scholarly journals From non-local Eringen’s model to fractional elasticity

2018 ◽  
Vol 24 (6) ◽  
pp. 1935-1953 ◽  
Author(s):  
Anton Evgrafov ◽  
José C. Bellido
Keyword(s):  
Riesz Potential ◽  
Heterogeneous Material ◽  
Research Literature ◽  
Stress Concentrations ◽  
Uniqueness Of Solutions ◽  
Numerical Studies ◽  
Smooth Kernels ◽  
Ill Posed ◽  
Non Local ◽  
Dimension One

Eringen’s model is one of the most popular theories in non-local elasticity. It has been applied to many practical situations with the objective of removing anomalous stress concentrations around geometric shape singularities, which appear when local modelling is used. Despite the great popularity of Eringen’s model within the mechanical engineering community, even the most basic questions such as the existence and uniqueness of solutions have been rarely considered in research literature for this model. In this work we focus on precisely these questions, proving that the model is in general ill-posed in the case of smooth kernels, the case which appears rather often in numerical studies. We also consider the case of singular, non-smooth kernels and for the paradigmatic case of Riesz potential we establish the well-posedness of the model in fractional Sobolev spaces. For such a kernel, in dimension one the model reduces to the well-known fractional Laplacian. Finally, we discuss possible extensions of Eringen’s model to spatially heterogeneous material distributions.

Numerical studies of the influence of textural gradients on the local stress concentrations around fibers in carbon/carbon composites

2008 ◽  
Vol 24 (12) ◽  
pp. 2194-2205 ◽  
Author(s):  
Romana Piat ◽  
Igor Tsukrov ◽  
Thomas Böhlke ◽  
Norbert Bronzel ◽  
Tilottama Shrinivasa ◽  
...  
Keyword(s):  
Local Stress ◽  
Carbon Composites ◽  
Stress Concentrations ◽  
Numerical Studies

New Results from Old Investigation: A Note on Fractional M-Dimensional Differential Operators. The Fractional Laplacian

2015 ◽  
Vol 18 (2) ◽  
Author(s):  
Humberto Prado ◽  
Margarita Rivero ◽  
Juan J. Trujillo ◽  
M. Pilar Velasco
Keyword(s):  
Fractional Integral ◽  
Fractional Laplacian ◽  
Singular Integrals ◽  
Differential Operators ◽  
Riesz Potential ◽  
Fractional Power ◽  
Potential Operators ◽  
Relevant Role ◽  
Non Local ◽  
Fractional Power Of Operators

AbstractThe non local fractional Laplacian plays a relevant role when modeling the dynamics of many processes through complex media. From 1933 to 1949, within the framework of potential theory, the Hungarian mathematician Marcel Riesz discovered the well known Riesz potential operators, a generalization of the Riemann-Liouville fractional integral to dimension higher than one. The scope of this note is to highlight that in the above mentioned works, Riesz also gave the necessary tools to introduce several new definitions of the generalized coupled fractional Laplacian which can be applied to much wider domains of functions than those given in the literature, which are based in both the theory of fractional power of operators or in certain hyper-singular integrals. Moreover, we will introduce the corresponding fractional hyperbolic differential operator also called fractional Lorentzian Laplacian.

A New Regularization Model Based on Non-Local Means for Image Deblurring

2013 ◽  
Vol 411-414 ◽  
pp. 1164-1169 ◽  
Author(s):  
Zhi Ming Wang ◽  
Hong Bao
Keyword(s):  
Image Denoising ◽  
Processing Speed ◽  
Operator Splitting ◽  
Image Deblurring ◽  
Local Similarity ◽  
Model Based ◽  
Local Means ◽  
Ill Posed ◽  
Non Local ◽  
Local Image

Image deblurring with noise is a typical ill-posed problem needs regularization. Various regularization models were proposed during several decades study, such as Tikhonov and TV. A new regularization model based non-local similarity constrains is proposed in this paper, which used l2 non-local norms and could be easily solved by fast non-local image denoising algorithm. By combining with Bregmanrized operator splitting (BOS) algorithm, a fast and efficient iterative three step image deblurring scheme is given. Experimental results show that proposed regularization model obtained better results on ten common test images than other similar regularization model including newly proposed NLTV regularization, both in deblurring performance (PSNR and MSSIM) and processing speed.

