Terms Of Constants Research Articles

A Quadruple Integral Involving the Hermite polynomial Hn(x): Derivation and Evaluation

A closed form expression of a quadruple integral involving the Hermite polynomial Hn(x) is derived. Special cases are expressed in terms of special functions and fundamental constants. All the results in this work are new.

Asymptotic of the smallest eigenvalues of the continuous Anderson Hamiltonian in $$d\le 3$$

We consider the continuous Anderson Hamiltonian with white noise potential on $(-L/2,L/2)^d$ in dimension $d\le 3$, and derive the asymptotic of the smallest eigenvalues when $L$ goes to infinity. We show that these eigenvalues go to $-\infty$ at speed $(\log L)^{1/(2-d/2)}$ and identify the prefactor in terms of the optimal constant of the Gagliardo-Nirenberg inequality. This result was already known in dimensions $1$ and $2$, but appears to be new in dimension $3$. We present some conjectures on the fluctuations of the eigenvalues and on the asymptotic shape of the corresponding eigenfunctions near their localisation centers.

Optical and radiation shielding features for some phospho-silicate glasses

Glass composition comprising of SiO2-Na2O-K2O-P2O5 with CaO/BaO were synthesised and characterized using XRD and UV-Vis spectroscopy. The optical features were analysed in terms of band gap (Eg), refractive index (n), molar refraction (RM), molar polarizability (αm), reflection loss (RLOSS), optical transmission (TOptical), metallization criterion (Mcriterion), dielectric constant (εStatic, εOptical), optical electronegativity (χ) and optical basicity (Ʌ). The Eg of glasses acquired using Tauc’s plot and ASF methods authenticates the applicability of both methods as equally good. The Eg value decreases, whereas n increases with an increase in alkaline earth metal oxides (CaO/BaO) content in the glass samples. The Mcriterion exhibits metallic nature of the glasses. The RM and αm decreases as CaO/BaO content increases; whereas RLOSS and TOptical remains constant for the glasses. The dielectric constants increase as CaO/BaO content increases. The photon attenuation parameters were investigated using MC simulations (PHITS and GEANT4) and theoretically using WinXCom. Among all glasses, S8 glass sample has highest μ/ρ, μ, Zeff, Neff and lowest mfp values. Further, S8 glass has low values of both stopping power (SP) and range (ℜp); as required for shielding from charged particles. The slow and fast neutron shielding ability also escalates with an increase in CaO/BaO content in glass matrix. Comparative analysis confirms that S8 glass sample possess superior radiation shielding competency not only for neutral radiations (photon and neutron beams), but also for charged particles (e, p, α and C-ion beams) as compared to several commercial shielding materials.

An electrochemical study of the binding interaction between chitosan and MPA-CdSe QDs for the development of biocompatible theranostic nanoprobe

The strength and stability of biopolymer-modified quantum dots (QDs) for designing biocompatible nanoprobes depends on the interaction between QDs and coating of interest. Hence, the quantitative determination of interaction parameters has a crucial role in their development. This paper focuses on an electrochemical approach to determine interaction and binding parameters between the chitosan and hydrophilic Mercaptopropionic acid (MPA) - CdSe QDs. MPA- CdSe QDs were synthesized by the hot injection method and characterized by several techniques. The cyclic voltammetry study revealed the reduction in oxidation peak current of redox solution with the addition of MPA- CdSe QDs (50 × 10−12 M to 350 × 10−12 M); however, the peak current was increased with the addition of chitosan (1 × 10−13 M to 50 × 10−13 M), without any change in the oxidation potential. This may be due to the interaction of the amino group of chitosan with the carboxylate group of MPA-CdSe QDs. The interaction was analyzed in terms of binding constant and no. of binding sites, which was 7.3 × 1015 L Mol−1and 1.3, respectively. Effect of scan rate on oxidation and reduction peak current confirms an irreversible electrode reaction. The interaction was further characterized with UV–Vis/Fluorescence spectroscopy, X-ray diffraction, and Fourier transform infrared spectroscopy. Biocompatibility of developed nano-biocomposite further evaluated by standard cell viability assay using Adenocarcinoma human alveolar basal epithelial cell line (A549) and Chinese hamster cell line (V79). Confocal microscopic studies and Z stacking were also performed to explore the efficacy of chitosan-coated MPA-CdSe QDs as a fluorescent agent for cell imaging.

