scholarly journals Dislocation patterning in a two-dimensional continuum theory of dislocations

2016 ◽  
Vol 93 (21) ◽  
Author(s):  
István Groma ◽  
Michael Zaiser ◽  
Péter Dusán Ispánovity
Keyword(s):  
Continuum Theory ◽  
Two Dimensional ◽  
Continuum Theory Of Dislocations

A General Continuum Theory With Microstructure for Wave Propagation in Elastic Laminated Composites

1974 ◽  
Vol 41 (1) ◽  
pp. 101-105 ◽  
Author(s):  
G. A. Hegemier ◽  
T. C. Bache
Keyword(s):  
Wave Propagation ◽  
Continuum Model ◽  
Laminated Composites ◽  
Continuum Theory ◽  
Velocity Spectrum ◽  
Two Dimensional ◽  
One Dimensional ◽  
General Continuum ◽  
Hierarchy Of Models ◽  
Dimensional Wave

A continuum theory with microstructure for wave propagation in laminated composites, proposed in previous works concerning propagation normal and parallel to the laminates, is extended herein to the general two-dimensional case. Continuum model construction is based upon an asymptotic scheme in which dominant signal wavelengths are assumed large compared to typical composite microdimensions. A hierarchy of models is defined by the order of truncation of the obtained asymptotic sequence. Particular attention is given to the lowest order dispersive theory. The phase velocity spectrum of the general theory is investigated for one-dimensional wave propagation at various propagation angles with respect to the laminates. Retention of all terms in the asymptotic sequence is found to yield the exact elasticity spectrum, while spectral collation of the lowest order dispersive theory with the first three modes of the exact theory gives excellent agreement.

TETRACRITICAL ISING MODEL COUPLED TO THE TWO-DIMENSIONAL GRAVITY

1992 ◽  
Vol 07 (19) ◽  
pp. 4487-4499
Author(s):  
ALOK KUMAR ◽  
JNANADEVA MAHARANA
Keyword(s):  
Ising Model ◽  
Central Charge ◽  
Continuum Theory ◽  
Two Dimensional ◽  
Operator Approach ◽  
Modular Invariant ◽  
Lax Operator ◽  
Dimensional Gravity ◽  
Ade Classification ◽  
The Continuum

Nonperturbative string equations are found explicitly for a central charge c=4/5 model coupled to the two-dimensional quantum gravity in the Lax operator approach proposed by Douglas. These string equations are used to derive the scaling behavior of several correlation functions on the sphere and it is shown that they agree with the calculations of the continuum theory. The model, identified with the diagonal modular invariant in the ADE classification, corresponds to the tetracritical Ising model.

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