Certain cases of elastic equilibrium of a composed wedge with an interface crack

2020 ◽  
Vol 25 (12) ◽  
pp. 2199-2209
Author(s):  
Konstantin B Ustinov
Keyword(s):  
Half Plane ◽  
Edge Crack ◽  
Elastic Equilibrium ◽  
Restrictive Condition ◽  
Uniform Loading ◽  
The Matrix ◽  
Remote Loading ◽  
The Common ◽  
Inclined Edge Crack ◽  
Crack Faces

Problems of interface cracks starting from the common corner points of pairs of perfectly glued wedges of different isotropic elastic materials are addressed. It is demonstrated that for a few particular configurations and a restrictive condition imposed on values of elastic constants (corresponding to vanishing of the second Dundurs parameter), the problem of elastic equilibrium may be solved by Khrapkov’s method. These configurations are: (i) the wedges forming a half-plane; (ii) the wedges forming a plane; (iii) one of the wedges being a half-plane. In all cases, the external boundaries are supposed to be free of stresses. By applying Mellin’s transform for all three configurations the problem has been reduced to vector Riemann’s problem, and the matrix coefficient has been factorized for the case of the mentioned restrictive condition. The first configuration, i.e. the problem of an inclined edge crack located along the boundary separating two wedges of different elastic isotropic materials forming a half-plane is considered in more detail. The solution has been obtained for both uniform (corresponding to remote loading) and non-uniform (loading applied at the crack faces) problems. Numerical results are presented and compared with the available results obtained by other authors for particular cases. The obtained solutions appear especially valuable for analysing extreme cases of parameters.

scholarly journals On Exact and Approximate Approaches for Stochastic Receptor-Ligand Competition Dynamics—An Ecological Perspective

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1014
Author(s):  
Polly-Anne Jeffrey ◽  
Martín López-García ◽  
Mario Castro ◽  
Grant Lythe ◽  
Carmen Molina-París
Keyword(s):  
Summary Statistics ◽  
Steady State Distribution ◽  
State Distribution ◽  
Cellular Receptors ◽  
Stochastic Description ◽  
The Matrix ◽  
Common Resource ◽  
A Cell ◽  
The Common ◽  
Cellular Medium

Cellular receptors on the cell membrane can bind ligand molecules in the extra-cellular medium to form ligand-bound monomers. These interactions ultimately determine the fate of a cell through the resulting intra-cellular signalling cascades. Often, several receptor types can bind a shared ligand leading to the formation of different monomeric complexes, and in turn to competition for the common ligand. Here, we describe competition between two receptors which bind a common ligand in terms of a bi-variate stochastic process. The stochastic description is important to account for fluctuations in the number of molecules. Our interest is in computing two summary statistics—the steady-state distribution of the number of bound monomers and the time to reach a threshold number of monomers of a given kind. The matrix-analytic approach developed in this manuscript is exact, but becomes impractical as the number of molecules in the system increases. Thus, we present novel approximations which can work under low-to-moderate competition scenarios. Our results apply to systems with a larger number of population species (i.e., receptors) competing for a common resource (i.e., ligands), and to competition systems outside the area of molecular dynamics, such as Mathematical Ecology.

scholarly journals LOCALIZATION OF UROMUCOID IN HUMAN KIDNEY AND IN SECTIONS OF HUMAN KIDNEY STONE WITH THE FLUORESCENT ANTIBODY TECHNIQUE

1965 ◽  
Vol 13 (3) ◽  
pp. 155-160 ◽  
Author(s):  
H. J. KEUTEL
Keyword(s):  
Kidney Stones ◽  
Kidney Stone ◽  
Fluorescent Antibody ◽  
Human Kidney ◽  
Fluorescent Antibody Technique ◽  
Renal Tubules ◽  
Antibody Technique ◽  
The Matrix ◽  
Normal Human ◽  
The Common

Fluorescent labeled antibodies were used for the demonstration of uromucoid. This urine specific mucoprotein is demonstrably present only in the epithelial cells of the proximal segments of the normal human renal tubules and in the matrix of human kidney stones of all the common crystalline compositions.

