Mathematical Model of Fan-Head Shear Rupture Mechanism

2013 ◽  
Vol 592-593 ◽  
pp. 121-124 ◽  
Author(s):  
Boris Tarasov ◽  
Mikhail A. Guzev
Keyword(s):  
Mathematical Model ◽  
Failure Process ◽  
Shear Resistance ◽  
Point Of View ◽  
The Self ◽  
The Core ◽  
Frictional Strength ◽  
Shear Rupture ◽  
Intact Rock Mass ◽  
Rupture Mechanism

Today frictional shear resistance along pre-existing ruptures (faults) is considered as the lower limit on rock shear strength for confined conditions. The paper proposes a mathematical model of recently identified shear rupture mechanism which can provide propagation of faults through the highly confined intact rock mass at shear stress levels significantly less than frictional strength of pre-existing faults. The model demonstrates that due to the self-unbalancing structure of the rupture head, representing the core of this mechanism, the failure process caused by the mechanism is always spontaneous and violent. It allows a novel point of view for understanding the nature of spontaneous failure processes including earthquakes.

Fan-Hinged Shear as a Unique Mechanism of Dynamic Shear Ruptures

2016 ◽  
Vol 258 ◽  
pp. 165-168
Author(s):  
Boris Tarasov ◽  
Mikhail Guzev ◽  
Vladimir Sadovskiy ◽  
Alexander Losev
Keyword(s):  
Mathematical Model ◽  
Shear Resistance ◽  
Rupture Propagation ◽  
Dynamic Shear ◽  
Tensile Cracks ◽  
Frictional Strength ◽  
Shear Rupture ◽  
Rupture Mechanism ◽  
Unique Mechanism ◽  
Low Shear

Recently a new fan-hinged shear rupture mechanism has been identified as a unique mechanism of dynamic shear ruptures. In the fan-mechanism, the shear rupture propagation is driven by a fan-shaped rupture head consisting of an echelon of intercrack (domino-like) blocks formed due to the consecutive creation of small tensile cracks in the rupture tip. The fan-structure propagates through the intact material as a wave and has a number of extraordinary features, one of which is extremely low shear resistance of the rupture head (below the frictional strength). Here we present a mathematical model elucidating the principles of this new mechanism. The model will support comprehensive studies of unique features of the discovered phenomenon.

On the displacements of the contours of the optic-electronic space images. Mathematical modeling of displacement

2017 ◽  
Vol 992 (4) ◽  
pp. 32-38 ◽  
Author(s):  
E.G. Voronin
Keyword(s):  
Mathematical Modeling ◽  
Remote Sensing ◽  
Mathematical Model ◽  
Point Of View ◽  
Design Features ◽  
Space Images ◽  
Electronic Imaging ◽  
Measuring Accuracy ◽  
Physical Laws

The article opens a cycle of three consecutive publications dedicated to the phenomenon of the displacement of the same points in overlapping scans obtained adjacent CCD matrices with opto-electronic imagery. This phenomenon was noticed by other authors, but the proposed explanation for the origin of displacements and the resulting estimates are insufficient, and developed their solutions seem controversial from the point of view of recovery of the measuring accuracy of opticalelectronic space images, determined by the physical laws of their formation. In the first article the mathematical modeling of the expected displacements based on the design features of a scanning opto-electronic imaging equipment. It is shown that actual bias cannot be forecast, because they include additional terms, which may be gross, systematic and random values. The proposed algorithm for computing the most probable values of the additional displacement and ways to address some of the systematic components of these displacements in a mathematical model of optical-electronic remote sensing.

Pathways to Success Through Identity-Based Motivation

2015 ◽  
Author(s):  
Daphna Oyserman
Keyword(s):  
The Self ◽  
The Core ◽  
Very Young Children ◽  
The Future ◽  
Identity Based ◽  
Future Self ◽  
Fidelity Measures ◽  
The Individual ◽  
Taking Action ◽  
Minimal Effort

Everyone can imagine their future self, even very young children, and this future self is usually positive and education-linked. To make progress toward an aspired future or away from a feared future requires people to plan and take action. Unfortunately, most people often start too late and commit minimal effort to ineffective strategies that lead their attention elsewhere. As a result, their high hopes and earnest resolutions often fall short. In Pathways to Success Through Identity-Based Motivation Daphna Oyserman focuses on situational constraints and affordances that trigger or impede taking action. Focusing on when the future-self matters and how to reduce the shortfall between the self that one aspires to become and the outcomes that one actually attains, Oyserman introduces the reader to the core theoretical framework of identity-based motivation (IBM) theory. IBM theory is the prediction that people prefer to act in identity-congruent ways but that the identity-to-behavior link is opaque for a number of reasons (the future feels far away, difficulty of working on goals is misinterpreted, and strategies for attaining goals do not feel identity-congruent). Oyserman's book goes on to also include the stakes and how the importance of education comes into play as it improves the lives of the individual, their family, and their society. The framework of IBM theory and how to achieve it is broken down into three parts: how to translate identity-based motivation into a practical intervention, an outline of the intervention, and empirical evidence that it works. In addition, the book also includes an implementation manual and fidelity measures for educators utilizing this book to intervene for the improvement of academic outcomes.

