Mesoscopic model for colloidal particles, powders and granular solids

A simulation model is presented, comprising elastic spheres with a short range attraction. Besides conservative forces, radial- and shear friction, and radial noise are added. The model can be used to simulate colloids, granular solids and powders, and the parameters may be related to experimental systems via the range of attraction and the adhesion energy. The model shares the simplicity and speed of Dissipative Particle Dynamics (DPD), yet the predictions are rather non-trivial. We demonstrate that the model predicts the correct scaling relations for fracture of granular solids, and we present a schematic phase diagram. This shows liquid-vapor coexistence for sufficiently large interaction range, with a surface tension that follows Ising criticality. For smaller interaction range only solid-vapor coexistence is found, but for very small attractive interaction range stable liquid-vapor coexistence reappears due to pathological stability of the solid phase. At very low temperature the model forms a glassy state.Comment: 12 pages, 6 figures, accepted by Physical Review E, typos correcte

From Molecular Dynamics to hydrodynamics - a novel Galilean invariant thermostat

This article proposes a novel thermostat applicable to any particle-based dynamic simulation. Each pair of particles is thermostated either (with probability P) with a pairwise Lowe-Andersen thermostat, or (with probability 1-P) with a thermostat that is introduced here, which is based on a pairwise interaction similar to the Nose-Hoover thermostat. When the pairwise Nose-Hoover thermostat dominates (low P), the liquid has a high diffusion coefficient and low viscosity, but when the Lowe-Andersen thermostat dominates, the diffusion coefficient is low and viscosity is high. This novel Nose-Hoover-Lowe-Andersen thermostat is Galilean invariant and preserves both total linear and angular momentum of the system, due to the fact that the thermostatic forces between each pair of the particles are pairwise additive and central. We show by simulation that this thermostat also preserves hydrodynamics. For the (non-interacting) ideal gas at P=0, the diffusion coefficient diverges and viscosity is zero, while for P>0 it has a finite value. By adjusting probability P, the Schmidt number can be varied by orders of magnitude. The temperature deviation from the required value is at least an order of magnitude smaller than in Dissipative Particle Dynamics (DPD), while the equilibrium properties of the system are very well reproduced. Applications of this thermostat include all standard molecular dynamic simulations of dense liquids and solids with any type of force field, as well as hydrodynamic simulation of multi-phase systems with largely different bulk viscosities, including surface viscosity, and of dilute gases and plasmas

Consumers don't play dice, influence of social networks and advertisements

Empirical data of supermarket sales show stylised facts that are similar to stock markets, with a broad (truncated) Levy distribution of weekly sales differences in the baseline sales [R.D. Groot, Physica A 353 (2005) 501]. To investigate the cause of this, the influence of social interactions and advertisements are studied in an agent-based model of consumers in a social network. The influence of network topology was varied by using a small-world network, a random network and a Barabasi-Albert network. The degree to which consumers value the opinion of their peers was also varied. On a small-world and random network we find a phase-transition between an open market and a locked-in market that is similar to condensation in liquids. At the critical point, fluctuations become large and buying behaviour is strongly correlated. However, on the small world network the noise distribution at the critical point is Gaussian, and critical slowing down occurs which is not observed in supermarket sales. On a scale-free network, the model shows a transition between a gas-like phase and a glassy state, but at the transition point the noise amplitude is much larger than what is seen in supermarket sales. To explore the role of advertisements, a model is studied where imprints are placed on the minds of consumers that ripen when a decision for a product is made. The correct distribution of weekly sales returns follows naturally from this model, as well as the noise amplitude, the correlation time and cross-correlation of sales fluctuations. For particular parameter values, simulated sales correlation shows power law decay in time. The model predicts that social interaction helps to prevent aversion, and that products are viewed more positively when their consumption rate is higher.Comment: Accepted for publication in Physica

Minority Game of price promotions in fast moving consumer goods markets

A variation of the Minority Game has been applied to study the timing of promotional actions at retailers in the fast moving consumer goods market. The underlying hypotheses for this work are that price promotions are more effective when fewer than average competitors do a promotion, and that a promotion strategy can be based on past sales data. The first assumption has been checked by analysing 1467 promotional actions for three products on the Dutch market (ketchup, mayonnaise and curry sauce) over a 120-week period, both on an aggregated level and on retailer chain level. The second assumption was tested by analysing past sales data with the Minority Game. This revealed that high or low competitor promotional pressure for actual ketchup, mayonnaise, curry sauce and barbecue sauce markets is to some extent predictable up to a forecast of some 10 weeks. Whereas a random guess would be right 50% of the time, a single-agent game can predict the market with a success rate of 56% for a 6 to 9 week forecast. This number is the same for all four mentioned fast moving consumer markets. For a multi-agent game a larger variability in the success rate is obtained, but predictability can be as high as 65%. Contrary to expectation, the actual market does the opposite of what game theory would predict. This points at a systematic oscillation in the market. Even though this result is not fully understood, merely observing that this trend is present in the data could lead to exploitable trading benefits. As a check, random history strings were generated from which the statistical variation in the game prediction was studied. This shows that the odds are 1:1,000,000 that the observed pattern in the market is based on coincidence.Comment: 19 pages, 10 figures, accepted for publication in Physica