Tuesday, February 19, 2019

Superconducting order in organic charge transfer salts

A long-standing question for superconductivity in organic charge transfer salts concerns the symmetry of the superconducting order parameter. Is it unconventional (i.e. not s-wave) and if so are there nodes in the energy gap? Over the years there have been a wide range of claims, both theoretical and experimental.

Most recently a combined theory-STM experiment claimed the symmetry was d + s and that there were 8 nodes on the Fermi surface.

Two of my UQ colleagues recently posted a nice preprint that comes to a different conclusion.
Microwave Conductivity Distinguishes Between Different d-wave States: Umklapp Scattering in Unconventional Superconductors 
D. C. Cavanagh, B. J. Powell

Microwave conductivity experiments can directly measure the quasiparticle scattering rate in the superconducting state. We show that this, combined with knowledge of the Fermi surface geometry, allows one to distinguish between closely related superconducting order parameters, e.g., dx2y2 and dxy superconductivity. We benchmark this method on YBa2Cu3O7δ and, unsurprisingly, confirm that this is a dx2y2 superconductor. We then apply our method to κ-(BEDT-TTF)2Cu[N(CN)2]Br, which we discover is a dxy superconductor.
In 2005 Ben Powell  (and others) showed that the simplest RVB theory gives such an order parameter with nodes required by symmetry.
[Aside: in our paper, this is denoted d_x2-y2, but that is because of how the x-y axes are defined].

Thursday, February 14, 2019

Does a temperature dependent Hamiltonian make sense?

At the fundamental level, we think of a Hamiltonian as independent of temperature. It is describing the energy of all possible states of the system in the absence of any environment.

However, when one does mean-field theory (e.g. for an Ising model or BCS theory) the Hamiltonian involves temperature-dependent parameters that are determined self consistently.

I have been thinking about this because one of the proposed effective minimal Hamiltonians for spin crossover compounds is an Ising model with a temperature dependent field.
My immediate reaction was that this must be some sort of mean-field theory.
However, I now realise that is not the case.

Effective Hamiltonians can be temperature dependent without invoking any approximations. Temperature-dependent interactions can arise when one integrates out some degrees of freedom.

One can see this by simply considering the case of a system with two degrees of freedom x and q. The partition function can be written as a path integral where there is an action which involves the integral of the Lagrangian in imaginary time from 0 to 1/T where T is the temperature.
Integrating out x one obtains an effective action for q that will depend on temperature.

Here are three cases where this can be done explicitly.

1. The spin boson model. One integrates out the harmonic oscillators, leading to a ``Feynman-Vernon influence functional'' that is temperature dependent.

2. A two-state system in which each state has a series of sub-states (e.g. spin states or vibrational states). Consider the simple Hamiltonian.

This corresponds to the case of spin-crossover systems and one sees how one can end up with an Ising type model with a "field" that is related to the free energy difference between the two spin states.

3. A one-dimensional chain of spin-crossover molecules which have an elastic interaction that depends on the spin state. This is treated in
Elastic interaction among transition metals in one-dimensional spin-crossover solids 
K. Boukheddaden, S. Miyashita, and M. Nishino

The classical phonons are integrated out and one is left with an Ising chain of pseudo-spins in an external ``field'' where the "exchange" interaction and field depend on temperature.
[See equation (13) in the paper].

Tuesday, February 12, 2019

Public perceptions of condensed matter physics

Why are string theorists celebrities who write best-selling books and popular documentaries?
Why are cosmology and particle physics seen as "fundamental" and answering profound questions about "why we are here?" as they push back the frontiers of knowledge with their great intellects and imagination. In contrast, condensed matter physics gets little public attention and is not seen as exciting, "fundamental", or intellectually challenging.

