Variational calculations on the energy levels of graphene quantum antidots

The critical properties of the two-dimensional Ising and Blume-Capel model on directedsmall-world lattices with quenched connectivity disorder are investigated. The disordered system is simulated by applying the Monte Carlo method with heat bath update algorithm and histogram re-weighting techniques. The critical temperature, as well as the critical exponents are obtained. For both models the critical parameters have been obtained for several values of the rewiring probability p. It is found that these disorder systems do not belong to the same universality class as two-dimensional ferromagnetic model on regular lattices. In particular, the Blume-Capel model, with zero crystal field interaction, on a directedsmall-world lattice presents a second-order phase transition for p < p _c , and a first-order phase transition for p > p _c , where p _c  ≈ 0.25. The critical exponents for p < p _c are different from those of the same model on a regular lattice, but are identical to the exponents of the Ising model on directedsmall-world lattice.     

Polaronic effects in one-dimensional quantum antidot arrays

We study the effect of polaronic corrections arising from theelectron-longitudinal optical phonon interaction on the energyspectrum of a two-dimensional electron system with a one-dimensionalperiodic antidot array geometry created by a weak electrostaticmodulation potential, and subjected to a weak magnetic fieldmodulation as well as a uniform strong perpendicular staticmagnetic field. To incorporate the effects of electron-phononinteractions within the framework of Fröhlich polaron theory, wefirst apply a displaced-oscillator type unitary transformation todiagonalise the relevant Fröhlich Hamiltonian, and we thendetermine the parameters of this transformation together with theparameter included in the electronic trial wave function . On thebasis of this technique, it has been shown that the polaroniccorrections have non-negligible effects on the electronic spectrumof a two-dimensional electron system with a quantum antidot array,since switching such an interaction results in shifting thedegeneracy restoring points of Landau levels wherein the flatbandcondition is fulfilled, thus suppressing the Weiss oscillations.     

Distribution of eigenvalues for the discontinuous boundary-value problem with functional-manypoint conditions

In this study, we investigate the boundary-value problem with eigenvalue parameter generated by the differential equation with discontinuous coefficients and boundary conditions which contains not only endpoints of the considered interval, but also a point of discontinuity, a finite number of internal points and abstract linear functionals. So our problem is not a pure boundary-value one. We single out a class of linear functionals and find simple algebraic conditions on the coefficients which guarantee the existence of an infinite number of eigenvalues. Also, the asymptotic formulas for the eigenvalues are found. The results obtained in this paper are new, even in the case of boundary conditions either without internal points or without linear functionals.     

Synthesis,photophysical and antioxidant properties of carbazole-based bis-thiosemicarbazones

Research on Chemical Intermediates - Utilizing Schiff base condensation of the 9-ethylcarbazole-3,6-dicarbaldehyde and thiosemicarbazides, four new N-ethylcarbazole-based bis-thiosemicarbazone...     

Two-particle Wigner functions in a one-dimensional Calogero-Sutherland potential

We calculate the Wigner distribution function for the Calogero-Sutherland system which consists of harmonic and inverse-square interactions. The Wigner distribution function is separated out into two parts corresponding to the relative and center-of-mass motions. A general expression for the relative Wigner function is obtained in terms of the Laguerre polynomials by introducing a new identity between Hermite and Laguerre polynomials.     

ASYMPTOTIC BEHAVIOUR OF EIGENVALUES FOR THE DISCONTINUOUS BOUNDARY-VALUE PROBLEM WITH FUNCTIONAL-TRANSMISSION CONDITIONS

In this study, the boundary-value problem with eigenvalue parameter generated by the differential equation with discontinuous coefficients and boundary conditions which contains not only endpoints of the considered interval, but also point of discontinuity and linear functionals is investigated. So, the problem is not pure boundary-value. The authors single out a class of linear functionals and find simple algebraic conditions on coefficients, which garantee the existence of innnit number eigenvalues. Also the asymptotic formulas for eigenvalues are found.     

Regular boundary value problems with a discontinuous coefficient,functional-multipoint conditions,and a linear spectral parameter

We consider a linear differential equation which includes a linear abstract operator, with a piecewise constant coefficient at the principal differential term, together with multipoint boundary-transmission conditions, including linear functionals. The spectral parameter appears linearly in the equation and may appear also linearly in the boundary-transmission conditions. We prove an isomorphism and coerciveness of the problem with respect to the spectral parameter and the space variable.     

Synthesis,photophysical and antioxidant properties of pyrrolo[3,2-c]carbazole and dipyrrolo[3,2-c:2′,3′-g]carbazole compounds

Research on Chemical Intermediates - The synthesis of (6-ethyl-1,6-dihydropyrrolo[3,2-c]carbazol-2-yl)methanol 5 and...     

Bridging the Time Gap: A Copper/Zinc Oxide/Aluminum Oxide Catalyst for Methanol Synthesis Studied under Industrially Relevant Conditions and Time Scales

Long‐term stability of catalysts is an important factor in the chemical industry. This factor is often underestimated in academic testing methods, which may lead to a time gap in the field of catalytic research. The deactivation behavior of an industrially relevant Cu/ZnO/Al₂O₃ catalyst for the synthesis of methanol is reported over a period of 148 days time‐on‐stream (TOS). The process was investigated by a combination of quasi in situ and ex situ analysis techniques. The results show that ZnO is the most dynamic species in the catalyst, whereas only slight changes can be observed in the Cu nanoparticles. Thus, the deactivation of this catalyst is driven by the changes in the ZnO moieties. Our findings indicate that methanol synthesis is an interfacially mediated process between Cu and ZnO.