Field test and numerical studies of the scissors-AVLB type bridge

2014 ◽  
Vol 62 (1) ◽  
pp. 103-112
Author(s):  
W. Krason ◽  
J. Malachowski
Keyword(s):  
High Mobility ◽  
Armed Forces ◽  
Careful Consideration ◽  
Discrete Models ◽  
Stress Concentrations ◽  
Bridge Span ◽  
Numerical Studies ◽  
The Republic ◽  
Loading Modes ◽  
Wheel Track

Abstract Scissor bridges are characterized by high mobility and modular structure. A single module-span consists of two spanning parts of the bridge; two main trucks and the support structure. Pin joints are used between modules of the single bridge span. Some aspects of the experimental test and numerical analysis of the scissor-AVLB type bridge operation are presented in this paper. Numerical analyses, presented here, were carried out for the scissors-type BLG bridge with treadways extended as compared to the classical bridge operated up to the present in the Armed Forces of the Republic of Poland. A structural modification of this kind considerably affects any changes in the effort of the force transmitting structure of the bridge. These changes may prove to be disadvantageous to the whole structure because of torsional moments that additionally load the treadways. Giving careful consideration to such operational instances has been highly appreciated because of the possibility of using this kind of bridges while organizing the crossing for vehicles featured with various wheel/track spaces (different from those used previously). The BLG bridge was numerically analysed to assess displacements and distributions of stresses throughout the bridge structure in different loading modes. Because of the complexity of the structure in question and simplifications assumed at the stage of constructing geometric and discrete models, the deformable 3D model of the scissors-type bridge needs verification. Verification of the reliability of models was performed by comparing deflections obtained in the different load modes that corresponded with tests performed on the test stand. It has been shown that the examined changes in conditions of loading the treadways of the bridge are of the greatest effect to the effort of the area of the joint which is attached to the girder bottom. Stress concentrations determined in the analysis are not hazardous to safe operation of the structure

scholarly journals Spatial externality and indeterminacy

2019 ◽  
Vol 14 (1) ◽  
pp. 102
Author(s):  
Emmanuelle Augeraud-Véron ◽  
Arnaud Ducrot
Keyword(s):  
Existence And Uniqueness ◽  
Supply And Demand ◽  
Uniqueness Of Solutions ◽  
Long Distance ◽  
Gaussian Kernels ◽  
Demand Curves ◽  
Uniqueness Of The Solution ◽  
Non Local ◽  
Spatial Externality ◽  
The Impact

We study conditions for existence and uniqueness of solutions in some space-structured economic models with long-distance interactions between locations. The solution of these models satisfies non local equations, in which the interactions are modeled by convolution terms. Using properties of the spectrum location obtained by studying the characteristic equation, we derive conditions for the existence and uniqueness of the solution. This enables us to characterize the degree of indeterminacy of the system being considered. We apply our methodology to a theoretical one-sector growth model with increasing returns, which takes into account technological interdependencies among countries that are modeled by spatial externalities. When symmetric interaction kernels are considered, we prove that conditions for which indeterminacy occurs are the same as the ones needed when no interactions are taken into account. For Gaussian kernels, we study the impact of the standard deviation parameter on the degree of indeterminacy. We prove that when some asymmetric kernels are considered, indeterminacy can occur with classical assumptions on supply and demand curves.

scholarly journals Existence and Uniqueness of Solutions of the Semiclassical Einstein Equation in Cosmological Models

2021 ◽  
Author(s):  
Paolo Meda ◽  
Nicola Pinamonti ◽  
Daniel Siemssen
Keyword(s):  
Einstein Equation ◽  
Existence And Uniqueness ◽  
Inversion Formula ◽  
Initial Conditions ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Expectation Values ◽  
Uniqueness Of Solutions ◽  
Stress Energy ◽  
Non Local