There is a helpful and stimulating paper
Prestige Asymmetry in American Physics: Aspirations, Applications, and the Purloined Letter Effect
Joseph D. Martin
Why do similar scientific enterprises garner unequal public approbation? High energy physics attracted considerable attention in the late-twentieth-century United States, whereas condensed matter physics – which occupied the greater proportion of US physicists – remained little known to the public, despite its relevance to ubiquitous consumer technologies.... popular emphasis on the mundane technological offshoots of condensed matter physics and its focus on human-scale phenomena have rendered it more recondite than its better-known sibling field. News reports about high energy physics emphasize intellectual achievement; reporting on condensed matter physics focuses on technology. And whereas frontier-oriented rhetoric of high energy physics communicates ideals of human potential, discoveries that smack of the mundane highlight human limitations and fail to resonate with the widespread aspirational vision of science – a consequence I call “the purloined letter effect.”
What is this "purloined letter"??
Understanding prestige asymmetry requires discerning how the values communicated in the discourse of scientific discovery relate to the values and expectations of the surrounding society. Many in the United States see science as a source of faith in both individual potential and collective possibility, and look to it as a way to overcome human limitations. John H. Evans has documented “faith in science producing meaning” .... Science functions for many as “a source of societal hope – a way to save our society from its troubles, in the same way that societies have looked to other saviors, like religion”... Some rhetoric of scientific discovery, however, undercuts the narrative of science as a testament to human potential. When discoveries are presented as evidence that we have missed something obvious, it highlights our failings and limitations alongside our accomplishments. We can only recognize such achievements by also acknowledging our collective failure to discover earlier what was in front of our eyes all along. In these instances, scientific discoveries fail to promote the values that evidence suggests best resonate with consumers of scientific media. I call this the purloined letter effect, after Edgar Allan Poe’s 1844 short story in which a stolen letter hidden in plain sight is uncovered in a way that exposes the police, who had failed to find it, as mulish and unimaginative.
This narrative of "science as salvation", particularly in popular books, has also been discussed by Mary Midgley and by Gregory Schrempp. More recently Ian Hesketh has argued that Big History is in this genre.

Martin illustrates his argument by considering press reports about different Nobel Prizes.
Steven Weinberg, Sheldon Glashow, and Abdus Salam’s prize for electroweak unification .... Both the LA Times and the Tribune ... gave prominent billing to Weinberg’s and Glashow’s statements about the fundamental importance of their work for understanding the way the universe works – and its manifest absence of practical applications. The .. [New York Times] toasted “a theory so profound as to affect man’s perception of existence” . 
The 1970s condensed matter prizes all recognized fundamental contributions, in particular theoretical developments in magnetism and work on the quantum properties of solids. US papers nevertheless routinely described these contributions as undergirding technological developments, with efforts to explain the content of the research either perfunctory or absent. 
The 1977 prize recognized theorists Philip Anderson, John Van Vleck, and Nevill Mott. The Nobel committee cited them “for their fundamental theoretical investigations of the electronic structure of magnetic and disordered systems.” The NY Times reported that the winners “were cited for work underlying the development of computer memories, office copying machines and many other devices of modern electronics,” and made little effort to clarify the theoretical work behind the prize. The AP report pointed to lasers, better glass, and copper IUDs ... Reuters tied the laureates’ “‘solid state’ physics theories” to “computer memories, pocket calculators, modern radios, office copiers, and solar energy converters” The emphasis was not only squarely on technology, but disproportionately on the work-a-day technologies that were becoming part of the furniture of Cold War America. High energy physics changed our perceptions of our very existence; condensed matter was the physics of photocopiers.
I thank Andrew Zangwill for bringing the paper to my attention.

I think that condensed matter physics is intellectually challenging and exciting. Furthermore, as it is all about emergence and complexity it addresses fundamental questions and produces concepts and methodologies that are not just relevant to making widgets but addressing important issues in a wide range of intellectual endeavors from biology to sociology.

Thursday, February 7, 2019

A critique of DFT calculations for spin crossover materials

A basic question concerning spin crossover compounds is what are the energy difference and entropy difference between the low spin (LS) and high spin (HS) states.

The relative magnitude of these two quantities determines the crossover temperature from the LS to HS state.
From experiment typical values of the energy difference Delta H are of the order of 1-5 kcal/mol (4-20 kJ/mol). Entropy differences are typically about 30-60 kJ/mol/K. (See table 1 in the Kepp paper below).
This relatively small difference in energy presents a challenge for computational quantum chemistry,
such as calculations based on density functional theory, because of the strong electron correlations associated with the transition metal ions,

Over the past few years some authors have done nice systematic studies of a wide range of compounds with a wide range of DFT exchange-correlation (XC) functionals. Here I will focus on two papers.

