Search results for " Boundary"

Ammonites on the Brink of Extinction: Diversity, Abundance, and Ecology of the Order Ammonoidea at the Cretaceous/Paleogene (K/Pg) Boundary

2015

We examined the stratigraphic distribution of ammonites at a total of 29 sites around the world in the last 0.5 myr of the Maastrichtian. We demarcated this interval using biostratigraphy, magnetostratigraphy, cyclostratigraphy, and data on fossil occurrences in relation to the K/Pg boundary in sections without any facies change between the highest ammonites and the K/Pg boundary. The ammonites at this time represent all four Mesozoic suborders comprising six superfamilies, 31 (sub)genera, and 57 species. The distribution of ammonites is dependent on the environmental setting. Recent data suggest that ammonites persisted to the boundary and some species may have survived for several tens of…

Investigation of TiO<sub>2</sub> Ceramic Surface Conductivity Using Conductive Atomic Force Microscopy

2012

Dense TiO2 (rutile) ceramic samples were prepared by sintering compacts of titanium dioxide anatase powder at 1500 °C for 5h. Sintered samples were polished and annealed in vacuum at 1000 °C for 1h. Structural properties of the samples were studied by X-ray diffraction, polarized light and scanning electron microscopy. The surface topography and local electrical conductivity of the samples were investigated by atomic force microscopy technique under atmospheric conditions. Enhanced electrical conductivity was observed at grain boundaries while the polished, vacuum annealed grains surface showed non-homogeneous conductivity.

TiO2 nanostructures prepared by ferrocene/cobalt catalyst agents

2008

We present the growth and characterization of TiO2 nanocrystals. Nanostructured growth is obtained in a low-pressure CVD system by using an organometallic precursor Ti(OC3H7)4 as both the Ti and O source catalyzed by both ferrocene (an organometallic precursor) and cobalt metallic clusters prepared by the microwave-assisted polyol method. Two kinds of TiO2 structures were obtained in the cobalt clusters: a) pine-tree like (with short-leaf structure) and b) long-leaf structures as large as a few micrometers in size and both under 10 nm in thickness. Long-leaf TiO2 structures were grown at cobalt grain boundaries. For the growth conditions utilized, the TiO2 structures are composed of both an…

Thin obstacle problem : Estimates of the distance to the exact solution

2018

We consider elliptic variational inequalities generated by obstacle type problems with thin obstacles. For this class of problems, we deduce estimates of the distance (measured in terms of the natural energy norm) between the exact solution and any function that satisfies the boundary condition and is admissible with respect to the obstacle condition (i.e., they are valid for any approximation regardless of the method by which it was found). Computation of the estimates does not require knowledge of the exact solution and uses only the problem data and an approximation. The estimates provide guaranteed upper bounds of the error (error majorants) and vanish if and only if the approximation c…

Nonlinear nonhomogeneous Neumann eigenvalue problems

2015

We consider a nonlinear parametric Neumann problem driven by a nonhomogeneous differential operator with a reaction which is $(p-1)$-superlinear near $\pm\infty$ and exhibits concave terms near zero. We show that for all small values of the parameter, the problem has at least five solutions, four of constant sign and the fifth nodal. We also show the existence of extremal constant sign solutions.

On the number of solutions of a Duffing equation

1991

The exact number of solutions of a Duffing equation with small forcing term and homogeneous Neumann boundary conditions is given. Several bifurcation diagrams are shown.

Fixed point theorems on ordered metric spaces and applications to nonlinear elastic beam equations

2012

In this paper, we establish certain fixed point theorems in metric spaces with a partial ordering. Presented theorems extend and generalize several existing results in the literature. As application, we use the fixed point theorems obtained in this paper to study existence and uniqueness of solutions for fourth-order two-point boundary value problems for elastic beam equations.

A boundary min-max principle as a tool for boundary element formulations

1991

Abstract A min-max principle for elastic solids, expressed in terms of the unknown boundary displacements and tractions, is presented. It is shown that its Euler-Lagrange equations coincide with the classical boundary integral equations for displacements and for tractions. This principle constitutes a suitable starting point for a symmetric sign-definite formulation of the boundary element method.

Multiplicity of solutions for two-point boundary value problems with asymptotically asymmetric nonlinearities

1996

Porous medium equation with absorption and a nonlinear boundary condition

2002

where is a bounded domain with smooth boundary, @=@ is the outer normal derivative, m ? 1; p; and q are positive parameters and u0 is in L∞( ). Problems of this form arise in mathematical models in a number of areas of science, for instance, in models for gas or :uid :ow in porous media [3] and for the spread of certain biological populations [13]. In the semilinear case (that is for m=1), there is an extensive literature about global existence and blow-up results for this type of problems, see among others, [5,9,16] and the literature therein. For the degenerate case (that is for m = 1), with a nonlinear boundary condition, local existence and uniqueness of weak solutions which are limit o…