Brittle Fracture: The Continuum Approach

2006 ◽  
pp. 290-364
Keyword(s):  
Brittle Fracture ◽  
Continuum Approach ◽  
The Continuum

Confirming the continuum theory of dynamic brittle fracture for fast cracks

Nature ◽  
10.1038/16891 ◽  
1999 ◽  
Vol 397 (6717) ◽  
pp. 333-335 ◽  
Author(s):  
Eran Sharon ◽  
Jay Fineberg
Keyword(s):  
Brittle Fracture ◽  
Continuum Theory ◽  
Dynamic Brittle Fracture ◽  
The Continuum

On the range of validity of the continuum approach for nonlinear diffusional mixing of multilayers

1999 ◽  
Vol 79 (8) ◽  
pp. 1757-1768 ◽  
Author(s):  
Z. ERDELYI, D. L. BEKE, P. NEMES, G. A
Keyword(s):  
Continuum Approach ◽  
The Continuum

scholarly journals Liouville quantum gravity — holography, JT and matrices

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Thomas G. Mertens ◽  
Gustavo J. Turiaci
Keyword(s):  
String Theory ◽  
Generating Functions ◽  
Preliminary Evidence ◽  
Quantum Deformation ◽  
Dilaton Gravity ◽  
Continuum Approach ◽  
Genus Zero ◽  
Explicit Formulas ◽  
Liouville Gravity ◽  
The Continuum

Abstract We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries. We find explicit formulas describing the gravitational dressing of bulk and boundary correlators in the disk. Their structure has a striking resemblance with observables in 2d BF (plus a boundary term), associated to a quantum deformation of SL(2, ℝ), a connection we develop in some detail. For the case of the (2, p) minimal string theory, we compare and match the results from the continuum approach with a matrix model calculation, and verify that in the large p limit the correlators match with Jackiw-Teitelboim gravity. We consider multi-boundary amplitudes that we write in terms of gluing bulk one-point functions using a quantum deformation of the Weil-Petersson volumes and gluing measures. Generating functions for genus zero Weil-Petersson volumes are derived, taking the large p limit. Finally, we present preliminary evidence that the bulk theory can be interpreted as a 2d dilaton gravity model with a sinh Φ dilaton potential.

scholarly journals VERIFICATION OF ROCK FALLS MODEL USING THE CONTINUUM APPROACH

2018 ◽  
Vol 10 (1) ◽  
pp. 7-13
Author(s):  
Evgeny KAMENETSKY ◽  
◽  
Natalya ORLOVA ◽  
Keyword(s):  
Continuum Approach ◽  
Rock Falls ◽  
The Continuum

An Attempt to Provide a Unified Treatment of Tribology Through Load Carrying Capacity, Transport, and Continuum Mechanics

1980 ◽  
Vol 102 (2) ◽  
pp. 153-164 ◽  
Author(s):  
M. Godet ◽  
D. Play ◽  
D. Berthe
Keyword(s):  
High Temperature ◽  
Continuum Mechanics ◽  
Carrying Capacity ◽  
Load Carrying Capacity ◽  
Third Body ◽  
Continuum Approach ◽  
Load Carrying ◽  
Solid Liquid ◽  
Film Lubrication ◽  
The Continuum

This paper attempts to give a unified treatment of experiments obtained with solid, liquid and boundary lubricants, different plastics, high temperature steels and elastomers. The argument is centered around third body role, load-carrying capacity, transport and continuum mechanics. This study suggests that an extension to general tribology of the continuum approach used in full film lubrication could be profitable.

Delusions: The Continuum Versus Category Debate

2003 ◽  
Vol 37 (5) ◽  
pp. 505-511 ◽  
Author(s):  
Richard Mullen
Keyword(s):  
Literature Review ◽  
Continuum Hypothesis ◽  
False Belief ◽  
Continuum Approach ◽  
Medline Search ◽  
High Prevalence ◽  
Belief Content ◽  
The Continuum ◽  
Versus Category

Objective: In this paper I critically review the recently developed idea that delusions are best considered as part of a continuum along with more ordinary human beliefs. Method: A literature review of the area was guided by a Medline search, and supplemented with material already known to the author. Claims that recent research supports the continuum hypothesis is critiqued. Results: The argument and evidence advanced for the continuum approach to delusions depends largely on: (i) inadequacies of prevailing definitions of delusion, particularly in the light of evidence that delusional conviction is often not absolute; and (ii) the high prevalence of unusual beliefs in community populations. To the extent that the delusion construct contains much in addition to conviction and unusual or false belief content, the continuity approach is weak. The category of delusions continues to have some validity. Conclusion: Both categorical and continuous approaches to delusions have validity that depends at any time on our immediate clinical or scientific needs. No definitive resolution of the category versus continuum debate is likely to emerge.

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