The structure of optimal solutions for harvesting a renewable resource

We consider the problem of optimal harvesting of a renewable resource whose dynamics are governed by logistic growth and whose payoff is proportional to the harvest. We consider both the case of a finite and an infinite time horizon and analyse the structure of the optimal solutions and their dependence on the parameters of the model. We show that the optimal policy can only have one of three structures: (1) maximal harvesting effort until the resource is depleted, (2) zero harvesting during an initial time interval followed by a subsequent switch to maximal harvesting effort, or (3) a singular solution, which corresponds to an intermediate level of harvesting, accompanied by the most rapid approach path. All three scenarios emerge, with minor variations, with finite and infinite time horizons, depending on the particular combination of parameters of the system. We characterize the conditions under which the singular solution is optimal and present suggestions for designing an optimal and sustainable harvesting strategy. Recommendations for Resource Managers :

• We have rigorously explored a standard optimal harvesting model and its steady states.
• We show that three different types of solutions may emerge: (i) maximal harvesting eventually leading to a complete depletion of the stock; (ii) maximal harvesting with a potential period of idleness leading to a positive stock; (iii) an initial phase of either no or full harvesting followed by a period of intermediate harvesting intensity leading to a positive stock (singular solution).
• With some modifications, similar results hold for a finite planning horizon.
• Which of these three scenarios emerges in the finite horizon case depends not only on the parameter values but also on the length of the planning horizon.

     

Light harvesting hexamolybdenum cluster integrated with the 3D ordered semiconductor inverse opals for optoelectronic property

Solar energy-harvesting materials have significantly contributed to the development of energy-saving applications for several decades. We have mainly used a new concept composed of the electrophoretic deposition technique and photonic crystal structural engineering to understand the tunable light-absorption and electronic conduction properties. A hexamolybdenum cluster compound (denoted as the Mo₆ cluster) was successfully functionalized on a tin pyrophosphate semiconductor integrated within an inverse opal photonic crystal. The size of the periodical pores, surface modification, and chemical composition of the infiltration material of the inverse opal film have been investigated to control the photonic bandgap in the visible range and the efficiency of the deposited Mo₆ cluster. The photoactive Mo₆ clusters act as a visible light harvester and generate an efficient photo-induced current upon light absorption that is enhanced by a slow photon effect occurring at the photonic stopband edges. The electron and proton are transferred in the inorganic-organic network via hydrogen bonds by a hopping mechanism to generate a rapid photoconductivity response during light irradiation. Specific attention focused on the role of humidity and temperature regarding the reproducibility of the experiments and the photosensitivity of the nanocomposite. The suitable tunable photo-induced conduction property in organic-inorganic materials opens a new opportunity for the applicability of cluster-based compounds in visible optoelectronic devices.     

Photophysics of Iridium(III) (2-phenylpyridine)(2,2’,6,2”-terpyridine) Chloride Encapsulated within the Zinc(II) Polyhedral MOF,USF-2

Photoactive metal-organic frameworks (MOFs) provide an important class of functional porous materials for a wide range of applications including light harvesting, photocatalysis and photodynamic therapy. Two strategies have been employed in the development of photoactive MOFs, one in which the photoactive element is incorporated as an element of the framework itself and the other in which the photoactive element serves as a guest within the MOF cavities. Transition metal polyimines have now been non-covalently incorporated within the cavities of a large number of MOFs with the Ru^II-polyimine being the most widely examined guest complex. Previous studies have demonstrated that the nature of the cavity modulates the Ru-polyimine photophysics. Here, an Ir^III(terpyridine)(phenylpyridine)Cl complex has been encapsulated within the Zn-polyhedral MOF, USF-2. Unlike the Ru-polyimines, the excited state photophysics associated with the encapsulated Ir polyimine shows very little change in either the steady state emission and emission lifetime. The slight decrease in emission lifetime is attributed to energy transfer between encapsulated Ir complexes. These results indicate that transition metal polyimines that exhibit excited state structural changes demonstrate the largest perturbations upon confinement.     

Dynamics of a Discrete Two-species Competitive Model with Michaelies-Menten Type Harvesting in the First Species

In this paper, we use a semidiscretization method to derive a discrete two-species competitive model with Michaelis-Menten type harvesting in the first species. First, the existence and local stability of fixed points of the system are investigated by employing a key lemma. Subsequently, the transcritical bifurcation, period-doubling bifurcation and pitchfork bifurcation of the model are investigated by using the Center Manifold Theorem and bifurcation theory. Finally, numerical simulations are presented to illustrate corresponding theoretical results.     

Light-Harvesting Artificial Cells for the Generation of ATP and NADPH†

The bottom-up construction of self-powered artificial cells is significant to understand the energy supply and metabolism of nature cells. Here, we demonstrate an efficient manner to build thylakoid-containing artificial cells, which continuously convert light energy into chemical energy to supply adenosine 5’-triphosphate (ATP) under light illumination. The production of ATP supplies energy to promote the biological enzyme cascade reactions, where glucose is transformed into glucose 6-phosphate (G6P) under the catalysis of hexokinase (HK). G6P was further converted to gluconolactone 6-phosphate (PG) in the presence of 6-phosphate dehydrogenase (G6PDH), meanwhile NADP⁺ was converted to nicotinamide adenine dinucleotide phosphate (NADPH). The self-powered artificial cells were demonstrated to generate ATP and NADPH successively, which provided a way for building more complicated artificial cells.