The Cavalcante-Tenenblat equation - Does the equation admits physical significance?

The main purpose of the given paper is to analyze a less studied third order non-linear partial differential equation, the so-called Cavalcante-Tenenblat equation (CTE) in the following form: .Since general class of solutions are of basic interest a complete characterization of the group properties is given. The traveling wave ‘ansatz’ restricts the solution manifold to special class of solutions and hence, a generalize algorithm is necessary.We determine the Lie point symmetry vector fields and calculate similarity ‘ansätze’. Further, we also derive a few non-linear transformations and some similarity solutions are obtained explicitly. Due to the complexity of some similarity solutions a numerical procedure is of advantage.Moreover, the non-classical case (potential symmetries) is studied to the first time and further, we show how the CTE leads to approximate symmetries and we apply the method to the first time. We call the disturbed equation the CTE-ε equation and we show how to derive new class of solutions.Finally, the equation does not pass the Painlevé-test and is therefore not soluble by the Inverse Scattering Transform Method (IST).Hence, suitable alternative (algebraic) approaches are necessary to derive class of solutions explicitly.     

Structural and conductivity studies of CsKSO4Te(OH)6 and Rb1.25K0.75SO4Te(OH)6 materials

The crystal structures of the title compounds were solved using the single-crystal X-ray diffraction technique. At room temperature CsKSO₄Te(OH)₆ was found to crystallize in the monoclinic system with Pn space group and lattice parameters: ; ; ; β=106.53(2)°; ; Z=4 and . The structural refinement has led to a reliability factor of R₁=0.0284 (wR₂=0.064) for 7577 independent reflections. Rb_1.25K_0.75SO₄Te(OH)₆ material possesses a monoclinic structure with space group P2₁/a and cell parameters: ; ; ; β=106.860(10)°; ; Z=4 and . The residuals are R₁=0.0297 and wR₂=0.0776 for 3336 independent reflections. The main interest of these structures is the presence of two different and independent anionic groups (TeO₆⁶⁻ and SO₄²⁻) in the same crystal.Complex impedance measurements (Z^*=Z^′—iZ^″) have been undertaken in the frequency and temperature ranges 20-10⁶ Hz and 400-600 K, respectively. The dielectric relaxation is studied in the complex modulus formalism M^*.     

Solution of Dirac Equation with Generalized Hylleraas Potential

We employ the parametric generalization of the Nikiforov-Uvarov method to solve the Alhaidari formalism of the Dirac equation with a generalized Hylleraas potential of the form V(r) = V0(a+exp(λr))/(b+ exp(λr)) + V1(d+exp(λr))/(b+exp(λr)).We obtain the bound state energy eigenvalue and the corresponding eigenfunction expressed in terms of the Jacobi polynomials.By choosing appropriate parameter in the potential model,the generalized Hylleraas potential reduces to the well known potentials as special cases.     

Fractional charges and fractional spins for composite fermions in quantum electrodynamics

By using the Faddeev-Senjanovic path integral quantization method, we quantize the composite fermions in quantum electrodynamics (QED). In the sense of Dirac’s conjecture, we deduce all the constraints and give Dirac’s gauge transformations (DGT). According to that the effective action is invariant under the DGT, we obtain the Noether theorem at the quantum level, which shows the fractional charges for the composite fermions in QED. This result is better than the one deduced from the equations of motion for the statistical potentials, because this result contains both odd and even fractional numbers. Furthermore, we deduce the Noether theorem from the invariance of the effective action under the rotational transformations in 2-dimensional (x, y) plane. The result shows that the composite fermions have fractional spins and fractional statistics. These anomalous properties are given by the constraints for the statistical gauge potential.     

A high-efficiency spin polarizer based on edge and surface disordered silicene nanoribbons

Using the tight-binding formalism, we explore the effect of weak disorder upon the conductance of zigzag edge silicene nanoribbons (SiNRs), in the limit of phase-coherent transport. We find that the fashion of the conductance varies with disorder, and depends strongly on the type of disorder. Conductance dips are observed at the Van Hove singularities, owing to quasilocalized states existing in surface disordered SiNRs. A conductance gap is observed around the Fermi energy for both edge and surface disordered SiNRs, because edge states are localized. The average conductance of the disordered SiNRs decreases exponentially with the increase of disorder, and finally tends to disappear. The near-perfect spin polarization can be realized in SiNRs with a weak edge or surface disorder, and also can be attained by both the local electric field and the exchange field.     

Two matrix algorithms for eigenmodes of a Bessel-Gauss resonator

A Bessel-Gauss resonator (BGR) was proposed to produce the Bessel Gauss beams. In this paper transverse profiles and their corresponding losses of the BGR are computed by use of the entire matrix formalism and the transfer matrix method, and the computation results from two algorithms are compared. The computation results show that for the BGR there is no inconsistence in the mode fields yielded by two methods, and the transfer matrix methods are more accurate in the mode losses than the entire matrix formalism, which lead to a believable conclusion that the BGR with a convex-spherical mirror easily produces the fundamental Bessel-Gauss mode of good quality.     

Surface and interfacial waves in anisotropic elastic quasicrystals

We present the Stroh formalism for two-dimensional subsonic steady-state motion of anisotropic quasicrystals. Using this new formalism and a series of identities and properties which follow, we investigate subsonic surface and interfacial waves in anisotropic quasicrystals. Our results suggest that there exist at most three subsonic surface wave speeds. This interesting observation is quite different from the unique surface wave speed known for anisotropic crystals. The degenerate case of decagonal quasicrystalline materials is discussed in detail.