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- Inheritances, social classes, and wealth distributionPublication . Patricio, Pedro; Araujo, NunoWe consider a simple theoretical model to investigate the impact of inheritances on the wealth distribution. Wealth is described as a finite resource, which remains constant over different generations and is divided equally among offspring. All other sources of wealth are neglected. We consider different societies characterized by a different offspring probability distribution. We find that, if the population remains constant, the society reaches a stationary wealth distribution. We show that inequality emerges every time the number of children per family is not always the same. For realistic offspring distributions from developed countries, the model predicts a Gini coefficient of G approximate to 0.3. If we divide the society into wealth classes and set the probability of getting married to depend on the distance between classes, the stationary wealth distribution crosses over from an exponential to a power-law regime as the number of wealth classes and the level of class distinction increase.
- Convection patterns gradients of non-living and living micro-entities in hydrogelsPublication . Canadas, Raphaël F.; Patricio, Pedro; Brancato, Virginia; Gasperini, Luca; Caballero, David; Pires, Ricardo A.; Costa, João; Pereira, Hélder; Yong, Ping; da Silva, Lucília P.; Chen, Jie; Kundu, Subhas C.; Araujo, Nuno; Reis, Rui L.; Marques, AP; Oliveira, Joaquim M.Inducing thermal gradients in two injected fluid systems results in the temporal formation of mixing conductive streams. If preserved through sol-gel transition, this mechanism can be used to drive and pattern non-living and living entities in mixed hydrogels. Interfaces are vital in nature, where gradients of non-living and living entities build distinct yet continuous integrated living tissues. However, the common tissue fabrication methodologies often result in dissimilar interfaces, lacking continuity through the interfaced engineered tissues. Thus, there is an urgent need for the fabrication of heterotypic but continuous engineered tissues with spatial control over biomimetic features. Here, we demonstrate the influence of gel injection temperature on the patterning of gradients of non-living and living entities. The experimental part was confirmed by numerical modelling, showing the formation of convective lines which spatially drive microscale microparticle and cells when different temperatures are applied in the sequential injection of two gels. Based on this finding, pure gellan gum (GG) and blended GG with methacrylated gelatin (Ge1MA) systems were used to program the formation of gradient features in hydrogels, such as microparticle and cells distribution patterns, polymeric bioactivity, degradation, controlled release, and stiffness. The correlation between gel injection temperature and gradients formation can be applied to tissue interface modelling, regeneration, drug release systems, and broader materials engineering fields.
- Smoluchowski equations for linker-mediated irreversible aggregationPublication . Tavares, Jose; Antunes, Goncalo C.; Dias, Cristóvão; da Gama, M. M. Telo; Araujo, NunoWe developed a generalized Smoluchowski framework to study linker-mediated aggregation, where linkers and particles are explicitly taken into account. We assume that the bonds between linkers and particles are irreversible, and that clustering occurs through limited diffusion aggregation. The kernel is chosen by analogy with single-component diffusive aggregation but the clusters are distinguished by their number of particles and linkers. We found that the dynamics depends on three relevant factors, all tunable experimentally: (i) the ratio of the diffusion coefficients of particles and linkers; (ii) the relative number of particles and linkers; and (iii) the maximum number of linkers that may bond to a single particle. To solve the Smoluchoski equations analytically we employ a scaling hypothesis that renders the fraction of bondable sites of a cluster independent of the size of the cluster, at each instant. We perform numerical simulations of the corresponding lattice model to test this hypothesis. We obtain results for the asymptotic limit, and the time evolution of the bonding probabilities and the size distribution of the clusters. These findings are in agreement with experimental results reported in the literature and shed light on unexplained experimental observations.