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Robert S. Farr

Publications and source records attributed to Robert S. Farr.

4 recordsLinked to original sources

Ab initio simulation of market dynamics

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, but is required as a medium of exchange. A collection of such actors are then simulated interacting through market rules which create a double auction for each of the goods. This framework captures the self-consistent, rational behavior of independent actors, including how they make compromises between purchases of different goods; so goes beyond price-demand curves, and also generates the small-scale fluctuations from individual trades. We find that stable price formation requires a model that includes time-preference for the actors. Fluctuations in prices show a distribution with algebraic tails. Including inflation expectations leads to complex, damped or un-damped price oscillations. We attempt to model the dynamics of input-output economic models, but find it difficult to keep prices stable with the assumptions employed.

physics.soc-ph

Easily repairable networks

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 show that for networks on the square and triangular lattice, this bound is achievable and results in a network with exactly three levels of structural hierarchy. We extend our results to networks subject to repeated attacks, in which the repairs themselves must be repairable. We find that, in exchange for a modest increase in repair cost, such networks are able to withstand any number of attacks.

physics.soc-ph

Random close packing fractions of lognormal distributions of hard spheres

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 case of lognormal distributions of sphere sizes and mixtures of such populations. We show that the results compare well to two much slower algorithms for directly simulating spheres in three dimensions, and show that the algorithm is fast enough to tackle inverse problems in particle packing: designing size distributions to meet required criteria. The one-dimensional method used in this paper is implemented as a computer code in the C programming language, available at http://sourceforge.net/projects/spherepack1d/ under the terms of the GNU general public licence (version 2).

cond-mat.mtrl-sci

Close packing density of polydisperse hard spheres

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 physics and engineering. However, the particle size distribution of a real granular material is never monodisperse. Here we present a simple but accurate approximation for the random close packing density of hard spheres of any size distribution, based upon a mapping onto a one-dimensional problem. To test this theory we performed extensive simulations for mixtures of elastic spheres with hydrodynamic friction. The simulations show a general (but weak) dependence of the final (essentially hard sphere) packing density on fluid viscosity and on particle size, but this can be eliminated by choosing a specific relation between mass and particle size, making the random close packed volume fraction well-defined. Our theory agrees well with the simulations for bidisperse, tridisperse and log-normal distributions, and correctly reproduces the exact limits for large size ratios.

cond-mat.soft