Optical signature of magnetoelectric polarizability of topological insulators

The discovery of topological insulators has opened a new chapter of condensed matter physics. Recently, several experiments have confirmed that the magnetoelectric susceptibility of a topological insulator with time-reversal symmetry is quantized in terms of the fine-structure constant. To realize such measurements, a number of challenges have been overcome; particularly, high-precision time-domain terahertz polarimetry is devised. Here an experiment is proposed to observe the topological magnetoelectric effect. Based on the generalized multisphere Mie theory, it is shown that the optical activity of a cluster of topological insulator spheres elevates as metal spheres are deliberately brought near to them: The destructive interference of fields of the induced electric dipoles allows fields of the induced magnetic dipoles, which originate from the topological magnetoelectric effect, to play a prominent role. For example, for clusters of ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ and $\mathrm{InSb}$ spheres, the elevated azimuth and ellipticity angles are about $\ifmmode\pm\else\textpm\fi{}{20}^{\ensuremath{\circ}}$. Such a giant optical activity serves as an optical bridge to the determination of the fine-structure constant.

A quadruple integral involving the product of generalized parabolic cylinder functions 𝐷ᵥ(𝛽𝑥)𝐷ᵤ(𝛼𝑧): Derivation and evaluation

The aim of the present document is to evaluate a quadruple integral involving the product of the generalized Parabolic Cylinder functions D v ( β x ) D u ( α z ) D_{v}(\beta x)D_{u}(\alpha z) expressed in terms of the Hurwitz-Lerch zeta function. Special cases are evaluated in terms of fundamental constants. All the results in this work are new.

Benzoselenadiazole containing donor–acceptor–donor receptor as a superior and selective probe for fluoride in DMSO

Benzoselenodiazole/benzothiadiazole unit containing donor–acceptor-donor (D-A-D) fluorescent chemosensors (1-Se and 1-S) have been designed, synthesized, and characterized by spectroscopic techniques viz NMR and Mass spectrometry. The addition of F– selectively induces a prominent ‘naked-eye’ color change for 1-Se from yellow to red and from light-green to reddish-orange for 1-S in DMSO. These probes also show selectivity towards F– in presence of other interfering anions, for instances, I–, H2PO4–, CN–, Cl–, CH3COO–, Br–, PhCOO–, HSO4–, and NO3– which is established by UV–Vis and FL spectroscopic studies. Furthermore, 1-Se is found to be more selective and sensitive towards F– over 1-S in terms of binding constant and detection limit. The sensing mechanism is found to occur through the deprotonation of the –NH proton of benzimidazole group by F– which is confirmed by various spectroscopic techniques, such as, 1H NMR, 19F spectroscopy, and DFT studies. The macroscopic studies, such as DLS, FEG-TEM, and DOSY NMR revealed that 1-Se forms aggregate in solution through hydrogen bonding interaction which decumulates upon the addition of F– in solution.

Stabilizing deep tomographic reconstruction: Part B. Convergence analysis and adversarial attacks

SummaryDue to lack of the kernel awareness, some popular deep image reconstruction networks are unstable. To address this problem, here we introduce the bounded relative error norm (BREN) property, which is a special case of the Lipschitz continuity. Then, we perform a convergence study consisting of two parts: (1) a heuristic analysis on the convergence of the analytic compressed iterative deep (ACID) scheme (with the simplification that the CS module achieves a perfect sparsification), and (2) a mathematically denser analysis (with the two approximations: [1] AT is viewed as an inverse A-1 in the perspective of an iterative reconstruction procedure and [2] a pseudo-inverse is used for a total variation operator H). Also, we present adversarial attack algorithms to perturb the selected reconstruction networks respectively and, more importantly, to attack the ACID workflow as a whole. Finally, we show the numerical convergence of the ACID iteration in terms of the Lipschitz constant and the local stability against noise.