Benchmarking Density Functional Methods for Calculation of State Energies of First Row Spin-Crossover Molecules 
Jordi Cirera, Mireia Via-Nadal, and Eliseo Ruiz

Theoretical Study of Spin Crossover in 30 Iron Complexes 
Kasper P. Kepp

First, these studies are refreshing and important. Too many computational chemistry calculations are dubious because they do not do systematics. 
Here I will just discuss the first paper.

Cirera et al. use 8 different XC functionals to study 20 different compounds. They find that only one (!) functional (TPSSh) correctly gives a low spin ground state for all the compounds, i.e. Delta H is positive.

The figure below nicely summarises the results.

Before one gets too excited that one has now found the "right" functional, one should note that when one uses TPSSh to calculate the crossover temperature there is little correlation with the experimental values.

To put all this in a broader context consider the hierarchal figure below which is in the spirit of the metaphor of Jacob's ladder proposed by John Perdew. [The figure is from here]. However, I do not think Jacob's ladder is the best Biblical metaphor.

This highlights the ad hoc nature of DFT based calculations and that one is a long way from anything that should seriously be considered to be a true ab initio calculation.

It should also be noted that all these calculations are for a single molecule in vacuum. However, the experiments are in the solid state (or solution) and so the energetics can be shifted by electrostatic screening and/or solvation. The crossover temperature (which can become a first-order phase transition) may also be shifted by intermolecular elastic interactions.

Wednesday, February 6, 2019

Ideas worth throwing out?

Unfortunately, like many universities, UQ has become a construction site in the rush to build shiny new buildings, particularly to accommodate the ever increasing expansion of senior management and nice facilities to ``enhance the student experience.''
An extra floor was added to the physics building for the Office of the Executive Dean of Science.
Faculty and grad student offices are being shuffled around campus to accommodate this construction. I am now making my third move in less than eighteen months. I took this opportunity to downsize and toss a lot of old files. While filling a dumpster I saw something I thought was pretty ironic and funny.

Tuesday, February 5, 2019

What is condensed matter physics?

What do condensed matter physicists study?

High school students are often taught there are three states of matter: solids, liquids, and gases. However, this is misleading as there are many more states of matter. Liquid crystals, superconductors, and ferromagnets are distinct states of matter that do not fit in the high school classification. Condensed matter physics (CMP) is concerned with practically any material system that involves a large number (say at least a million) of interacting atoms or molecules. We can consider this to be a complex system because there are many different ways of arranging the constituents (atoms or molecules) of the system.

What approaches and techniques do condensed matter physicists use to study and understand these systems?

CMP provides a coherent intellectual framework for a multi-faceted approach to investigate and understand complex material systems.
First, one can look at the material at many different scales ranging from the microscopic level (scale of individual atoms and molecules) to the mesoscopic (roughly thousands of atoms or molecules, micrometer scale) to the macroscopic (what can be seen with the naked eye). The different scales can be different system sizes, length scales, energy scales, and time scales.
At every scale one can use different tools and approaches, which fall into three broad categories: experimental, theoretical, and computational. All three are intellectually and technically challenging. All are important.

There are several distinct parts to this.
Synthesis and fabrication: one has to make a sample of the material. This involves chemistry. Making large clean samples is an art in itself.
Characterisation: this concerns testing that one actually has a sample of chemical composition and purity desired.
Property measurement: this concerns determining what the physical properties (for example, crystal structure or electrical resistance) of the sample are. Often one varies external conditions such as temperature, magnetic field, and pressure, and determines how the properties of interest vary with these parameters. Some of the most interesting condensed matter physics happens under extreme conditions: low temperatures, high magnetic fields, or high pressures.

Theory and model building
The fundamental question that one is trying to answer is: How do the material properties emerge from the chemical composition and atomic structure of the material? In particular, what are the physical mechanisms responsible for the different states of matter found in the material? In CMP it is found that these questions are best understood in terms of deciding on the essential system components and  physical interactions between them that occur at different length and energy scales. Constructing (or dreaming up!) the simplest possible model for these interactions is a real art.

This has several aspects often requiring the use of state-of-the-art supercomputers and algorithms. One is broadly known as quantum chemistry and concerns starting with a knowledge of the basic chemical composition and calculating from quantum theory the properties of the system. In spite of massive advances in computational power and algorithms over the past 60 years, one is still confined to relatively small numbers of atoms and/or unreliable approximation schemes.
The second computational side is calculating properties of the theoretical models that can be compared to experiment. Even for "simple" models usually requires either massive computational power on small systems or unreliable approximation schemes.

