Similarity solutions for magneto-forced-unsteady free convective laminar boundary-layer flow

The group theoretic method is applied for solving problem of a unsteady free-convective laminar boundary-layer flow on a non-isothermal vertical plate under the effect of an external velocity and a magnetic field normal to the plate. The application of two-parameter transformation group reduces the number of independent variables, by two, and consequently the system of governing partial differential equations with the boundary and initial conditions reduces to a system of ordinary differential equations with appropriate corresponding conditions. The Runge–Kutta shooting method used to find the numerical solution of the velocity field, shear stress, heat transfer and heat flux has been obtained. The effect of the magnetic field on the velocity field and the Prandtl number on the heat transfer and heat flux has been discussed.     

Estimation of the confidence limits for the quadratic forms in normal variables using a simple Gaussian distribution approximation

Summary  In this paper a simple Gaussian approximation of the distribution of the weighted sum of squared normal variables is proposed. The proposed approximation is computationally less complex compared to other known approximations. However, the convergence towards Gaussian distribution is guaranteed provided the weights comply with certain limit conditions. The suggested approximation is applied to the calculation of confidence limits of the quadratic forms in normal variables. These problems can be encountered in a number of statistical decision making tasks. The accuracy of the estimated confidence limit is investigated on several simulation examples.     

Intertwined Hamiltonians in two-dimensional curved spaces

The problem of intertwined Hamiltonians in two-dimensional curved spaces is investigated. Explicit results are obtained for Euclidean plane, Minkowski plane, Poincaré half plane (AdS₂), de Sitter plane (dS₂), sphere, and torus. It is shown that the intertwining operator is related to the Killing vector fields and the isometry group of corresponding space. It is shown that the intertwined potentials are closely connected to the integral curves of the Killing vector fields. Two problems are considered as applications of the formalism presented in the paper. The first one is the problem of Hamiltonians with equispaced energy levels and the second one is the problem of Hamiltonians whose spectrum is like the spectrum of a free particle.     

OPTIMIZATION OF THE SYNTHESIS OF ACRYLAMIDE HYDROGEL BY γ-RAY IRRADIATION

Hydrogels have been synthesized from 10%, 20%, 30%, 40%, 50% and 60% aqueous solutions of acrylamide monomer by gamma radiation employing doses in the range of 0.2-30 kGy from a Co-60 source. The effect of solution concentration, γ-ray dose, pH and time was studied in order to observe the optimizing conditions in the characterization of hydrogels. Gel fraction increases with dose for all concentrations indicating hundred-percentage conversion of gel at doses ≥5 kGy for homogenous solutions in the range of 20%-50% concentration. On the other hand, 10% solution provides conversion less than 86% even at 30 kGy, whereas 60% monomer makes an inhomogeneous solution which stile gives about 100% gel fraction. Swelling of hydrogels under water with respect to time varies with both the doses and concentrations due to the change of crosslinking density in the gels. The maximum volume change of hydrogels during swelling and water desorption mainly occurs within 24 h. Swelling is also enhanced with the rise of pH due to change of ionic content of the solvent. Considering the amount of gel fraction and the properties of hydrogel, the samples prepared from 20% solution at 5kGy show better results. Moreover, the effect of bacteria on hydrogel was found to be nil, suggesting a prohibition of growth of microorganism in it.     

Topological Strings and (Almost) Modular Forms

The B-model topological string theory on a Calabi-Yau threefold X has a symmetry group Γ, generated by monodromies of the periods of X. This acts on the topological string wave function in a natural way, governed by the quantum mechanics of the phase space H ³(X). We show that, depending on the choice of polarization, the genus g topological string amplitude is either a holomorphic quasi-modular form or an almost holomorphic modular form of weight 0 under Γ. Moreover, at each genus, certain combinations of genus g amplitudes are both modular and holomorphic. We illustrate this for the local Calabi-Yau manifolds giving rise to Seiberg-Witten gauge theories in four dimensions and local IP ₂ and IP ₁ × IP ₁. As a byproduct, we also obtain a simple way of relating the topological string amplitudes near different points in the moduli space, which we use to give predictions for Gromov-Witten invariants of the orbifold .     

