In Nature this week

1. Parsi Genes and their databasing K S Jayaraman writes about the efforts of a Bangalore based company to generate the database of genetic information of Parsis and use the information for the study of diseases:
   

   Fleeing persecution by invading Arabs, the Parsis arrived in India from Persia 1,200 years ago, around the same time that a few hundred Vikings arrived in Iceland. They speak a unique Indian dialect and their religion forbids marriage outside the community, so they have remained relatively inbred.

   “I realized four years ago that I was sitting on a goldmine or a powder keg,” says Villoo Morawala Patell, a Parsi and molecular biologist who founded the biotech company Avesthagen in 1998. Patell says she refers to a powder keg because of the fear that Parsis will soon become extinct because of inbreeding (the population has shrunk to its present size from a high of 115,000 in 1941).

   However, the project is not without its critiques:

   Studies suggest that there has been some mixing of Parsi genes with those of other Indians. “It is a bit of a gamble,” says Indraneel Mittra, director of the Bhopal Memorial Hospital and Research Centre in India. “My feeling is that the Parsis are not as pure as Icelanders, and in any case I do not know how fruitful the Icelandic study has been.”

2. The Darwin delay myth, or, is it? Did Darwin really delay his publication of the origin of species for fears of its reception by the public and the estabishment? A historian says no; however, some Darwin scholars seem to take objections to the methodology used in arriving at that answer:
   

   Kohn points out that searching for explicit references to a “delay” is a simplistic approach to the problem, and that other factors should be considered. For example, Darwin often criticized religion in his notebooks, which suggests that he would have been aware of the probable implications of his theory for religion. It is hard to see how the absence of specific references to a delay rules out any influence of cultural and societal factors on Darwin’s decisions, agrees David Quammen, author of The Reluctant Mr Darwin.

3. How mathematical can you get with a renaissance painting? A leading historian of science advances interesting, if controversial theories as to the identities of the people portrayed  in a Renaissance painting, The Flagellation:
   

   King is undaunted by the criticism he has received, and believes that some art historians will dismiss his work because they can’t understand it. “The epigram and painting are mathematical in nature,” he says. “No art historian has ever looked at the basic geometry of the painting”.

   But even an expert with mathematical training, such as Kemp, says that drawing any conclusions from measurements alone is fraught with problems. Part of the difficulty is deciding what to measure and where to measure it from and to, especially on a complicated painting like The Flagellation. “You are likely to hit something,” Kemp says. “I want to see direct evidence.” Such evidence might be lines drawn underneath the paint.

   Like other art historians approached by Nature, Ellen Handy of the City College of New York worries that King may be jumping too quickly to conclusions, but she acknowledges that art history often ignores mathematics. “Ironically, many of those who consider themselves as art historians don’t have the training that the artists of the time did,” she says. Many Renaissance artists, such as Piero, were skilled geometricians. “We are not. We can learn from those who have that mathematical training now.”

   Architect James Bradburne, also a cultural historian and director general of the Palazzo Strozzi in Florence, acknowledges that proof may never be found, but supports King’s ideas nevertheless: “If this is accepted even as a plausible hypothesis, then it says that scientific objects can legitimately be treated as historical documents, in the same way as paintings themselves have been. Scientific objects can be considered part of the puzzle.”

   Be sure to take a look at the article at least for the nice pictures of the painting as well as the medieval scientific instrument called astrolabe.

4. Systems biology and simplicity in biology Eric Werner reviews three books on systems biology and finds one of them most practical, while the author of one of the books reviewed, Uri Alon, writes how it is possible to discover general principles in biology.
5. Seeing without eyes No, we are not discussing some Rig Vedic poetry here. Herman Batelan and Kees Uiterwaal, in a News and Views piece, describe one such technique of seeing, namely using electric fields, and apparently, some fish (like sharks) do. Here is the abstract of the piece:
   

   Images of nanoscale structures can be constructed using the flow of electrons ejected from a metal probe tip by a fast laser pulse. The technique adds new dimensions to established methods of microscopy.

   Don’t miss the tip-enhanced electron emission microscopic picture of a nanoscale gold (grain boundary?) groove.

