as a sweat shop worker in your paper production factory. Give them a broad education that will equip them for jobs outside academia.

Students and postdocs.
Be realistic. Don’t live in denial. But don’t get depressed and enjoy your life in science while it lasts. Take opportunities to learn a broader skill set that will equip you for broader job options.
Bail out sooner than later. There are many good job opportunities outside academia. You are not a failure if you don’t win the lottery.

How should the system change?
I am not endorsing the status quo.
I would be happy to see some of the money spent on the large numbers Ph.D student and postdoc positions redirected towards longer term staff such as technical staff and junior faculty positions. Shrinking some large research groups might be good for everyone.

I also think some of this problem is an unfortunate reflection of broader issues of increasing inequality, and a "winner takes all" mentality in many Western societies.

I welcome comments.

Tuesday, July 19, 2016

Value of student pre-reading quizzes. II

Following up on my previous post, below are some selected comments I got from students in my thermodynamics class last semester. 
A couple (in bold) comment on how the lectures help understand the reading.
But, there is an interesting follow up. Since the students now have their grades I received the student evaluations. Some complained strongly that the lectures were poor/useless because they just repeated what was in the reading. Others complained that I did not answer all the questions they raised in the reading. 

I am sure I can do better, but this just highlights to me that it is impossible to keep all students happy. 
For some you go too fast, some too slow. 
For some you give too much detail, others not enough detail. 
For some you follow the book too closely, for others not closely enough. 
For some you repeat things too much, for others not enough.

I would really like to go through the derivations and maths in class. It's so much harder to read than it is to see it being written on the board.

Some things are much easier for me to understand after the lectures. The constant K is exponential decay depending on the change of G and inversely to the T. I'll understand Q2 better after the lecture.

The most interesting was definitely the section on the construction of the phase diagrams from the free energy graphs over various temperatures. I've used phase diagrams extensively before, but have never been taught how they are constructed bar experimental measurements of the temperatures at which solidification begins and ends over a range of compositions. It's great to finally see a theory-based, thermodynamic construction that supports the experimental measurements.

The section on the Eutectic point and eutectic phase changes was confusing at first, then really cool and interesting when I understood. This really strikes me as being a useful application of thermodynamics!

I have just studied phase diagrams for solid solutions in MECH2300 so it was nice to get a better look behind the curtain at what gives the phase diagrams their shape. Thanks Gibbs.

I wish I could learn PHYS2020 through Osmosis

I felt that the section on the osmotic pressure and the derivation of the equation was a little bit rushed and difficult to follow. Also, who lead the Israelites through a semipermeable membrane? ......Osmoses. Get it? Cus... Cus... yeah alright... that's all.

I never had any idea diffusion to was just due to a pressure difference. Now that i think about it it maes sense but it never even crossed my mind why this occured other than simply because mixing would increase entropy and the membrane was permeable. This new interpretation of the event is really interesting.

Of all the reading I was very pleased to see a derivation of the Saha eequation and how basic chemical equilibrium equations were able to be applied to other areas of physics. I've seen the equation arise extensively is astrophysics and it was nice to see how such a seemingly complex relation could be derived so simply by applying the versatility of thermodynamics in physics.

I found the derivation of Le Chatlier's principle to be extremely interesting, as we were taught this qualitatively in Year 12 chemistry, and the derivation was easy to follow and made sense and it was nice to see where this actually comes from

Magnets; how do they work? In all seriousness, paramagnetism and ferromagnetism have come up a couple times, yet we've never covered these in lectures.  Would you be able to go over a brief explanation of them and what they have to do with magnetic dipole moment?

I couldn't pull my head around the magnetic phase boundary, something about it threw me and even after reading it several times I still didn't really understand what was going on.

Friday, July 15, 2016

Universal distributions for wealth distribution from physical ideas

I finally read most of an interesting Colloquium article in Reviews of Modern Physics
Statistical mechanics of money, wealth, and income 
Victor M. Yakovenko and J. Barkley Rosser, Jr.

[I mentioned the review 2 years ago in a post about the science of economic inequality].

It reviews the history and concept of econophysics, pointing out how some of the founders of statistical mechanics actually had a vision for its application to economics and sociology. Most of the review is about analogues with statistical mechanics that use the notion of money as a conserved quantity that is exchanged by individuals, leading to Boltzmann type distributions for wealth and income.
I found the article a nice accessible introduction to the field.

What is impressive is that the simple exponential distribution (Boltzmann) does describe empirical data over two orders of magnitude. Furthermore, the analysis gives some insight into economic inequality. This is summarised in the following sentences from the abstract and the figure below showing data from the USA.
Data analysis of the empirical distributions of wealth and income reveals a two-class distribution. The majority of the population belongs to the lower class, characterized by the exponential (“thermal”) distribution, whereas a small fraction of the population in the upper class is characterized by the power-law (“superthermal”) distribution. The lower part is very stable, stationary in time, whereas the upper part is highly dynamical and out of equilibrium.

Another result that is interesting is the income of spouses seems to be uncorrelated leading to the distribution shown below for total household income. The solid line is the simple functional form following from two uncorrelated Boltzmann distributions.