Finally, an important challenge is that of intellectual synthesis and critical evaluation. Here, one tries to bring together the results of all these complementary investigations to gain a coherent picture of the material and its properties. Inevitably, there are inconsistencies, sometimes minor and sometimes major. Investigators then have to decide in which element the problem lies.

I think CMP is more complex, challenging, and full of surprises than other areas of physics, such as atomic physics, elementary particle physics, fluid mechanics, and optics. There is a lot more that is unknown in CMP and a lot more that can go wrong.

Friday, February 1, 2019

My biggest questions about spin crossover compounds

Most of the questions are inter-related. Most have been discussed in earlier posts.

How do we tune physical properties (e.g. hysteresis width) by varying chemical composition?

How do we understand two-step transitions? Are they associated with spatially inhomogeneous arrangements of the spin?

Are spin ice phases possible?

What is the physical origin of the intermolecular interactions that lead to a first-order transition?
Is it electronic (magnetic) and/or elastic?
Are there long-range interactions? Are they crucial?

Is there a simple way to understand the change in vibrational spectra (and thus entropy) associated with the transition?

What is the role of spatial anisotropy?

What is the simplest possible effective model Hamiltonian that captures the physical properties above?
Can the elastic degrees of freedom be "integrated out" to give a "simple" Ising model?
How do the model parameters depend on structural and chemical composition?

Thursday, January 31, 2019

Postdocs are not junior faculty

Over the past decade, I have noticed a disturbing trend in Australian universities: postdocs are now often expected to be like junior faculty. Specifically, they are expected to apply for grants, recruit and supervise Ph.D. students, be involved in public outreach, help with teaching, engage with industry, ... This is quite different from the traditional role of a postdoc: purely to do research and not worry about money, teaching, and admin.

I don't think anyone is winning from this change. First, it is creating a lot more stress and anxiety for the postdocs. Second, their research productivity and quality are lower because they are distracted and spending significant time not doing research. Thus, the funding agency that is actually supporting them to do research is getting less for their money.

I think this change has been caused by several factors.
First, the job market for tenure-track positions has got even more competitive (from extreme to ridiculous) and so there is a hope that if you get a grant and have done some teaching experience (with stellar student evaluations) then you will have a better chance of getting a permanent position. Second, university management and funding agencies really want to promote the myth of scientific careers. Postdocs are "Early Career Researchers'' and so applying for grants etc. is just part of the ``natural'' progression in them developing into an independent faculty member. Management hopes that if postdocs believe this myth they will be highly motivated workers. They also see getting grants as a random process and the more applicants the better. More grants means more income from overhead and more status for the university ...
This career myth denies the painful reality that the vast majority of Ph.D. students and postdocs will not get permanent positions in research universities. If you are in doubt about this just do the following for your own department: divide the number of new tenure-track faculty hired each year (on average) by the number of Ph.D.'s graduated each year (on average).

The best thing for the vast majority would be to focus on doing some excellent research, enjoy what they are doing, gain diverse skills, and keep an eye out for exit strategies. The main hope for this to happen is for senior faculty to encourage them in these directions.

Tuesday, January 29, 2019

Why is condensed matter physics important and interesting?

I am trying to get some momentum in writing A Very Short Introduction to Condensed Matter Physics. The intended audience is the intellectually curious person with little background in science. My goal is to convince them that CMP is important and interesting. I can think of several reasons.

1. CMP is intimately connected with everyday technology ranging from liquid crystal displays to computer chips.
2. CMP comprises the majority of physics (employees, papers, conferences, ...) and has significant interaction with areas of science and engineering.
3. CMP is a rich source of creative ideas, concepts, and techniques that represent a significant intellectual achievement and are relevant to many other intellectual endeavors.
4. CMP is full of surprises. We keep discovering new unanticipated phases of matter.
5. CMP presents significant scientific challenges: theoretical, computational, and experimental (from characterisation to sample synthesis).

I am going to focus on 3.
However, it is interesting that the traditional route is 1. Furthermore, different people (including reviewers of the book proposal) are quite divided about 1. versus 3.
[More on that later following this article].

What are the big picture ideas of condensed matter, that are significant intellectual achievements in their own right and particularly relevant to other endeavors?
Here are a few suggestions. It provides very concrete systems to address, at both the mathematical and experimental level, the following issues, which turn out to be often inter-related.

