Search results for "Function"
showing 10 items of 14432 documents
On the Computational Aspects of a Symmetric Multidomain Boundary Element Method Approach for Elastoplastic Analysis
2011
The symmetric boundary element method (SBEM) is applied to the elasto-plastic analysis of bodies subdivided into substructures. This methodology is based on the use of: a multidomain SBEM approach, for the evaluation of the elastic predictor; a return mapping algorithm based on the extremal paths theory, for the evaluation of inelastic quantities characterizing the plastic behaviour of each substructure; and a transformation of the domain inelastic integrals of each substructure into corresponding boundary integrals. The elastic analysis is performed by using the SBEM displacement approach, which has the advantage of creating system equations that only consist of nodal kinematical unknowns…
Identification of stiffness,dissipation and input parameters of randomly excited non-linear systems: Capability of restricted potential models (RPM)
2006
Abstract A dynamic identification technique in the time domain for time invariant systems under random external forces is presented. This technique is based on the use of the class of restricted potential models (RPM), which are characterized by a non-linear stiffness and a special form of damping, that is a product of the input power spectral density (PSD) matrix and the velocity gradient of a non-linear function of the total mechanical energy. By applying It o ^ stochastic differential calculus and by specific analytical manipulations, some algebraic equations, depending on the response statistics and on the mechanic parameters that characterize RPM, are obtained. These equations can be u…
Contrasting probabilistic and anti-optimization approaches in an applied mechanics problem
2003
Probabilistic and non-probabilistic, anti-optimization analyses of uncertainty are contrasted in this study. Specifically, the comparison of these two competing approaches is conducted for an uniform column, with initial geometric imperfection, subjected to an impact axial load. The reliability of the column is derived for the cases when the initial imperfections posses either (a) uniform probability density, (b) truncated exponential density or (c) generic truncated probability density. The problem is also analyzed in the context of an interval analysis. It is shown that in, the most important near-unity reliability range these two approaches tend to each other. Since the interval analysis…
Itô calculus extended to systems driven by -stable Lévy white noises (a novel clip on the tails of Lévy motion)
2007
Abstract The paper deals with probabilistic characterization of the response of non-linear systems under α -stable Levy white noise input. It is shown that, by properly selecting a clip in the probability density function of the input, the moments of the increments of Levy motion process remain all of the same order ( d t ) , like the increments of the Compound Poisson process. It follows that the Ito calculus extended to Poissonian input, may also be used for α -stable Levy white noise input processes. It is also shown that, when the clip on the tails of the probability of the increments of the Levy motion approaches to infinity, the Einstein–Smoluchowsky equation is restored. Once these c…
One-dimensional families of projections
2008
Let m and n be integers with 0 < m < n. We consider the question of how much the Hausdorff dimension of a measure may decrease under typical orthogonal projections from onto m-planes provided that the dimension of the parameter space is one. We verify the best possible lower bound for the dimension drop and illustrate the sharpness of our results by examples. The question stems naturally from the study of measures which are invariant under the geodesic flow.
A regularized Newton method for locating thin tubular conductivity inhomogeneities
2011
We consider the inverse problem of determining the position and shape of a thin tubular object, such as for instance a wire, a thin channel or a curve-like crack, embedded in some three-dimensional homogeneous body from a single measurement of electrostatic currents and potentials on the boundary of the body. Using an asymptotic model describing perturbations of electrostatic potentials caused by such thin objects, we reformulate the inverse problem as a nonlinear operator equation. We establish Frechet differentiability of the corresponding operator, compute its Frechet derivative and set up a regularized Newton scheme to solve the inverse problem numerically. We discuss our implementation…
The Calderón Problem for a Space-Time Fractional Parabolic Equation
2020
In this article we study an inverse problem for the space-time fractional parabolic operator $(\partial_t-\Delta)^s+Q$ with $0<s<1$ in any space dimension. We uniquely determine the unknown bounded...
Explanation, motivation and question posing routines in university mathematics teachers' pedagogical discourse: a commognitive analysis
2015
This paper investigates the teaching practices used by university mathematics teachers when lecturing, a topic within university mathematics education research which is gaining an increasing intere ...
Jacobian of solutions to the conductivity equation in limited view
2022
Abstract The aim of hybrid inverse problems such as Acousto-Electric Tomography or Current Density Imaging is the reconstruction of the electrical conductivity in a domain that can only be accessed from its exterior. In the inversion procedure, the solutions to the conductivity equation play a central role. In particular, it is important that the Jacobian of the solutions is non-vanishing. In the present paper we address a two-dimensional limited view setting, where only a part of the boundary of the domain can be controlled by a non-zero Dirichlet condition, while on the remaining boundary there is a zero Dirichlet condition. For this setting, we propose sufficient conditions on the bounda…
Activity-Centered Design: An Appropriation Issue
2011
When designing workplace computer systems one must take human activity into account. It has become standard practice to approach this issue through user-centered design. The aim of this paper is to stimulate thought on activity-centered design and to propose the concept of appropriation as a fundamental principle of this design approach. This orientation aims to take into consideration the constituent function of tools during conception. We will take the design of computer systems dedicated to customer relations as an example.