A Non‐Gaussian Ornstein–Uhlenbeck Process for Electricity Spot Price Modeling and Derivatives Pricing

A mean‐reverting model is proposed for the spot price dynamics of electricity which includes seasonality of the prices and spikes. The dynamics is a sum of non‐Gaussian Ornstein–Uhlenbeck processes with jump processes giving the normal variations and spike behaviour of the prices. The amplitude and frequency of jumps may be seasonally dependent. The proposed dynamics ensures that spot prices are positive, and that the dynamics is simple enough to allow for analytical pricing of electricity forward and futures contracts. Electricity forward and futures contracts have the distinctive feature of delivery over a period rather than at a fixed point in time, which leads to quite complicated expressions when using the more traditional multiplicative models for spot price dynamics. In a simulation example it is demonstrated that the model seems to be sufficiently flexible to capture the observed dynamics of electricity spot prices. The pricing of European call and put options written on electricity forward contracts is also discussed.     

Revealing the mechanisms behind SnO2 nanoparticle formation and growth during hydrothermal synthesis: an in situ total scattering study

The formation and growth mechanisms in the hydrothermal synthesis of SnO(2) nanoparticles from aqueous solutions of SnCl(4)·5H(2)O have been elucidated by means of in situ X-ray total scattering (PDF) measurements. The analysis of the data reveals that when the tin(IV) chloride precursor is dissolved, chloride ions and water coordinate octahedrally to tin(IV), forming aquachlorotin(IV) complexes of the form [SnCl(x)(H(2)O)(6-x)]((4-x)+) as well as hexaaquatin(IV) complexes [Sn(H(2)O)(6-y)(OH)(y)]((4-y)+). Upon heating, ellipsoidal SnO(2) nanoparticles are formed uniquely from hexaaquatin(IV). The nanoparticle size and morphology (aspect ratio) are dependent on both the reaction temperature and the precursor concentration, and particles as small as ~2 nm can be synthesized. Analysis of the growth curves shows that Ostwald ripening only takes place above 200 °C, and in general the growth is limited by diffusion of precursor species to the growing particle. The c-parameter in the tetragonal lattice is observed to expand up to 0.5% for particle sizes down to 2-3 nm as compared to the bulk value. SnO(2) nanoparticles below 3-4 nm do not form in the bulk rutile structure, but as an orthorhombic structural modification, which previously has only been reported at pressures above 5 GPa. Thus, adjustment of the synthesis temperature and precursor concentration not only allows control over nanoparticle size and morphology but also the structure.     

Direct numerical simulation of surfactant-stabilized emulsions

A 3D lattice Boltzmann model for two-phase flow with amphiphilic surfactant was used to investigate the evolution of emulsion morphology and shear stress in starting shear flow. The interfacial contributions were analyzed for low and high volume fractions and varying surfactant activity. A transient viscoelastic contribution to the emulsion rheology under constant strain rate conditions was attributed to the interfacial stress. For droplet volume fractions below 0.3 and an average capillary number of about 0.25, highly elliptical droplets formed. Consistent with affine deformation models, gradual elongation of the droplets increased the shear stress at early times and reduced it at later times. Lower interfacial tension with increased surfactant activity counterbalanced the effect of increased interfacial area, and the net shear stress did not change significantly. For higher volume fractions, co-continuous phases with a complex topology were formed. The surfactant decreased the interfacial shear stress due mainly to advection of surfactant to higher curvature areas. Our results are in qualitative agreement with experimental data for polymer blends in terms of transient interfacial stresses and limited enhancement of the emulsion viscosity at larger volume fractions where the phases are co-continuous.     

A Survey of Multicomponent Mass Diffusion Flux Closures for Porous Pellets: Mass and Molar Forms

Heterogeneous catalysis is of paramount importance in many areas of gas conversion and processing in chemical engineering industries. In porous pellets, the catalytic reactions may be affected by diffusional limitations such that the global rate can be different from the intrinsic reaction rate. In the literature, a number of multicomponent diffusion flux closures have been applied to characterize the diffusion process within different units in chemical process plants. The main purpose of this paper is to outline the derivation of the different diffusion flux models: the rigorous Maxwell–Stefan and dusty gas models, and the simpler Wilke and Wilke–Bosanquet models. Usually the diffusion fluxes are derived and presented with respect to the molar average velocity definition. In this study, also the diffusion flux closures with respect to the mass average velocity definition is outlined. Thus, if the temperature equation and the momentum equation are used in the pellet model, a consistently closed set of pellet equations is obtained on mass basis holding only the mass average velocity. On the other hand, for the closed set of pellet equations on molar basis, the component balances hold the molar averaged velocity whereas the temperature and momentum equations hold the mass average velocity due to the physical laws applied deriving these fundamental balances. Nevertheless, the Maxwell–Stefan and dusty gas models are manipulated and put on the convenient Fickian form. The second purpose of this article is the evaluation of the diffusion flux closures derived. For this purpose, a transient model is developed to describe the evolution of the species composition, pressure, velocity, temperature, total concentration, and fluxes within a spherical pellet. The catalyst problem has been simulated for the methanol dehydration process producing dimethyl ether (DME), with computed efficiency factor values in the range 0.06–0.6 for pellet pore diameters of 0.1–100 nm. Identical results are expected for the mole and mass based pellet equations. However, deviations are obtained in the component fractions comparing the mass and mole based pellet model formulations where the mass fluxes were described according to the Wilke and Wilke–Bosanquet models. On the other hand, the rigorous Maxwell–Stefan and dusty gas models gave identical results.     