A. Qualitative distinctions are defined by discontinuities. (Different phases of matter).

B. Simple models of complex systems. (Landau theory of phase transitions; Effective Hamiltonians).

C. Universality versus particularity. (Universality classes for critical phenomena).

D. Emergence and the hierarchal nature of reality. (Effective interactions. Renormalisation.)

What do you think are the great intellectual achievements of condensed matter that people need to know about?

Friday, January 25, 2019

Strategies for minimal effective Hamiltonians

An important step in understanding any class of complex materials is to find/discover the simplest possible effective Hamiltonian that can be used to describe the main properties of interest (e.g. a phase diagram).
Doing this well is a non-trivial and subjective process. I am thinking about this because I am currently trying to figure out the appropriate Hamiltonian for spin-crossover compounds.

Here are some key elements of the process. 
"Simplest possible" means having the fewest possible degrees of freedom and parameters.

1. What are the key degrees of freedom (molecular orbitals, vibrations, spins, ...)?
2. What are the key interactions and the associated Hamiltonian?
3. What approximation scheme can be used to calculate properties of the many-body Hamiltonian (ground state, thermodynamics, electronic, magnetic, ...)?
4. How do the calculated properties compare to experiment?
5. Can we estimate the values of the Hamiltonian parameters from the comparison of the calculated properties with experiments? 
6. Can we estimate the values of the Hamiltonian parameters from ab initio electronic structure methods, such as those based on density functional theory (DFT)?

Inevitably, things do not work out perfectly, sometimes qualitatively and always somewhat quantitatively. Then one has to face the difficult task of deciding what the problem is and what the next step is. There are several options.

A. There are some missing degrees of freedom in the original Hamiltonian.
B. There are some missing interactions.
C. The approximation scheme used to calculate properties was not reliable enough.
D. There is a problem with the experiments.
E. This is really the best one can hope to do and you should move on to other problems. i.e, know when to quit and face the law of diminishing returns.

This plethora of options is why falsifiability is so hard in the theory of strongly correlated electron materials. But, it does not mean we should give up on it.

The flow diagram below is one way of looking at the process. Some people like the picture. Others do not. As usual, real science is not quite so algorithmic.

Tuesday, January 22, 2019

Post-colonial science

Today there are many threats to science playing an appropriate role in education, public policy, and general public discourse. Some include anti-vaccination campaigns, climate change denial, young earth creationism, "health" products, ...
In the Western world issues such as these rightly get considerable attention. However, in the Majority World there is an issue that does considerable harm and is growing significantly. The basic claims are along the following lines. Modern science did not first arise in Europe but was already present in ancient cultures, often in religious texts. Post-colonial nations need to be proud of this heritage and this "science" should be an integral part of science education. Nations need to embrace their own methods and epistemologies consistent with their culture.

I recently become aware of just how prevalent these views are and the powerful political forces promoting them. You can get some of the flavour from this recent newspaper article and watching some of this video.

A relevant book is
Lost Discoveries: The Ancient Roots of Modern Science—from the Babylonians to the Maya
(Aside: The author, Dick Teresi wrote The God Particle with Leon Lederman.)
This book is authoritatively quoted in a recent book by a prominent South Asian political leader.
A helpful and critical review of Teresi's book is in Science. Basically, it is bad history. There is no doubt that various ancient civilisations did develop some pre-cursors of various aspects of modern mathematics, science, and technology. However, they were never comparable in scope, coherence, conceptual framework, and longevity to what happened in the "scientific revolution" in Europe. A very detailed debunk of some specific claims was given by Meera Nanda, and unfortunately received a vicious response.

So what is the source of the problem here?
I think several very distinct entities get conflated: colonialism, Western civilisation, science, technology, the greed and duplicity of some multinational corporations, and modernism.
A particularly tragic example of this conflation was arguably instrumental in the AIDS-HIV denialism of the South African government from 1999-2008. It was probably responsible for the death of hundreds of thousands of people.

Colonialism was a brutal system which ruthlessly exploited, humiliated, raped, and murdered millions of people across the globe. (See for example). Countless nations today labour under that horrific legacy. No doubt the colonising powers had a patronising view of the "natives", claiming they were bringing them the great achievements of Western civilisation such as science and modernism, and they ruthlessly used technology to maximise their exploitative agenda.
The subtle interplay between scientific, colonial, and theological ideas is described by Sarah Irving in
Natural Science and the Origins of the British Empire.

