Positive numerical splitting method for the Hull and White 2D Black–Scholes equation

We consider the locally one‐dimensional backward Euler splitting method to solve numerically the Hull and White problem for pricing European options with stochastic volatility in the presence of a mixed derivative term. We prove the first‐order convergence of the time‐splitting. The parabolic equation degenerates on the boundary x = 0 and we apply a fitted finite volume scheme to the equation to resolve the degeneracy and derive the fully discrete problem as we also investigate the discrete maximum principle. Numerical experiments illustrate the efficiency of our difference scheme. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 822–846, 2015     

Colloidal hybrid heterostructures based on II–VI semiconductor nanocrystals for photocatalytic hydrogen generation

Hydrogen generated through the photochemical cleavage of water using renewable solar energy is considered to be an environmentally friendly chemical fuel of the future, which neither results in air pollution nor leads to the emission of greenhouse gases. The photocatalytic materials for water cleavage are required to perform at least two fundamental functions: light harvesting of the maximal possible part of the solar energy spectrum and a catalytic function for efficient water decomposition into oxygen and hydrogen. Photocatalytic systems based on colloidal semiconductor nanocrystals offer a number of advantages in comparison with photoelectrochemical cells based on bulk electrodes: (i) a broad range of material types are available; (ii) higher efficiencies are expected due to short distance charge transport; (iii) large surface areas are beneficial for the catalytic processes; (iv) flexibility in fabrication and design which also allows for tuning of the electronic and optical properties by employing quantum confinement effects. The presence of co-catalysts on colloidal semiconductors is an important part of the overall design of the photocatalytic colloidal systems necessary to maximize the water splitting efficiency. This review article discusses the rational choice of colloidal nanoheterostructured materials based on light-harvesting II–VI semiconductor nanocrystals combined with a variety of metal and/or non-metal co-catalysts, with optimized light harvesting, charge separation, and photocatalytic functions.     

Enhancing the Water Splitting Efficiency of Sn‐Doped Hematite Nanoflakes by Flame Annealing

The effect of flame annealing on the water‐splitting properties of Sn decorated hematite (α‐Fe₂O₃) nanoflakes has been investigated. It is shown that flame annealing can yield a considerable enhancement in the maximum photocurrent under AM 1.5 (100 mW cm^?2) conditions compared to classic furnace annealing treatments. Optimizing the annealing time (10 s at 1000 °C) leads to a photocurrent of 1.1 mA cm^?2 at 1.23 V (vs. RHE) with a maximum value 1.6 mA cm^?2 at 1.6 V (vs. RHE) in 1 M KOH. The improvement in photocurrent can be attributed to the fast direct heating that maintains the nanoscale morphology, leads to optimized Sn decoration, and minimizes detrimental substrate effects.     

A Doping Technique that Suppresses Undesirable H2 Evolution Derived from Overall Water Splitting in the Highly Selective Photocatalytic Conversion of CO2 in and by Water

Photocatalytic conversion of CO₂ to reduction products, such as CO, HCOOH, HCHO, CH₃OH, and CH₄, is one of the most attractive propositions for producing green energy by artificial photosynthesis. Herein, we found that Ga₂O₃ photocatalysts exhibit high conversion of CO₂. Doping of Zn species into Ga₂O₃ suppresses the H₂ evolution derived from overall water splitting and, consequently, Zn‐doped, Ag‐modified Ga₂O₃ exhibits higher selectivity toward CO evolution than bare, Ag‐modified Ga₂O₃. We observed stoichiometric amounts of evolved O₂ together with CO. Mass spectrometry clarified that the carbon source of the evolved CO is not the residual carbon species on the photocatalyst surface, but the CO₂ introduced in the gas phase. Doping of the photocatalyst with Zn is expected to ease the adsorption of CO₂ on the catalyst surface.     

Construction of Shallow Surface States through Light Ni Doping for High‐Efficiency Photocatalytic Hydrogen Production of CdS Nanocrystals

Ni‐doped CdS nanowires were synthesized by a simple one‐step method. X‐ray diffraction, X‐ray photoelectron spectroscopy, and photoluminescence spectroscopy confirmed that light Ni doping can form shallow surface states due to the presence of substitutional Ni ions, and heavy Ni doping can form deep surface states due to the presence of interstitial Ni ions. Surface photovoltage spectroscopy and transient photovoltage measurements revealed that the shallow surface states can prolong the lifetime of the photogenerated charge carriers, whereas the deep surface states lead to recombination of the photogenerated charge carriers. The relationship between different surface states and the photocatalytic performance of CdS nanocrystals are discussed. The enhanced density of shallow surface states due to light Ni doping significantly promotes photocatalytic H₂ production.     

