Preparation and characterization of LiAl_xCo_yNi_1-x-yO₂ particles

Lithium-aluminum-cobalt-nickel oxide LiAlxCoyNi1xyO2 particles, generally used as cathode of lithium battery, were prepared by chemical coprecipitation from an aqueous solution of LiOH, Al(NO3)3, Co(NO3)2 and Ni(NO3)2 with NH4OH. XRD, SEM and FTIR were used to examine the effect of nickel content on the product. FTIR patterns showed that increase in nickel content decreased the absorption strength of the peak of spinel structure of the product, attributed to the occupation by nickel in the aluminum sites. Particle size and electrical properties of the lithium-aluminum-cobalt-nickel oxide (abbreviated as LACNO) particles were also determined.     

Differential Independence of <Emphasis Type="Italic">Γ</Emphasis> and <Emphasis Type="Italic">ζ</Emphasis>

In a celebrated theorem H?lder proved that the Euler Γ-function is differential transcendental, i.e. Γ(z) is not a solution of any (non-trivial) algebraic ordinary differential equation with coefficients that are complex numbers; and we extend his methods to the Riemann ζ-function. Moreover, we conjecture that Γ and ζ are differential independent, i.e. Γ(z) is not a solution of any such algebraic differential equation—even allowing coefficients that are differential polynomials in ζ(z). However, we are able to demonstrate only the partial result that Γ(z) and ζ(sin 2πz) are differential independent.     

“Frictionless” and “frictional” ThermoElastic Dynamic Instability (TEDI) of sliding contacts

Recently, we found that a new form of coupled instability, named ThermoElastic Dynamic Instability (TEDI), can occur by interaction between frictional heating and the natural dynamic modes of sliding bodies. This is distinct from the classical dynamic instabilities (DI) which is produced by an interaction between the frictional forces at the sliding interface and the natural modes of vibration of the bodies if the friction coefficient is sufficiently high, and also from ThermoElastic Instability (TEI), which is due to the interaction of frictional heating and thermal expansion, leading for example to low pitched brake noise above some critical speed. This result was relative to an highly idealized system, comprising an elastic layer sliding over a rigid plane including both dynamic and thermoelastic effects, but neglecting shear waves at the interface due to frictional tractions (from which the denomination “frictionless TEDI”). We demonstrate here that including these shear waves destabilizes both the shear and dilatational vibration modes of the system at arbitrarily small friction coefficients and speeds, where DI and TEI are predicted to be stable. A detailed study of the new modes and transient simulations show that for low pressures and high speed, the system tends towards the results of the previous model (“frictionless TEDI”), i.e. the tendency to a state in which the layer bounces over the plane, with alternating periods of sliding contact and separation. In the case of low speeds and high pressures, viceversa, the system is dominated by the modes near the resonance of the shear and dilatational modes, with a resulting complex behaviour, but generally leading to stick-slip regimes, reducing the jumping mode of “frictionless TEDI”, because stick reduces or stops frictional heating production.     

Electrorheological response of SnO<Subscript>2</Subscript> and Y<Subscript>2</Subscript>O<Subscript>3</Subscript> nanoparticles in silicon oil

The electrorheological properties (ER) of some fluids containing particles change extensively under the external electrical field. This phenomenon is applicable in many industries and equipments, such as clutches and motor driven rotor, which would transfer the spin to a drive shaft through a thin layer of electrorheological fluid. In this investigation, the effects of external electrical field on ER properties of non-Newtonian fluids (silicon oil) with the addition of SnO₂ and Y₂O₃ nanoparticles were studied. The ER properties were measured for a wide range of SnO₂ and Y₂O₃ nanoparticle concentrations and DC electrical voltages using concentric cylinder rotary rheometer. Based on the results, ER properties of nanofluids, e.g., apparent viscosity, shear stress, and yield stress, were enhanced by applying electrical field and increasing SnO₂ and Y₂O₃ concentrations.

