Gravitational collapse in higher dimensional Husain space–time

We investigate exact solution in higher dimensional Husain model for a null fluid source with pressure p and density ρ are related by the following relations (i) p  =  kρ, (ii) (variable modified Chaplygin) and (iii) p  =  kρ^α (polytropic). We have studied the nature of singularity in gravitational collapse for the above equations of state and also for different choices of the of the parameters k and B namely, (i) k  =  0, B  =  constant (generalized Chaplygin), (ii) B  =  constant (modified Chaplygin). It is found that the nature of singularity is independent of these choices of different equation of state except for variable Chaplygin model. Choices of various parameters are shown in tabular form. Finally, matching of Szekeres model with exterior Husain space–time is done.     

Performance of a 80 W copper vapor laser with “alignment free” unstable CAT-EYE resonator and other configurations using intra-cavity apertures

Performance of a kinetically enhanced copper vapor laser (KE-CVL) with various stable/unstable “alignment free” CAT-EYE resonator configurations are presented here in this paper. The laser used in the experiment was a 45 mm bore (∼2 l discharge volume) kinetically enhanced copper vapor laser developed in our laboratory and capable of generating maximum power of ∼80 W (at ∼9.8 kHz). The efficiency of the laser was ∼1.4% and beam divergence of ∼3.5 mrad in a plane-plane standard multimode cavity. For the first time performance of unstable CAT-EYE resonator is demonstrated with a CVL/KE-CVL. On using unstable CAT-EYE resonator the divergence of the laser beam reduced to ∼0.22 mrad (∼20-fold reduction as compared to conventional plane-plane cavity), ∼40 W output power and with excellent misalignment tolerance. The laser output power was found to be within ∼5% drift/decline with misalignment angle of about 4 mrad between the mirrors. This is a significant improvement in comparison to standard conventional unstable resonator (M ∼ 50) CVL where ∼0.5 mrad divergence is achieved with power drift/decline of about 45% at ∼4 mrad misalignment angle.Off-axis unstable CAT-EYE unstable resonator was also demonstrated for the first time with further reduction in beam divergence to ∼0.13 mrad and with output power of ∼28 W. The misalignment tolerance was found to be highest in case of off-axis unstable CAT-EYE resonator with decline/drift in laser power of only ∼10% for misalignment angle as high as ∼8 mrad. Performance with intra-cavity apertures in plane-plane type CAT-EYE resonator for transverse mode control is also presented for the first time in CVLs. It is observed that the laser beam divergence reduces significantly to 1.25 mrad (a factor of 2) on using an aperture of ∼3.5 mm at the CAT-EYE reflector as compared to its normal (R = F = d) configuration without aperture. In case of stable CAT-EYE resonator the average beam divergence reduces from 8 mrad to 4 mrad (factor of 2) on using intra-cavity aperture of about 3 mm. It was also observed that high misalignment tolerance was retained on using intra-cavity apertures in almost all the CAT-EYE resonators. Use of intra-cavity mesh was also demonstrated for the first time with stable CAT-EYE resonator for improving the beam focus-ability. Average beam divergence was reduced by a factor of 2.5 (from 8 mrad to 3 mrad) on using intra-cavity mesh. These new configurations in CAT-EYE resonators in KE-CVLs are found to be effective in improving and controlling the laser beam divergence significantly with additional characteristic of high misalignment tolerance.     

Order parameter description of electrochemical-hydrodynamic interactions in nanochannels

A novel phase-field model is developed for the quantitative modeling of the complex electrochemical-hydrodynamic interactions in narrow fluidic confinements. Through an order parameter variation, this model captures the underlying excluded volume effects, solvation interactions, and preferential polarizabilities in a self-consistent fashion, without resorting to computationally prohibitive molecular dynamics simulations. Agreement with molecular dynamics predictions is found to be quantitative.     

Development of electron-proton density functionals for multicomponent density functional theory

We present a strategy for the development of electron-proton density functionals in multicomponent density functional theory, treating electrons and selected nuclei quantum mechanically without the Born-Oppenheimer approximation. An electron-proton functional is derived using an explicitly correlated electron-proton pair density. This functional provides accurate hydrogen nuclear densities, thereby enabling reliable calculations of molecular properties. This approach is potentially applicable to relatively large molecular systems with key hydrogen nuclei treated quantum mechanically.     

