Notations, Spectroscopic Parameters, Energy Levels and Their Relationship to Effective Hamiltonian Formalism of Diatomic Molecules

This paper presents a part of the culmination of the collective efforts in developing a cohesive and consolidated enunciation of the spectroscopic parameters and their relationship to effective molecular Hamiltonians for diatomic formalism, linear four-atomic formalism and quasi-linearity, Watson Hamiltonian and the complexities in symmetric and asymmetric top spectral structures. All these considered together present a beautiful and consistent picture of molecular spectroscopy. In this paper we deal with the diatomic formalism. This paper forms our tribute to Professor K. Narahari Rao and in the second part of the paper we convoy our gratitude to him with a summary of his more than half century of work and an obituary. We will deal with other forms of molecular species which will be connected to optical pumping and/or interstellar space.     

Operational characteristics of dual gain single cavity Nd:YVO4 laser

Operational characteristics of a dual gain single cavity Nd:YVO₄ laser have been investigated. With semiconductor diode laser pump power of 2 W, 800 mW output was obtained with a slope efficiency of 49%. Further, by changing the relative orientation of the two crystals the polarization characteristics of the output could be varied. In particular by keeping the two Nd:YVO₄ crystals with their c-axes orthogonal to each other and adjusting the gain of the crystals so that both operate at approximately the same power level, completely unpolarized beams could be obtained.     

Interpenetrated molecules: crown-ether and linear organic molecule supramolecular architectures

In this review, pseudorotaxanes and rotaxanes structured out of simple crown ethers and linear organic molecules with positively charged nitrogen centres (i.e., quaternary pyridinium groups, viologens like paraquat and also extended viologens, imidazolium groups, benzimidazolium groups, bis-benzimidazolium groups and their derivatives) are described. Some selected examples of such systems are assembled here with respect to their properties and applications.     

Redefining the transparency order

In this paper, we consider the multi-bit Differential Power Analysis (DPA) in the Hamming weight model. In this regard, we revisit the definition of Transparency Order (\(\mathsf {TO}\)) from the work of Prouff (FSE 2005) and find that the definition has certain limitations. Although this work has been quite well referred in the literature, surprisingly, these limitations remained unexplored for almost a decade. We analyse the definition from scratch, modify it and finally provide a definition with better insight that can theoretically capture DPA in Hamming weight model for hardware implementation with precharge logic. At the end, we confront the notion of (revised) transparency order with attack simulations in order to study to what extent the low transparency order of an s-box impacts the efficiency of a side channel attack against its processing. To the best of our knowledge, this is the first time that such a critical analysis is conducted (even considering the original notion of Prouff). It practically confirms that the transparency order is indeed related to the resistance of the s-box against side-channel attacks, but it also shows that it is not sufficient alone to directly achieve a satisfying level of security. Regarding this point, our conclusion is that the (revised) transparency order is a valuable criterion to consider when designing a cryptographic algorithm, and even if it does not preclude to also use classical countermeasures like masking or shuffling, it enables to improve their effectiveness.     

Waves on the surface of a falling power-law fluid film

Waves that occur at the surface of a falling film of thin power-law fluid on a vertical plane are investigated. Using the method of integral relations an evolution equation is derived for two types of waves equation which are possible under long wave approximation. This equation reveals the presence of both kinematic and dynamic wave processes which may either act together or singularly dominate the wave field depending on the order of different parameters. It is shown that, at a small flow rate, kinematic waves dominate the flow field and the energy is acquired from the mean flow during the interaction of the waves, while, for high flow rate, inertial waves dominate and the energy comes from the kinematic waves. It is also found that this exchange of energy between kinematic and inertial waves strongly depends on the power-law index n. Linear stability analysis predicts the contribution of different terms in the wave mechanism. Further, it is found that the surface tension plays a double role: for a kinematic wave process, it exerts dissipative effects so that a finite amplitude case may be established, but for a dynamic wave process it yields dispersion. Further, it is shown that the non-Newtonian character n plays a vital role in controlling the role of the term that contains surface tension in the above processes.     

FeCl3 catalysed two consecutive aminomethylation at the α-position of the β-dicarbonyl compounds: an easy access to hexahydropyrimidines and its spiro analogues

Multicomponent synthesis of 1,3-diaryl-hexahydropyrimidines by a one-pot reaction of 1,3-dicarbonyl compounds, amines and formaldehyde catalysed by FeCl₃ in dichloromethane at room temperature (25-30 °C) has been reported. Double amino methylation occurs at the α-position of the 1,3-dicabonyl compounds/β-keto esters. The same methodology leads to spiro compounds with indane-1,3-dione. In this reaction, six molecules condense in one pot to form six new covalent bonds, thus, creating high atom economy. This is the first report of the synthesis of the substituted hexahydropyrimidines involving β-keto esters and its spiro analogues with indane-1,3-dione.     

