302 citations · 507 across the 14 of their papers we have counts for
15 papers
Ab initio simulation of market dynamics
Robert S. Farr
We provide simple models for the utility function (or psychology) of an actor trading a multitude of goods for money. In this framework, money has no intrinsic consumption value, b…
A phase transition creates the geometry of the continuum from discrete space
Robert Stanley Farr, Thomas M. A. Fink
Models of discrete space and space-time that exhibit continuum-like behavior at large lengths could have profound implications for physics. They may tame the infinities that arise…
The flow and evolution of ice-sucrose crystal mushes
Andrew Gilbert, Felix Oppong, Robert Farr
We study the rheology of suspensions of ice crystals at moderate to high volume fractions in a sucrose solution in which they are partially soluble; a model system for a wide class…
Optimal counter-current exchange networks
Robert S Farr, Yong Mao
We present a general analysis of exchange devices linking their efficiency to the geometry of the exchange surface and supply network. For certain parameter ranges, we show that th…
Eigenvalues of neutral networks: interpolating between hypercubes
T. Reeves, R. S. Farr, J. Blundell +2
A neutral network is a subgraph of a Hamming graph, and its principal eigenvalue determines its robustness: the ability of a population evolving on it to withstand errors. Here we…
Easily repairable networks
Robert S. Farr, John L. Harer, Thomas M. A. Fink
We introduce a simple class of distribution networks which withstand damage by being repairable instead of redundant. We prove a lower bound for the expected cost of repair, and sh…
Optimisation of fractal spaceframes under gentle compressive load
Daniel Rayneau-Kirkhope, Yong Mao, Robert Farr
The principle of hierarchical design is a prominent theme in many natural systems where mechanical efficiency is of importance. Here we establish the properties of a particular hie…
Random close packing fractions of lognormal distributions of hard spheres
Robert S. Farr
We apply a recent one-dimensional algorithm for predicting random close packing fractions of polydisperse hard spheres [Farr and Groot, J. Chem. Phys. 133, 244104 (2009)] to the ca…
Bifurcations in the optimal elastic foundation for a buckling column
Daniel Rayneau-Kirkhope, Robert Farr, K. Ding +1
We investigate the buckling under compression of a slender beam with a distributed lateral elastic support, for which there is an associated cost. For a given cost, we study the op…
Estimate for the fractal dimension of the Apollonian gasket in d dimensions
R. S. Farr, E. Griffiths
We adapt a recent theory for the random close packing of polydisperse spheres in three dimensions [R. S. Farr and R. D. Groot, J. Chem. Phys. {\bf 131} 244104 (2009)] in order to p…
Fractal space frames and metamaterials for high mechanical efficiency
R. S. Farr, Y. Mao
A solid slender beam of length , made from a material of Young's modulus and subject to a gentle compressive force , requires a volume of material proportional to $L^{3}f…
Sintering behavior of two roughened crystals just after contact
R. S. Farr, M. J. Izzard
We consider two spherical, roughened crystals with approximately isotropic surface free energy which are brought into contact and begin to sinter. We argue that the geometry immedi…
Fractal design for an efficient shell strut under gentle compressive loading
R. S. Farr
Because of Euler buckling, a simple strut of length and Young modulus requires a volume of material proportional to in order to support a compressive force $F…
Fractal design for efficient brittle plates under gentle pressure loading
R. S. Farr
We consider a plate made from an isotropic but brittle elastic material, which is used to span a rigid aperture, across which a small pressure difference is applied. The problem we…
Close packing density of polydisperse hard spheres
Robert S. Farr, Robert D. Groot
The most efficient way to pack equally sized spheres isotropically in 3D is known as the random close packed state, which provides a starting point for many approximations in physi…