Search results for " solution"
showing 10 items of 3084 documents
The effect of elastic strain on the microstructure of free surfaces of stressed minerals in contact with an aqueous solution
2001
The influence of gradients in bulk elastic strain energy on the dissolution and growth behaviour of minerals in rocks is commonly considered negligible. We experimentally observed, however, that regular arrays of macroscopically visible etch grooves may develop on the originally smooth free surfaces of soluble crystals held in an undersaturated aqueous solution if the crystals are only elastically stressed. These grooves are oriented perpendicular to the compressive stress. They disappear soon after the stress is taken off. The formation of the grooves is well explained by recent theories on the instability of the surface of stressed solids. Development of such instabilities could significa…
Crystallographic preferred orientation development by dissolution–precipitation creep
2000
Abstract Crystallographic preferred orientations (CPOs) in deformed rocks are commonly interpreted as resulting from crystal plastic deformation mechanisms, where deformation is achieved by the movement of dislocations. In this paper we investigate the possibility of CPO-development by dissolution–precipitation creep or pressure solution. A numerical model is presented, which simulates the development of a grain aggregate that deforms by reaction-controlled dissolution–precipitation creep. Grains are simulated as rectangular boxes that change their shape by growth, or dissolution of their surfaces, depending on the normal stresses acting on the individual surfaces. Grains can also rotate du…
Stress fields in general composite laminates
1996
A direct approach is employed to obtain a general boundary integral formulation for the analysis of composite laminates subjected to uniform axial strain. The integral equations governing the problem are directly deduced from the reciprocity theorem, employing the generalized orthotropic elasticity fundamental solutions expressly inferred. The solution is achieved by the boundary element method, which gives, once the traction-free boundary conditions and the interfacial continuity conditions are enforced, a linear system of algebraic equations. The formulation does not present restrictions with regard to the laminate stacking sequence and it does not require any aprioristic assumption. The …
Purification of recovered phosphoric acid by extracting aluminium with di-2-ethylhexyl phosphoric acid
2021
AbstractThe extraction of aluminium from dilute phosphoric acid with di-2-ethylhexyl phosphoric acid (DEHPA) was optimized using response surface methodology. The optimization was based on the experimental three-level central composite face-centred design (CCF) and was conducted on real-life samples. The three variables included were pH, extractant concentration and aqueous to organic phase ratio (AO). Under the optimized conditions (pH 2.5, 0.6 M DEHPA and AO ratio 1:2), extraction efficiency of 99% for aluminium in four extraction stages is achieved. The purified phosphoric acid solution can then be utilized by the fertilizing industry. Stripping tests for organic phase loaded with alumin…
Nonlinear Nonhomogeneous Elliptic Problems
2019
We consider nonlinear elliptic equations driven by a nonhomogeneous differential operator plus an indefinite potential. The boundary condition is either Dirichlet or Robin (including as a special case the Neumann problem). First we present the corresponding regularity theory (up to the boundary). Then we develop the nonlinear maximum principle and present some important nonlinear strong comparison principles. Subsequently we see how these results together with variational methods, truncation and perturbation techniques, and Morse theory (critical groups) can be used to analyze different classes of elliptic equations. Special attention is given to (p, 2)-equations (these are equations driven…
THE MINIMIZING TOTAL VARIATION FLOW WITH MEASURE INITIAL CONDITIONS
2004
In this paper we obtain existence and uniqueness of solutions for the Cauchy problem for the minimizing total variation flow when the initial condition is a Radon measure in ℝN. We study limit solutions obtained by weakly approximating the initial measure μ by functions in L1(ℝN). We are able to characterize limit solutions when the initial condition μ=h+μs, where h∈L1(ℝN)∩L∞(ℝN), and μs=αℋk⌊ S,α≥0,k is an integer and S is a k-dimensional manifold with bounded curvatures. In case k<N-1 we prove that the singular part of the solution does not move, it remains equal to μs for all t≥0. In particular, u(t)=δ0 when u(0)=δ0. In case k=N-1 we prove that the singular part of the limit solution …
Dielectric and Elastic Parameters of LixNa1-xTa0.1Nb0.9O3 Ferroelectric Solid Solution Ceramics
2011
Results of the studies of electric and elastic parameters as functions of concentration in ferroelectric LiхNa1-хTa0.1Nb0.9O3 (x = 0–0.16) solid solutions and comparative studies of the elastic properties by acoustic and contact probe techniques are reported. The electric and elastic properties of LiхNa1-хTa0.1Nb0.9O3 solid solutions are shown to be rather sensitive to structural distortion at concentration-induced structural phase transitions. The values of elastic modules obtained from acoustic measurements are found to be in good agreement with those obtained by contact probe techniques.
Stylolite interfaces and surrounding matrix material: Nature and role of heterogeneities in roughness and microstructural development
2010
Rough pressure solution interfaces, like stylolites, are one of the most evident features of localized slow deformation in rocks of the upper crust. There is a general consensus that the development of these rough structures is a result of localized, stress enhanced, dissolution of material along a fluid filled interface, but little is known on the initiation of this roughness. The aim of this article is to reveal the role of heterogeneities initially present in the host-rock on roughness initiation. This should give insights on whether stylolite roughness is generated by a stress-induced instability or by the presence of disorder in the material (i.e. quenched noise). We use a microstructu…
Rate Effects of AOT-Stabilized Microemulsions on Reactions of Ligand Substitution in Cationic Palladium(II) Complexes
1998
Rate data for the substitution reactions of the coordinated ligand X (=2,2‘-bipyridine or 4,4‘-dimethyl-2,2‘-bipyridine) of the palladium(II) complex [Pd(en)X]2+, where en = ethylenediamine, by en or N,N-dimethylethylenediamine in heptane−AOT−water microemulsions have been obtained at 25.0 °C as a function of the AOT concentration at the constant R (=[H2O]/[AOT]) values of 3, 8, and 20 or 30. The overall second-order rate constants are higher in microemulsions than in bulk water and decrease significantly as both the AOT concentration (at constant R) and the molar ratio R (at a given [AOT]) increase. The quantitative analysis of the kinetic data, made by applying the pseudophase model, lead…
Experimental and theoretical study on the substitution reactions of aryl 2,4-dinitrophenyl carbonates with quinuclidines
2006
Abstract The reactions of quinuclidines with phenyl, 4-methylphenyl, and 4-chlorophenyl 2,4-dinitrophenyl carbonates are kinetically evaluated in aqueous solution. The Bronsted-type plots (log kN vs pKa of quinuclidinium ions) are linear. The magnitude of the slopes and validated theoretical scales of electrophilicity and nucleophilicity confirm the concerted nature of these reactions.