Solvent- and Substrate-Induced Chiroptical Inversion in Amphiphilic,Biocompatible Glycoconjugate Supramolecules: Shape-Persistent Gelation,Self-Healing,and Antibacterial Activity

We have shown solvent- and substrate-dependent chiral inversion of a few glycoconjugate supramolecules. (Z)-F-Gluco, in which d -glucosamine has been attached chemically to Cbz-protected l -phenylalanine at the C terminus, forms a self-healing hydrogel through intertwining of the nanofibers wherein the gelators undergo lamellar packing in the β-sheet secondary structures with a single chiral handedness. Dihybrid (Z)-F-gluco nanocomposite gel was prepared by in-situ formation of silver nanoparticles AgNPs in the gel; this enhances the mechanical properties of the composite gel through physical crosslinking without altering the packing pattern. In contrast, (Z)-L-gluco bearing an l -leucine moiety does not form a hydrogel but an organogel. Interestingly, the chiral handedness of the aggregates of (Z)-L-gluco can be reversed by choosing suitable solvents. In addition to self-healing behavior, (Z)-L-gluco gel revealed shape persistency. Further, (Z)-F-gluco hydrogel is benign, nontoxic, non-immunogenic, and non-allergenic in animal cells. AgNP-loaded (Z)-F-gluco hydrogel showed antibacterial activity against both Gram-positive and Gram-negative bacteria.     

On a family of elliptic curves of rank at least 2

Let C_m:y² = x³ ? m²x + p²q² be a family of elliptic curves over ?, where m is a positive integer and p, q are distinct odd primes. We study the torsion part and the rank of C_m(?). More specifically, we prove that the torsion subgroup of C_m(?) is trivial and the ?-rank of this family is at least 2, whenever m ? 0 (mod 3), m ? 0 (mod 4) and m ≡ 2 (mod 64) with neither p nor q dividing m.

     

Co-Assembly between Fmoc Diphenylalanine and Diphenylalanine within a 3D Fibrous Viscous Network Confers Atypical Curvature and Branching

Supramolecular polymer co-assembly is a useful approach to modulate peptide nanostructures. However, the co-assembly scenario where one of the peptide building blocks simultaneously forms a hydrogel is yet to be studied. Herein, we investigate the co-assembly formation of diphenylalanine (FF), and Fmoc-diphenylalanine (FmocFF) within the 3D network of FmocFF hydrogel. The overlapping peptide sequence between the two building blocks leads to their co-assembly within the gel state modulating the nature of the FF crystals. We observe the formation of branched microcrystalline aggregates with an atypical curvature, in contrast to the FF assemblies obtained from aqueous solution. Optical microscopy reveal the sigmoidal kinetic growth profile of these aggregates. Microfluidics and ToF-SIMS experiments exhibit the presence of co-assembled structures of FF and FmocFF in the crystalline aggregates. Molecular dynamics simulation was used to decipher the mechanism of co-assembly formation.     

C−C Bond Formation of Benzyl Alcohols and Alkynes Using a Catalytic Amount of KOtBu: Unusual Regioselectivity through a Radical Mechanism

We report a C?C bond‐forming reaction between benzyl alcohols and alkynes in the presence of a catalytic amount of KO^tBu to form α‐alkylated ketones in which the C=O group is located on the side derived from the alcohol. The reaction proceeds under thermal conditions (125 °C) and produces no waste, making the reaction highly atom efficient, environmentally benign, and sustainable. Based on our mechanistic investigations, we propose that the reaction proceeds through radical pathways.     

Hierarchically porous organic polymers: highly enhanced gas uptake and transport through templated synthesis

Porous organic polymers (POPs) possessing meso- and micropores can be obtained by carrying out the polymerization inside a mesoporous silica aerogel template and then removing the template after polymerization. The total pore volume (tpv) and specific surface area (ssa) can be greatly enhanced by modifying the template (up to 210% increase for tpv and 73% for ssa) as well as by supercritical processing of the POPs (up to an additional 142% increase for tpv and an additional 32% for ssa) to include larger mesopores. The broad range of pores allows for faster transport of molecules through the hierarchically porous POPs, resulting in increased diffusion rates and faster gas uptake compared to POPs with only micropores.