Biocatalytic Photosynthesis with Water as an Electron Donor

Efficient harvesting of unlimited solar energy and its conversion into valuable chemicals is one of the ultimate goals of scientists. With the ever‐increasing concerns about sustainable growth and environmental issues, numerous efforts have been made to develop artificial photosynthetic process for the production of fuels and fine chemicals, thus mimicking natural photosynthesis. Despite the research progress made over the decades, the technology is still in its infancy because of the difficulties in kinetic coupling of whole photocatalytic cycles. Herein, we report a new type of artificial photosynthesis system that can avoid such problems by integrally coupling biocatalytic redox reactions with photocatalytic water splitting. We found that photocatalytic water splitting can be efficiently coupled with biocatalytic redox reactions by using tetracobalt polyoxometalate and Rh‐based organometallic compound as hole and electron scavengers, respectively, for photoexcited [Ru(bpy)₃]²⁺. Based on these results, we could successfully photosynthesize a model chiral compound (L ‐glutamate) using a model redox enzyme (glutamate dehydrogenase) upon in situ photoregeneration of cofactors.     

Supramolecular Water Oxidation with Ru–bda‐Based Catalysts

Extremely slow and extremely fast new water oxidation catalysts based on the Ru–bda (bda=2,2′‐bipyridine‐6,6′‐dicarboxylate) systems are reported with turnover frequencies in the range of 1 and 900 cycles s^?1, respectively. Detailed analyses of the main factors involved in the water oxidation reaction have been carried out and are based on a combination of reactivity tests, electrochemical experiments, and DFT calculations. These analyses give a convergent interpretation that generates a solid understanding of the main factors involved in the water oxidation reaction, which in turn allows the design of catalysts with very low energy barriers in all the steps involved in the water oxidation catalytic cycle. We show that for this type of system π‐stacking interactions are the key factors that influence reactivity and by adequately controlling them we can generate exceptionally fast water oxidation catalysts.     

A Cost‐Effective 3D Hydrogen Evolution Cathode with High Catalytic Activity: FeP Nanowire Array as the Active Phase

Iron is the cheapest and one of the most abundant transition metals. Natural [FeFe]‐hydrogenases exhibit remarkably high activity in hydrogen evolution, but they suffer from high oxygen sensitivity and difficulty in scale‐up. Herein, an FeP nanowire array was developed on Ti plate (FeP NA/Ti) from its β‐FeOOH NA/Ti precursor through a low‐temperature phosphidation reaction. When applied as self‐supported 3D hydrogen evolution cathode, the FeP NA/Ti electrode shows exceptionally high catalytic activity and good durability, and it only requires overpotentials of 55 and 127 mV to afford current densities of 10 and 100 mA cm², respectively. The excellent electrocatalytic performance is promising for applications as non‐noble‐metal HER catalyst with a high performance–price ratio in electrochemical water splitting for large‐scale hydrogen fuel production.     

Photocatalytic Water Oxidation by a Pyrochlore Oxide upon Irradiation with Visible Light: Rhodium Substitution Into Yttrium Titanate

A stable visible‐light‐driven photocatalyst (λ≥450 nm) for water oxidation is reported. Rhodium substitution into the pyrochlore Y₂Ti₂O₇ is demonstrated by monitoring Vegard′s law evolution of the unit‐cell parameters with changing rhodium content, to a maximum content of 3 % dopant. Substitution renders the solid solutions visible‐light active. The overall rate of oxygen evolution is comparable to WO₃ but with superior light‐harvesting and surface‐area‐normalized turnover rates, making Y₂Ti_1.94Rh_0.06O₇ an excellent candidate for use in a Z‐scheme water‐splitting system.     

Nanocomposites of Tantalum‐Based Pyrochlore and Indium Hydroxide Showing High and Stable Photocatalytic Activities for Overall Water Splitting and Carbon Dioxide Reduction

Nanocomposites of tantalum‐based pyrochlore nanoparticles and indium hydroxide were prepared by a hydrothermal process for UV‐driven photocatalytic reactions including overall water splitting, hydrogen production from photoreforming of methanol, and CO₂ reduction with water to produce CO. The best catalyst was more than 20 times more active than sodium tantalate in overall water splitting and 3 times more active than Degussa P25 TiO₂ in CO₂ reduction. Moreover, the catalyst was very stable while generating stoichiometric products of H₂ (or CO) and O₂ throughout long‐term photocatalytic reactions. After the removal of In(OH)₃, the pyrochlore nanoparticles remained highly active for H₂ production from pure water and aqueous methanol solution. Both experimental studies and density functional theory calculations suggest that the pyrochlore nanoparticles catalyzed the water reduction to produce H₂, whereas In(OH)₃ was the major active component for water oxidation to produce O₂.