However, one can decry European colonialism but affirm good things about Western civilisation such as science.
One can decry how technology [based on science] is used to harm people but still affirm science.
Modernism is a particular world view or philosophical framework that claims scientific foundations. One can embrace science without embracing modernism.

I consider postcolonialism an understandable struggle for post-colonial nations to find an identity and direction in the era of globalisation. Somehow these nations need to honor the good parts of their own culture and history [including an accurate assessment of their scientific achievements], accept some good achievements of the West [science, democracy, rule of law, individual freedoms] without uncritically accepting dubious aspects of the West [consumerism, neoliberalism, narcissism, arrogance, ....].

Friday, January 18, 2019

First-order transitions and critical points in spin-crossover compounds

An interesting feature of spin-crossover compounds is that the transition from low-spin to high-spin with increasing temperature is usually a first-order phase transition. This is associated with hysteresis and the temperature range of the hysteresis varies significantly between compounds.
If there was no interaction between the transition metal ions the transition would be a smooth crossover. This is nicely illustrated in a figure taken from the paper below.

Abrupt versus Gradual Spin-Crossover in FeII(phen)2(NCS)2 and FeIII(dedtc)3 Compared by X-ray Absorption and Emission Spectroscopy and Quantum-Chemical Calculations 
Stefan Mebs, Beatrice Braun, Ramona Kositzki, Christian Limberg, and Michael Haumann

For the first compound, the transition is abrupt [much earlier work found a narrow hysteresis region of about 0.15 K]. For the second compound, the transition is a crossover.

The authors fit their data to an empirical equation that has a parameter n, describing the "interactions". You have to read the Supplementary Material to find the details. This equation cannot describe hysteresis.

 However, there is an elegant analytical theory going back to a paper by Wajnflasz and Pick from 1971. This is nicely summarised in the first section of a paper by Kamel Boukheddaden, Isidor Shteto, Benoit Hôo, and François Varret.
The system can be described by the Ising model

where the Ising spin denotes the high- and low-spin states. Delta is the energy difference between them and ln g the entropy difference.
The mean-field Hamiltonian for q nearest neighbours is

There are two independent dimensionless variables, d and r. Solving for the fraction of high-spin states (HS) versus temperature gives the graphs below for different values of d.
The vertical arrows show the hysteresis region for a specific value of d=2. 
As d increases the hysteresis region gets smaller. Above the critical value of d=r/2, the crossover temperature T0=Delta/ln g is larger than the mean-field critical temperature Tc= qJ, and the transition is no longer first-order but a crossover.
Using DFT-based quantum chemistry the authors calculate the change in vibrational frequencies and the associated entropy change for the SCO transition in a single molecule. The values for compound 1 and 2 are 0.68  and 0.21 meV/K respectively. The spin entropy changes are 0.21and 0.22 meV/K respectively. The total entropy changes are thus 0.89 and 0.43 meV/K respectively. The values of Delta are 175 and 125 meV, respectively. The corresponding crossover temperatures are 210 and 360 K, compared to the experimental values of 176 and 285 K.

If we assume that J is roughly the same for both compounds then the fact that the entropy change is half as big for compound 2, means r is twice as big. This naturally explains why the second compound has a smooth crossover, compared to the first, which is very close to the critical point.

Tuesday, January 15, 2019

Thinking skills for scientists (and engineers)

I keep coming back to the basic claim that the key ingredient of education is learning to think in particular ways. [n.b. In science, I am not at all playing up theory over experiment. You have to learn to think about what experiment to do and how to think about your results.].

In the past year, several people brought to my attention that MIT recently reviewed their engineering curricula. It is interesting that a key element is to teach students 11 ways of thinking. The list is worth reading and contemplating.

I have two minor comments. Although I affirm this as an admirable goal. I think the list is incredibly ambitious (even for MIT students) both in scope and content. But, maybe that is a good thing.
What do you think?

One of the 11 ways is Systems Thinking
Predicting emergence of the whole by examining inter-related entities in context, in the face of complexity and ambiguity, for homogeneous systems and systems that integrate multiple technologies.
Again, I love it. But, some would even argue you cannot predict emergence...