Evaluation of one‐ and two‐equation low‐Re turbulence models. Part II—Vortex‐generator jet and diffusing S‐duct flows

This second segment of the two‐part paper systematically examines several turbulence models in the context of two flows, namely a vortex flow created by an inclined jet in crossflow, and the flow field in a diffusing S‐shaped duct. The test cases are chosen on the basis of availability of high‐quality and detailed experimental data. The tested turbulence models are integrated to solid surfaces and consist of: Rodi's two‐layer k–ε model, Wilcox's k–ω model, Menter's two‐equation shear–stress‐transport model, and the one‐equation model of Spalart and Allmaras. The objective of the study is to establish the prediction accuracy of these turbulence models with respect to three‐dimensional separated flows with streamline curvature. At the same time, the study establishes the minimum spatial resolution requirements for each of these turbulence closures, and identifies the proper low‐Mach‐number preconditioning and artificial diffusion settings of a Reynolds‐averaged Navier–Stokes algorithm for optimum rate of convergence and minimum adverse impact on prediction accuracy. Copyright © 2003 John Wiley & Sons, Ltd.     

HAMILTON OPERATORS AND HOMOTHETIC MOTIONS IN R^3

Quaternion is a division ring. It is shown that planes passing through the origin can be made a field with the quaternion product in R3. The Hamiltonian operators help us define the homothetic motions on these planes. New characterizations for these motions are investigated.     

CFD simulation of two‐ and three‐dimensional free‐surface flow

The paper describes the implementation of moving‐mesh and free‐surface capabilities within a 3‐d finite‐volume Reynolds‐averaged‐Navier–Stokes solver, using surface‐conforming multi‐block structured meshes. The free‐surface kinematic condition can be applied in two ways: enforcing zero net mass flux or solving the kinematic equation by a finite‐difference method. The free surface is best defined by intermediate control points rather than the mesh vertices. Application of the dynamic boundary condition to the piezometric pressure at these points provides a hydrostatic restoring force which helps to eliminate any unnatural free‐surface undulations. The implementation of time‐marching methods on moving grids are described in some detail and it is shown that a second‐order scheme must be applied in both scalar‐transport and free‐surface equations if flows driven by free‐surface height variations are to be computed without significant wave attenuation using a modest number of time steps. Computations of five flows of theoretical and practical interest—forced motion in a pump, linear waves in a tank, quasi‐1d flow over a ramp, solitary wave interaction with a submerged obstacle and 3‐d flow about a surface‐penetrating cylinder—are described to illustrate the capabilities of our code and methods. Copyright © 2003 John Wiley & Sons, Ltd.     

Raviart–Thomas and Brezzi–Douglas–Marini finite‐element approximations of the shallow‐water equations

An analysis of the discrete shallow‐water equations using the Raviart–Thomas and Brezzi–Douglas–Marini finite elements is presented. For inertia–gravity waves, the discrete formulations are obtained and the dispersion relations are computed in order to quantify the dispersive nature of the schemes on two meshes made up of equilateral and biased triangles. A linear algebra approach is also used to ascertain the possible presence of spurious modes arising from the discretization. The geostrophic balance is examined and the smallest representable vortices are characterized on both structured and unstructured meshes. Numerical solutions of two test problems to simulate gravity and Rossby modes are in good agreement with the analytical results. Copyright © 2007 John Wiley & Sons, Ltd.     

Comments on ‘‘Design of aluminium boom and arm for an excavator”

This paper comments on the recently published work dealing with the problem in the design of the backhoe excavator working device. It also includes remarks on the inadequacy in the problem approach to the device weight optimization and synthesis, and highlights mistakes in the mathematical model. This work points out the demand for a much wider approach to the optimization problem of the backhoe excavator working device.     

Enhanced CO<Subscript>2</Subscript> Storage and Sequestration in Deep Saline Aquifers by Nanoparticles: Commingled Disposal of Depleted Uranium and CO<Subscript>2</Subscript>

Geological storage of anthropogenic CO₂ emissions in deep saline aquifers has recently received tremendous attention in the scientific literature. Injected buoyant CO₂ accumulates at the top part of the aquifer under a sealing cap rock. Potential buoyant movement of CO₂ has caused some concern that the high-pressure CO₂ could breach the seal rock. However, CO₂ will diffuse into the brine underneath and generate a slightly denser fluid that may induce instability and convective mixing. Onset times of instability and convective mixing performance depend on the physical properties of the rock and fluids, such as permeability and density contrast. We present the novel idea of adding nanoparticles (NPs) to injected CO₂ to increase density contrast between the CO₂-rich brine and the underlying resident brine and, consequently, decrease onset time of instability and increase convective mixing. The analyses show that 0.001 volume fraction of NPs added to the CO₂ stream shortens onset time of mixing by approximately 80% and increases convective mixing by 50%. If it thus originally takes 5 years for the overlying CO₂ to start convective mixing, by adding NPs, onset time of mixing reduces to 1 year, and after initiation of convective mixing, mixing improves by 50%. A reduction of the CO₂ leakage risk ensues. In addition to other metallic NPs, use of processed depleted uranium oxide (DU) as the NPs is also proposed. DU-NPs are potentially stable and might be safely commingled with CO₂ to store in saline aquifers.     

