Enhancement of Near-Cloaking. Part II: The Helmholtz Equation

The aim of this paper is to extend the method of Ammari et al. (Commun. Math. Phys., 2012) to scattering problems. We construct very effective near-cloaking structures for the scattering problem at a fixed frequency. These new structures are, before using the transformation optics, layered structures and are designed so that their first scattering coefficients vanish. Inside the cloaking region, any target has near-zero scattering cross section for a band of frequencies. We analytically show that our new construction significantly enhances the cloaking effect for the Helmholtz equation.     

A 3D numerical simulation of mixed convection of a magnetic nanofluid in the presence of non-uniform magnetic field in a vertical tube using two phase mixture model

In this paper, results of applying a non-uniform magnetic field on a ferrofluid (kerosene and 4 vol% Fe₃O₄ ) flow in a vertical tube have been reported. The hydrodynamics and thermal behavior of the flow are investigated numerically using the two phase mixture model and the control volume technique. Two positive and negative magnetic field gradients have been examined. Based on the obtained results the Nusselt number can be controlled externally using the magnetic field with different intensity and gradients. It is concluded that the magnetic field with negative gradient acts similar to Buoyancy force and augments the Nusselt number, while the magnetic field with positive gradient decreases it. Also with the negative gradient of the magnetic field, pumping power increases and vice versa for the positive gradient case.     

Computational singular perturbation with non-parametric tabulation of slow manifolds for time integration of stiff chemical kinetics

This paper presents a novel tabulation strategy for the adaptive numerical integration of chemical kinetics using the computational singular perturbation (CSP) method. The strategy stores and reuses CSP quantities required to filter out fast dissipative processes, resulting in a non-stiff chemical source term. In particular, non-parametric regression on low-dimensional slow invariant manifolds (SIMs) in the chemical state space is used to approximate the CSP vectors spanning the fast chemical subspace and the associated fast chemical time-scales. The relevant manifold and its dimension varies depending on the local number of exhausted modes at every location in the chemical state space. Multiple manifolds are therefore tabulated, corresponding to different numbers of exhausted modes (dimensions) and associated radical species. Non-parametric representations are inherently adaptive, and rely on efficient approximate-nearest-neighbor queries. As the CSP information is only a function of the non-radical species in the system and has relatively small gradients in the chemical state space, tabulation occurs in a lower-dimensional state space and at a relatively coarse level, thereby improving scalability to larger chemical mechanisms. The approach is demonstrated on the simulation of homogeneous constant pressure H₂–air and CH₄–air ignition, over a range of initial conditions. For CH₄–air, results are shown that outperform direct implicit integration of the stiff chemical kinetics while maintaining good accuracy.     

First-Order Intertwining Operators with Position Dependent Mass and <Emphasis Type="Italic">η</Emphasis>-Weak-Pseudo-Hermiticity Generators

A Hermitian and an anti-Hermitian first-order intertwining operators are introduced and a class of η-weak-pseudo-Hermitian position-dependent mass (PDM) Hamiltonians are constructed. A corresponding reference-target η-weak-pseudo-Hermitian PDM—Hamiltonians’ map is suggested. Some η-weak-pseudo-Hermitian -symmetric Scarf II and periodic-type models are used as illustrative examples. Energy-levels crossing and flown-away states phenomena are reported for the resulting Scarf II spectrum. Some of the corresponding η-weak-pseudo-Hermitian Scarf II- and periodic-type-isospectral models ( -symmetric and non- -symmetric) are given as products of the reference-target map.     

Optical corrosion meter

In a previous study, a mathematical model relating surface and bulk behaviours of metals in aqueous solution has been developed. The model was established based on principles of holographic interferometry for measuring microsurface dissolution, i.e. mass loss, and on those of electrochemistry for measuring the bulk electronic current, i.e. corrosion current. In the present work, an optical corrosion meter was built based on the above model. The corrosion meter consists of an electrochemical cell in which the sample is immersed in aqueous solution. Furthermore, the corrosion meter has a holographic camera with a thermoplastic film for in situ processing of holograms in order to obtain real-time holographic interferoms of the sample in the electrochemical cell. Results of the present work indicate that optical holography is a very useful technique for measuring the corrosion current density of different alloys in aqueous solutions. As a result, the corrosion current density of aluminium, stainless steel, and low-carbon steel in 1 M KCl, 1 M NaCl, and 1 M NaOH solutions were obtained. A comparison between the corrosion data of samples showed that the corrosion current density of the stainless steel in 1 M NaCl is nearly three-folds higher than that of the aluminium in 1 M KCl and the low-carbon steel in 1 M NaOH.     

