scholarly journals Matrix integrals & finite holography

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Dionysios Anninos ◽  
Beatrix Mühlmann
Keyword(s):  
Critical Exponents ◽  
Continuum Theory ◽  
Point Of View ◽  
Leading Order ◽  
Minimal Models ◽  
Point Evaluation ◽  
Brst Cohomology ◽  
Matrix Integrals ◽  
The Matrix ◽  
The Continuum

Abstract We explore the conjectured duality between a class of large N matrix integrals, known as multicritical matrix integrals (MMI), and the series (2m − 1, 2) of non-unitary minimal models on a fluctuating background. We match the critical exponents of the leading order planar expansion of MMI, to those of the continuum theory on an S2 topology. From the MMI perspective this is done both through a multi-vertex diagrammatic expansion, thereby revealing novel combinatorial expressions, as well as through a systematic saddle point evaluation of the matrix integral as a function of its parameters. From the continuum point of view the corresponding critical exponents are obtained upon computing the partition function in the presence of a given conformal primary. Further to this, we elaborate on a Hilbert space of the continuum theory, and the putative finiteness thereof, on both an S2 and a T2 topology using BRST cohomology considerations. Matrix integrals support this finiteness.

scholarly journals Effective Action and Measure in Matrix Model of IIB Superstrings

1997 ◽  
Vol 12 (31) ◽  
pp. 2331-2340 ◽  
Author(s):  
L. Chekhov ◽  
K. Zarembo
Keyword(s):  
Matrix Model ◽  
Effective Action ◽  
Continuum Limit ◽  
Auxiliary Field ◽  
Large N ◽  
The Matrix ◽  
Reparametrization Invariance ◽  
The Continuum ◽  
Induced Measure

We calculate an effective action and measure induced by the integration over the auxiliary field in the matrix model recently proposed to describe IIB superstrings. It is shown that the measure of integration over the auxiliary matrix is uniquely determined by locality and reparametrization invariance of the resulting effective action. The large-N limit of the induced measure for string coordinates is discussed in detail. It is found to be ultralocal and, thus, is possibly irrelevant in the continuum limit. The model of the GKM type is considered in relation to the effective action problem.

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

scholarly journals The matrix element method at next-to-leading order

2012 ◽  
Vol 2012 (11) ◽  
Author(s):  
John M. Campbell ◽  
Walter T. Giele ◽  
Ciaran Williams
Keyword(s):  
Matrix Element ◽  
Leading Order ◽  
Matrix Element Method ◽  
The Matrix ◽  
Element Method

On the Properties of Gelatin-Dye Phosphors and the Continuum Theory of Szent-Gyorgyi

Science ◽  
1948 ◽  
Vol 107 (2787) ◽  
pp. 566-567
Author(s):  
Michael Kasha
Keyword(s):  
Continuum Theory ◽  
The Continuum

Fibre-Matrix Interface Development during High Temperature Exposition of Long Fibre Reinforced SiOC Matrix

2013 ◽  
Vol 592-593 ◽  
pp. 401-404
Author(s):  
Zdeněk Chlup ◽  
Martin Černý ◽  
Adam Strachota ◽  
Martina Halasova ◽  
Ivo Dlouhý
Keyword(s):  
High Temperature ◽  
Crack Formation ◽  
Fracture Behaviour ◽  
Point Of View ◽  
Reinforced Composites ◽  
Matrix Interface ◽  
Significant Damage ◽  
The Matrix ◽  
Fibre Matrix ◽  
Fibre Reinforced Composites

The fracture behaviour of long fibre reinforced composites is predetermined mainly by properties of fibre-matrix interface. The matrix prepared by pyrolysis of polysiloxane resin possesses ability to resist high temperatures without significant damage under oxidising atmosphere. The application is therefore limited by fibres and possible changes in the fibre matrix interface. The study of development of interface during high temperature exposition is the main aim of this contribution. Application of various techniques as FIB, GIS, TEM, XRD allowed to monitor microstructural changes in the interface of selected places without additional damage caused by preparation. Additionally, it was possible to obtain information about damage, the crack formation, caused by the heat treatment from the fracture mechanics point of view.