The three-loop anomalous dimension and the four-loop β-function for mathcal{N} = 1 SQED regularized by higher derivatives

For mathcal{N} = 1 SQED with Nf flavors regularized by higher derivatives in the general ξ-gauge we calculate the three-loop anomalous dimension of the matter superfields defined in terms of the bare coupling constant and demonstrate its gauge independence. After this the four-loop β-function defined in terms of the bare coupling constant is obtained with the help of the NSVZ equation, which is valid for these renormalization group functions in all loops. Next, we calculate the three-loop anomalous dimension and the four-loop β-function defined in terms of the renormalized coupling constant for an arbitrary subtraction scheme supplementing the higher derivative regularization. Then we construct a renormalization prescription for which the results coincide with the ones in the overline{mathrm{DR}} -scheme and describe all NSVZ schemes in the considered approximation. Also we demonstrate the existence of a subtraction scheme in which the anomalous dimension does not depend on Nf, while the β-function contains only terms of the first order in Nf. This scheme is obtained with the help of a finite renormalization compatible with a structure of quantum corrections and is NSVZ. The existence of such an NSVZ scheme is also proved in all loops.

Apsidal motion in massive eccentric binaries in NGC 6231

Context. The measurement of the apsidal motion in close eccentric massive binary systems provides essential information to probe the internal structure of the stars that compose the system. Aims. Following the determination of the fundamental stellar and binary parameters, we make use of the tidally induced apsidal motion to infer constraints on the internal structure of the stars composing the binary system HD 152219. Methods. The extensive set of spectroscopic, photometric, and radial velocity observations allowed us to constrain the fundamental parameters of the stars together with the rate of apsidal motion of the system. Stellar structure and evolution models were further built with the Clés code testing different prescriptions for the internal mixing occurring inside the stars. The effect of stellar rotation axis misalignment with respect to the normal to the orbital plane on our interpretation of the apsidal motion in terms of internal structure constants is investigated. Results. Made of an O9.5 III primary star (M1 = 18.64 ± 0.47 M⊙, R1 = 9.40−0.15+0.14 R⊙, Teff,1 = 30 900 ± 1000 K, Lbol,1 = (7.26 ± 0.97)×104 L⊙) and a B1-2 V-III secondary star (M2 = 7.70 ± 0.12 M⊙, R2 = 3.69 ± 0.06 R⊙, Teff,2 = 21 697 ± 1000 K, Lbol,2 = (2.73 ± 0.51)×103 L⊙), the binary system HD 152219 displays apsidal motion at a rate of (1.198 ± 0.300)° yr−1. The weighted-average mean of the internal structure constant of the binary system is inferred: k̄2 = 0.00173 ± 0.00052. For the Clés models to reproduce the k2-value of the primary star, a significantly enhanced mixing is required, notably through the turbulent mixing, but at the cost that other stellar parameters cannot be reproduced simultaneously. Conclusions. The difficulty to reproduce the k2-value simultaneously with the stellar parameters as well as the incompatibility between the age estimates of the primary and secondary stars are indications that some physics of the stellar interior are still not completely understood.

Quasi-Freestanding Bilayer Borophene on Ag(111).

The lattice structure of monolayer borophene depends sensitively on the substrate yet is metallic independent of the environment. Here, we show that bilayer borophene on Ag(111) shares the same ground state as its freestanding counterpart that becomes semiconducting with an indirect bandgap of 1.13 eV, as evidenced by an extensive structural search based on first-principles calculations. The bilayer structure is composed of two covalently bonded v1/12 boron monolayers that are stacked in an AB mode. The interlayer bonds not only localize electronic states that are otherwise metallic in monolayer borophene but also in part decouple the whole bilayer from the substrate, resulting in a quasi-freestanding system. More relevant is that the predicted bilayer model of a global minimum agrees well with recently synthesized bilayer borophene on Ag(111) in terms of lattice constant, topography, and moiré pattern.

