Generalized Conditional Symmetries,Related Solutions and Conservation Laws of the Grad-Shafranov Equation with Arbitrary Flow

The generalized conditional symmetry (GCS) method is applied to the case of a generalized Grad-Shafranov equation (GGSE) with incompressible flow of arbitrary direction. We investigate the conditions which yield the GGSE that admits a special class of second-order GCSs. Three GCS generators and the associated families of invariant solutions are pointed out. Several plots of the level sets or flux surfaces of the new solutions are displayed. These results extend the recent solutions with 5 parameters recently obtained on the basis of Lie-point symmetries. They could be useful in the study of plasma equilibrium, of transport phenomena, and of magnetohydrodynamic stability. Futher, by making use of the multiplier’s method, three nontrivial conservation laws that are admitted by the concerned equation and which involve arbitrary functions, are highlighted.     

Characterization of magnetic nano-fluids via Mössbauer spectroscopy

The laser pyrolysis became a useful tool, providing various ways, in production of nano materials. The iron Mössbauer spectroscopy is one very accurate method in evidencing the physical properties and related processes in the nano scale compounds. The effect of pressure, laser spot area and induced combustion, of gas mixture and laser power on the phase composition and inside particle distribution, grain size as well as the related phenomena were investigated by temperature dependent Mössbauer spectroscopy. A selection of most relevant properties is presented and discussed in details.     

The exterior Dirichlet problem for a quasilinear elliptic boundary value problem suggested by plane shear flow

We study the existence of a classical solution of the exterior Dirichlet problem for a class of quasilinear elliptic boundary value problems that are suggested by plane shear flow. In this connection only bounded solutions which tend to zero at infinity are of interest. A priori bounds on solutions and constructive existence proofs are given. Finally, we prove the existence of a unique bounded solution of the shear flow and we show, under certain hypotheses about the asymptotic behavior of the nonlinearity, that this solution tends to zero at infinity. As an example, we consider the case of the parabolic shear flow.     

On the time evolution of transmittivity in magnetic fluids

When a magnetic fluid is subjected to a magnetic field, a part of the magnetic particles in the fluid agglomerates to form chains. Thus, the ferrofluid becomes optically anisotropic. In this work we describe optically observed patterns in some magnetic fluid films in applied parallel magnetic fields and optical effects of these, especially the optical transmittance. The most interesting experimental observation is that concerning the time dependence of relative transmittivity . For kerosene base ferrofluids relax rapidly at coupling and decoupling magnetic field, but for a transformer-oil magnetic fluid the relaxation times can attain (5–10) minutes, depending on the intensity of applied magnetic field.     

Quasi-phase-matching engineering for spatial control of entangled two-photon states

We show that transverse engineering of quasi-phase-matched geometries can be used to tailor the spatial mode function that describes the quantum state of photon pairs generated in spontaneous parametric down-conversion. We study several geometries and reveal how properly engineered gratings affect, in particular, the spatial correlations embedded in two-photon entangled states.     

Explicit Formulae for Some Kazhdan-Lusztig Polynomials

We consider the Kazhdan-Lusztig polynomials P _u,v (q) indexed by permutations u, v having particular forms with regard to their monotonicity patterns. The main results are the following. First we obtain a simplified recurrence relation satisfied by P _u,v (q) when the maximum value of v S_n occurs in position n – 2 or n – 1. As a corollary we obtain the explicit expression for P_{e,3 4 ... n 1 2}(q) (where e denotes the identity permutation), as a q-analogue of the Fibonacci number. This establishes a conjecture due to M. Haiman. Second, we obtain an explicit expression for P_{e, 3 4 ... (n – 2) n (n – 1) 1 2}(q). Our proofs rely on the recurrence relation satisfied by the Kazhdan-Lusztig polynomials when the indexing permutations are of the form under consideration, and on the fact that these classes of permutations lend themselves to the use of induction. We present several conjectures regarding the expression for P _u,v (q) under hypotheses similar to those of the main results.     

Quasistatic Crack Growth in Nonlinear Elasticity

In this paper, we prove a new existence result for a variational model of crack growth in brittle materials proposed in [19]. We consider the case of n-dimensional nonlinear elasticity, for an arbitrary n1, with a quasiconvex bulk energy and with prescribed boundary deformations and applied loads, both depending on time.     

Antibacterial and Photocatalytic Properties of ZnO Nanoparticles Obtained from Chemical versus Saponaria officinalis Extract-Mediated Synthesis

In the present work, the properties of ZnO nanoparticles obtained using an eco-friendly synthesis (biomediated methods in microwave irradiation) were studied. Saponaria officinalis extracts were used as both reducing and capping agents in the green nanochemistry synthesis of ZnO. Inorganic zinc oxide nanopowders were successfully prepared by a modified hydrothermal method and plant extract-mediated method. The influence of microwave irradiation was studied in both cases. The size, composition, crystallinity and morphology of inorganic nanoparticles (NPs) were investigated using dynamic light scattering (DLS), powder X-ray diffraction (XRD), SEM-EDX microscopy. Tunings of the nanochemistry reaction conditions (Zn precursor, structuring agent), ZnO NPs with various shapes were obtained, from quasi-spherical to flower-like. The optical properties and photocatalytic activity (degradation of methylene blue as model compound) were also investigated. ZnO nanopowders’ antibacterial activity was tested against Gram-positive and Gram-negative bacterial strains to evidence the influence of the vegetal extract-mediated synthesis on the biological activity.