Geometry and quadratic nonlinearity of charge transfer complexes in solution using depolarized hyper-Rayleigh scattering

We report large quadratic nonlinearity in a series of 1:1 molecular complexes between methyl substituted benzene donors and quinone acceptors in solution. The first hyperpolarizability, β(HRS), which is very small for the individual components, becomes large by intermolecular charge transfer (CT) interaction between the donor and the acceptor in the complex. In addition, we have investigated the geometry of these CT complexes in solution using polarization resolved hyper-Rayleigh scattering (HRS). Using linearly (electric field vector along X direction) and circularly polarized incident light, respectively, we have measured two macroscopic depolarization ratios D=I(2ω,X,X)/I(2ω,Z,X) and D(')=I(2ω,X,C)/I(2ω,Z,C) in the laboratory fixed XYZ frame by detecting the second harmonic scattered light in a polarization resolved fashion. The experimentally obtained first hyperpolarizability, β(HRS), and the value of macroscopic depolarization ratios, D and D('), are then matched with the theoretically deduced values from single and double configuration interaction calculations performed using the Zerner's intermediate neglect of differential overlap self-consistent reaction field technique. In solution, since several geometries are possible, we have carried out calculations by rotating the acceptor moiety around three different axes keeping the donor molecule fixed at an optimized geometry. These rotations give us the theoretical β(HRS), D and D(') values as a function of the geometry of the complex. The calculated β(HRS), D, and D(') values that closely match with the experimental values, give the dominant equilibrium geometry in solution. All the CT complexes between methyl benzenes and chloranil or 1,2-dichloro-4,5-dicyano-p-benzoquinone investigated here are found to have a slipped parallel stacking of the donors and the acceptors. Furthermore, the geometries are staggered and in some pairs, a twist angle as high as 30° is observed. Thus, we have demonstrated in this paper that the polarization resolved HRS technique along with theoretical calculations can unravel the geometry of CT complexes in solution.     

Mechanistic studies on the oxidation of ascorbic acid and hydroquinone by a {Mn4O6}4+ core in aqueous media

Described in this work is the kinetics of oxidation of ascorbic acid and hydroquinone by a tetranuclear Mn(IV) oxidant, [Mn(4)(μ-O)(6)(bipy)(6)](4+) (1(4+), bipy =2,2(/)-bipyridine), in aqueous solution over a wide pH range 1.5-6.0. In particular, below pH 3.0, protonation on the oxo-bridge of 1(4+) results in the formation of [Mn(4)(μ-O)(5)(μ-OH)(bipy)(6)](5+) (1H(5+)) as an additional oxidant over 1(4+). Both ascorbic acid and ascorbate whereas only hydroquinone and none of its protolytic species were found to be reactive reducing agents in these reactions. Analysis of the rate data clearly established that the oxo-bridge protonated oxidant 1H(5+) is kinetically far more superior to 1(4+) in oxidizing ascorbic acid and hydroquinone. Rates of these reactions are substantially lowered in D(2)O-enriched media in comparison to that in H(2)O media. An initial one electron one proton transfer electroprotic rate step could be mechanistically conceived. DFT studies established that among the two sets of terminal and central Mn(IV) atoms in the tetranuclear oxidant, one of the two terminal Mn(IV) is reduced to Mn(III) at the rate step that we can intuitively predict considering the probable positive charge distribution on the Mn(IV) atoms.     

Analysis of blood flow through a modelled artery with an aneurysm

The intention of the present work is to carry out a systematic analysis of flow features in a tube, modelled as artery, having a local aneurysm in presence of haematocrit. The arterial model is treated to be axi-symmetric and rigid. The blood, flowing through the modelled artery, is treated to be Newtonian and non-homogeneous. For a thorough quantitative analysis of the flow characteristics such as wall pressure, flow velocity, wall shear stress, the unsteady incompressible Navier-Stokes equations in cylindrical polar co-ordinates under the laminar flow conditions are solved by using the finite-difference method. Finally, the numerical illustrations presented in this paper provide an effective measure to estimate the combined influence of haematocrit and aneurysm on flow characteristics. It is found that the magnitude of wall shear stress and also the length of separation increase with increasing values of the haematocrit parameter. The length of flow separation increases but the peak value of wall shear stress decreases with the increasing length of aneurysm. The peak value of wall shear stress as well as the length of separation increases with the increasing height of the aneurysm.