AbstractWe prove existence and uniqueness of solutions of the semiclassical Einstein equation in flat cosmological spacetimes driven by a quantum massive scalar field with arbitrary coupling to the scalar curvature. In the semiclassical approximation, the backreaction of matter to curvature is taken into account by equating the Einstein tensor to the expectation values of the stress-energy tensor in a suitable state. We impose initial conditions for the scale factor at finite time, and we show that a regular state for the quantum matter compatible with these initial conditions can be chosen. Contributions with derivative of the coefficient of the metric higher than the second are present in the expectation values of the stress-energy tensor and the term with the highest derivative appears in a non-local form. This fact forbids a direct analysis of the semiclassical equation, and in particular, standard recursive approaches to approximate the solution fail to converge. In this paper, we show that, after partial integration of the semiclassical Einstein equation in cosmology, the non-local highest derivative appears in the expectation values of the stress-energy tensor through the application of a linear unbounded operator which does not depend on the details of the chosen state. We prove that an inversion formula for this operator can be found, furthermore, the inverse happens to be more regular than the direct operator and it has the form of a retarded product, hence, causality is respected. The found inversion formula applied to the traced Einstein equation has thus the form of a fixed point equation. The proof of local existence and uniqueness of the solution of the semiclassical Einstein equation is then obtained applying the Banach fixed point theorem.

scholarly journals An experimental study of the bearing capacity of wall models with openings under one and two-way loading

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Barei Abdul ◽  
Victor Ledenev ◽  
Yaroslav Savinov ◽  
Yaya Keyta
Keyword(s):  
Bearing Capacity ◽  
Functional Dependencies ◽  
Stress Concentrations ◽  
Factors Affecting ◽  
Numerical Studies ◽  
Destruction Mechanism ◽  
Wall Models ◽  
Experimental Values ◽  
Stability Of Structures ◽  
Classical Calculation

The results of an experimental and numerical studies of the stress-strain state of wall models under one and two way action are presented. The mechanisms of destruction of walls with openings are described. The functional dependencies between the destructive loads of the onset of crack formation and the influencing parameters are obtained. It is shown that the openings are stress concentrators, leading to the occurrence of micro and macro damage, the appearance and development of cracks, and in some cases to the loss of stability of structures (walls). The obtained influence functions can be included in traditional calculation methods with the aim of clarifying them. The factors affecting the process of cracking and fracture are given. Their modeling will allow to predict and prevent adverse events. Practical methods for regulating stresses, forces, and displacements that reduce the influence of various concentrators are considered. The analysis of the destruction mechanism of wall models carried out in this article allows one to study the influence of the size, position, and shape of window openings on the bearing capacity of walls. For example, the presence of stress concentrations in the region of the corners of square openings and their absence in round ones. The system of indicators of the sentry type ICh-10 made it possible to control the deformation of models from the plane of the walls, which is especially important under conditions of lateral pinching. The experimental values of the strength of the walls with openings compared with the calculated ones, which made it possible to see the degree of simplification of the classical calculation models used in design practice.

Numerical Studies on Non-Boiling Two-Phase Flows in Microtubes and Microchannels: A Review

2010 ◽  
Author(s):  
V. Talimi ◽  
Y. S. Muzychka
Keyword(s):  
Heat Transfer ◽  
Pressure Drop ◽  
Flow Pattern ◽  
Research Literature ◽  
Heat Transfer Characteristics ◽  
Liquid Slug ◽  
Two Phase Flows ◽  
Two Phase ◽  
Numerical Studies ◽  
Slug Flows

Numerical studies on the hydrodynamic and heat transfer characteristics of two-phase flows in small tubes and channels are reviewed. These flows are gas-liquid and liquid-liquid slug flows. The review is categorized into two groups of studies: circular and non-circular channels. Different aspects such as slug formation, slug shape, flow pattern, pressure drop and heat transfer are of interest. According to this review, there are some large gaps in the research literature, including pressure drop and heat transfer in liquid-liquid slug flows. Gaps in research are also found in applications of non-circular ducts, pressure drop and heat transfer in meandering microtubes and microchannels for both of gas-liquid and liquid-liquid two-phase flows.

scholarly journals Γ-convergence of non-local, non-convex functionals in one dimension

2019 ◽  
Vol 22 (07) ◽  
pp. 1950077
Author(s):  
Haïm Brezis ◽  
Hoai-Minh Nguyen
Keyword(s):  
Open Interval ◽  
One Dimension ◽  
Monotonicity Condition ◽  
Convex Functionals ◽  
Non Local ◽  
Γ Convergence ◽  
Dimension One

We study the [Formula: see text]-convergence of a family of non-local, non-convex functionals in [Formula: see text] for [Formula: see text], where [Formula: see text] is an open interval. We show that the limit is a multiple of the [Formula: see text] semi-norm to the power [Formula: see text] when [Formula: see text] (respectively, the [Formula: see text] semi-norm when [Formula: see text]). In dimension one, this extends earlier results which required a monotonicity condition.

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