Heterogeneous contributions can jeopardize cooperation in the public goods game.

When studying social dilemma games, a crucial question arises regarding the impact of general heterogeneity on cooperation, which has been shown to have positive effects in numerous studies. Here, we demonstrate that heterogeneity in the contribution value for the focal public goods game can jeopardize cooperation. We show that there is an optimal contribution value in the homogeneous case that most benefits cooperation depending on the lattice. In a heterogeneous scenario, where strategy and contribution coevolve, cooperators making contributions higher than the optimal value end up harming those who contribute less. This effect is notably detrimental to cooperation in the square lattice with von Neumann neighborhood, while it can have no impact in other lattices. Furthermore, in parameter regions where a higher-contributing cooperator cannot normally survive alone, the exploitation of lower-value contribution cooperators allows their survival, resembling a parasitic behavior. To obtain these results, we examined the effect of various distributions for the contribution values in the initial condition and we conducted Monte Carlo simulations.

A single active ring model with velocity self-alignment.

Cellular tissue behavior is a multiscale problem. At the cell level, out of equilibrium, biochemical reactions drive physical cell-cell interactions in a typical active matter process. Cell modeling computer simulations are a robust tool to explore countless possibilities and test hypotheses. Here, we introduce a two-dimensional, extended active matter model for biological cells. A ring of interconnected self-propelled particles represents the cell. Neighboring particles are subject to harmonic and bending potentials. Within a characteristic time, each particle's self-velocity tends to align with its scattering velocity after an interaction. Translational modes, rotational modes, and mixtures of these appear as collective states. Using analytical results derived from active Brownian particles, we identify effective characteristic time scales for ballistic and diffusive movements. Finite-size scale investigation shows that the ring diffusion increases linearly with its size when in collective movement. A study on the ring shape reveals that all collective states are present even when bending forces are weak. In that case, when in a translational mode, the collective velocity aligns with the largest ring's direction in a spontaneous polarization emergence.

Symbiotic behaviour in the public goods game with altruistic punishment.

Finding ways to overcome the temptation to exploit one another is still a challenge in behavioural sciences. In the framework of evolutionary game theory, punishing strategies are frequently used to promote cooperation in competitive environments. Here, we introduce altruistic punishers in the spatial public goods game. This strategy acts as a cooperator in the absence of defectors, otherwise it will punish all defectors in their vicinity while bearing a cost to do so. We observe three distinct behaviours in our model: i) in the absence of punishers, cooperators (who don't punish defectors) are driven to extinction by defectors for most parameter values; ii) clusters of punishers thrive by sharing the punishment costs when these are low; iii) for higher punishment costs, punishers, when alone, are subject to exploitation but in the presence of cooperators can form a symbiotic spatial structure that benefits both. This last observation is our main finding since neither cooperation nor punishment alone can survive the defector strategy in this parameter region and the specificity of the symbiotic spatial configuration shows that lattice topology plays a central role in sustaining cooperation. Results were obtained by means of Monte Carlo simulations on a square lattice and subsequently confirmed by a pairwise comparison of different strategies' payoffs in diverse group compositions, leading to a phase diagram of the possible states.

Phase transitions in hard-core lattice gases on the honeycomb lattice.

We study lattice gas systems on the honeycomb lattice where particles exclude neighboring sites up to order k (k=1,...,5) from being occupied by another particle. Monte Carlo simulations were used to obtain phase diagrams and characterize phase transitions as the system orders at high packing fractions. For systems with first-neighbors exclusion (1NN), we confirm previous results suggesting a continuous transition in the two-dimensional Ising universality class. Exclusion up to second neighbors (2NN) lead the system to a two-step melting process where, first, a high-density columnar phase undergoes a first-order phase transition with nonstandard scaling to a solidlike phase with short-range ordered domains and, then, to fluidlike configurations with no sign of a second phase transition. 3NN exclusion, surprisingly, shows no phase transition to an ordered phase as density is increased, staying disordered even to packing fractions up to 0.98. The 4NN model undergoes a continuous phase transition with critical exponents close to the three-state Potts model. The 5NN system undergoes two first-order phase transitions, both with nonstandard scaling. We, also, propose a conjecture concerning the possibility of more than one phase transition for systems with exclusion regions further than 5NN based on geometrical aspects of symmetries.

Modeling of Droplet Evaporation on Superhydrophobic Surfaces.

When a drop of water is placed on a rough surface, there are two possible extreme regimes of wetting: the one called Cassie-Baxter (CB) with air pockets trapped underneath the droplet and the one called the Wenzel (W) state characterized by the homogeneous wetting of the surface. A way to investigate the transition between these two states is by means of evaporation experiments, in which the droplet starts in a CB state and, as its volume decreases, penetrates the surface's grooves, reaching a W state. Here we present a theoretical model based on the global interfacial energies for CB and W states that allows us to predict the thermodynamic wetting state of the droplet for a given volume and surface texture. We first analyze the influence of the surface geometric parameters on the droplet's final wetting state with constant volume and show that it depends strongly on the surface texture. We then vary the volume of the droplet, keeping the geometric surface parameters fixed to mimic evaporation and show that the drop experiences a transition from the CB to the W state when its volume reduces, as observed in experiments. To investigate the dependency of the wetting state on the initial state of the droplet, we implement a cellular Potts model in three dimensions. Simulations show very good agreement with theory when the initial state is W, but it disagrees when the droplet is initialized in a CB state, in accordance with previous observations which show that the CB state is metastable in many cases. Both simulations and the theoretical model can be modified to study other types of surfaces.