Some aspects of mathematical and chemical modeling of complex chemical processes

Some theoretical questions involved in the mathematical modeling of the kinetics of complex chemical process are discussed. The analysis is carried out for the homogeneous oxidation of ethylbenzene in the liquid phase. Particular attention is given to the determination of the general characteristics of chemical systems from an analysis of mathematical models developed on the basis of linear algebra

Functional integral for non-Lagrangian systems

A novel functional integral formulation of quantum mechanics for non-Lagrangian systems is presented. The new approach, which we call "stringy quantization," is based solely on classical equations of motion and is free of any ambiguity arising from Lagrangian and/or Hamiltonian formulation of the theory. The functionality of the proposed method is demonstrated on several examples. Special attention is paid to the stringy quantization of systems with a general A-power friction force $-\kappa[\dot{q}]^A$. Results for $A = 1$ are compared with those obtained in the approaches by Caldirola-Kanai, Bateman and Kostin. Relations to the Caldeira-Leggett model and to the Feynman-Vernon approach are discussed as well.Comment: 14 pages, 7 figures, corrected typo

Electronic and structural properties of alkali doped SWNT

Comprehensive experiments on structural and transport properties of alkali intercalated single walled carbon nanotubes (SWNT) are presented. The increasing electron density was measured as a shift of the Drude-edge in optical reflectivity in-situ with progressive doping. In saturation-doped samples the Drude-edge shifts into the visible (to 25,000 - 30,000 cm— 1 for potassium and rubidium doped samples) and the samples have a golden-brown color, similar to stage I graphite. X-ray diffraction reveals a crystalline rope structure with expanded lattice constant, similar to results of Duclaux et al. The change in the low temperature divergence of the resistivity after degassing at high temperature and high vacuum and after K-doping is studied in-situ

Apparent rippling with honeycomb symmetry and tunable periodicity observed by scanning tunneling microscopy on suspended graphene

Suspended graphene is difficult to image by scanning probe microscopy due to the inherent van-der-Waals and dielectric forces exerted by the tip which are not counteracted by a substrate. Here, we report scanning tunneling microscopy data of suspended monolayer graphene in constant-current mode revealing a surprising honeycomb structure with amplitude of 50$-$200 pm and lattice constant of 10-40 nm. The apparent lattice constant is reduced by increasing the tunneling current $I$, but does not depend systematically on tunneling voltage $V$ or scan speed $v_{\rm scan}$. The honeycomb lattice of the rippling is aligned with the atomic structure observed on supported areas, while no atomic corrugation is found on suspended areas down to the resolution of about $3-4$ pm. We rule out that the honeycomb structure is induced by the feedback loop using a changing $v_{\rm scan}$, that it is a simple enlargement effect of the atomic resolution as well as models predicting frozen phonons or standing phonon waves induced by the tunneling current. Albeit we currently do not have a convincing explanation for the observed effect, we expect that our intriguing results will inspire further research related to suspended graphene.Comment: 10 pages, 7 figures, modified, more detailed discussion on errors in vdW parameter

Ordered low-temperature structure in K4C60 detected by infrared spectroscopy

Infrared spectra of a K4C60 single-phase thin film have been measured between room temperature and 20 K. At low temperatures, the two high-frequency T1u modes appear as triplets, indicating a static D2h crystal-field stabilized Jahn-Teller distortion of the (C60)4- anions. The T1u(4) mode changes into the known doublet above 250 K, a pattern which could have three origins: a dynamic Jahn-Teller effect, static disorder between "staggered" anions, or a phase transition from an orientationally-ordered phase to one where molecular motion is significant.Comment: 4 pages, 2 figures submitted to Phys. Rev.

Charge transfer and Fermi level shift in p-doped single-walled carbon nanotubes

The electronic properties of p-doped single-walled carbon nanotube (SWNT) bulk samples were studied by temperature-dependent resistivity and thermopower, optical reflectivity, and Raman spectroscopy. These all give consistent results for the Fermi level downshift (Delta E(F)) induced by doping. We find Delta E(F) approximate to 0.35 eV and 0.50 eV for concentrated nitric and sulfuric acid doping respectively. With these values, the evolution of Raman spectra can be explained by variations in the resonance condition as E(F) moves down into the valence band. Furthermore, we find no evidence for diameter-selective doping, nor any distinction between doping responses of metallic and semiconducting tubes

Nanosegregation in Na2C60

There is continuous interest in the nature of alkali metal fullerides containing C(4)(60) and C(2)(60), because these compounds are believed to be nonmagnetic Mott–Jahn–Teller insulators. This idea could be verified in the case of A(4)C(60), but Na(2)C(60) is more controversial. By comparing the results of infrared spectroscopy and X-ray diffraction, we found that Na(2)C(60) is segregated into 3-10 nm large regions. The two main phases of the material are insulating C(60) and metallic Na(3)C(60). We found by neutron scattering that the diffusion of sodium ions becomes faster on heating. Above 470 K Na(2)C(60) is homogeneous and we show IR spectroscopic evidence of a Jahn–Teller distorted C(2)(60) anion

Small oscillations of a chiral Gross-Neveu system

We study the small oscillations regime (RPA approximation) of the time-dependent mean-field equations, obtained in a previous work, which describe the time evolution of one-body dynamical variables of a uniform Chiral Gross-Neveu system. In this approximation we obtain an analytical solution for the time evolution of the one-body dynamical variables. The two-fermion physics can be explored through this solution. The condition for the existence of bound states is examined.Comment: 21pages, Latex, 1postscript figur