On a boundary variational inequality of the second kind modelling a friction problem

A scalar contact problem with friction governed by the Yukawa equation is reduced to a boundary variational inequality. The presence of the non‐differentiable friction functional causes some difficulties when approximated. We present two methods to overcome this difficulty. The first one is a regularization leading to a non‐linear boundary variational equation, for which we propose an iterative procedure, whereas the second method is based on the boundary mixed variational formulation involving Lagrange multipliers. We propose Uzawa's algorithm to compute the saddle point of the corresponding boundary Lagrangian and investigate the discretization of various formulations by the boundary element Galerkin method. Convergence of the boundary element solution is proved and a convergence order is obtained. Copyright © 2002 John Wiley & Sons, Ltd.     

Solid-liquid equilibria of three binary systems: {1-Ethyl-3-methylimidazolium hexafluorophosphate + 2-phenylimidazole, or 4,5-diphenylimidazole or 2,4,5-triphenylimidazole}

The phase diagrams of binary mixtures formed by 1-ethyl-3-methylimidazolium hexafluorophosphate ([emim][PF₆]) and 2-phenylimidazole or 4,5-diphenylimidazole or 2,4,5-triphenylimidazole has been established using differential scanning calorimetry. Solutions containing 2,4,5-triphenylimidazole display phase splitting at high temperature range.     

A fracture criterion of rubber-like materials under plane stress conditions

In this work, we attempt to derive a fracture criterion for filled and unfilled elastomer vulcanizates and thermoplastics from a set of experimental data. Firstly, fracture criteria reported in the literature have been applied to experimental data obtained from tests including various loading modes (simple tension, equal biaxial tension and biaxial tension) and performed on four materials: a natural rubber (NR), a styrene butadiene rubber (SBR), a polyurethane (PU) and a thermoplastic elastomer (TPE).

Then, a new failure criterion based on an equivalent elongation concept is proposed. This equivalent elongation seems to be linearly dependent on a given biaxiality ratio n=(ln(λ_2b)/ln(λ_1b)), which leads to expressing the principal elongations at break as functions of both the biaxiality n and two experimental parameters. Quite good agreement is highlighted when comparing the failure experimental data with the proposed criterion for the tested elastomers.     

Mg2Ru2Cl10O·16H2O

Mg₂Ru₂Cl₁₀O·16H₂O {dimagnesium μ‐oxo‐bis­[penta­chloro­ruthenate(IV)] hexa­deca­hydrate} crystallizes in the monoclinic system (space group P2₁/c). The structure consists of layers of [Ru₂Cl₁₀O]⁴⁻ anions, [Mg(H₂O)₆]²⁺ cations and water mol­ecules stacked along the a axis. Only the O atom bonded to Ru occupies the 2a site with symmetry. All the other atoms occupy general 4e sites. The crystal structure is stabilized by O—H⋯O and O—H⋯Cl inter­actions.     

Solvent extraction of thorium from mixed organic — aqueous nitric acid media by try-n-octylphosphine oxide

The extraction equilibria of Th in tri-n-octylphosphine oxide (TOPO)–HNO₃–H₂O systems have been investigated in the absence and presence of water-miscible alcohols and acetone. The influence of TOPO concentration in an inert diluent (toluene) and the concentration of nitric acid and the water-miscible additives have been systematically examined. The slopes of the log-log plots of D_Th vs. the TOPO concentration (up to 0.02M) are found to be close to 3 over a wide range of polar phase compositions leading to a coordination number of 11 for Th. The D_Th values were determined as a function of the concentration of uranyl nitrate in the aqueous phase, while the effect of additives was also examined in the absence and presence of uranyl nitrate in the polar phase. The results show that at TOPO concentrations above about 2.5 · 10^–3 M (about 1%) in toluene, polymerization of the solvent occurs.     

Covering cycles andk-term degree sums

We show that if , for every stable set , then the vertex set ofG can be covered withk–1 cycles, edges or vertices. This settles a conjecture by Enomoto, Kaneko and Tuza.     

Mechanical properties of polyamide-12 layered silicate nanocomposites and their relations with structure

The mechanical properties of polyamide-12/Cloisite 30B (PA12/C30B) nanocomposites prepared by melt compounding were studied as a function of clay volume fraction φ under various processing conditions. All measured mechanical characteristics, Young's modulus, yield stress, strain at break and stress at break, exhibit a transition at φ_p1%, identified with a percolation threshold. Also, the linear and non-linear mechanical properties appeared to depend on the degree of exfoliation of the structure, which can be tuned by the processing conditions. The three-phase Ji's theoretical model was used to predict Young's modulus as a function of clay concentration, focusing on the influence of the degree of exfoliation. Experimental yield stress data were fitted to Pukanszky's model and discussed in terms of PA12/C30B interfacial adhesion.     

Thermal diagnostics of highly heated surfaces using water-spray cooling

Spray cooling of heated surfaces is common in many industrial applications, notably steelmaking, because of its high heat dissipating ability. Control of the surface heat flux rate contributes to better products; it is shown that the heat transfer rate depends on the mass fraction of liquid. Quantitative information regarding the parameters affecting spray cooling is relatively scarce. The rate of heat transfer from a plate due to impinging of an array of water jets was investigated numerically through the solution of heat conduction equation. The simulation is carried out for eight different sprayers, in the range of ejected fluid pressure between 1 bar and 3 bars. Experimental data are used to study the influence of the function g(x, y), of dispersed water, on heat transfer variations across the surface at the temperature of 600°C. Curves were generated showing time histories of the steel temperature for the removal of high heat fluxes of the order of 300 W/cm². It was also observed that for lower temperatures, the predicted local heat transfer coefficient increased significantly. In memory of H. Mzad’s father Mebrouk.     

Mean distance and minimum degree

We prove that in a graph of order n and minimum degree d, the mean distance μ must satisfy . This asymptotically confirms, and improves, a conjecture of the computer program GRAFFITI. The result is close to optimal; examples show that for any d, μ may be larger than n/(d + 1). © 1997 John Wiley & Sons, Inc. J Graph Theory 25: 95–99, 1997