Ferronematics: On the development of the continuum theory approach

1990 ◽  
Vol 85 (1-3) ◽  
pp. 74-76 ◽  
Author(s):  
S.V. Burylov ◽  
Yu.L. Raikher
Keyword(s):  
Continuum Theory ◽  
Theory Approach ◽  
The Continuum

scholarly journals MYSTERY AS A META-GENRE IN THE DRAMA OF THE TWENTIETH CENTURY

2021 ◽  
pp. 18-26
Author(s):  
K. Oliinyk
Keyword(s):  
Twentieth Century ◽  
World Order ◽  
Semantic Content ◽  
Point Of View ◽  
Dramatic Works ◽  
Life And Death ◽  
The Matrix ◽  
General Feeling ◽  
The Aesthetic ◽  
Definition Of

The article examines the specificity of existence of the renewed mystery genre as a meta genre in the twentieth century. The main literary study views on the definition of ancient and medieval / Christian ritual mystery are analyzed. The beginning of the twentieth century was full of a general feeling of catastrophe and tragic hopelessness. In artistic terms, the consequence of this was the activation of Christian issues, motives, plots, religious genres (miracles, morality and mystery). The most universal from the point of view of the ideological message and content for the writers of the twentieth century. was the matrix of the medieval mystery, which retained the ritual basis in its primary structure. This made it possible for the multilevel organization of the action and the space for it. The genre of medieval mystery is being modified, it ceases to be a purely form of religious action and acquires the quality of a meta genre. There is a transition from the religious sphere to the secular one, and the aesthetic one is replacing the didactic load. Mystery begins to exist on the edge of genres as a synthetic formation, showing intentions to “help” other genres. A large number of dramatic works of the twentieth century. ("Forest Song" by Lesia Ukrainka, "Iconostasis of Ukraine" by Vіra Vovk) comes close to the mystery, using its archetypal components: the ideas of faith in the absolute beginning, governing the eternal rotation of life and death, world order and harmony, death and rebirth, transformations of the human soul, chosenness and initiation associated with trials, sacrifice, deepening into mysticism. Such works are a certain imitation with elements of mythological or religious subjects. So, the twentieth century, actualizes a certain involvement of the semantic content of dramas to the mysteries, bringing the mystery to the level of the meta genre.

Free Energy of Granular Materials in Static Equilibrium

1979 ◽  
Vol 46 (4) ◽  
pp. 944-945 ◽  
Author(s):  
M. Shahinpoor ◽  
G. Ahmadi
Keyword(s):  
Free Energy ◽  
Granular Materials ◽  
Continuum Theory ◽  
Gravitational Effect ◽  
Experimental Results ◽  
Static Equilibrium ◽  
The Continuum

We employ the continuum theory of granular materials due to Goodman and Cowin and some experimental results due to P. G. Nutting to arrive at a functional from for the free energy of granular materials in static equilibrium. The results obtained indicate the dominance of gravitational effect, modify and enlarge the results previously obtained by J. T. Jenkins.

Dislocation Threading Through an Epitaxial Film: an Analysis Based on the Peierls-Nabarro Concept

1993 ◽  
Vol 308 ◽  
Author(s):  
G. E. Beltz ◽  
L. B. Freund
Keyword(s):  
Critical Thickness ◽  
Epitaxial Film ◽  
Continuum Theory ◽  
Dislocation Core ◽  
Critical Layer Thickness ◽  
Cutoff Parameter ◽  
Mismatch Strain ◽  
Realistic Description ◽  
Cutoff Radius ◽  
The Continuum

ABSTRACTThe Peierls-Nabarro theory of crystal dislocations is applied to estimate the critical thickness of a strained layer bonded to a substrate for a given mismatch strain. Previous analyses were based on the continuum theory of elastic dislocations, and hence depended on the artificial core cutoff parameter r0. The Peierls-Nabarro theory makes use of an interplanar shear law, which leads to a more realistic description of the stresses and displacements in the vicinity of a dislocation core, thus eliminating the need for the core cutoff parameter. The dependence of the critical layer thickness on the mismatch strain in films with a diamond cubic lattice is found to be similar to that predicted by the continuum elastic dislocation theory, provided that a core cutoff radius equal to about one-tenth the Burgers displacement is used.

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