Classical Integral Approach Research Articles

A Dual Approach for Model Construction of Two-Dimensional Horizontal Flow

The two-dimensional horizontal flow model in the classical integration approach is integrated from the three-dimensional Navier-Stokes system of equations. Using the classical theory, the integral is taken directly from the bed to the free water surfaces. Consequently, the effects between the channel bed and free water surface, in the process of integration, was disappeared. However, with the proposed dual-process approach, the integral can be performed locally several times. The receiving equations thus allow to contain many physical phenomena which may be lost in the classical integral process. As a result, the derived model based on the proposed dual approach will be more complex and accurate than the classical one. In this paper, the authors perform twice integrals. The improved two-dimensional horizontal flow model was received from the dual approach which allows the calculation of flow parameters, which, having the unusual phenomena in the channel as solid objects, liquids containing other added ingredients, external forces, reversals, and so on.

Quantification of corrugation in simulated graphene by electron tomography techniques

Electron tomography (ET) can be used to determine the shape, and therefore the properties, of an object. It deals with retrieving tridimensional (3D) information from bidimensional (2D) projections of the object under study. While ET has been used widely in biology, its application to the nanoscale world is relatively recent because of the limitations in resolution and aberration of electron microscopes. At atomic scale, classical tomography reconstruction can be replaced by tomography through points reconstruction, that is, the 3D information can be obtained by applying image processing techniques to the projections and by using geometrical models instead of the classical integral approach. In this paper, a methodology for the study of corrugated graphene will be presented. It will be shown how to apply tomographic techniques to the determination of the corrugations in graphene layers with error in 3D location in the range of pm.

Energy dissipation under multiaxial thermomechanical fatigue loading

The paper presents an approach to the energy dissipation calculation under arbitrary multiaxial thermomechanical fatigue (TMF) loading. In such an approach the total area of plastic hysteresis loops is taken as a measure of dissipated energy. The calculation is based on the concept of the developed temperature dependent Prandtl type operator. Energy dissipation is associated to irreversible dislocation movements represented by slider shifts of three independent operators. The dissipated energy is then obtained continuously at any time by collecting dissipated energy increments of each operator. It is shown that the multiaxial operator approach gives us the same total energy of plastic deformation as compared to the classical integration approach. Furthermore, the presented approach enables to automatically split the obtained dissipated energy between the “true” dissipated energy and the elastically “stored” energy. In order to satisfy the request for a minimum number of dedicated material tests, the approach assumes fixed principal directions. Therefore, the proportional as well as non-proportional loading conditions are addressed in the same manner, which is currently the main deficiency of the approach.

Variations on Higher‐Order Shoaling

Variations on the classical integral approach to shoaling may be categorized in terms of the choice of steady‐wave theory and, more importantly, the choice of dependent variables and conservation laws. One‐variable models (wave height) appear to underpredict both wave height and wave number, and assume that both undertow current and setup are zero. Models with two variables (wave height and undertow current) and three variables (wave height, undertow current, and setup) provide almost identical predictions of wave height, wave number, and undertow current. Setup, which is assumed to be zero in one‐ and two‐variable models, is predicted by three‐variable models. Fourier 18 predictions of the shoaling evolution of wave height, wave number, undertow current, and setup of the mean water level are presented for a range of deep‐water incident wave heights.