On the micro mechanics of one-dimensional normal compression

Discrete-element modelling has been used to investigate the micro mechanics of one-dimensional compression. One-dimensional compression is modelled in three dimensions using an oedometer and a large number of particles, and without the use of agglomerates. The fracture of a particle is governed by the octahedral shear stress within the particle due to the multiple contacts and a Weibull distribution of strengths. Different fracture mechanisms are considered, and the influence of the distribution of fragments produced for each fracture on the global particle size distribution and the slope of the normal compression line is investigated. Using the discrete-element method, compression is related to the evolution of a fractal distribution of particles. The compression index is found to be solely a function of the strengths of the particles as a function of size

Aspiring to the fittest and promotion of cooperation in the prisoner's dilemma game

Strategy changes are an essential part of evolutionary games. Here we introduce a simple rule that, depending on the value of a single parameter $w$, influences the selection of players that are considered as potential sources of the new strategy. For positive $w$ players with high payoffs will be considered more likely, while for negative $w$ the opposite holds. Setting $w$ equal to zero returns the frequently adopted random selection of the opponent. We find that increasing the probability of adopting the strategy from the fittest player within reach, i.e. setting $w$ positive, promotes the evolution of cooperation. The robustness of this observation is tested against different levels of uncertainty in the strategy adoption process and for different interaction network. Since the evolution to widespread defection is tightly associated with cooperators having a lower fitness than defectors, the fact that positive values of $w$ facilitate cooperation is quite surprising. We show that the results can be explained by means of a negative feedback effect that increases the vulnerability of defectors although initially increasing their survivability. Moreover, we demonstrate that the introduction of $w$ effectively alters the interaction network and thus also the impact of uncertainty by strategy adoptions on the evolution of cooperation.Comment: 7 two-column pages, 5 figures; accepted for publication in Physical Review

Restricted connections among distinguished players support cooperation

We study the evolution of cooperation within the spatial prisoner's dilemma game on a square lattice where a fraction of players $\mu$ can spread their strategy more easily than the rest due to a predetermined larger teaching capability. In addition, players characterized with the larger teaching capability are allowed to temporarily link with distant opponents of the same kind with probability $p$, thus introducing shortcut connections among the distinguished. We show that these additional temporary connections are able to sustain cooperation throughout the whole range of the temptation to defect. Remarkably, we observe that as the temptation to defect increases the optimal $\mu$ decreases, and moreover, only minute values of $p$ warrant the best promotion of cooperation. Our study thus indicates that influential individuals must be few and sparsely connected in order for cooperation to thrive in a defection prone environment.Comment: 6 two-column pages, 6 figures; accepted for publication in Physical Review

On Phase Transitions to Cooperation in the Prisoner's Dilemma

Game theory formalizes certain interactions between physical particles or between living beings in biology, sociology, and economics, and quantifies the outcomes by payoffs. The prisoner's dilemma (PD) describes situations in which it is profitable if everybody cooperates rather than defects (free-rides or cheats), but as cooperation is risky and defection is tempting, the expected outcome is defection. Nevertheless, some biological and social mechanisms can support cooperation by effectively transforming the payoffs. Here, we study the related phase transitions, which can be of first order (discontinous) or of second order (continuous), implying a variety of different routes to cooperation. After classifying the transitions into cases of equilibrium displacement, equilibrium selection, and equilibrium creation, we show that a transition to cooperation may take place even if the stationary states and the eigenvalues of the replicator equation for the PD stay unchanged. Our example is based on adaptive group pressure, which makes the payoffs dependent on the endogeneous dynamics in the population. The resulting bistability can invert the expected outcome in favor of cooperation.Comment: For related work see http://www.soms.ethz.ch

Impact of aging on the evolution of cooperation in the spatial prisoner's dilemma game

Aging is always present, tailoring our interactions with others and postulating a finite lifespan during which we are able to exercise them. We consider the prisoner's dilemma game on a square lattice, and examine how quenched age distributions and different aging protocols influence the evolution of cooperation when taking the life experience and knowledge accumulation into account as time passes. In agreement with previous studies, we find that a quenched assignment of age to players, introducing heterogeneity to the game, substantially promotes cooperative behavior. Introduction of aging and subsequent death as a coevolutionary process may act detrimental on cooperation but enhances it efficiently if the offspring of individuals that have successfully passed their strategy is considered newborn. We study resulting age distributions of players, and show that the heterogeneity is vital yet insufficient for explaining the observed differences in cooperator abundance on the spatial grid. The unexpected increment of cooperation levels can be explained by a dynamical effect that has a highly selective impact on the propagation of cooperator and defector states.Comment: 7 two-column pages, 5 figures; accepted for publication in Physical Review