6. Electrons in plutonium A high temperature (600 K, ) phase of plutonium, I understand, is characterized by a 25% increase in its atomic volume as compared to its room temperature(300 K, ) phase. Shim et al trace this characteristic to the underlying electronic structure.
   

   The 5f duality similarly has a quantum-mechanical origin, but this time it is in the ‘correlated electron’ problem. Electrons have the same negative charge and so repel each other electrostatically. In simple, crystalline metals, this effect is weak, and the effect of all other electrons on one individual electron can be calculated using an averaged effective repulsive potential.This ’self-consistent mean-field approximation’ predicts itinerant electronic states, and provides generally accurate predictions of a metal’s bonding, phase stability, equation of state, and so on. But where electrons are more strongly localized (atomic), the approximation starts to fail. New approaches must take into account not only how electron wavefunctions dance round each other in a correlated fashion so as to lower the total energy of the system, but also phenomena, such as the Pauli repulsion between two electrons of the same spin, that affect the metal’s magnetic properties.

   I understand that the theoretical approach that Shim et al use to explain the size anamoly is called the dynamical mean-field method, and it overcomes the disadvantages of the usual mean field methods which predict the size correctly, but also predict (wrongly) the plutonium phase to be magnetic. The News and Views section explain all these and much more very lucidly.

7. The handedness at the molecular level An interesting paper about the determination of chirality of a small organic molecule and the News and Views piece that comments on the work:
   

   Were he alive today, Lord Kelvin would be impressed with the work of Haesler et al. … Kelvin was the first to introduce the word ‘chirality’, meaning right- or left-handedness, into science, and was equally adept at experimental and theoretical physics. He would have enjoyed the combination of exquisite instrumentation and advanced theoretical simulation with which the authors have confirmed the absolute configuration (handedness) of a small organic molecule designed to possess structural chirality of the utmost delicacy.

Have a science-filled week!

Some notes on GB migration — I

The following are the notes of Chapter 3 of Grain boundary migration in metals: Thermodynamics, kinetics, applications by Guenter Gottstein and Lasar S Shvindlerman, CRC Press, New York 1999.

Grain boundary displacement vs. non-zero diffusive flux across a boundary

Grain boundaries are structures that separate regions of the same phase and crystal structure which differ in their orientation. Thus, a displacement of grain boundary corresponds to the growth of one at the expense of another grain. This displacement also distinguishes the grain boundary migration from the shrinkage/growth of grains due to a diffusive motion.

Consider a case in which a non-zero flux across the grain boundary leads to a growth of a grain at the cost of the other. In such a case, with respect to an external frame of reference, the grain boundary remains stationary, while the opposite faces of the grains move. On the other hand, during the grain boundary displacement, when atoms from one grain make a jump to another, they change their orientation to that of the grain to which they are jumping to. Thus, there is a non-zero net exchange of lattice sites across the boundary, which results in the grain boundary displacement.

Do grain boundaries have specific properties?

Grain boundaries are usually defined to be layers of defined thickness separating phases of different orientations and the grain boundary phase is assumed to have an associated energy, entropy or mobility. However, in reality grain boundaries are only regions of discontinuities in crystal orientation; thus, for example, depending on the constraints of the adjacent crystalline surfaces, the grain boundary mobility can be different for motions in opposite directions.

Is there a theory of grain boundary migration?

No; all theories are attempts to describe grain boundary motion in terms of the rate of atoms crossing the grain boundary with net energy gain.

Consider a very narrow–single layer wide– grain boundary; thus, each atomic jump displaces the boundary by the diameter of an atom . The grain boundary velocity in such a system is given by where are the jump frequencies in the respective directions.

If there is no difference in the Gibbs free energy of the two crystallites, , and hence there is no boundary migration. This leads us to the question as to what leads to such differences in Gibbs free energy; in other words, what is the driving force for GB migration? That question has to wait for the next post.