Time-property least-squares spectral method for population balance equations

In multiphase chemical reactor analysis the dispersed phase distribution plays a major role in obtaining reliable predictions. The population balance equation is a well established equation for describing the evolution of the dispersed phase. However, the numerical solution of this type of equations is computationally intensive. In this work, a time-property least squares spectral method is presented for solving the population balance equation including breakage and coalescence processes. In this problem, both property and time are coupled in the least squares minimization procedure. Spectral convergence of the L ² least squares functional and L ² error norms in time-property is verified using a smooth solution to the population balance equation.     

NMR study and quantum mechanical calculations on the 2-[(2-aminoethyl)amino]-ethanol-H2O-CO2 system

13C and 1H NMR spectra were obtained for AEEA (2-[(2-aminoethyl)amino]-ethanol)-H2O-CO2 systems and quantum mechanical calculations were carried out for the different AEEA species. The results suggest that the main AEEA species under the conditions studied are free amine, primary carbamate, and secondary carbamate. There is also some indication that a dicarbamate species is formed, this species does however only appear to be formed in small amounts. Comparison between experimental data and quantum mechanical calculations suggest that most AEEA species take on conforms with some degree of intramolecular hydrogen bonding.     

Single-crystal growth and characterization of disilver(I) monofluorophosphate(V), Ag2PO3F: crystal structure, thermal behavior, vibrational spectroscopy, and solid-state 19F, 31P, and 109Ag MAS NMR spectroscopy

Single crystals of disilver(I) monofluorophosphate(V), Ag2PO3F (1), were obtained by slow evaporation of a diluted aqueous Ag2PO3F solution. Compound 1 adopts a new structure type and crystallizes in the monoclinic space group C2/c with eight formula units and lattice parameters of a = 9.2456(8) A, b = 5.5854(5) A, c = 14.7840(13) A, and beta = 90.178(2) degrees. The crystal structure of 1 [R(F2 > 2sigma(F2) = 0.0268, wR(F2 all) = 0.0665] is composed of three crystallographically independent Ag+ cations and PO3F2- anions as single building units. The oxygen environment around each of the Ag+ cations is different, with one Ag+ in distorted octahedral (d(Ag-O) = 2.553 A), one in nearly rectangular (d(Ag-O) = 2.445 A), and one in distorted tetrahedral (d(Ag-O) = 2.399 A) coordination. Additional Ag-F contacts to more remote F atoms located at distances >2.80 A augment the coordination polyhedra for the two latter Ag+ cations. The monofluorophosphate anion deviates slightly from C3v symmetry and exhibits the characteristic differences in bond lengths, with a mean of 1.510 A for the P-O bonds and one considerably longer P-F bond of 1.575(2) A. Compound 1 was further characterized by vibrational spectroscopy (Raman and IR) and solid-state 19F, 31P, and 109Ag MAS NMR spectroscopy. The value for the isotropic one-bond P-F coupling constant in 1 is 1JPF = -1045 Hz. Thermal analysis (TG, DSC) revealed a reversible phase transition at 308 degrees C, which is very close to the decomposition range of 1. Under release of POF3, Ag4P2O7 and Ag3PO4 are the thermal decomposition products at temperatures above 450 degrees C.     

First nucleophilic aromatic substitution of annelated pyrazole.

3-Chloropyrazolo[3,4-c]quinoline 5, 3-chloropyrazolo[3,4-c]isoquinoline 6, 1,2-dihydro-1,2-dimethylpyrazolo[3,4-c]quinolin-3-one 8, and 1,2-dihydro-1,2-dimethylpyrazolo[3,4-c]isoquinolin-3-one 10 were obtained by acid-induced nucleophilic aromatic substitution (S(N)H) of H-3 in N-hydroxypyrazolo[3,4-c]quinoline 1b and in N-hydroxy pyrazolo[3,4-c]isoquinoline 3b. In the acid-induced chlorination, 3b was far more reactive than 1b, whereas the related N-hydroxypyrazolo[4,3-c]quinoline 2b and N-hydroxypyrazolo[4,3-c]isoquinoline 4b were completely unreactive toward S(N)H under identical conditions.     

Dual nuclear magnetic resonance for probing intrinsic bone structure and a potential gut–bone axis in ovariectomized rats

Currently, the existence of a gut–bone axis receives massive attention, and while sound premises and indirect proofs exist for the gut–bone axis concept, few studies have provided actual data linking the gut and bone physically. This study aimed to exploit the versatile nature of nuclear magnetic resonance (NMR) to link NMR relaxometry data on bone mineralization with NMR spectroscopic profiling of gut metabolites. For this purpose, sample material was obtained from a 6-week intervention study with ovariectomized (OVX) rats (n = 49) fed with seven different diets varying in calcium content (0.2–6.0 mg/kg) and prebiotic fiber content (0–5.0% w/w). This design ensured a span in (i) calcium available for bone mineralization and (ii) metabolic activity in the gut. After termination of the intervention, longitudinal (T₁), transverse (T₂) relaxation, and mechanical bone strength were measured on the excised femur bones. A PLS model with high predictability (Q² = 0.86, R² = 0.997) was demonstrated between T₂ decay curves and femur mechanical strength. Correlations were established between bone T₂ populations and gut short-chain fatty acids. In conclusion, the present dual NMR approach showed strong correlation between T₂ relaxation and mechanical strength of the bone, and when metabolic activity in the gut was modulated by inulin, the potential existence of a gut–bone axis was demonstrated.