Effect of Al<Subscript>2</Subscript>O<Subscript>3</Subscript> phases on the enhancement of thermal conductivity and viscosity of nanofluids in engine oil

Thermal conductivity of α-Al₂O₃ was measured using hot wire method. α-Al₂O₃ (20 nm in size) was synthesized by microwave method for which, the results were compared with commercially available γ-Al₂O₃. Thermal conductivity of nanofluids was investigated considering, it is dependency on Al₂O₃ phase. It was observed that by adding 3 wt% of nano γ-Al₂O₃ and α-Al₂O₃ to the engine oil, thermal conductivity increases by 37 and 31%, respectively. The corresponding viscosity increase for the same amount of nano γ-Al₂O₃ and α-Al₂O₃ were 36 and 38%, respectively. It was concluded that the differences in thermal conductivity originate from higher specific surface area of γ-Al₂O₃ compared to the α-Al₂O₃ which is the result of porosity difference, obtained during the synthesis process.     

Stress distribution in an infinite transversally isotropic body with a rigid elliptical inclusion in a uniform thermal flux

Universidade de Beira Interior, Portugal: and S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of the Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31. No. 11, pp. 3–10, November, 1995.     

Uniqueness of quantum Markov chains associated with an XY-model on a cayley tree of order 2

We propose the construction of a quantum Markov chain that corresponds to a “forward” quantum Markov chain. In the given construction, the quantum Markov chain is defined as the limit of finite-dimensional states depending on the boundary conditions. A similar construction is widely used in the definition of Gibbs states in classical statistical mechanics. Using this construction, we study the quantum Markov chain associated with an XY-model on a Cayley tree. For this model, within the framework of the given construction, we prove the uniqueness of the quantum Markov chain, i.e., we show that the state is independent of the boundary conditions.     

Attractors of the sine-Gordon equation in the field of a quasiperiodic external force

The well-known sine-Gordon equation, supplemented with small damping and small quasiperiodic external force, is studied under the zero Dirichlet boundary conditions at the endpoints of a finite interval. The main assumption is that all frequencies of the external force are in 1:1 resonance with certain eigenfrequencies of the unperturbed equation; i.e., the socalled fundamental multifrequency resonance is observed. It is shown that in this case, by an appropriate choice of the parameters of the external force, one can make it so that the boundary value problem has a stable invariant torus of any finite dimension that bifurcates from zero on any preassigned finite set of spatial modes. It is also shown (by numerical analysis) that in a number of cases the above-mentioned torus coexists with a chaotic attractor.     

Non-linear peristaltic transport of a second-order fluid through a porous medium

The present paper investigates phenomena brought about into the classic peristaltic mechanism by inclusion of non-Newtonian effects through a porous space in a channel. The peristaltic motion of a second-order fluid through a porous medium was studied for the case of a planar channel with harmonically undulating extensible walls. The system of the governing nonlinear PDE is solved by using the perturbation method to second-order in dimensionless wavenumber. The analytic solution has been obtained in the form of a stream function from which the axial pressure gradient has been derived. The flow is investigated in a wave frame of reference moving with velocity of the wave. Numerical calculations are carried out for the pressure rise and frictional force. The features of the flow characteristics are analyzed by plotting graphs and discussed in detail.     

Super spline spaces of smoothnessr and degreed≥3r+2

The problem of computing the dimension of spaces of splines whose elements are piecewise polynomials of degreed withr continuous derivatives globally has attracted a great deal of attention recently. We contribute to this theory by obtaining dimension formulae for certain spaces of super splines, including the case where varying amounts of additional smoothness is enforced at each vertex. We also explicitly construct minimally supported bases for the spaces. The main tool is the Bernstein-Bézier method.Communicated by Klaus Höllig.     

On some integro-differential operators in the class of harmonic functions and their applications

We study properties of integro-differential operators generalizing the operators of the Riemann-Liouville and Caputo fractional differentiation in the class of harmonic functions. The properties obtained are applied to examine some local and nonlocal boundary value problems for the Laplace equation in the unit ball.     

Locally one-dimensional difference schemes for the fractional order diffusion equation

Locally-one-dimensional difference schemes for the fractional diffusion equation in multidimensional domains are considered. Stability and convergence of locally one-dimensional schemes for this equation are proved.