An adaptive wavelet space‐time SUPG method for hyperbolic conservation laws

This article concerns with incorporating wavelet bases into existing streamline upwind Petrov‐Galerkin (SUPG) methods for the numerical solution of nonlinear hyperbolic conservation laws which are known to develop shock solutions. Here, we utilize an SUPG formulation using continuous Galerkin in space and discontinuous Galerkin in time. The main motivation for such a combination is that these methods have good stability properties thanks to adding diffusion in the direction of streamlines. But they are more expensive than explicit semidiscrete methods as they have to use space‐time formulations. Using wavelet bases we maintain the stability properties of SUPG methods while we reduce the cost of these methods significantly through natural adaptivity of wavelet expansions. In addition, wavelet bases have a hierarchical structure. We use this property to numerically investigate the hierarchical addition of an artificial diffusion for further stabilization in spirit of spectral diffusion. Furthermore, we add the hierarchical diffusion only in the vicinity of discontinuities using the feature of wavelet bases in detection of location of discontinuities. Also, we again use the last feature of the wavelet bases to perform a postprocessing using a denosing technique based on a minimization formulation to reduce Gibbs oscillations near discontinuities while keeping other regions intact. Finally, we show the performance of the proposed combination through some numerical examples including Burgers’, transport, and wave equations as well as systems of shallow water equations.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 2062–2089, 2017     

A numerical method for solving linear integral equations of the second kind on the non-rectangular domains based on the meshless method

The main purpose of this article is to describe a numerical scheme for solving two-dimensional linear Fredholm integral equations of the second kind on a non-rectangular domain. The method approximates the solution by the discrete collocation method based on radial basis functions (RBFs) constructed on a set of disordered data. The proposed method does not require any background mesh or cell structures, so it is meshless and consequently independent of the geometry of domain. This approach reduces the solution of the two-dimensional integral equation to the solution of a linear system of algebraic equations. The error analysis of the method is provided. The proposed scheme is also extended to linear mixed Volterra–Fredholm integral equations. Finally, some numerical examples are presented to illustrate the efficiency and accuracy of the new technique.     

On some new analytical solutions for the nonlinear long–short wave interaction system

This paper deals with exact soliton solutions of the nonlinear long–short wave interaction system, utilizing two analytical methods. The system of coupled long–short wave interaction equations is investigated with the help of two analytical methods, namely, the generalized \(\tan (\phi /2)\)-expansion method and He’s semi-inverse variational method. Moreover, in this paper we generalize two aforementioned methods which give new soliton wave solutions. As a consequence, solutions are including solitons, kink, periodic and rational solutions. Moreover, dark, bright and singular solition solutions of the coupled long–short wave interaction equations have been found. All solutions have been verified back into its corresponding equation with the aid of maple package program. We depicted the physical explanation of the extracted solutions with the free choice of the different parameters by plotting some 3D and 2D illustrations. Finally, we believe that the executed methods are robust and efficient than other methods and the obtained solutions in this paper can help us to understand the soliton waves in the fields of physics and mechanics.     

Approximate analysis and design of rectangular-lattice photonic crystals

We present a theoretical analysis of wave propagation in rectangular- and square-lattice photonic crystals by approximating the arbitrary refractive-index function with a staircase profile. This profile has a number of tunable parameters that allow one to fit the band structures of the staircase and the desired structure over a large frequency range. The staircase profile is such that its corresponding two-dimensional wave equation decomposes into two one-dimensional equations by means of a constant decoupling parameter. We show that basic features of the band structure and Bloch waves in photonic crystals can be analyzed theoretically through this simple approximation.     

Compact Fourier-transform volume holographic spectrometer for diffuse source spectroscopy

We present a new idea for diffuse source spectroscopy using a Fourier-transform volume holographic spectrometer formed by a Fourier-transform lens, a volume hologram, and a CCD. We show that this spectrometer can operate well under spatially incoherent light illumination. Furthermore, this spectrometer is less bulky, less sensitive to input alignment, and potentially more appropriate for implementation of highly sensitive spectrometers than conventional spectrometers.     

Diffraction efficiency of localized holograms in doubly doped LiNbO(3) crystals

The diffraction efficiency of M holograms superimposed in the volume of the recording medium is proportional to 1/M(2). We present a method, based on nondestructive localized holograms in a doubly doped LiNbO(3) crystal, that allows us to also record M holograms in the same volume without an exposure schedule or a diffraction efficiency that has 1/M dependence. We compare experimentally the final diffraction efficiency obtained with the localized and distributed recording methods.     