Boundary between two ideal layered crystals

Title: Friction between incommensurate crystals

Author: J. Friedel and P -G de Gennes

Bibliographic details: Philosophical Magazine, Volume 87, Number 1, 1 January 2007, pp. 39-49(11)

Abstract: We present an overview of friction processes expected between two ideal crystals of strong layers (graphite, MoS₂, etc.) when one crystal is rotated with respect to the other by a certain angle θ. We assume perfect conditions: no impurities; no preexisting dislocations in the bulk of the crystals; slow gliding velocities. Two regimes show up: (a) Weak coupling when , where are typical intra- (inter-) layer interactions. Here we expect weak friction, controlled by two-phonon processes, and analyzed by Sokoloff et al. However, we point out that surface waves at the interface also play a role. (b) Strong coupling where two orthogonal sets of screw disclinations should build up in the contact plane, as shown long ago by F.C. Frank. Here (to a first approximation) the dislocations are arranged in ladders, and we expect solid friction with a Peierls-Nabarro threshold stress.

Notes: A paper that needs careful reading (which, I haven’t done yet).

Note added on August 8, 2007:  A follow-up paper in Philosophical Magazine Letters.

Grain boundary migration in bcc metals

Title: Collective motion of atoms in grain boundary migration of a  bcc metal

Authors: L Zhou, N Zhou, and G Song

Bibliographic details: Philosophical Magazine, Volume 86, Number 36, 21 December 2006, pp. 5885-5895(11)

Abstract:

Molecular dynamics simulations of grain boundary (GB) migration of a bcc metal, tungsten, have been carried out. The GB is of asymmetrical 〈 110〉 tilt type. Detailed examinations of atomic processes in the migration, show that the GB migration consists mainly of GB dislocation glides. Furthermore, each motion of a GB dislocation involves a cooperative motion of about three atoms on each of the atomic planes perpendicular to the tilt axis, leading to their realignment from the receding grain to the advancing grain. This collective motion is not synchronized in all of the atomic planes, but appears to be in two or three adjacent planes, suggesting a kink mechanism for glides of the GB dislocations.

Notes: In this paper, the authors try to answer two specific questions regarding grain boundary migration in bcc metals using molecular dynamics simulations:

1. The number of atoms involved in each collective motion (and what determines the number); and,
2. The relationship between the collective mechanism and grain boundary dislocation mechanism.

There also seems to be indications of grain rotations at around 1.7 nm or so (which is not pursued in this paper). Finally, to answer the questions above–the grain boundary migration is via dislocation glide; each glide is associated with a collective motion of three atoms; further, the glide might also be associated with a kink motion.

In Nature this week

1. On the mundane applications of metamaterials: Katharine Sanderson feels that notwithstanding all the brouhaha surrounding metamaterials, their applications, if any, as and when they are found, will be rather mundane. Ouch!
2. Piers Coleman feels that the nexus between biology and physics will be found somewhere between the nano- and micro-metre scales;
3. Based on a paper of C R Hickenbroth et al on biasing chemical pathways using mechanical forces, Brad M Rosen and Virgil Percec, in a news and views piece, argue that mechanochemistry — triggering and controlling chemical reactions by the application of mechanical stress — holds a great promise.
4. Andrew Holmes pays tributes to the conducting polymers pioneer Alan Graham MacDiarmid, who passed away recently.

Have fun!

Split patterns in ordered precipitates

Do ordered () precipitates in the -rich () matrix undergo elastic stress driven splitting, or, is it particle coalescence which gives rise to split-looking patterns?

Luo et al, in a paper which is to appear in Acta Materialia, advance an altogether new mechanism, namely, nucleation of ordered particles at dislocations and the subsequent growth.

Even though the fact that ordered precipitates preferentially nucleate at dislocations in Ni-base alloys due to lattice mismatch is well known (See the 1966 classic paper of Ardell and Nicholson–with an appendix by Eshelby, for example), I have never come across any mention of the same in the context of particle splitting–though, from the paper, I understand that such a mechanism was discussed in the PhD thesis of Prof. Wang back in 1995.

Paper: Nucleation of ordered particles at dislocations and formation of split patterns

Authors: W Luo, C Shen and Y Wang

Abstract:

We investigated the effect of nucleation of ordered precipitates at dislocations and the subsequent growth of particle morphology through computer simulations using a phase-field model. The model treats simultaneously precipitates, dislocations and precipitate–dislocation interactions within a single algorithm. In particular, the model takes into account the structural discontinuity associated with a dislocation that leads to the formation of antiphase domains if the dislocation is within an ordered particle. Three long-range order parameters are used to describe the antiphase domains associated with L1₂ ordering and an additional set of non-conserved order parameters is introduced to characterize dislocations. We show that heterogeneous nucleation and subsequent growth of ordered precipitates at dislocations yield various “split” patterns, whose formation has been attributed to different mechanisms in literature.

