Global well‐posedness of the compressible Euler with damping in Besov spaces

In this paper, we consider the Cauchy problems for compressible Euler equations with damping. In terms of the Littlewood–Paley decomposition and Bony's para‐product formula, we prove the global existence, uniqueness and asymptotic behavior of the solution in the critical Besov space comparing with previous results. Copyright © 2012 John Wiley & Sons, Ltd.     

Spectral approximation for drainage of an Elastico‐viscous liquid and error analysis

A Fourier‐Galerkin spectral method is proposed and used to analyze a system of quasilinear partial differential equations governing the drainage of liquids of the Oldroyd four‐constant type. It is shown that, Fourier‐Galerkin approximations are convergent with spectral accuracy. An efficient and accurate algorithm based on the Fourier‐Galerkin approximations to the system of quasilinear partial differential equations are developed and implemented. Numerical results indicating the high accuracy and effectiveness of this algorithm are presented. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 492–505, 2012     

New (3+1)‐dimensional nonlinear equations with KdV equation constituting its main part: multiple soliton solutions

In thiswork,we present two new(3+1)‐dimensional nonlinear equationswith Korteweg‐de Vries equation constituting its main part. We show that the dispersive relation is distinct for each model, whereas the phase shift remains the same. We determine multiple solitons solutions, with distinct physical structures, for each established equation. The architectures of the simplified Hirota's method is implemented in this paper. The constraint conditions that fall out which must remain valid in order for themultiple solitons to exist are derived.Copyright © 2015 John Wiley & Sons, Ltd.     

Integral operators with Green's function type kernel

A variant of the Nyström method based on Simpson's rule is presented. This is designed to deal with integral operators with kernels k(s, t) that are not continuous along the diagonal s = t. A complete analysis is carried out, generalizations for other interpolatory quadrature rules are proposed; also a variant using Gaussian quadrature is considered and examples are given.     

Density functional theory study on a fluorescent chemosensor device of aza‐crown ether

Three derivatives of alkyl anthracene covalently bonded to aza‐18‐crown‐6 at the nitrogen position, anthracene(CH₂)_n, (n = 1–3) which act as an on–off fluorogenic photoswitch have been theoretically studied using a computational strategy based on density functional theory at B3LYP/6‐31 + G(d,p) method. The fully optimized geometries have been performed with real frequencies which indicate the minima states. The binding energies, enthalpies and Gibbs free energies have been calculated for aza‐18‐crown‐6 ( L ) and their metal complexes. The natural bond orbital analysis is used to explore the interaction of host–guest molecules. The absorption spectra differences between L and their metal ligands, the excitation energies and absorption wavelength for their excited states have been studied by time‐dependent density functional theory with the basis set 6‐31 + G(d,p). These fluorescent sensors and switchers based on photoinduced electron transfer mechanism have been investigated. The PET process from aza‐crown ether to fluorophore can be suppressed or completely blocked by the entry of alkali metal cations into the aza‐crown ether‐based receptor. Such a suppression of the PET process means that fluorescence intensity is enhanced. The binding selectivity studies of the aza‐crown ether part of L indicate that the presence of the alkali metal cations Li⁺, Na⁺ and K⁺ play an important role in determining the internal charge transfer and the fluorescence properties of the complexes. In addition, the solvent effect has been investigated. Copyright © 2014 John Wiley & Sons, Ltd.     

Muffin‐tin potentials in EXAFS analysis

Muffin‐tin potentials are the standard tool for calculating the potential surface of a cluster of atoms for use in the analysis of extended X‐ray absorption fine‐structure (EXAFS) data. The set of Cartesian coordinates used to define the positions of atoms in the cluster and to calculate the muffin‐tin potentials is commonly also used to enumerate the scattering paths used in the EXAFS data analysis. In this paper, it is shown that these muffin‐tin potentials are sufficiently robust to be used to examine quantitatively contributions to the EXAFS data from scattering geometries not represented in the original cluster.     

On the quantum Fermi accelerator and its relevance to ‘quantum chaos’

We discuss a quantum version of the Fermi acceleration model, which consists of a particle bouncing between a fixed and oscillating wall. The actual movement of the particle crucially depends on the boundary conditions of the Schrödinger equation. Under Dirichlet boundary conditions, the quantum system displays a regular behaviour, but its classical limit exhibits some unphysical attributes. Only for certain initial conditions does it correspond to the stable motion of a ball bouncing once for an integer number of wall oscillations. In the classical model that situation gives rise to regular islands imbedded in the chaotic sea.     

Flying qubits and entangled photons

Efficient generation of polarized single photons or entangled photon pairs is crucial for the implementation of quantum key distribution (QKD) systems. Self organized semiconductor quantum dots (QDs) are capable of emitting on demand one polarized photon or an entangled photon pair upon current injection. Highly efficient single‐photon sources consist of a pin structure inserted into a microcavity where single electrons and holes are funneled into an InAs QD via a submicron AlOx aperture, leading to emission of single polarized photons with record purity of the spectrum and non‐classicality of the photons. A new QD site‐control technique is based on using the surface strain field of an AlO_x current aperture below the QD. GaN/AlN QD based devices are promising to operate at room temperature and reveal a fine‐structure splitting (FSS) depending inversely on the QD size. Large GaN/AlN QDs show disappearance of the FSS. Theory also suggests QDs grown on (111)‐oriented GaAs substrates as source of entangled photon pairs.     

Post's Problem for Reducibilities of Bounded Complexity

In this paper we consider the we known method by E. Post of solving the problem of construction of recursively enumerable sets that have a degree intermediate between the degrees of recursive and complete sets with respect to a given reducibility. Post considered reducibilities ≤_m, ≤_btt, ≤_tt and ≤_T and solved the problem for al of them except ≤_T. Here we extend Post's original method of construction of incomplete sets onto two wide classes of sub‐Turing reducibilities what were studying in [1, 2].     

Derivation of macroscopic equations for individual cell‐based models: a formal approach

In this paper we review the theory of cells (particles) that evolve according to a dynamics determined by friction and that interact between themselves by means of suitable potentials. We derive by means of elementary arguments several macroscopic equations that describe the evolution of cell density. Some new results are also obtained—a formal derivation of a limit equation in the case of attractive potential as well as in the case of repulsive potential with a hard‐core part are presented. Finally we discuss the possible relevance of those results within the framework of individual cell‐based models. Several classes of potentials, including hard‐core, repulsive and potentials with attractive parts are discussed. The effect of noise terms in the equation is also considered. Copyright © 2005 John Wiley & Sons, Ltd.