Binding studies for the interaction between hazardous organophosphorus compound phosmet and lysozyme: Spectroscopic and In-silico analyses

Organophosphorus compounds are generally toxic compounds found uses in agriculture, pharmaceutics, and other industries. These organophosphorus compounds are life threatening and may cause mortalities on acute exposure. Also, some of these are well known nerve agents. Phosmet is one such organophosphorus compound with moderate nerve toxicity on prolonged exposure. Phosmet is widely used pesticide on various trees including apple, pear, peach, almond and vines like grape vine. Thus, phosmet is the major contaminant of most of the consumed fruits.The present study investigated the binding of phosmet with lysozyme to understand the toxicology and the transport of phosmet using various spectroscopic techniques, molecular modeling and enzymatic assay. The ability of lysozyme to act as a biomarker for phosmet can also be revealed by the current study. The UV–Visible spectrum of lysozyme in presence of phosmet indicated hyperchromicity in the absorbance peak of lysozyme. The fluorescence quenching of lysozyme in presence of phosmet involve predominantly static quenching. The complexation is further quantified in terms of a binding constant (Kb) and the number of sets of equivalent binding sites (n) with the help of double logarithmic regression curve. The Kb value of 103–104 M−1 and n value near 1 indicated that phosmet is binding through non-covalent forces in single set of equivalent binding sites. Static quenching was additionally confirmed by modified Stern-Volmer plot for lysozyme-phosmet interactions. Post binding protein conformation changes and the enhanced protein stability of lysozyme were showed by CD spectrum and melting curves of lysozyme. The FT-IR spectrum also revealed the changes in secondary structure content of protein on interaction with phosmet. The docked structure for binding of phosmet with lysozyme were achieved using molecular docking analysis with a glide score −5.273 k J/mol-1 that indicated towards moderate binding as suggested by other experimental studies. The enzymatic activity of lysozyme depicted an increase of 16% after binding with phosmet indicative of interaction with the active site.

Impact of Charge Transfer Complex on the Dielectric Relaxation Processes in Poly(methyl methacrylate) Polymer.

The impact of the charge transfer complex on the dielectric relaxation processes in free poly(methyl methacrylate) (PMMA) polymer sheets was investigated. The frequency dependence of dielectric properties was obtained over the frequency range 0.1 Hz–1 MHz at temperatures ranging between 303 K and 373 K for perylene dye and acceptors (picric acid (PA) and chloranilic acid (CLA)) in an in situ PMMA polymer. The TG/dTG technique was used to investigate the thermal degradation of the synthesized polymeric sheets. Additionally, the kinetic parameters have been assessed using the Coats–Redfern relation. The dielectric relaxation spectroscopy of the synthesized polymeric sheets was analyzed in terms of complex dielectric constant, dielectric loss, electrical modulus, electrical conductivity, and Cole–Cole impedance spectroscopy. α- and β-relaxation processes were detected and discussed. The σ(ω) dispersion curves of the synthesized polymeric sheets show two distinct regions with increasing frequency. The impedance data of the synthesized polymeric sheets can be represented by the equivalent circuit (parallel RC).

Anomalous dispersion in gravity theories

A wave pulse (be it a gravitational wave or a light wave) undergoes anomalous dispersion in a vacuum in flat spacetimes with an even number of spatial dimensions even if all the frequencies move at the same speed. Such an anomalous dispersion does not occur in spacetimes with an odd number of spatial dimensions. We study various gravity theories and show that dispersion-free propagation is possible in even number of spatial dimensions if the background is not the Minkowski but the de Sitter spacetime and the gravity theory is massive gravity with a tuned mass in terms of the cosmological constant. Mass and the cosmological constant conspire to get rid of the anomalous dispersion and restore Huygens' principle.