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.     

Sur les approximations « isotrope » et « anisotrope » de l''opérateur tangent pour les méthodes tangentes incrémentale et affineOn the ‘isotropic’ and ‘anisotropic’ approximations of the tangent operator in the incremental tangent and affine methods

Three localisation rules, TFA, the incremental tangent, and the affine method, are recalled and evaluated in the context of the elastoplastic micromechanical analysis of heterogeneous materials, composites or polycrystals. With the help of a severe example, it is shown how methods based on the complete anisotropic elastoplastic tangent operator yield very stiff predictions which are far from the reference solution; the same conclusion holds for the method using the elastic accommodation rule. On the other hand, using an isotropic form of the tangent operator delivers much better responses. The reasons for such differences are discussed, together with possible justifications for the choice of the isotropic form. To cite this article: J.-L. Chaboche, P. Kanouté, C. R. Mecanique 331 (2003).     

Evaluation of one‐ and two‐equation low‐Re turbulence models. Part I—Axisymmetric separating and swirling flows

This first segment of the two‐part paper systematically examines several turbulence models in the context of three flows, namely a simple flat‐plate turbulent boundary layer, an axisymmetric separating flow, and a swirling flow. The test cases are chosen on the basis of availability of high‐quality and detailed experimental data. The tested turbulence models are integrated to solid surfaces and consist of: Rodi's two‐layer k–ε model, Chien's low‐Reynolds number k–ε model, Wilcox's k–ω model, Menter's two‐equation shear‐stress‐transport model, and the one‐equation model of Spalart and Allmaras. The objective of the study is to establish the prediction accuracy of these turbulence models with respect to axisymmetric separating flows, and flows of high streamline curvature. At the same time, the study establishes the minimum spatial resolution requirements for each of these turbulence closures, and identifies the proper low‐Mach‐number preconditioning and artificial diffusion settings of a Reynolds‐averaged Navier–Stokes algorithm for optimum rate of convergence and minimum adverse impact on prediction accuracy. Copyright © 2003 John Wiley & Sons, Ltd.     

Equivalence of u–p and ζ–ψ formulations of the time-dependent Navier–Stokes equations

This paper deals with the non-stationary incompressible Navier--Stokes equations for two-dimensional flows expressed in terms of the velocity and pressure and of the vorticity and streamfunction. The equivalence of the two formulations is demonstrated, both formally and rigorously, by virtue of a condition of compatibility between the boundary and initial values of the normal component of velocity. This condition is shown to be the only compatibility condition necessary to allow for solutions of a minimal regularity, namely H¹ for the velocity, as in most current numerical schemes relying on spatial discretizations of local type.     

MAXIMAL ELEMENTS FOR GB-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅰ)

A new family of set-valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set-valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature. Contributed by DING Xie-ping Foundation items: the National Natural Science Foundation of China (19871059); the Natural Science Foundation of Education Department of Sichuan Province of China ([2000]25) Biography: DING Xie-ping (1938∼)     

MAXIMAL ELEMENTS FOR G-B-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅱ)

By applying existence theorems of maximal elements for a family of G_B-majorized mappings in a product space of G-convex spaces, some coincidence theorem, Fan-Browder type fixed point theorem and some existence theorems of solutions for a system of minimax inequalities are proved under noncompact setting of G-convex spaces. These theorems improve and generalize many important known results in literature. Contributed by Duping Xie-ping Foundation items: the National Natural Science Foundation of China (19871059); the Natural Science Foundation of Education Department of Sichuan Province ([2000]25) Biography: Duping Xie-ping (1938∼), Professor (E-mail: dingxip@sichu.edu.cn)     

Regularity and finite dimensionality of attractor for plate equation on R<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

This paper addresses the regularity and finite dimensionality of the global attractor for the plate equation on the unbounded domain. The existence of the attractor in the phase space has been established in an earlier work of the author. It is shown that the attractor is actually a bounded set of the phase space and has finite fractal dimensionality.