On the construction of supersymmetric quantum mechanical Hamiltonian

Starting from an arbitrary supersymmetric quantum mechanical Hamilonian (SSQM) (with unbroken spersymmetry) we construct a sequence of SSQM Hamiltonians, each one having the same energy spectrum as the original one with different eigenvectors. The alogorithm developed here is verified for a transcendental type superpotential.     

Simultaneous determination of glycerol and clavulanic acid in an antibiotic bioprocess using attenuated total reflectance mid infrared spectroscopy

Attenuated total reflectance mid infrared (ATR-MIR) spectroscopy is a potential technique for the near real-time monitoring of filamentous bioprocesses. Here we investigate the utility of ATR-MIR to monitor and predict concentrations of glycerol and product (clavulanic acid) in a complex antibiotic bioprocess. Streptomyces clavuligerus exhibits filamentous growth, thus, as biomass accumulates the process fluid becomes much more viscous, and develops pronounced non-Newtonian behaviour. A multivariate statistical technique, partial least square (PLS) has been used to develop models for the key analytes over the time course of the bioprocess. These models were then validated externally using unseen samples, not used in the original modelling exercise. Despite the heterogeneous nature of the bioprocess and the resulting complexity of the spectra, the models developed had high correlation coefficient values and low prediction error values of 0.302 and 0.009 for glycerol and clavulanic acid, respectively. The findings extend the use of ATR-MIR in these difficult fluids which are typical of filamentous industrial bioprocesses, and demonstrate the practical utility of the technique in the measurement of a range of analyte types, including those present at relatively modest levels compared to the concentrations of biomass and major substrates.     

Drive level dependency in quartz resonators

Common piezoelectric resonators such as quartz resonators have a very high Q and ultra stable resonant frequency. However, due to small material nonlinearities in the quartz crystal, the resonator is drive level dependent, that is, the resonator level of activity and its frequency are dependent on the driving, or excitation, voltage. The size of these resonators will be reduced to one fourth of their current sizes in the next few years, but the electrical power which is applied will not be reduced as much. Hence, the applied power to resonator size ratio will be larger, and the drive level dependency may play a role in the resonator designs.We study this phenomenon using the Lagrangian nonlinear stress equations of motion and Piola–Kirchhoff stress tensor of the second kind. Solutions are obtained using COMSOL for the AT-cut, BT-cut, SC-cut and other doubly rotated cut quartz resonators and the results compared well with experimental data. The phenomenon of the drive level dependence is discussed in terms of the voltage drive, electric field, power density and current density. It is found that the drive level dependency is best described in terms of the power density. Experimental results for the AT-, BT- and SC-cut resonators in comparison with our model results are presented. Results for new doubly rotated cuts are presented. The effects of spurious modes, quality factor and air damping on DLD are presented.     

Recent advances in continuous flow synthesis of heterocycles

In the current scenario, flow chemistry is emerging as a significant technology in the field of organic synthesis. This miniaturized protocol including microreactors facilitates excellent heat transfer, low solvent wastage, lesser reaction time, a safer environment for reagent handling and appreciable yields of desired products. Thus, this “enabling technology” has a great scope in the synthesis and preparation of a variety of heterocycles that require toxic reagents as starting materials. This review discusses the recent advances (2020–2021) in continuous flow strategy for synthesis and derivatization of variety of heterocyclic entities, of different ring size, using different approaches. This also highlights the advantages of different combined techniques like Microwave assisted heating, electrochemical flow cell, LED light source, NMR and FT-IR analysis, etc., that enables utilization of various mechanisms and real-time monitoring of reactions leading to improved results.

Graphic abstract

     

A mathematical criterion for a stable government†

The paper presents a mathematical model of the problem of the politico‐economic stability of a welfare state. The variables characterizing the state of a government are identified. A sufficient criterion which ensures the damping out of the effects arising due to arbitrary perturbations in the variables, is obtained. The model assumes the prevalence of normal conditions, that is, times free from unforeseen calamities such as severe earthquake, outbreak of epidemic on a large scale, invasion by another country, acute famine, etc.