Kinetics of lipase-catalyzed kinetic resolutions of racemic compounds: Reparameterization in terms of specificity constants

Lipases, which catalyze reactions by the Ping Pong bi bi mechanism, are commonly used in kinetic resolutions to produce pure enantiomers. Although expressions for the relative rates of reaction of the two enantiomers in such resolutions are well known, they are difficult to interpret in terms of the reaction mechanism. In the current work, we reparameterize these expressions in terms of specificity constants, resulting in parameters that are easier to relate to the reaction mechanism. Expressions are derived for three different combinations of chiral substrates and products in a reaction “A + B ⇌ P + Q”: A-Q resolution, B-Q resolution and A-P resolution. We show that the relative rates of reaction of the enantiomers depend on key “decision points”, represented by the free and substituted enzymes. The relative rates of the various reactions that leave a “decision point” are determined by selectivities, which are given by ratios of specificity constants, multiplied by the ratio of concentrations of the corresponding species. The enantiomeric ratio is only one of these selectivities.

Laser-coolable AcOH+ ion for CP -violation searches

The ${\mathrm{AcOH}}^{+}$ molecular ion is identified as a prospective system to search for $\mathcal{CP}$-violation effects. According to our study ${\mathrm{AcOH}}^{+}$ belongs to the class of laser-coolable polyatomic molecular cations implying a large coherence time in the experiments to study symmetry-violating effects of fundamental interactions. We perform both nuclear and high-level relativistic coupled cluster electronic structure calculations to express the experimentally measurable $\mathcal{T},\mathcal{P}$-violating energy shift in terms of fundamental quantities such as the nuclear magnetic quadrupole moment (MQM), electron electric dipole moment ($e\mathrm{EDM}$) and dimensionless scalar-pseudoscalar nuclear-electron interaction constant. We further express nuclear MQM in terms of the strength constants of $\mathcal{CP}$-violating nuclear forces: quantum chromodynamics vacuum angle $\overline{\ensuremath{\theta}}$ and quark chromo-EDMs. The equilibrium structure of ${\mathrm{AcOH}}^{+}$ in the ground and the four lowest excited electronic states was found to be linear. The calculated Franck-Condon factors and transition dipole moments indicate that the laser cooling using an optical cycle involving the first excited state is possible for the trapped ${\mathrm{AcOH}}^{+}$ ions with the Doppler limit estimated to be $\ensuremath{\sim}$4 nK. The lifetime of the ($0,{1}^{1},0$) excited vibrational state considered as a working one for MQM and $e\mathrm{EDM}$ search experiments is estimated to be $\ensuremath{\sim}0.4$ s.

Torsional Properties of Bundles with Randomly Packed Carbon Nanotubes.

Carbon nanotube (CNT) bundles/fibers possess promising applications in broad fields, such as artificial muscles and flexible electronics, due to their excellent mechanical properties. The as-prepared CNT bundles contain complex structural features (e.g., different alignments and components), which makes it challenging to predict their mechanical performance. Through in silico studies, this work assessed the torsional performance of CNT bundles with randomly packed CNTs. It is found that CNT bundles with varying constituent CNTs in terms of chirality and diameter exhibit remarkably different torsional properties. Specifically, CNT bundles consisting of CNTs with a relatively large diameter ratio possess lower gravimetric energy density and elastic limit than their counterpart with a small diameter ratio. More importantly, CNT bundles with the same constituent CNTs but different packing morphologies can yield strong variation in their torsional properties, e.g., up to 30%, 16% and 19% difference in terms of gravimetric energy density, elastic limit and elastic constants, respectively. In addition, the separate fracture of the inner and outer walls of double-walled CNTs is found to suppress the gravimetric energy density and elastic limit of their corresponding bundles. These findings partially explain why the experimentally measured mechanical properties of CNT bundles vary from each other, which could benefit the design and fabrication of high-performance CNT bundles.

