A Cox process with State-Dependent exponential pulses to model rainfall

A point process model based on a class of Cox processes is developed to analyse precipitation data at a point location. The model is constructed using state-dependent exponential pulses that are governed by an unobserved underlying Markov chain. The mathematical formulation of the model where both the arrival rate of the rain cells and the initial pulse depth are determined by the Markov chain is presented. Second-order properties of the rainfall depth process are derived and utilised in model assessment. A method of moment estimation is employed in model fitting. The proposed model is used to analyse 69 years of sub-hourly rainfall data from Germany and 15 years of English rainfall data. The results of the analysis using variants of the proposed model with fixed pulse lifetime and variable pulse duration are presented. The performance of the proposed model, in reproducing second-moment characteristics of the rainfall, is compared with that of two stochastic models where one has exponential pulses and the other has rectangular pulses. The proposed model is found to capture most of the empirical rainfall properties well and outperform the two alternative models considered in our analysis

Cascade synthesis of dihydrobenzofuran via Claisen rearrangement of allyl aryl ethers using FeCl3/MCM-41 catalyst

Dihydrobenzofuran as one of the active ingredients of the naturally occurring motif is synthesized by using in situ generation of ortho allyl phenols. Aryl allyl ethers on reacting with catalytic amounts of non noble metal iron (III) chloride supported on MCM-41 under moderate reaction conditions yield dihydrobenzofuran. First step via Claisen rearrangement gives ortho allyl phenol followed by its in situ cyclization to yield dihydrobenzofuran in very good yields. Both Lewis as well as Brønsted acidity of the catalyst as evidenced by Py-FTIR studies was found to catalyze the cascade synthesis of dihydrobenzofuran. The scope of the present strategy was successfully demonstrated for several substrates with varying electronic effects for the synthesis of corresponding dihydrobenzofuran with high yields in a range of 71–86%. Keywords: Claisen rearrangement, Dihydrobenzofuran, Aryl allyl ether, MCM-41, Ferric chlorid

Steering the Ester and γ‑Valerolactone Selectivities in Levulinic Acid Hydrogenation

Both alkyl esters and γ-valerolactone (GVL) derived from levulinic acid (LA) have applications as renewable transportation fuel/fuel additives. Non-noble metal cobalt supported on La₂O₃ catalyst was developed for efficient cascade LA hydrogenation to GVL via esterification. LA hydrogenation in methanol alone yielded methyl levulinate (MeLA) as a major product along with 43% of GVL. Interestingly, hydrogenation in water gave almost complete selectivity to GVL; nevertheless, it was associated with significant metal leaching. Suppression of metal leaching and enhancement in selectivity to GVL could be achieved by a methanol/water (95:5) solvent system. XRD analysis of La₂O₃-supported catalysts evidenced the characteristic peaks of a mixture of La₂O₃ and La­(OH)₃ phases. Basicity, as well as acidity, of the catalyst as determined by CO₂ and NH₃ TPD was due to these La₂O₃, Co–La, and La­(OH)₃ phases which played an important role in directing the product selectivity in levulinic acid hydrogenation. At the low temperature of 160 °C, almost equal selectivities of MeLA (47%) and GVL (43%) were observed, while higher temperature (200 °C) favored further hydrogenation of MeLA to GVL (75%). Similarly, with an increase in reaction time to 9 h, the GVL selectivity achieved was as high as 80%. The selectivity to MeLA and GVL in LA hydrogenation over Co/La₂O₃ catalyst can be altered by suitably adjusting the reaction conditions