Spectral theory and L∞-time decay estimates for Klein–Gordon equations on two half axes with transmission: The tunnel effect

Consider two copies N₁, N₂ of the interval [0, ∞]. Consider Klein-Gordon equations with (different) constant coefficients on ? × N_j ( = time × space). Assume the coincidence of the values of the solution at the boundary points of the N_j for all times and a transmission condition relating its first (one-sided) space derivatives at these points. Under a symmetry condition, we extend the spatial part of the equation and the transmission conditions to a self-adjoint operator (by Friedrichs extension) and reformulate our problem in terms of an abstract wave equation in a suitable Hilbert space. We derive an expansion of the solution in generalized eigenfunctions of this self-adjoint extension and show, that the L^∞-norms (in space) of the solution and its first k space derivatives at the time t decay for t → ∞ at least as const. t^¼, if the initial conditions satisfy a compatibility condition of order k derived in this paper. The loss of decay rate in comparison with the full line case (const. t^?½, cf. [28]) is caused by the tunnel effect. Further we show that an abstract wave equation in a Hilbert space with a Friedrichs extension as spatial part can always be derived from a stationarity principle for an associated action-type functional. This yields a physical legitimation of our model by the principle of stationary action and moreover a criterion for the physical interpretability of all models created by the linear interaction concept [4, 6, 8, 10], in particular for the coupling of media of different dimension (alternative to [13, 16] for similar models).     

Nonlinear Galerkin methods and mixed finite elements: two-grid algorithms for the Navier-Stokes equations

Summary. A nonlinear Galerkin method using mixed finite elements is presented for the two-dimensional incompressible Navier-Stokes equations. The scheme is based on two finite element spaces and for the approximation of the velocity, defined respectively on one coarse grid with grid size and one fine grid with grid size and one finite element space for the approximation of the pressure. Nonlinearity and time dependence are both treated on the coarse space. We prove that the difference between the new nonlinear Galerkin method and the standard Galerkin solution is of the order of $H^2$, both in velocity ( and pressure norm). We also discuss a penalized version of our algorithm which enjoys similar properties. Received October 5, 1993 / Revised version received November 29, 1993     

Graphene to graphite; a layer by layer experimental measurements and density function theory calculations of electric conductivity

ABSTRACT

We measured the electric conductivity of large (25?×?50?mm) graphene films as a function of number of layers in the range of 1–20 layers. We also calculated the energy gap for such samples using density function theory. Our results showed a conductivity slightly above that of ITO for monolayer graphene and an exponential decrease as the number of graphene layers increased. Both experimental and simulation results showed a convergence of graphene into graphite at as little as 18–20 layers.     

Critical properties of mixed spin-1 and spin-5/2 with equal and unequal crystal fields

The effects of assuming equal or unequal crystal fields (CF) on the phase diagrams of a mixed spin-1 and spin-5/2 system are investigated in terms of the recursion relations on the Bethe lattice (BL). The equal CF case was considered for the coordination numbers q=3, 4, and 6, while for q=3 the unequal CF case was also studied. It was found that for the equal CF case, the model exhibits second-order phase transitions and two compensation temperatures for all q, the reentrant behavior for q=4 and first-order phase transitions and tricritical point (TCP) for q=6. In the unequal CF case for q=3, the system yields first- and second-order phase transitions, TCP's, and three compensation temperatures. In addition, the TCP's in a very short range are classified as the stable and unstable ones depending on their free energies.     

The complex networks approach for authorship attribution of books

Authorship analysis by means of textual features is an important task in linguistic studies. We employ complex networks theory to tackle this disputed problem. In this work, we focus on some measurable quantities of word co-occurrence network of each book for authorship characterization. Based on the network features, attribution probability is defined for authorship identification. Furthermore, two scaling exponents, q-parameter and α-exponent, are combined to classify personal writing style with acceptable high resolution power. The q-parameter, generally known as the nonextensivity measure, is calculated for degree distribution and the α-exponent comes from a power law relationship between number of links and number of nodes in the co-occurrence network constructed for different books written by each author. The applicability of the presented method is evaluated in an experiment with thirty six books of five Persian litterateurs. Our results show high accuracy rate in authorship attribution.     

Solvothermal synthesis and characterization of α-Fe2O3 nanodiscs and Mn3O4 nanoparticles with 1,10-phenanthroline

α-Fe₂O₃ nanodiscs and Mn₃O₄ nanoparticles have been prepared by the 1,10-phenanthroline as complexing agent in the presence of sodium hydroxide under hydrothermal conditions. The products were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), and Fourier transform infrared (FT-IR) spectra. The average diameter of α-Fe₂O₃ nanodiscs is of 2 μm. In the case of Mn₃O₄ sample, the Mn₃O₄ crystallites are nanoparticles with an average size of 34 nm. A formation mechanism for the α-Fe₂O₃ and Mn₃O₄ nanomaterials was proposed.     

