Search results for "Weight function"
showing 10 items of 20 documents
The weight function for charges - A rigorous theoretical concept for Kelvin probe force microscopy
2016
A comprehensive discussion of the physical origins of Kelvin probe force microscopy (KPFM) signals for charged systems is given. We extend the existing descriptions by including the openloop operation mode, which is relevant when performing KPFM in electrolyte solutions. We define the contribution of charges to the KPFM signal by a weight function, which depends on the electric potential and on the capacitance of the tip-sample system. We analyze the sign as well as the lateral decay of this weight function for different sample types, namely, conductive samples as well as dielectric samples with permittivities both larger and smaller than the permittivity of the surrounding medium. Dependin…
A Space-Time Meshless Method for Heat Transfer Problems With High Discontinuities
2013
The aim of this research is the development of a space-time driscretization method based on Diffuse Approximation Meshless method. This method, devoted to transient heat transfer problems presenting high temporal discontinuities, avoids any Finite-Difference time stepping procedure. The space-time discretization proposed here seems to be convenient for continuous transient heat transfer. Nevertheless, for problems including temporal discontinuities, some spurious oscillations, whose amplitudes depend on source power, appear. A new weight function respecting the principle of causality, based on a modification of the involved node’s selection and a normalisation of the distances, is developed…
Fatigue fracture planes and expected principal stress directions under biaxial variable amplitude loading
2005
Fatigue behaviour under multiaxial variable amplitude loading can be examined by applying the failure criteria based on the critical plane approach. Positions of the critical plane can be determined in relation to the principal stress or strain directions. In the present paper, the expected directions of the principal stresses under proportional and non-proportional loading have been obtained by averaging the instantaneous values of the Euler angles through special weight functions. The known weight functions based on stress parameters appear not to be efficient for each loading or material being analysed. Thus, the authors consider new weight functions based on energy parameters. The prese…
Spectral Invariance and Submultiplicativity for the Algebras of S(M, g)-pseudo-differential Operators on Manifolds
2003
For appropriate triples (M, g, M), where M is an (in general non-compact) manifold, g is a metric on T*M, and M is a weight function on T* M, we developed in [5] a pseudo-differential calculus on.A.4 which is based on the S(M, g)-calculus of L. Hormander [30] in local models. Here we prove that the algebra of operators of order zero is a submultiplicative Ψ*-algebra in the sense of B. Gramsch [21] in \( \mathcal{L}\left( {{L^2}\left( M \right)} \right)\). For the basic calculus we generalized the concept of E. Schrohe [40] of so-called SG-compatible manifolds. In the proof of the existence of “order reducing operators” we apply a method from [4], and the proof of spectral invariance and sub…
On Multiresolution Transforms Based on Weighted-Least Squares
2014
This work is devoted to construct Harten’s multiresolution transforms using Weighted-Least squares for different discretizations. We establish a relation between the filters obtained using some decimation operators. Some properties and examples of filters are presented.
An alternative space-time meshless method for solving transient heat transfer problems with high discontinuous moving sources
2016
International audience; The aim of this work is the development of a space-time diffuse approximation meshless method (DAM) to solve heat equations containing discontinuous sources. This work is devoted to transient heat transfer problems with static and moving heat sources applied on a metallic plate and whose power presents temporal discontinuities. The space-time DAM using classical weight function is convenient for continuous transient heat transfer. Nevertheless, for problems including discontinuities, some spurious oscillations for the temperature field occur. A new weight function, respecting the principle of causality, is used to eradicate the physically unexpected oscillations.
Holder continuity of solutions for a class of nonlinear elliptic variational inequalities of high order
2001
ω-hypoelliptic differential operators of constant strength
2004
Abstract We study ω-hypoelliptic differential operators of constant strength. We show that any operator with constant strength and coefficients in E ω (Ω) which is homogeneous ω-hypoelliptic is also σ-hypoelliptic for any weight function σ=O(ω). We also present a sufficient condition in order to ensure that a differential operator admits a parametrix and, as a consequence, we obtain some conditions on the weights (ω,σ) to conclude that, for any operator P(x,D) with constant strength, the σ-hypoellipticity of the frozen operator P(x0,D) implies the ω-hypoellipticity of P(x,D). This requires the use of pseudodifferential operators.
Simulation investigations of the position of Fatigue Fracture Plane in materials with biaxial loads
1989
In the paper three methods of determination of the expected fatigue fracture plane position under random triaxial stress state have been presented. They are: weight function method, variance method and damage cumulation method. The weight function method for biaxial cyclic loadings has been analysed with digital simulation. The fatigue fracture plane position has been determined with mean values of the direction cosines of principal stress axes. Averaging has been done at angle values with use of weights. Eleven various weights have been presented and their usability has been analysed on the basis of experimental results obtained by Rotvel, and Nishihara-Kawamoto. The weights with good agre…
COMPARISON OF EXPERIMENTS WITH WEIGHTED DISTRIBUTIONS
1989
In this paper the standard statistical experiment in which a random sample is drawn from some distribution involving an unknown parameter θ is compared with experiments in which samples are obtained from different weighted versions of that distribution, so that the underlying probability of entering the sample is multiplied by some weight function. This comparison is carried out by means of the concepts of sufficiency and pairwise sufficiency as developed in Blackwell's theory of the comparison of statistical experiments. Many examples are presented which illustrate the wide variety of effects that weight functions can have on the information about θ.