scholarly journals Influence of Salt on the Self-Organization in Solutions of Star-Shaped Poly-2-alkyl-2-oxazoline and Poly-2-alkyl-2-oxazine on Heating

Polymers ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1152
Author(s):  
Tatyana Kirila ◽  
Anna Smirnova ◽  
Alla Razina ◽  
Andrey Tenkovtsev ◽  
Alexander Filippov
Keyword(s):  
Phase Separation ◽  
Salt Concentration ◽  
Monomer Unit ◽  
Salt Content ◽  
The Self ◽  
Self Organization ◽  
Phase Separation Temperature ◽  
The Core ◽  
Separation Temperature ◽  
Water Salt

The water–salt solutions of star-shaped six-arm poly-2-alkyl-2-oxazines and poly-2-alkyl-2-oxazolines were studied by light scattering and turbidimetry. The core was hexaaza[26]orthoparacyclophane and the arms were poly-2-ethyl-2-oxazine, poly-2-isopropyl-2-oxazine, poly-2-ethyl-2-oxazoline, and poly-2-isopropyl-2-oxazoline. NaCl and N-methylpyridinium p-toluenesulfonate were used as salts. Their concentration varied from 0–0.154 M. On heating, a phase transition was observed in all studied solutions. It was found that the effect of salt on the thermosensitivity of the investigated stars depends on the structure of the salt and polymer and on the salt content in the solution. The phase separation temperature decreased with an increase in the hydrophobicity of the polymers, which is caused by both a growth of the side radical size and an elongation of the monomer unit. For NaCl solutions, the phase separation temperature monotonically decreased with growth of salt concentration. In solutions with methylpyridinium p-toluenesulfonate, the dependence of the phase separation temperature on the salt concentration was non-monotonic with minimum at salt concentration corresponding to one salt molecule per one arm of a polymer star. Poly-2-alkyl-2-oxazine and poly-2-alkyl-2-oxazoline stars with a hexaaza[26]orthoparacyclophane core are more sensitive to the presence of salt in solution than the similar stars with a calix[n]arene branching center.

Mathematical model of the rupture mechanism of intracranial saccular aneurysms through daughter aneurysm formation and growth

2005 ◽  
Vol 27 (5) ◽  
pp. 459-465 ◽  
Author(s):  
Hui Meng ◽  
Yixiang Feng ◽  
Scott H. Woodward ◽  
Bernard R. Bendok ◽  
Ricardo A. Hanel ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Aneurysm Formation ◽  
Rupture Mechanism ◽  
Saccular Aneurysms

Kierkegaard, Metaphysics, and Love

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
George Pattison
Keyword(s):  
Sense Of Self ◽  
The Self ◽  
The Other ◽  
Gabriel Marcel ◽  
The Core ◽  
The Dead ◽  
Alternative Reading ◽  
The Way

AbstractNoting Heidegger’s critique of Kierkegaard’s way of relating time and eternity, the paper offers an alternative reading of Kierkegaard that suggests Heidegger has overlooked crucial elements in the Kierkegaardian account. Gabriel Marcel and Sharon Krishek are used to counter Heidegger’s minimizing of the deaths of others and to show how the deaths of others may become integral to our sense of self. This prepares the way for revisiting Kierkegaard’s discourse on the work of love in remembering the dead. Against the criticism that this reveals the absence of the other in Kierkegaardian love, the paper argues that, on the contrary, it shows how Kierkegaard conceives the self as inseparable from the core relationships of love that, despite of death, constitute it as the self that it is.

A note on design-based versus model-based variance estimation in stereology

2002 ◽  
Vol 34 (03) ◽  
pp. 484-490 ◽  
Author(s):  
Asger Hobolth ◽  
Eva B. Vedel Jensen
Keyword(s):  
Mathematical Model ◽  
Original Problem ◽  
Variance Estimation ◽  
Point Of View ◽  
Systematic Sampling ◽  
Variance Estimator ◽  
Shape Model ◽  
Model Based ◽  
Versus Model ◽  
Special Case

Recently, systematic sampling on the circle and the sphere has been studied by Gual-Arnau and Cruz-Orive (2000) from a design-based point of view. In this note, it is shown that their mathematical model for the covariogram is, in a model-based statistical setting, a special case of the p-order shape model suggested by Hobolth, Pedersen and Jensen (2000) and Hobolth, Kent and Dryden (2002) for planar objects without landmarks. Benefits of this observation include an alternative variance estimator, applicable in the original problem of systematic sampling. In a wider perspective, the paper contributes to the discussion concerning design-based versus model-based stereology.

Effective Properties of Superconducting and Superfluid Composites

1998 ◽  
Vol 12 (29n31) ◽  
pp. 3063-3073 ◽  
Author(s):  
Leonid Berlyand
Keyword(s):  
Mathematical Model ◽  
Linear Problem ◽  
Effective Properties ◽  
Point Of View ◽  
Periodicity Cell ◽  
Unit Size ◽  
Composite Media ◽  
Homogenization Procedure

We consider a mathematical model which describes an ideal superfluid with a large number of thin insulating rods and an ideal superconductor reinforced by such rods. We suggest a homogenization procedure for calculating effective properties of both composite media. From the numerical point of view the procedure amounts to solving a linear problem in a periodicity cell of unit size.

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