Calcium as the superior coating metal in functionalization of carbon fullerenes for high-capacity hydrogen storage

We explore theoretically the feasibility of functionalizing carbon nanostructures for hydrogen storage, focusing on the coating of C60 fullerenes with light alkaline-earth metals. Our first-principles density functional theory studies show that both Ca and Sr can bind strongly to the C60 surface, and highly prefer monolayer coating, thereby explaining existing experimental observations. The strong binding is attributed to an intriguing charge transfer mechanism involving the empty d levels of the metal elements. The charge redistribution, in turn, gives rise to electric fields surrounding the coated fullerenes, which can now function as ideal molecular hydrogen attractors. With a hydrogen uptake of >8.4 wt % on Ca32C60, Ca is superior to all the recently suggested metal coating elements.     

A Purified,Solvent‐Intercalated Precursor Complex for Wide‐Process‐Window Fabrication of Efficient Perovskite Solar Cells and Modules

A high‐purity methylammonium lead iodide complex with intercalated dimethylformamide (DMF) molecules, CH₃NH₃PbI₃?DMF, is introduced as an effective precursor material for fabricating high‐quality solution‐processed perovskite layers. Spin‐coated films of the solvent‐intercalated complex dissolved in pure dimethyl sulfoxide (DMSO) yielded thick, dense perovskite layers after thermal annealing. The low volatility of the pure DMSO solvent extended the allowable time for low‐speed spin programs and considerably relaxed the precision needed for the antisolvent addition step. An optimized, reliable fabrication method was devised to take advantage of this extended process window and resulted in highly consistent performance of perovskite solar cell devices, with up to 19.8 % power‐conversion efficiency (PCE). The optimized method was also used to fabricate a 22.0 cm², eight‐cell module with 14.2 % PCE (active area) and 8.64 V output (1.08 V/cell).     

A Purified,Solvent‐Intercalated Precursor Complex for Wide‐Process‐Window Fabrication of Efficient Perovskite Solar Cells and Modules

A high‐purity methylammonium lead iodide complex with intercalated dimethylformamide (DMF) molecules, CH₃NH₃PbI₃?DMF, is introduced as an effective precursor material for fabricating high‐quality solution‐processed perovskite layers. Spin‐coated films of the solvent‐intercalated complex dissolved in pure dimethyl sulfoxide (DMSO) yielded thick, dense perovskite layers after thermal annealing. The low volatility of the pure DMSO solvent extended the allowable time for low‐speed spin programs and considerably relaxed the precision needed for the antisolvent addition step. An optimized, reliable fabrication method was devised to take advantage of this extended process window and resulted in highly consistent performance of perovskite solar cell devices, with up to 19.8 % power‐conversion efficiency (PCE). The optimized method was also used to fabricate a 22.0 cm², eight‐cell module with 14.2 % PCE (active area) and 8.64 V output (1.08 V/cell).     

Preparation by high-energy milling, characterization, and catalytic properties of nanocrystalline TiO2

Titanium dioxide (TiO2) is widely used for applications in heterogeneous photocatalysis. We prepared nanocrystalline powders of the anatase as well as the rutile modification by high-energy ball milling of the coarse grained source materials for up to 4 h. The resulting average grain size was about 20 nm. The morphology of the powders was investigated with transmission electron microscopy, X-ray powder diffraction, and BET surface area determination. Measurements of the catalytic activity reveal a maximum as a function of the milling time at about 40 min. This maximum could be explained by a superposition of two counteracting effects. The first one is the increase of the specific surface area resulting in an increase of the catalytic activity, and the second one is a change of the electronic structure at the surface of the TiO2 particles corresponding to a reduction of the surface. The latter one was confirmed by light absorption experiments, X-ray photoelectron spectroscopy, and electron paramagnetic resonance spectroscopy.