Rafi Blumenfeld ...
... and theoretical physics: a never-ending story
✓ An `uncertainty principle' in granular mechanics.
Below is an excerpt on this issue from our review chapter, "Granular Systems", in The Oxford Handbook of Soft Condensed Matter (Oxford University Press, Oxford, UK, 2015):
"...these calculations are idealised and taking into consideration the redundancy is problematic. In real systems in mechanical equilibrium, exact redundancy is possible only when a grain has exactly two force-carrying contacts, in which case they must be equal, opposite and align along the line between the contacts. For grains with three contacts or more, it is impossible to determine the force directions in general with absolute accuracy and, in particular, whether those coincide exactly at a point. At most one can say that the forces apply very small torques to the grain because the `region of coincidence' (the shaded region in figure 5.10b) is small. Consequently, except for two-contact grains, the equations are never really redundant - they are at most negligible. It follows that the value of $z_c$ depends to some extent on the level of accuracy of the measurement of forces; the more accurate the measurement, the more torque balance equations need to be included and the higher the value of $z_c$.
This sounds strangely like an `uncertainty principle' - the more accurate the measurement the more equations one needs to determine the stresses. This `uncertainty principle' is also a manifestation of the inherent relation between the structure on the granular level and the stress field that the assembly supports ...".
✓ There seem to be intriguing connections between the formalism of statistical mechanics and the nature of reality, time and our perception of these two.
✓ Shahar Amitai has passed his viva with minor corrections. Congratulations Dr Amitai!
✓ Our reply to an interesting comment to our paper on the failure of the volume function in granular statistical mechanics (with Amitai, Jordan and Hihinashvili) has been published in Phys. Rev. Lett. "Reply to comment on "Failure of the Volume Function in Granular Statistical Mechanics and an Alternative Formulation"
✓ Paper (with S. Amitai) identifying different types of structural entropy in granular matter, calculating explicitly expectation values of measurable quantities and deriving an equation of state, appeared:
"Affine and topological structural entropies in granular statistical mechanics: Explicit calculations and equation of state"
✓ Organising an international Symposium (with Mike Cates, Mark Warner and Tom McLeish) 2nd Edwards Symposium: Challenges and Opportunities in Soft Matter , (September 6 - 8) Cambridge, UK
✓ Paper (with T. Matsushima) showing inherent universality-like behaviour and self-organisation of granular matter appeared:
"Fundamental structural characteristics of planar granular assemblies: self-organisation and scaling away friction and initial state"
✓ Paper (with J. Ma) showing stress chains bending backward appeared:
"Bending back stress chains and unique behaviour of granular matter in cylindrical geometries"
✓ Paper (with S. Amitai) on diffusion of finite size particles in porous media appeared:
"Modifying continuous-time random walks to model finite-size particle diffusion in granular porous media"
✓ Invited talks in conferences:
(ii) "The 2nd International Granular Flow Workshop", Guiyang, China, August 21 - 24 (Talk title: Granular statistical mechanics: different structural entropy sources, exact calculations, and the origin of N!)
(i) "From supercooled liquids to glasses: Current challenges for amorphous materials", Kavli Inst. of Theoretical Science, Beijing, August 7 - 18 (Talk title: Entropy in disordered particulate systems);
(iii) "The 10th National Conference on Soft Matter and Biophysics, Xiamen, China, March 25 - 28 (Opening talk, Title: Self-organisation of structural characteristics in packing of granular materials in 2D and implications)
These pages have grown uncontrollably from a modest beginning in 1993, when a home page was a rarity. I cannot pinpoint when exactly over the years was it that I lost the fight against this unstable self-(dis)organised growth. I was probably never in control.
You may notice that the pages are written in the old basic HTML format. This is because none of the current fancy new softwares, which essentially do all the nitty-gritty work, existed. Hence, there are no fancy java scripts, flashing lights and colours, background music, or automatically starting videos. This may be one of the last bastion of the HTML purists, uncluttered by sights or sounds.
As my friend Peter once put it:
"This is about delegation of responsibility. About trust. About subsidiarity.
It's a small-scale mirror of so many of our every day problems."
Anyway, my publication list is updated regularly ... after a fashion. The rest not so much. If your time is short, I recommend to browse my 'Selected publications' and then move to the less frequently updated 'research interests' page. Much of the latter is distilled into limericks at the bottom of this page. You are, of course, welcome to visit all the pages but be warned that there is always the possibility of getting lost in the overgrown meandering paths.
CV, publications, interests, and more
Often, when I finish developing a model or a theory, I write a limerick that summarises it. The weight and rythm are not always great, but they do describe, as accurately as possible in a limerick form, the modelling ideas and the relevant physics.
Below are the limericks I wrote so far, each with a link to a paper that the work produced, if it has.
On Force Chains paper
Force chains can be found
And in granular materials they abound
Now although isostaticity
Has caused great turbidity
That particular stress theory is sound
(RB April 2006)
On Stato-elasticity I (paper in preparation)
Some put their faith in Elasticity
Others swear on Isostaticity
But I stand before you
To tell you boldly
That Stato-elasticity is the one and only
(RB April 2008)
On Stato-elasticity II (paper in preparation)
A theory called Elasticity
Was challenged by Isostaticity
But I tell you boldly
That real packs mostly
Should follow Stato-elasticity
(RB April 2008)
On Couette flow of da Vinci fluids paper 1,
O' whirling sands in the cylinder flow
Layer by streamline they clump and they slow
Grains rub their neighbour
Dissipating much labour
And da Vinci fluids explain it, gung-ho!
(RB November 2010)
Polymer chain pullout with AFM paper 1, paper 2
Pick a polymer chain with the tip
Bond it tight, don't let it slip
It pulls out in a stutter
Here a jump, there a flutter
Thus, through the tube it would not zip
(RB April 2006)
Fractures propagating in disordered materials paper 1, paper 2
Fractures evolving in disordered matter
Spawn voids that expand, grow large and scatter
Swallowed by the crack
With a supersonic smack
They get to become part of the big antimatter
(RB September 2014)
On modeling Disordered Auxetics paper 1, paper 2
On pulling they swell, on pushing they dense
Auxetic materials defy common sense
They expand and dilate
Causing heated debate
But iso-auxeticity dispels the suspense
(RB June 2015)
On contact granular statistical mechanics I (paper in preparation)
One moment they're there and then they are gone
Inter-grain contacts do not linger on
Their dynamics mysterious
And their modelling spurious
But contact potential explains it, c'est bon!
(RB December 2015)
On contact granular statistical mechanics II (paper in preparation)
Shear them to slide and knock them to clap
Inter-grain contacts are an energy trap
Their dynamics obscure
To the theorist's pure
But contacture statistics fills out the gap
(RB December 2015)
On Sam Edwards paper
He pushed science to places unmanned
Made physics of squishies and sand
And all with some wit and Chablis glass in hand
(RB April 2016)
On Force Chains Curving Back paper
Back-curving stress chains in cylinders loop
Detected and measured in Behringer’s group
They leak to the cone
They branch on and on
And isostaticty explains all this soup
(Experimental figure courtesy of Jie Zhang)
(RB April 2016)
On Archimedes Law in penetration into granular media
Plunge a rod into the sand
Observe the turn, then linear band
The curve is robust
Its model a must
And, by Archimedes, we now understand
(RB August 2017)