A nonlocal Levinson beam model for free vibration analysis of zigzag single-walled carbon nanotubes including thermal effects

A nonlocal Levinson beam model is developed to study the free vibrations of a zigzag single-walled carbon nanotube (SWCNT) in thermal environments. The equivalent Young’s modulus and shear modulus for a zigzag SWCNT are derived using an energy-equivalent model. The present study illustrates that the vibration characteristics of an SWCNT are strongly dependent on the temperature change and on the chirality of a zigzag carbon nanotube. The investigation of the chirality and temperature effects on free vibration of carbon nanotubes may be used as a useful reference for the application and the design of nanoelectronic and nanodrive devices, nano-oscillators, and nanosensors, in which carbon nanotubes act as basic elements.     

Improvement of thermal and spectroscopic behavior of Er<Superscript>3+</Superscript>/Ce<Superscript>3+</Superscript> co-doped tellurite glass for lasing materials

Tellurite glasses (TeO₂–ZnO–Nb₂O₅) mono-doped Er³⁺ and co-doped Er³⁺/Ce³⁺ have been prepared using the melt-quenching technique. To evaluate the effect of Ce³⁺ on the structural, thermal stability of glass hosts and fluorescence properties of Er³⁺, X-ray diffraction patterns, Ftir spectra, differential scanning calorimeter curves, absorption spectra, fluorescence emission spectra, fluorescence lifetimes, up-conversion emission spectra of glass samples were measured and investigated. Using Judd–Ofelt theory, we calculated intensity parameters (Ω₂, Ω₄ and Ω₆), spontaneous emission probabilities, the radiative lifetime, luminescence branching factors and the quantum yield of luminescence for ⁴I_13/2 → ⁴I_15/2 transition. The co-doping with Ce³⁺ was effective on the suppression of up-conversion emission of Er³⁺ owing to the phonon-assisted energy transfer: Er³⁺:⁴I_11/2 + Ce³⁺:²F_5/2 → Er³⁺:⁴I_13/2 + Ce³⁺:²F_7/2 which contributed the effective enhancement of 1.53 µm fluorescence emission. The change in optical properties with the addition of Ce³⁺ ions have been discussed and compared with other glasses. Using the Mc Cumber method for the ⁴I_13/2 → ⁴I_15/2 transition, absorption cross-section, calculated emission cross-section, and gain cross-section values support that TZNEr1Ce1 glass is a potential material for developing broad-band and high-gain erbium-doped fiber amplifiers applied for 1.53 µm.     

Quantum Effect on the Energy Levels of Eu2+ Doped K2Ca2(SO4)3 Nanoparticles

Quantum confinement effect on the energy levels of Eu²⁺ doped K₂Ca₂(SO₄)₃ nanoparticles has been observed. The broad photoluminescence (PL) emission band of Eu²⁺ doped K₂Ca₂(SO₄)₃ microcrystalline sample observed at ～436 nm is found to split into two narrow well resolved bands, located at 422 and 445 nm in the nanostructure form of this material. This has been attributed to the reduction in the crystal field strength of the nanomaterials, which results in widening the energy band gap and splitting the broad 4f⁶5d energy level of Eu²⁺. Energy band gap values of the micro and nanocrystalline K₂Ca₂(SO₄)₃ samples were also determined by measuring the UV–visible absorption spectra. These values are 3.34 and 3.44 eV for the micro and nanocrystalline samples, respectively. These remarkable results suggest that activators having wide emission bands might be subjected to weak crystal strength via nanostructure materials to modify their electronic transitions. This might prove a powerful technique for producing new-advanced materials for use in the fields of solid state lasers and optoelectronic devises.