Modeling of bulk modulus of A2BX6 cubic crystals (A = K, Cs, Rb, TI, NH4; B = tetravalent cation; X = F, Cl, Br, I) using semi-empirical model

In this work, a semi-empirical relation was elaborated in terms of lattice constant (a∘) and product of ionic charges (ZaZbZx) for the calculation of bulk moduli (in GPa) of A2BX6 (A: large cation, B: transition metal and X: halide anions) structured materials. ZaZbZx and a∘ were related through bulk moduli through linear regression. These two parameters yield a straight regression line, when plotted but fall on different positions due the variation in bulk moduli values. The calculated values of bulk moduli (reflecting elastic characteristics) are in close agreement with the other available values. As, these values are only differing by average of 3% from values in the literature. Moreover, the regression resulted in good values of correlation coefficient (R = 0.77) and Probability (P = 0.001). These all show the accuracy and reliability of the current work. The technique adopted in this work will be helpful to material scientists for finding new materials with preferred elastic characteristics among structurally similar materials, also the calculated data will act as a reference for upcoming investigation of the studied compounds.

Capturing Free-Radical Polymerization by Synergetic Ab Initio Calculations and Topological Reactive Molecular Dynamics.

Photocurable polymers are used ubiquitously in 3D printing, coatings, adhesives, and composite fillers. In the present work, the free radical polymerization of photocurable compounds is studied using reactive classical molecular dynamics combined with a dynamical approach of the nonequilibrium molecular dynamics (D-NEMD). Different concentrations of radicals and reaction velocities are considered. The mechanical properties of the polymer resulting from 1,6-hexanediol dimethacrylate systems are characterized in terms of viscosity, diffusion constant, and activation energy, whereas the topological ones through the number of cycles (polymer loops) and cyclomatic complexity. Effects like volume shrinkage and delaying of the gel point for increasing monomer concentration are also predicted, as well as the stress-strain curve and Young's modulus. Combining ab initio, reactive molecular dynamics, and the D-NEMD method might lead to a novel and powerful tool to describe photopolymerization processes and to original routes to optimize additive manufacturing methods relying on photosensitive macromolecular systems.

Slow nucleosome dynamics set the transcriptional speed limit and induce RNA polymerase II traffic jams and bursts.

Nucleosomes are recognized as key regulators of transcription. However, the relationship between slow nucleosome unwrapping dynamics and bulk transcriptional properties has not been thoroughly explored. Here, an agent-based model that we call the dynamic defect Totally Asymmetric Simple Exclusion Process (ddTASEP) was constructed to investigate the effects of nucleosome-induced pausing on transcriptional dynamics. Pausing due to slow nucleosome dynamics induced RNAPII convoy formation, which would cooperatively prevent nucleosome rebinding leading to bursts of transcription. The mean first passage time (MFPT) and the variance of first passage time (VFPT) were analytically expressed in terms of the nucleosome rate constants, allowing for the direct quantification of the effects of nucleosome-induced pausing on pioneering polymerase dynamics. The mean first passage elongation rate γ(hc, ho) is inversely proportional to the MFPT and can be considered to be a new axis of the ddTASEP phase diagram, orthogonal to the classical αβ-plane (where α and β are the initiation and termination rates). Subsequently, we showed that, for β = 1, there is a novel jamming transition in the αγ-plane that separates the ddTASEP dynamics into initiation-limited and nucleosome pausing-limited regions. We propose analytical estimates for the RNAPII density ρ, average elongation rate v, and transcription flux J and verified them numerically. We demonstrate that the intra-burst RNAPII waiting times tin follow the time-headway distribution of a max flux TASEP and that the average inter-burst interval [Formula: see text] correlates with the index of dispersion De. In the limit γ→0, the average burst size reaches a maximum set by the closing rate hc. When α≪1, the burst sizes are geometrically distributed, allowing large bursts even while the average burst size [Formula: see text] is small. Last, preliminary results on the relative effects of static and dynamic defects are presented to show that dynamic defects can induce equal or greater pausing than static bottle necks.