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Abstract:
Photocatalytic CO2 reduction has emerged as a promising strategy for converting solar energy into valuable chemicals, capturing the attention of scientists across various disciplines. Organic and inorganic perovskites, particularly methylammonium lead bromide (MAPbBr3), have demonstrated potential in this field due to their remarkable visible-light response and carrier transport properties. However, the catalytic performance of pristine MAPbBr3 has been limited by severe charge recombination, hindering its applicability in photocatalytic systems. Here, we show that a MAPbBr3/Bi2WO6 (MA/BWO) heterojunction significantly enhances photocatalytic CO2 reduction performance compared to individual pristine MA or BWO. This enhancement is evidenced by the superior performance of the 25% MA/BWO composite, which exhibits CO and CH4 release rates of 1.82 μmol/g/h and 0.08 μmol/g/h, respectively. This improvement is attributed to the direct Z-scheme heterojunction formed between MAPbBr3 and Bi2WO6, which facilitates efficient charge separation and suppresses charge recombination. The results challenge the previous understanding of MAPbBr3-based photocatalysts and demonstrate a novel approach for developing highly active organic and inorganic perovskite photocatalysts. The successful application of the MA/BWO heterojunction in photocatalytic CO2 reduction expands the scope of organic and inorganic perovskites in the field of renewable energy conversion. By providing a broader perspective, our findings contribute to the ongoing efforts towards sustainable energy solutions, appealing

Abstract:
Dynamical systems in which geometrically extended model cells produce and interact with diffusible (morphogen) and nondiffusible (extracellular matrix) chemical fields have proved very useful as models for developmental processes. The embryonic vertebrate limb is an apt system for such mathematical and computational modeling since it has been the subject of hundreds of experimental studies, and its normal and variant morphologies and spatiotemporal organization of expressed genes are well known. Because of its stereotypical proximodistally generated increase in the number of parallel skeletal elements, the limb lends itself to being modeled by Turing-type systems which are capable of producing periodic, or quasiperiodic, arrangements of spot- and stripe-like elements. This chapter describes several such models, including, (i) a system of partial differential equations in which changing cell density enters into the dynamics explicitly, (ii) a model for morphogen dynamics alone, derived from the latter system in the “morphostatic limit” where cell movement relaxes on a much slower time-scale than cell differentiation, (iii) a discrete stochastic model for the simplified pattern formation that occurs when limb cells are placed in planar culture, and (iv) several hybrid models in which continuum morphogen systems interact with cells represented as energy-minimizing mesoscopic entities. Progress in devising computational methods for handling 3D, multiscale, multimodel simulations of organogenesis is discussed, as well as for simulating reaction–diffusion dynamics in domains of irregular shape.

Abstract:
A recently proposed mathematical model of a “core” set of cellular and molecular interactions present in the developing vertebrate limb was shown to exhibit pattern-forming instabilities and limb skeleton-like patterns under certain restrictive conditions, suggesting that it may authentically represent the underlying embryonic process (Hentschel et al., Proc. R. Soc. B 271, 1713–1722, 2004). The model, an eight-equation system of partial differential equations, incorporates the behavior of mesenchymal cells as “reactors,” both participating in the generation of morphogen patterns and changing their state and position in response to them. The full system, which has smooth solutions that exist globally in time, is nonetheless highly complex and difficult to handle analytically or numerically. According to a recent classification of developmental mechanisms (Salazar-Ciudad et al., Development 130, 2027–2037, 2003), the limb model of Hentschel et al. is “morphodynamic,” since differentiation of new cell types occurs simultaneously with cell rearrangement. This contrasts with “morphostatic” mechanisms, in which cell identity becomes established independently of cell rearrangement. Under the hypothesis that development of some vertebrate limbs employs the core mechanism in a morphostatic fashion, we derive in an analytically rigorous fashion a pair of equations representing the spatiotemporal evolution of the morphogen fields under the assumption that cell differentiation relaxes faster than the evolution of the overall cell density (i.e., the morphostatic limit of the full system). This simple reaction–diffusion system is unique in having been derived analytically from a substantially more complex system involving multiple morphogens, extracellular matrix deposition, haptotaxis, and cell translocation. We identify regions in the parameter space of the reduced system where Turing-type pattern formation is possible, which we refer to as its “Turing space.” Obtained values of the parameters are used in numerical simulations of the reduced system, using a new Galerkin finite element method, in tissue domains with nonstandard geometry. The reduced system exhibits patterns of spots and stripes like those seen in developing limbs, indicating its potential utility in hybrid continuum-discrete stochastic modeling of limb development. Lastly, we discuss the possible role in limb evolution of selection for increasingly morphostatic developmental mechanisms.

Keywords:
Limb development, Chondrogenesis, Mesenchymal condensation, Reaction–diffusion model