Utilization of standardless analysis algorithms using WDXRF and XRD for Egyptian iron ore identification

On the basis of fundamental parameter approaches, the validity of standardless wavelength dispersive X‐ray fluorescence (WDXRF) and X‐ray powder diffraction algorithms was confirmed for analyzing Egyptian iron ore samples collected from two different locations, Aswan and Baharyia. The studied Egyptian iron ores represent different depositional environments and consequently exhibit variable mineralogical and chemical compositions. In the case of WDXRF analysis, the ground powders of iron ore samples were mixed and pressed with low contamination binder in a mass ratio of wax: sample = 4: 0.9 g at 120 kN cm^?2. A standardless method for quantitative WDXRF was employed, which requires accurate determination of the amount of organic material in the sample. On the basis of differential thermal analysis, a new method is introduced for the determination of loss of ignition. With the application of the proposed method and standardless quantitative analysis, results for 12 elements in iron ores were obtained: Fe, Mn, Mg, Si, Al, Ca, Na, K, S, Ba, Zn, and Cl. The reliability and precision of the adopted procedure were tested against a standard reference material ‘Iron ore concentrate (SRM 690, NIST, USA)’. The quantitative analysis results of the certified reference material were found acceptable. Depending on the WDXRF results, the powder samples were directly introduced to X‐ray powder diffraction goniometry, and the phase compositions were quantitatively determined by using a standardless analysis program based on Rietveld method. The main phases of all iron ore samples are the hematite and goethite, whereas other phases are found with varying ratios, namely quartz, nordstrandite, rhodochrosite, kaolinite, todorokit, bassanit, andydrite, and hydroxyapatite. Copyright © 2012 John Wiley & Sons, Ltd.     

Synthesis of some new triamide derivatives via Ugi five-component reaction in aqueous solution

Triamide derivatives have been synthesized in good yields in a novel, one-pot, five-component, and efficient process by the reaction of Z-oxazolone, water, primary amines, aldehydes, isocyanides, in the presence of catalytic amount of KAl(SO₄)₂·12H₂O (alum) as a non-toxic, reusable, inexpensive, and easily available reagent via Ugi reaction in aqueous solution.     

Functionalization of (<Emphasis Type="Italic">n</Emphasis>, 0) CNTs (<Emphasis Type="Italic">n</Emphasis> = 3–16) by uracil: DFT studies

Density functional theory (DFT) calculations were performed to investigate stabilities and properties for uracil (U)-functionalized carbon nanotubes (CNTs). To this aim, the optimized molecular properties were evaluated for (n, 0) models of CNTs (n = 3–16) in the original and U-functionalized forms. The results indicated that the dipole moments and energy gaps were independent of tubular diameters whereas the binding energies showed that the U-functionalization could be better achieved for n = 8–11 curvatures of (n, 0) CNTs. Further studies based on the evaluated atomic-scale properties, including quadrupole coupling constants (C _Q ), indicated that the electronic properties of atoms could detect the effects of diameters variations of (n, 0) CNTs, in which the effects were very much significant for the atoms around the U-functionalization regions. Finally, the achieved results of singular U, original CNTs, and CNT-U hybrids were compared to each other to demonstrate the stabilities and properties for the U-functionalized (n, 0) CNTs.     

Real‐Time and Broadband Terahertz Wave Scattering Manipulation via Polarization‐Insensitive Conformal Graphene‐Based Coding Metasurfaces

Here, for the first time, the real‐time and broadband manipulation of terahertz (THz) waves are acquired by introducing a multifunctional graphene‐based coding metasurface (GBCM). The designed structure consists of subwavelength patterned graphene units whose operational statuses can be dynamically switched between two digital states of “0” and “1”. By engineering the spatial distribution of chemical potentials across the GBCM, various scattering patterns having single, two, four, and numerous reflection beams are elaborately achieved just within one planar structure. To compute the far‐field pattern of GBCM, an inverse discrete Fourier transform (IDFT) is established, providing a fast and efficient design method. The proposed GBCM provides a low reflection bellow ?10 dB over a broad frequency band ranging from 1 THz to 1.9 THz. In addition, the metasurface retains its low reflection behavior in a wide range of incident wave angles for both TE and TM polarizations. According to conformal invariance of graphene sheets, the stealth property of GBCM is well preserved while wrapping around a curved object. The proposed technique of real‐time scattering manipulation leads to multifunctional THz devices, opening new routes contributing to numerous applications such as imaging and stealth technology.