Simple and New Method for the Synthesis of β-Acetamido Ketones on a Solid Surface

Diels–Alder reactions of 3-vinylindoles were carried out with methyl acrylate and N-phenylmaleimide as dienophiles under microwave conditions to furnish unreported tetrahydrocarbazoles regio- and stereoselectively in good yields. Further dehydrogenation resulted in new substituted carbazoles.     

Accurate determination of microparticle size using Fourier transform of light scattering spectrum over wavenumber

We discovered that the far-field light scattering spectra of microparticles over wavenumber at a certain angle could be decomposed into periodic components, with an oscillation frequency linearly dependent on the particle size at each angle. Based on this observation, we propose and experimentally demonstrate a new Fourier transform technique for microparticle size determination. This technique is simple, fast, robust in its data processing algorithm, and flexible in its detection system.     

A novel reusable ionic liquid chemically bonded fused-silica fiber for headspace solid-phase microextraction/gas chromatography-flame ionization detection of methyl tert-butyl ether in a gasoline sample

A novel ionic liquid (IL) bonded fused-sil-ica fiber for headspace solid-phase microextraction (HS-SPME)/gas chromatography-flame ionization detection (GC-FID) of methyl tert-butyl ether (MTBE) in a gasoline sample was prepared and used. The new proposed chemically bonded fiber has better thermal stability and durability than its corresponding physically coated fiber. Another advantage is that no spacer was used for the purpose of bonding the IL to the surface of the fused-silica. The latter advantage makes the preparation of these fibers easier with lower cost than those prepared using sol–gel method. The ionic liquid 1-methyl-3-(3-trimethoxysilyl propyl) imidazolium bis(trifluoromethylsulfonyl) imide was synthesized and cross linked to the surface of the fused-silica fiber. Then, the chemically IL-modified fibers were applied to the headspace extraction of MTBE. The chemically IL-modified fibers showed improved thermal stability at temperatures up to 220 °C relative to the physically IL-modified fibers (180 °C). The chemically bonded IL film on the surface of the fused-silica fiber was durable over 16 headspace extractions without any significant loss of the IL film. The calibration graph was linear in a concentration range of 2–240 μg L⁻¹ (R² = 0.996) with the detection limit of 0.1 μg L⁻¹ level. The reproducibility (RSD %, n = 6) of the new IL bonded fused-silica fiber (8.9%) was better than the physically coated fiber (12%) suggesting that the proposed chemically IL-modified fiber is more robust than the physically IL-modified fiber. The optimum extraction conditions were the followings: 40 °C extraction temperature, 12 min extraction time, 30 s desorption time and sample agitation at 200 rpm.     

A new disposable ionic liquid based coating for headspace solid-phase microextraction of methyl tert-butyl ether in a gasoline sample followed by gas chromatography-flame ionization detection

A new ionic liquid (IL) based solid-phase microextraction (SPME) fiber was investigated and used for headspace (HS) extraction of methyl tert-butyl ether (MTBE) in a gasoline sample. Using the new IL coated HS-SPME fiber with the combination of gas chromatography-flame ionization detection (GC-FID); sub-to-low μg L⁻¹ concentrations of MTBE were detected. Four different ILs including 1-butyl-3-methylimidazolium tetraflouroborate ([C₄C₁IM] [BF₄]), 1-octyl-3-methylimidazolium tetraflouroborate ([C₈C₁IM] [BF₄]), 1-octyl-3-methylimidazolium hexaflourophosphate ([C₈C₁IM] [PF₆]) and 1-ethyl-3-methylimidazolium ethylsulphate ([C₂C₁IM] [ETSO₄]) were synthesized and examined for extraction, preconcentration and determination of MTBE. It was observed that [C₈C₁IM] [BF₄] showed the highest extraction efficiency and possessed the best extractability for MTBE. The fiber coating takes up the compounds from the sample by absorption in the case of liquid coatings. The calibration graph was linear in a concentration range of 1-120 μg L⁻¹ (R² > 0.994) with the detection limit of 0.09 μg L⁻¹ level. The new IL-coated fiber was applied successfully for the determination of MTBE in a gasoline sample with good recoveries between 90 and 95%.