Quasinormal modes of BTZ black hole and Hawking‐like radiation in graphene

The Bañados‐Teitelboim‐Zanelli (BTZ) black hole model corresponds to a solution of (2+1)‐dimensional Einstein gravity with negative cosmological constant, and by a conformal rescaling its metric can be mapped onto the hyperbolic pseudosphere surface (Beltrami trumpet) with negative curvature. Beltrami trumpet shaped graphene sheets have been predicted to emit Hawking radiation that is experimentally detectable by a scanning tunnelling microscope. Here, for the first time we present an analytical algorithm that allows variational solutions to the Dirac Hamiltonian of graphene pseudoparticles in BTZ black hole gravitational field by using an approach based on the formalism of pseudo‐Hermitian Hamiltonians within a discrete‐basis‐set method. We show that our model not only reproduces the exact results for the real part of quasinormal mode frequencies of (2+1)‐dimensional spinless BTZ black hole, but also provides analytical results for the real part of quasinormal modes of spinning BTZ black hole, and also offers some predictions for the observable effects with a view to gravity‐like phenomena in a curved graphene sheet.

     

Synthesis of dipyrrolo[2,3-a:1′,2′,3′-fg]acridin-12(1H)-ones

Acylation reactions of 4,6-dimethoxyindoles with glyoxyloyl chlorides were achieved by the use of graphite powder in 1,2-dichloroethane at reflux. The products were monoketones as a result of decarbonylation, rather than the expected 1,2-diketones. Treatment of these monoketones with base led to their cyclisation and elimination of methanol to afford the novel dipyrrolo[2.3-a:1′,2′,3′-fg]acridin-12(1H)-ones.     

Determination of sulpha-drugs with ion-selective membrane electrodes--II

Two liquid-membrane electrodes, one sensitive to Cu(2+) and the other to Ag(+), were used for the determination of various sulpha-drugs with pK(a) > or = 6 (as the sodium salts) by potentiometric titration with CuSO(4) and AgNO(3). The construction and basic characteristics of these two electrodes are discussed.     

The stability of magnetobipolarons in low-dimensional systems

We investigate the stability condition of large bipolarons confined in a parabolic potential containing certain parameters and a uniform magnetic field. The variational wave function is constructed as a product form of electronic parts, consisting of center of mass and internal motion, and a part of coherent phonons generated by Lee-Low-Pines transformation from the vacuum. An analytical expression for the bipolaron energy is found, from which the ground and excited-state energies are obtained numerically by minimization procedure. The bipolaron stability region is determined by comparing the bipolaron energy with those of two separate polarons, which is already calculated within the same approximation. It is shown that the results obtained for the ground state energy of bipolarons reduce to the existing works in zero magnetic field. In the presence of a magnetic field, the stability of bipolarons is examined, for three types of low-dimensional system, as function of certain parameters, such as the magnetic-field, the electron-phonon coupling constant, Coulomb repulsion and the confinement strength. Numerical solutions for the energy levels of the ground and first excited states are examined as functions of the same parameters. Received 7 March 2002 and Received in final form 22 April 2002 Published online 25 June 2002     

Performance assessment of the photon enhanced thermionic emitter and heat engine system

Journal of Thermal Analysis and Calorimetry - The aim of this research is to show the potential application of a photon enhanced thermionic emitter (PETE)–irreversible heat engine (HE) hybrid...     

Methoxy-activated indole-7-carbohydrazides; synthesis,antioxidant, and anticancer properties

Indole has been known as a key heterocyclic motif in the development of new structures for both chemical and biological properties. In this current study, a new range of indole-7-carbohydrazides has been successfully synthesized starting from the readily available 3-phenyl and 2,3-diphenyl 4,6-dimethoxyindoles. The structures of the novel compounds were confirmed by utilizing ¹H NMR, ¹³C NMR, FT-IR, high-resolution mass spectrometry, and single crystal X- ray diffraction techniques. In addition, the indole-7-carbohydrazides showed promising antioxidant results in preliminary screens. Some of the new compounds generated from dimethoxy indoles were also screened for their anticancer activity against SH-SHY5Y (human neuroblastoma), AGS (human gastric adenocarcinoma), and MDA-MB-231 (human breast adenocarcinoma) cell lines. The results revealed that the compound 12 was the promising candidate, showing cytotoxic effects on both neuroblastoma, stomach, and breast cancer cells.     

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.     

Bromination of 4,6-dimethoxyindoles

The bromination of activated 4,6-dimethoxyindoles can be carried out effectively provided that an electron-withdrawing group is also present. Thus the range of products includes 2-bromo-7-formyl or 2-bromo-7-acetylindoles 13a–c and 16, 7-bromo-2-acetylindole 21, 2,5-dibromo-7-acetylindole 17, 2,5-dibromo-N-sulfonylindole 27, and 2,7-dibromo-N-acetylindole 24. Acetyl and sulfonyl protecting groups on nitrogen can be removed to give 2-bromoindoles 28a–b, 2,5-dibromoindole 29, and 2,7-dibromoindole 4.