On the supersymmetric nonlinear evolution equations

Supersymmetrization of a nonlinear evolution equation in which the bosonic equation is independent of the fermionic variable and the system is linear in fermionic field goes by the name B-supersymmetrization. We provide B-supersymmetric extension of a number of quasilinear and fully nonlinear evolution equations and demonstrate that the supersymmetric system follows from the usual action principle. We observe that B-supersymmetrization can also be realized using a generalized Noetherian symmetry such that the resulting set of Lagrangian symmetries coincides with symmetries of the field equations. Following this viewpoint we derive conservation laws for the supersymmetric pair of equations. We attempt to realize the bosonic and fermionic fields in terms of bright and dark solitons. The interpretation sought by us has its origin in the classic work of Bateman who introduced a reverse-time system with negative friction to bring linear dissipative systems within the framework of variational principle.     

Electron Rydberg wave packets in one-dimensional atoms

An expression for the transition probability or form factor in one-dimensional Rydberg atom irradiated by short half-cycle pulse was constructed. In applicative contexts, our expression was found to be more useful than the corresponding result given by Landau and Lifshitz. Using the new expression for the form factor, the motion of a localized quantum wave packet was studied with particular emphasis on its revival and super-revival properties. Closed form analytical expressions were derived for expectation values of the position and momentum operators that characterized the widths of the position and momentum distributions. Transient phase-space localization of the wave packet produced by the application of a single impulsive kick was explicitly demonstrated. The undulation of the uncertainty product as a function of time was studied in order to visualize how the motion of the wave packet in its classical trajectory spreads throughout the orbit and the system becomes nonclassical. The process, however, repeats itself such that the atom undergoes a free evolution from a classical, to a nonclassical, and back to a classical state.     

Primary cosmic-ray nucleon spectrum from the atmospheric gamma-ray and muon data

Summary The available experimental inclusive cross-sections for single-pion and kaon production in proton-proton collisions between 0.01 and 2 TeV incident-proton laboratory energy have been used to determine a phenomenological form for the inclusive cross-sections. This has been used together with the recent high-precision measurements of atmospheric gamma-ray and single-muon spectra between 0.002 to 50 TeV to derive the primary nucleon spectrum in the formI(E)=I ₀E-γ up to the primary energy ≥100 TeV. The parametersI ₀ and γ, vary in the range 1.75┌2.7 and 2.63┌2.78, respectively.

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Riassunto Sono state usate le sezioni d'urto inclusive sperimentali disponibili per la produzione di pioni singoli e kaoni negli urti protone-protone ad una energia del protone incidente nel laboratorio compresa tra 0.01 e 2 TeV per determinare una forma fenomenologica per la sezione d'urto inclusiva. Questa è stata usata assieme a recenti misure ad alta precisione dei raggi gamma e degli spettri di muoni singoli tra 0.002 e 50 TeV per derivare lo spettro primario dei nucleoni nella formaI(E)=I ₀E-γ fino a un'energia primaria ≥100 TeV. I parametriI ₀ e γ variano nell'intervallo 1.75┌2.7 e 2.63┌2.78 rispettivamente.

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Резуме Имеущиеся экспериментальные инклюзивные поперечные сечения для рождения отельных пионов и каонов в протон-протонных соударениях при энергиях падающих протонов в лабораторной системе коорлинат от 0.01 до 2 ГэВ используются для определения феноменологической формы для инклюзивного поперечного сечения. Эти результаты вместе с недавними измерениями спектров атмосферных гамма-лучей и отдельных мюонов в области от 0.002 до 50 ТэВ используются затем для получения спектра первичных нуклонов в видеI(E)=I ₀E-γ вплоть до первичной энергии ≥100 ТэВ. ПараметрыI ₀ и γ нзменяются соответственно в областях 1.75┌2.7 и 2.63┌2.78.

     

Modulation of electronic couplings within Ru2-polyyne frameworks

Dimers of [Ru(2)(Xap)(4)] bridged by 1,3,5-hexatriyn-diyl (Xap are 2-anilinopyridinate and its aniline substituted derivatives), [Ru(2)(Xap)(4)](2)(μ-C(6)) (1), were prepared. Compounds 1 reacted with 1 equiv of tetracyanoethene (TCNE) to yield the cyclo-addition/insertion products [Ru(2)(Xap)(4)](2){μ-C≡CC(C(CN)(2))-C(C(CN)(2))C≡C} (2) and 1 equiv of Co(2)(dppm)(CO)(6) to yield the η(2)-Co(2) adducts to the middle C≡C bond, [Ru(2)(Xap)(4)](2)(μ-C(6))(Co(2)(dppm)(CO)(4)) (3). Voltammetric and spectroelectrochemical studies revealed that (i) two Ru(2) termini in 1 are sufficiently coupled with the monoanion (1(-)) as a Robin-Day class II/III mixed valence species; (ii) the coupling between two Ru(2) is still significant but somewhat weakened in 3; and (iii) the coupling between two Ru(2) is completely removed by the insertion of TCNE in 2. The attenuation of electronic couplings in 2 and 3 was further explored with both the X-ray diffraction study of representative compounds and spin-unrestricted DFT calculations.     

First order intervalley scattering in silicon inversion layers

The mobility limited by first order intervalley scattering in a quantized silicon inversion layer is calculated by an iterative solution of the Boltzmann equation incorporating both scattering-out and scattering-in terms. The mobility values are found to be much smaller than those based on a relaxation-time model considering scattering-out only.     

Copper complexes with a flexible piperazinyl arm: nuclearity driven catecholase activity and interactions with biomolecules

Three new Cu(II) complexes, [Cu(HL¹)(pyridine)(H₂O)](ClO₄)₂·2MeOH (1), [Cu₂(HL¹)₂(NO₃)₂](NO₃)₂·3H₂O (2) and [Cu(HL₂)(NO₃)₂]·MeCN (3), have been synthesized from two Schiff base ligands [HL¹ = 1-phenyl-3-((2-(piperazin-4-yl)ethyl)imino)but-1-en-1-ol and HL² = 4-((2-(piperazin-1-yl)ethyl)imino)pent-2-en-2-ol] using the chair conformer of a flexible piperazinyl moiety. Structural analysis reveals that 1 and 3 are monomeric Cu(II) complexes consisting of five- and six-coordinate Cu(II), respectively, whereas 2 is a dinuclear Cu(II) complex consisting of two different Cu(II) centers, one square planar with the other distorted octahedral. Screening tests were conducted to quantify the binding of 1–3 towards DNA and BSA as well as the DNA cleavage activity of these complexes using gel electrophoresis. Enzyme kinetic studies were also performed for the complexes mimicking catecholase-like activities. Antibacterial activities of these complexes were also examined towards Methicillin-Resistant Staphylococcus aureus bacteria. The results reflect that 2 is more active than the monomeric complexes, which is further corroborated by density functional theory study.     

Starspots,stellar cycles and stellar flares: Lessons from solar dynamo models

We theoretically investigate the multistable behavior of a hybrid optomechanical system,in which a charged mechanical resonator is coupled via Coulomb interaction to an optomechanical cavity containing an optical parametric amplifier(OPA).It is shown that the multistable behavior of the mean intracavity photon number can be controlled flexibly by adjusting the nonlinear gain parameter of the OPA,the phase of the field pumping the OPA,the power and frequency of the field driving the cavity,and the Coulomb coupling strength between the two charged mechanical resonators.In particular,the increase of the nonlinear gain parameter can result in a transition from testability to Instability.Moreover,the effect of the Coulomb coupling strength on the bistable behavior of the steady-state positions of the two mechanical resonators is discussed.