     

A Comparison of Pair Potential for Some Polar and Non-Polar Mesogenic Molecules

Asymmetry of pair potential plays a crucial role in the formation of mesophases in molecular systems. Variation of such asymmetry is closely related to the constituents of the molecules as well as their positions. To investigate the asymmetry as well as its effect on molecular behavior, a few polar biphenyl and non-polar 2,5 disubstituted pyridine derivatives have been chosen. The intermolecular interaction energy between a pair of molecules has been calculated with the help of a standard method as prescribed by Claverie (Claverie, P. (1978). Elaborations of approximate formulas for interactions between large molecules: Applications in organic chemistry. In: B. Pullman (Eds.), Inter Molecular Interactions from Diatomic to Biopolymers, J. Wiley & Sons Ltd.: Hoboken, NJ, 217–226.). Molecular geometry of all the selected systems was fully optimized without any constraint, and the net atomic charge and the dipole moment on each atomic center was calculated using the Gaussian03 program with density functional B3LYP method using 6-31G** as the basis set. The dispersion and the short range repulsion energy terms have been calculated using semiempirical Kitaigorodskii's “6-exp” formula. An attempt has been made to explain the phase sequences on the basis of the ratios of various interaction energy terms.

Supplemental materials are available for this article. Go to the publisher's online edition of Molecular Crystals and Liquid Crystals to view the free supplemental file.     

Parametric identification of fractional-order nonlinear systems

Nonlinear Dynamics - This work presents a new method for the identification of fractional-order nonlinear systems from time domain data. A parametric identification technique for integer-order...     

Acid‐Triggered Degradable Reagents for Differentiation of Adaptive and Innate Immune Responses to Leishmania‐Associated Sugars

Lipopolysaccharides (LPS) of Leishmania spp are known to alter innate immune responses. However, the ability of these sugars to specifically alter adaptive T‐cell responses is unclear. To study cap sugar–T‐cell interactions, pathogen mimics (namely glycodendrimer‐coated latex beads with acid‐labile linkers) were synthesized. Upon lysosomal acidification, linker breakdown releases glycodendrimers for possible loading on antigen presenting molecules to induce T‐cell growth. T‐cell proliferation was indeed higher after macrophage exposure to mannobioside or ‐trioside‐containing glycodendrimers than to non‐functionalized beads. Yet, blocking phagolysosomal acidification only reduced T‐cell proliferation with macrophages exposed to beads with an acid‐labile‐linker and not to covalently‐linked beads. These sugar‐modified reagents show that oligosaccharides alone can drive T‐cell proliferation by acidification‐requiring presentation, most significantly in NKT receptor (CD160)‐restricted T cells.     

Estimation of mesogenic character of disubstituted pyridine derivatives on the basis of intermolecular interaction energy calculations

Two pyridine derivative “2-(4-butoxyphenyl)-5-hexyl pyridine” (Cpd 1) and “3-(4-butoxyphenyl)-6-hexyl pyridine” (Cpd 2) differing only in the relative position of nitrogen have been examined quantum mechanically to understand the possible reason of their different mesogenic character. The studies include geometry optimization, evaluation of interaction energy between a molecular pair at minimum energy configuration and tendency of ordering at various interacting conditions. It has been found that in Cpd 1, the phenyl and pyridine rings are almost coplanar with the butoxy tail while Cpd 2 differs significantly from planarity. Cpd 1 therefore stacks more closely than Cpd 2. An attempt has been made to correlate the results of intermolecular interaction energy calculation with the mesogenic behavior of the respective molecules.     

Dynamics of cascade three-level system interacting with the classical and quantized field

We study the exact solutions of the cascade three-level atom interacting with a single mode classical and quantized field with different initial conditions of the atom. For the semiclassical model, it is found that if the atom is initially in the middle level, the time-dependent populations of the upper and lower levels are always equal. This dynamical symmetry exhibited by the classical field is spoiled on quantization of the field mode. To reveal this non-classical effect, a Euler matrix formalism is developed to solve the dressed states of the cascade Jaynes-Cummings model (JCM). Possible modification of such an effect on the collapse and revival phenomenon is also discussed by taking the quantized field in a coherent state