A Crack Model of a Bone Cement Interface

1984 ◽  
Vol 106 (3) ◽  
pp. 235-243 ◽  
Author(s):  
J. P. Clech ◽  
L. M. Keer ◽  
J. L. Lewis
Keyword(s):  
Bone Cement ◽  
Cohesive Zone ◽  
Edge Crack ◽  
Crack Problem ◽  
Bimaterial Interface ◽  
Fracture Mechanisms ◽  
Homogeneous Material ◽  
Crack Model ◽  
Cement Interface ◽  
Crack Faces

This paper is concerned with the fracture mechanics of a bone-cement interface that includes a cohesive zone effect on the crack faces. This accounts for the experimentally observed strengthening mechanism due to the mechanical interlock between the crack faces. Edge crack models are developed where the cohesive zone is simulated by a continuous or a discrete distribution of linear or nonlinear springs. It is shown that the solution obtained by assuming a homogeneous material is fairly close to the exact solution for the bimaterial interface edge crack problem. On the basis of that approximation, the analysis is conducted for the problem of two interacting edge cracks, one at the interface, and the other one in the cement. The small crack that was observed to initiate in the cement, close to the bone-cement interface, does not affect much the mode I stress-intensity factor at the tip of the interface crack. However it may grow, leading to a catastrophic breakdown of the cement. The analysis and following discussion point out an interdependency between bone-cement interface strength and cement strength not previously appreciated. The suggested crack models provide a framework for quantifying the fracture mechanisms at the bone-cement interface.

scholarly journals Fast and Robust Orientation of Cryo-Electron Microscopy Images

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Guoliang Xu ◽  
Xia Wang ◽  
Ming Li ◽  
Zhucui Jing
Keyword(s):  
Sparse Matrix ◽  
Three Dimensional ◽  
Image Plane ◽  
Real Space ◽  
Computation Method ◽  
Common Line ◽  
The Matrix ◽  
Common Lines ◽  
The Common ◽  
Dimensional Object

AbstractWe present an efficient and reliable algorithm for determining the orientations of noisy images obtained fromprojections of a three-dimensional object. Based on the linear relationship among the common line vectors in one image plane, we construct a sparse matrix, and show that the coordinates of the common line vectors are the eigenvectors of the matrix with respect to the eigenvalue 1. The projection directions and in-plane rotation angles can be determined fromthese coordinates. A robust computation method of common lines in the real space using aweighted cross-correlation function is proposed to increase the robustness of the algorithm against the noise. A small number of good leading images, which have the maximal dissimilarity, are used to increase the reliability of orientations and improve the efficiency for determining the orientations of all the images. Numerical experiments show that the proposed algorithm is effective and efficient.

scholarly journals Differences in Wear and Material Integrity of NAO and Low-Steel Brake Pads under Severe Conditions

Materials ◽  
2021 ◽  
Vol 14 (19) ◽  
pp. 5531
Author(s):  
Edouard A. T. Davin ◽  
Anne-Lise Cristol ◽  
Arnaud Beaurain ◽  
Philippe Dufrénoy ◽  
Neomy Zaquen
Keyword(s):  
Heat Treatment ◽  
Gray Cast Iron ◽  
Organic Matrix ◽  
Third Body ◽  
Test Program ◽  
Brake Pads ◽  
The Matrix ◽  
Disc Configuration ◽  
Crack Faces ◽  
Reduced Scale

In this study, through severe reduced-scale braking tests, we investigate the wear and integrity of organic matrix brake pads against gray cast iron (GCI) discs. Two prototype pad materials are designed with the aim of representing a typical non-metal NAO and a low-steel (LS) formulation. The worn surfaces are observed with SEM. The toughness of the pad materials is tested at the raw state and after a heat treatment. During braking, the LS-GCI disc configuration produces heavy wear. The friction parts both keep their macroscopic integrity and wear appears to be homogeneous. The LS pad is mostly covered by a layer of solid oxidized steel. The NAO-GCI disc configuration wears dramatically and cannot reach the end of the test program. The NAO pad suffers many deep cracks. Compacted third body plateaus are scarce and the corresponding disc surface appears to be very heterogeneous. The pad materials both show similar strength at the raw state and similar weakening after heat treatment. However, the NAO material is much more brittle than the LS material in both states, which seems to favor the growth of cracks. The observations of crack faces suggest that long steel fibers in the LS material palliate the brittleness of the matrix, even after heat damage.

scholarly journals Common Factors in Fraction-Free Matrix Decompositions

2020 ◽  
Author(s):  
Johannes Middeke ◽  
David J. Jeffrey ◽  
Christoph Koutschan
Keyword(s):  
Normal Form ◽  
Common Factors ◽  
Reduction Process ◽  
Triangular Matrices ◽  
Specific Data ◽  
Matrix Decompositions ◽  
The Matrix ◽  
The Common

AbstractWe consider LU and QR matrix decompositions using exact computations. We show that fraction-free Gauß–Bareiss reduction leads to triangular matrices having a non-trivial number of common row factors. We identify two types of common factors: systematic and statistical. Systematic factors depend on the reduction process, independent of the data, while statistical factors depend on the specific data. We relate the existence of row factors in the LU decomposition to factors appearing in the Smith–Jacobson normal form of the matrix. For statistical factors, we identify some of the mechanisms that create them and give estimates of the frequency of their occurrence. Similar observations apply to the common factors in a fraction-free QR decomposition. Our conclusions are tested experimentally.

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