Soret and Dufour Effects on Double-Diffusive Free Convection Over a Vertical Truncated Cone in Porous Media with Variable Wall Heat and Mass Fluxes

This work studies the Soret and Dufour effects on the double-diffusive free convection over a downward-pointing vertical truncated cone with variable wall heat and mass fluxes in fluid-saturated porous media. A coordinate transformation is used to derive the nondimensional boundary-layer governing equations, and the obtained nonsimilar equations are then solved by the cubic spline collocation method. Results for local surface temperature and the local surface concentration are presented as functions of Soret parameters, Dufour parameters, power-law exponents, buoyancy ratios, and Lewis numbers. Results show that increasing the Dufour parameter tends to increase the local surface temperature, while it tends to decrease the local surface concentration. An increase in the Soret number leads to a decrease in the local surface temperature for buoyancy assisting flows, while it leads to an increase in the local surface temperature for buoyancy opposing flows. Increasing the Soret number tends to increase the local surface concentration. Moreover, the local surface temperature and the local surface concentration of the truncated cones with higher power-law exponents are lower than those with lower exponents.     

Study of Heat Transport in Bénard-Darcy Convection with g-Jitter and Thermo-Mechanical Anisotropy in Variable Viscosity Liquids

The effects of temperature-dependent viscosity, gravity modulation and thermo-mechanical anisotropies on heat transport in a low-porosity medium are studied using the Ginzburg–Landau model. The effect of gravity modulation is to decrease the Nusselt number, Nu and variable viscosity leads to increase in Nu. The thermo-mechanical anisotropies have opposite effect on Nu with thermal anisotropy decreasing the heat transport.     

A Note on the Legendre Series Solution of the Biharmonic Equation for Cylindrical Problems

The solution of cylindrical problems is addressed. A series solution is considered of the biharmonic equation, in which the series terms of the stress function Φ are expressions based upon Legendre polynomials and logarithmically singular functions. An explicit form of a polynomial supplementing each logarithmically singular part of the series solution is obtained.     

An Incompressible Fluid in a Weakly Deformable Shell. Part I: Analysis of the Model

We consider the flow of a viscous incompressible fluid in a pipe when the boundary is a deformable shell of Naghdi type. We prove that the corresponding system of partial differential equations has a solution when the deformation of the shell is smooth and small enough. We propose an algorithm that uncouples the unknowns and prove its convergence.     

Nonlinear analysis of laser droplet generation by means of 0–1 test for chaos

We apply the recently improved version of the 0–1 test for chaos to real experimental time series of laser droplet generation process. In particular two marginal regimes of dripping are considered: spontaneous and forced dripping. The outcomes of the test reveal that both spontaneous and forced dripping time series can be characterized as chaotic, which coincides with the previous analysis based on nonlinear time series analysis.     

On <Emphasis Type="Italic">C</Emphasis><Superscript><Emphasis Type="Italic">r</Emphasis></Superscript>-closing for flows on orientable and non-orientable 2-manifolds

We provide an affirmative answer to the C ^r -Closing Lemma, r ≥ 2, for a large class of flows defined on every closed surface.     

Spherical T-Duality

We introduce spherical T-duality, which relates pairs of the form (P, H) consisting of a principal SU(2)-bundle \({P \rightarrow M}\) and a 7-cocycle H on P. Intuitively spherical T-duality exchanges H with the second Chern class c ₂(P). Unless \({dim(M) \leq 4}\), not all pairs admit spherical T-duals and the spherical T-duals are not always unique. Nonetheless, we prove that all spherical T-dualities induce a degree-shifting isomorphism on the 7-twisted cohomologies of the bundles and, when \({dim(M) \leq 7}\), also their integral twisted cohomologies and, when \({dim(M) \leq 4}\), even their 7-twisted K-theories. While spherical T-duality does not appear to relate equivalent string theories, it does provide an identification between conserved charges in certain distinct IIB supergravity and string compactifications.     

Synthesis of nanoplate bismuth oxychloride—a visible light active material

We have synthesized bismuth oxychloride (BiOCl) by wet chemical route. Characterization of the synthesized samples has been carried out using XRD, SEM with EDAX, HRTEM, FT-IR, Raman Spectroscopy, PL and UV. XRD and SEM analysis confirms crystallite size varying from 20–40 nm. FTIR spectrum indicates that the prepared material is highly pure and there is no water molecule present. Raman and photoluminescence spectrum of the bismuth oxychloridenanoplate demonstrated strong blue light emission which brings them in a special class of materials which work under visible light exposure. UV-Vis spectroscopy shows very less charge carriers transit time under visible light thus confirming excellent photocatalytic properties of material.     

On cutting sequences of the <Emphasis Type="Italic">L</Emphasis>-shaped translation surface tiled by three squares

We consider a symbolic coding of bi-infinite non periodic geodesics on the L-shaped translation surface tiled by three squares. Each bi-infinite non periodic geodesic is associated with a cutting sequence corresponding to the sequence of labeled saddle connections hit. We prove that there is a relationship between the cutting sequences and the actions of some affine automorphisms of the translation surface. We also get an explicit formula to determine the direction of a bi-infinite non periodic geodesic by using the corresponding cutting sequence.