Chemical fracture and distribution of extreme values

When a corrosive solution reaches the limits of a solid sample, a chemical fracture occurs. An analytical theory for the probability of this chemical fracture is proposed and confirmed by extensive numerical experiments on a two dimensional model. This theory follows from the general probability theory of extreme events given by Gumbel. The analytic law differs from the Weibull law commonly used to describe mechanical failures for brittle materials. However a three parameters fit with the Weibull law gives good results, confirming the empirical value of this kind of analysis.Comment: 7 pages, 5 figures, to appear in Europhysics Letter

Statistical mechanics of systems with heterogeneous agents: Minority Games

We study analytically a simple game theoretical model of heterogeneous interacting agents. We show that the stationary state of the system is described by the ground state of a disordered spin model which is exactly solvable within the simple replica symmetric ansatz. Such a stationary state differs from the Nash equilibrium where each agent maximizes her own utility. The latter turns out to be characterized by a replica symmetry broken structure. Numerical results fully agree with our analytic findings.Comment: 4 pages, 1 Postscript figure. Revised versio

Conditional strategies and the evolution of cooperation in spatial public goods games

The fact that individuals will most likely behave differently in different situations begets the introduction of conditional strategies. Inspired by this, we study the evolution of cooperation in the spatial public goods game, where besides unconditional cooperators and defectors, also different types of conditional cooperators compete for space. Conditional cooperators will contribute to the public good only if other players within the group are likely to cooperate as well, but will withhold their contribution otherwise. Depending on the number of other cooperators that are required to elicit cooperation of a conditional cooperator, the latter can be classified in as many types as there are players within each group. We find that the most cautious cooperators, such that require all other players within a group to be conditional cooperators, are the undisputed victors of the evolutionary process, even at very low synergy factors. We show that the remarkable promotion of cooperation is due primarily to the spontaneous emergence of quarantining of defectors, which become surrounded by conditional cooperators and are forced into isolated convex "bubbles" from where they are unable to exploit the public good. This phenomenon can be observed only in structured populations, thus adding to the relevance of pattern formation for the successful evolution of cooperation.Comment: 7 two-column pages, 7 figures; accepted for publication in Physical Review

New methods for unmixing sediment grain size data

Grain size distribution (GSD) data are widely used in Earth sciences and although large data sets are regularly generated, detailed numerical analyses are not routine. Unmixing GSDs into components can help understand sediment provenance and depositional regimes/processes. End-member analysis (EMA), which fits one set of end-members to a given data set, is a powerful way to unmix GSDs into geologically meaningful parts. EMA estimates end-members based on covariability within a data set and can be considered as a nonparametric approach. Available EMA algorithms, however, either produce suboptimal solutions or are time consuming. We introduce unmixing algorithms inspired by hyperspectral image analysis that can be applied to GSD data and which provide an improvement over current techniques. Nonparametric EMA is often unable to identify unimodal grain size subpopulations that correspond to single sediment sources. An alternative approach is single-specimen unmixing (SSU), which unmixes individual GSDs into unimodal parametric distributions (e.g., lognormal). We demonstrate that the inherent nonuniqueness of SSU solutions renders this approach unviable for estimating underlying mixing processes. To overcome this, we develop a new algorithm to perform parametric EMA, whereby an entire data set can be unmixed into unimodal parametric end-members (e.g., Weibull distributions). This makes it easier to identify individual grain size subpopulations in highly mixed data sets. To aid investigators in applying these methods, all of the new algorithms are available in AnalySize, which is GUI software for processing and unmixing grain size data

Discrete element modelling of rock communition in a cone crusher using a bonded particle model

It is known that discrete element method modelling (DEM) of rock size reduction can be achieved by two approaches: the population balance model (PBM) and the bonded particle model (BPM). However, only PBM has been successfully used in DEM modelling cone crusher in the literature. The aim of this paper is to explore the feasibility of using the BPM to represent the size reduction of rock experienced within the cone crusher chamber. The feed rock particles were represented by isotropic dense random packing agglomerates. The simulation results were compared with the PBM simulation results, and it was shown that the BPM cone crusher model was able to satisfactorily replicate the performance of a cone crusher as well and it can provide more accurate prediction of the percentage of the fine products. In addition, the novel contribution here is that the rock feed material comprises particles of realistic shapes which break into more realistically shaped fragments compared with the fragments with defined shapes in the PBM model