Temperature shift of the CdxHg1−xTe energy gap

The temperature coefficient of the Cd_xHg_1?xTe energy gap dE_g/dT as a sum of lattice dilatation and the phonon-electron interaction terms has been calculated as the function of molar composition x, for 0?x?0.3, in the temperature range 4.2–300 K. A non-linear dependence of $\text{d}\text{E}{}_{\mathrm{g}}\text{d}\text{T}$ vs x and a strong effect of temperature on $\text{d}\text{E}{}_{\mathrm{g}}\text{d}\text{T}$ values have been obtained and a comparison with experimental data is discussed.     

Effect of quadratic interactions on the resonance raman scattering of T × t2 jahn-teller systems

Raman excitation profiles and depolarization dispersion curves are calculated for T × t₂ Jahn-Teller systems that are subject to quadratic vibronic (Renner-Teller) coupling as well as frequency changes of the active vibrational mode.     

Absorption,resonance, and near‐resonance Raman studies of the tetracyanoquinodimethane neutral and its monoanion in terms of density functional theory and complete active space self‐consistent field methods

The electronic structure of the 1¹B_1u and 1²B_3u excited electronic states of the tetracyanoquinodimethane (TCNQ) neutral and its charged derivative are studied within the framework of complete active space self‐consistent field (CASSCF) and Becke's three‐parameter hybrid method with Lee–Yang–Parr correlation functional (B3LYP) methods applied to the level aug‐cc‐p‐VDZ basis set. Both CASSCF/aug‐cc‐p‐VDZ and B3LYP/aug‐cc‐p‐VDZ treatments provide the ground‐state and the excited state geometries; these are then used to assess the Franck–Condon (FC) parameters in the 1¹B_1u state of the neutral TCNQ and in the 1²B_3u state of the TCNQ monoanion. The quality of numerical results is then tested on the base of available experimental near‐resonance and resonance Raman data. The studies are performed in terms of the vibronic model, which takes both FC and mode‐mixing (Dushinsky) effects into account. This somewhat simplified vibronic model leads to very good agreement between the theory and the Raman experiments concerning both neutral TCNQ and its monoanion. In particular, the calculated excitation profiles of the ν₂ = 2215 cm^?1, ν₄ = 1389 cm^?1, ν₅ = 1195 cm^?1, and ν₉ = 336 cm^?1 fundamentals are shown to be in excellent agreement with those for the TCNQ monoanion. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Absorption and magnetic circular dichroism (MCD) studies of 1,4,5,8-naphthalenetetracarboxy diimides in terms of CASSCF method and FC theory

The electronic and geometrical structures of the low-energy states of 1,4,5,8-naphthalenetetracarboxylic dianhydride parent diimide (1) are studied in terms of the complete active space self-consistent field (CASSCF) method employed at different level with respect to the size and the quality of the active space. In the framework of the vibronic model based on the Franck–Condon (FC) effect the absorption and magnetic circular dichroism (MCD) spectra are studied in the excitation region corresponding to two low-energy 1¹A_g → 1¹B_2u and 1¹A_g → 1¹B_3u electronic transitions in diimides. In that (visible) excitation region the CASSCF computations with the 5π[4n]5π active space (i.e., the naphthalene-like π orbitals enriched by the four lone pair orbitals of the oxygen atoms) were found to reproduce very well the empirical absorption and the MCD spectra measured for the dicyclohexyl-N,N^′-substituted diimide (2). At the same CASSCF/5π[4n]5π level, the electronic absorption of diimides in the near UV excitation region were attributed to the 1¹A_g → 2¹B_1u, 1¹A_g → 2¹B_3u and 1¹A_g → 2¹B_2u electronic transitions; the latter two are mostly localized on the “diimide chromophore”. For these transitions the calculated magneto-optical characteristics, such as sign pattern and intensity distribution in the MCD spectrum, were found to be consistent with that experimentally observed for the diimide 2 compound.     

The diamond covering property axiom

The Covering Property Axiom, which attempts to capture some of the combinatorics of the Sacks model, the model obtained from by countable support iteration of length of the Sacks forcing, seems to miss a Suslin tree. We add a diamond polish to the axiom to remedy this.     

Non-standard coupled extensional and bending bias tests for planar pantographic lattices. Part I: numerical simulations

In dell’Isola et al. (Zeitschrift für Angewandte Math und Physik 66(6):3473–3498, 2015, Proc R Soc Lond A Math Phys Eng Sci 472(2185), 2016), the concept of pantographic sheet is proposed. The aim is to design a metamaterial showing: (i) a large range of elastic response; (ii) an extreme toughness in extensional deformation; (iii) a convenient ratio between toughness and weight. However, these required properties must coexist with non-detrimental mechanical characteristics in the presence of other kinds of imposed displacements. The aim of this paper is to prove via numerical simulations that pantographic sheets may effectively resist to coupled bending and extensional deformations. The four-parameter model introduced shows its versatility as it is able to encompass all the considered types of (large) deformations. The numerical integration scheme which we use is based on the same concepts exploited in Turco et al. (Zeitschrift für Angewandte Math und Physik 67(4):1–28, 2016): They prove that the Hencky-type discretization is very efficient also in nonlinear large deformations and large displacements regimes. In Part II of this paper, we will show that the used models are very effective to describe experimental evidence.     

Theory of depolarization dispersion of inversely polarized modes in heme proteins

A new polarization phenomenon observed recently in resonance Raman scattering from heme proteins is explained by vibronic interactions between split Q_x, Q_y, and B_x, B_y electronic states in porphyrin rings. Analytical formulas are presented which account well for the observed depolarization dispersion of the 1585 cm^?1 and 1310 cm^?1 a_2g modes in ferrocytochrome c.     

Generation of self-similar processes for simulation studies of telecommunication networks

It is generally accepted that self-similar processes may provide better models for teletraffic in modern telecommunication networks than Poisson processes. If stochastic self-similarity of teletraffic is not taken into account, it can lead to inaccurate conclusions about the performance of networks. Thus, an important requirement for conducting simulation studies of networks is the ability to generate long synthetic self-similar sequences of incremental processes, to transform them into interevent time intervals, and to do this accurately and quickly. A fast generator for count processes based on wavelets is described. Then a method for transformation of count processes into interevent processes proposed by Leroux and Hassan [1] and an alternative method, that is, inverting the empirical distribution directly, are studied. A case study is discussed to show how long sequences are needed in the steady-state simulation of queueing models with self-similar input processes. This is compared with simulation run lengths of the same queueing models fed by Poisson processes.