Very interesting indeed!

Maximally fast algorithm for Cahn-Hilliard equation

Here is a follow-up paper on the unconditionally stable time step for diffuse interface methods.

Paper: Maximally fast coarsening algorithms

Authors: Mowei Cheng and Andrew D. Rutenberg

Abstract:

We present maximally fast numerical algorithms for conserved coarsening systems thatare stable and accurate with a growing natural time step . We compare the scaling structure obtained from our maximally fast conserved systems directly against the standard fixed time-step Euler algorithm, and find that the error scales as —so arbitrary accuracy can be achieved. For non-conserved systems, only effectively finite time steps are accessible for similar unconditionally stable algorithms.

Computational physics course notes online

The lecture notes of an upper-division Introduction to Computational Physics course in html and pdf formats:

A complete set of lecture notes for an upper-division computational physics course. Topics covered include scientific programming in C, the numerical solution of ordinary and partial differential equations, particle-in-cell codes, and Monte Carlo methods.

I especially liked the programming methodology adopted in the course, namely,

…write our own programs–completely from scratch–in a high-level language.

And, what is more, I liked the choice of programming language much more:

Of the above languages, we can immediately rule out C++, because object-orientation is an unnecessary complication (at least, for our purposes), and FORTRAN 90, because of the absence of an inexpensive compiler. The remaining options are FORTRAN 77 and C. I have chosen to use C (augmented by some of the useful, non-object-orientated features of C++) in this course, simply because I find the archaic features of FORTRAN 77 too embarrassing to teach students in the 21st century.

And, whatever little I read of the lecture notes I liked too. Take a look!

PS:- For those of you coming from a physics background, there are also other lecture notes of Prof. Richard Fitzpatrick that are available online here.

Unconditonally stable time steps for diffuse interface equations

Paper: Fast and accurate coarsening simulation with an unconditionally stable time step

Authors: Benjamin P. Vollmayr-Lee and Andrew D. Rutenberg

Abstract:

We present Cahn-Hilliard and Allen-Cahn numerical integration algorithms that are unconditionally stable and so provide significantly faster accuracy-controlled simulation. Our stability analysis is based on Eyre’s theorem and unconditional von Neumann stability analysis, both of which we present. Numerical tests confirm the accuracy of the von Neumann approach, which is straightforward and should be widely applicable in phase-field modeling. For the Cahn-Hilliard case, we show that accuracy can be controlled with an unbounded time step that grows with time as . We develop a classification scheme for the step exponent and demonstrate that a class of simple linear algorithms gives . For this class the speedup relative to a fixed time step grows with , the linear size of the system, as . With conservative choices for the parameters controlling accuracy and finite-size effects we find that an lattice can be integrated 300 times faster than with the Euler method.

The Eyre’s theorem referred to in the abstract is described in this report (ps file).

A review of domain coarsening using phase field models

Here is a review of Cahn-Hilliard and Allen-Cahn models with specific reference to coarsening studies:

Author: Bray, A.J.

Source: Advances In Physics, Volume 43, Number 3, May/June 1994, pp. 357-459 (103)

Abstract:

The theory of phase-ordering dynamics, that is the growth of order through domain coarsening when a system is quenched from the homogeneous phase into a broken-symmetry phase, is reviewed, with the emphasis on recent developments. Interest will focus on the scaling regime that develops at long times after the quench. How can one determine the growth laws that describe the time dependence of characteristic length scales, and what can be said about the form of the associated scaling functions? Particular attention will be paid to systems described by more complicated order parameters than the simple scalars usually considered, for example vector and tensor fields. The latter are needed, for example, to describe phase ordering in nematic liquid crystals, on which there have been a number of recent experiments. The study of topological defects (domain walls, vortices, strings and monopoles) provides a unifying framework for discussing coarsening in these different systems

The review collects all the important results pertaining to the mathematical aspects of the problem and describes them in a very lucid fashion, making it a very pleasant read indeed.