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- Maximum thermodynamic power coefficient of a wind turbinePublication . Tavares, Jose; Patricio, PedroAccording to the centenary Betz-Joukowsky law, the power extracted from a wind turbine inopen flow cannot exceed 16/27 of the wind transported kinetic energy rate. This limit is usuallyinterpreted as an absolute theoretical upper bound for the power coefficient of all wind turbines,but it was derived in the special case of incompressible fluids. Following the same steps of Betzclassical derivation, we model the turbine as an actuator disk in a one dimensional fluid flowbut consider the general case of a compressible reversible fluid, such as air. In doing so, we areobliged to use not only the laws of mechanics but also and explicitly the laws of thermodynamics.We show that the power coefficient depends on the inlet wind Mach numberM0,andthatitsmaximum value exceeds the Betz-Joukowsky limit. We have developed a series expansion forthe maximum power coefficient in powers of the Mach number M0that unifies all the cases (compressible and incompressible) in the same simple expression: 𝜂max= 16∕27 + 8∕243M20.
- 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.