Stochastic conservation laws: Weak-in-time formulation and strong entropy condition

This article is an attempt to complement some recent developments on conservation laws with stochastic forcing. In a pioneering development, Feng and Nualart [8] have developed the entropy solution theory for such problems and the presence of stochastic forcing necessitates introduction of strong entropy condition. However, the authors' formulation of entropy inequalities are weak-in-space but strong-in-time. In the absence of a priori path continuity for the solutions, we take a critical outlook towards this formulation and offer an entropy formulation which is weak-in-time and weak-in-space.     

Electronic Transport and Thermopower in 2D and 3D Heterostructures—A Theory Perspective

The impact of interfaces and heterojuctions on the electronic and thermoelectric transport properties of materials is discussed herein. Recent progress in understanding electronic transport in heterostructures of 2D materials ranging from graphene to transition metal dichalcogenides, their homojunctions (grain boundaries), lateral heterojunctions (such as graphene/MoS₂ lateral interfaces), and vertical van der Waals heterostructures is reviewed. Work on thermopower in 2D heterojunctions, as well as their applications in creating devices such as resonant tunneling diodes (RTDs), is also discussed. Last, the focus turns to work in 3D heterostructures. While transport in 3D heterostructures has been researched for several decades, here recent progress in theory and simulation of quantum effects on transport via the Wigner and non‐equilibrium Green's functions approaches is reviewed. These simulation techniques have been successfully applied toward understanding the impact of heterojunctions on transport properties and thermopower, which finds applications in energy harvesting, and electron resonant tunneling, with applications in RTDs. In conclusion, tremendous progress has been made in both simulation and experiments toward the goal of understanding transport in heterostructures and this progress will soon be parlayed into improved energy converters and quantum nanoelectronic devices.     

An expedient solvent-free C-benzylation of 4-hydroxycoumarin with styrenes

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Zwitterionic‐Type Molten Salt‐Catalyzed Multicomponent Reactions: One‐Pot Synthesis of Substituted Imidazoles Under Solvent‐Free Conditions

4‐(1‐Imidazolium) butane sulfonate is an excellent catalyst for the synthesis of 2,4,5‐trisubstituted and 1,2,4,5‐tetrasubstituted imidazoles through the condensation of 1,2‐dicarbonyl compounds, aldehydes, and ammonium acetate or amine via multicomponent condensation strategy under solvent‐free conditions. The key advantages of this process are high yields, reusability of catalyst, environmental friendliness, easy work‐up and purification of products by nonchromatographic methods.     

Studies on organotin compounds using the Del Re method III. Variations in tin-chlorine,tin-carbon and tin-hydrogen stretching frequencies and tin-chlorine bond distance in organotin compounds

The concept of bond order has been extended to Del Re calculations, and the bond orders of tin-chlorine and tin-carbon bonds in Me_4-nSnCl_n (n = 1 to 4) type compounds have been calculated. The tin-chlorine bond order increases progressively from 0.922 in Me₃SnCl to 0.977 in SnCl₄, and correlates satisfactorily with the experimental tin-chlorine bond distances. The tin-carbon bond order, on the other hand, remains almost constant, in agreement with the constancy of tin-carbon bond distance in the series. The average tin-chlorine, tin-carbon and tin-hydrogen stretching frequencies in similar compounds vary linearly with the calculated bond polarities indicating variation in bond polarity to be the dominating factor. The unusually low values of the tin-carbon stretching frequency for the tin-vinyl bond compared to the tin-methyl bond in Me₃ViSn and Et₂Vi₂Sn can also be explained in terms of larger polarity of the tin-vinyl bond in these compounds.     

On electrophoresis of a pH‐regulated nanogel with ion partitioning effects

The electrophoresis of a polyelectrolyte nanoparticle, whose charge condition depends on the salt concentration and pH of the suspended medium as well as the dielectric permittivity difference, is analyzed. The present nonlinear model for the electrophoresis of this pH‐regulated polyelectrolyte (PE) particle is based on the consideration of full set of governing equations of fluid and ion transport coupled with the equation for electric field. The Born energy of the ions are incorporated to account for the difference in the dielectric permittivity of the PE and the electrolyte. The governing equations are computed numerically through a control volume approach. The nonlinear effects are highlighted by comparing with the existing linear model as well as results based on the first‐order perturbation analysis valid for a weak applied field. The ion partitioning effect arising due to the difference in self energy of ions between the two media, have a strong impact on the mobility of the PE. The ion partitioning effect attenuates the penetration of counterions in the PE, which enhances the electric force and hence, results in a larger mobility of the PE. The nonlinear effects due to the double layer polarization and relaxation are intensified due to the ion partitioning effect. The ion partitioning effect influences the association/dissociation of PE functional group by tuning the hydrogen/hydroxide ions. Present study shows that the ion partitioning effect is profound for higher salt concentration and/or higher volume density of PE functional groups.     

An expedient one-pot sequential three-component reaction for the stereoselective synthesis of functionalized spiro-sulfamidate imine fused δ-lactone scaffold

A convenient one-pot three-component transformation between 4-aryl-5H-1,2,3-oxathiazole-2,2-dioxides, trans-β-aryl/alkyl-substituted acroleins and paraformaldehyde in CH₂Cl₂ at room temperature in the presence of commercially available l-proline and DBU as the organocatalysts has been successfully realized for the first time via a Michael-condensation-hemiacetalization sequence process. The resulting functionalized spiro-sulfamidate imine fused δ-lactone scaffolds were obtained via in situ oxidation of spiro-δ-lactols by PCC in good to excellent overall yields and moderate to good diastereomeric ratio (up to ?5:1 dr). Moreover, a synthetically useful intermediate trans–cis-β-amino-α-azido compound has been successfully achieved through our procedure.     

A Facile Synthesis of 2,2,4‐Trisubstituted‐1,2‐Dihydroquinolines Catalyzed by Zinc Triflate under Solvent‐Free Conditions

An efficient process has been developed for the synthesis of 2,2,4‐trisubstituted‐1,2‐dihydroquinolines in good yields through a simple one‐pot condensation between anilines and ketones in the presence of zinc triflate as a catalyst at room temperature under solvent‐free conditions.