Derivation of a Continuum Model for the Long-Range Elastic Interaction on Stepped Epitaxial Surfaces in $2+1$ Dimensions

2009 ◽  
Vol 69 (5) ◽  
pp. 1393-1414 ◽  
Author(s):  
Haoyun Xu ◽  
Yang Xiang
Keyword(s):  
Long Range ◽  
Continuum Model ◽  
Elastic Interaction

LONG–RANGE MAGNETIC ORDER IN La2NiO4+δ UNDER SMALL OXYGEN EXCESS

1993 ◽  
Vol 07 (01n03) ◽  
pp. 178-181
Author(s):  
YURY G. POGORELOV
Keyword(s):  
Long Range ◽  
Continuum Model ◽  
Magnetic Order ◽  
Oxide Compound ◽  
Range Magnetic Order ◽  
Magnetic Symmetry ◽  
Oxygen Excess ◽  
The Stability ◽  
Effect Of Oxygen ◽  
Long Range Magnetic Order

Within a continuum model based on the microscopic magnetic symmetry of Ni 2+ ion (spin S = 1) in the metal-oxide compound La 2 NiO 4+δ, a theoretical analysis is made of the stability of antiferromagnetic long-range order under the effect of oxygen interstitials at δ ≪ 1. It is shown that the Néel temperature dicreases significantly with growing δ though does not become zero, in contrast to that in the structurally isomorhic compound La 2 CuO 4+δ (but Cu 2+ spin S = 1/2).

A Numerical Scheme for Generalized Peierls-Nabarro Model of Dislocations Based on the Fast Multipole Method and Iterative Grid Redistribution

2015 ◽  
Vol 18 (5) ◽  
pp. 1282-1312 ◽  
Author(s):  
Aiyu Zhu ◽  
Congming Jin ◽  
Degang Zhao ◽  
Yang Xiang ◽  
Jingfang Huang
Keyword(s):  
Boundary Conditions ◽  
Long Range ◽  
Numerical Scheme ◽  
Fast Multipole Method ◽  
Dislocation Core ◽  
Elastic Interaction ◽  
Epitaxial Thin Films ◽  
Fast Multipole ◽  
Multipole Method ◽  
Grid Points

AbstractDislocations are line defects in crystalline materials. The Peierls-Nabarro models are hybrid models that incorporate atomic structure of dislocation core into continuum framework. In this paper, we present a numerical method for a generalized Peierls-Nabarro model for curved dislocations, based on the fast multipole method and the iterative grid redistribution. The fast multipole method enables the calculation of the long-range elastic interaction within operations that scale linearly with the total number of grid points. The iterative grid redistribution places more mesh nodes in the regions around the dislocations than in the rest of the domain, thus increases the accuracy and efficiency. This numerical scheme improves the available numerical methods in the literature in which the long-range elastic interactions are calculated directly from summations in the physical domains; and is more flexible to handle problems with general boundary conditions compared with the previous FFT based method which applies only under periodic boundary conditions. Numerical examples using this method on the core structures of dislocations in Al and Cu and in epitaxial thin films are presented.

Continuum Model for Ion Gating in Cochlear Hair Cells

1997 ◽  
Vol 50 (11S) ◽  
pp. S210-S215
Author(s):  
Charles R. Steele
Keyword(s):  
Flow Rate ◽  
Continuum Model ◽  
Mechanical Response ◽  
Elastic Interaction ◽  
Physical Parameters ◽  
Cochlear Hair Cells ◽  
Ion Flow ◽  
Basic Fluid ◽  
Spring Force ◽  
Flow Through

The details of ion flow in cells are important for the macro mechanical response of sensory organs, as in the inner ear of vertebrates. A continuum model for the flow of an ionized fluid through a pore in an elastic wall is considered. With this, the electro-mechanical behavior is readily computed. An interesting result is that two equilibria exist for the flow through a pore with a soft elastic entrance region. At one equilibrium point, the entrance opening is more restricted and the corresponding ion flow rate is much lower. Thus it appears that the tendency of ion channels to pop from an open to a closed state may be a consequence of basic fluid-elastic interaction. With the simple continuum model, various effects can be explored. One is the presence of an external spring force, corresponding to the force of the tip fiber between stereocilia. Another is the effect of an adjacent membrane and pore. The input physical parameters are reasonable and the results for flow rate are consistent with experimental measurements.

Signatures of long-range elastic interaction in textured materials

2000 ◽  
Vol 62 (9) ◽  
pp. 5265-5269
Author(s):  
T. Lookman ◽  
A. Saxena ◽  
D. A. Dimitrov ◽  
A. R. Bishop ◽  
R. C. Albers
Keyword(s):  
Long Range ◽  
Elastic Interaction ◽  
Textured Materials

scholarly journals Equivalent plastic strain gradient plasticity with grain boundary hardening and comparison to discrete dislocation dynamics

2015 ◽  
Vol 471 (2184) ◽  
pp. 20150388 ◽  
Author(s):  
E. Bayerschen ◽  
M. Stricker ◽  
S. Wulfinghoff ◽  
D. Weygand ◽  
T. Böhlke
Keyword(s):  
Plastic Strain ◽  
Yield Strength ◽  
Grain Boundary ◽  
Continuum Model ◽  
Equivalent Plastic Strain ◽  
Elastic Interaction ◽  
Dislocation Dynamics ◽  
Discrete Dislocation Dynamics ◽  
Discrete Dislocation ◽  
The Continuum

The gradient crystal plasticity framework of Wulfinghoff et al. (Wulfinghoff et al. 2013 Int. J. Plasticity 51, 33–46. ( doi:10.1016/j.ijplas.2013.07.001 )), incorporating an equivalent plastic strain γ eq and grain boundary (GB) yielding, is extended with GB hardening. By comparison to averaged results from many discrete dislocation dynamics (DDD) simulations of an aluminium-type tricrystal under tensile loading, the new hardening parameter of the continuum model is calibrated. Although the GBs in the discrete simulations are impenetrable, an infinite GB yield strength, corresponding to microhard GB conditions, is not applicable in the continuum model. A combination of a finite GB yield strength with an isotropic bulk Voce hardening relation alone also fails to model the plastic strain profiles obtained by DDD. Instead, a finite GB yield strength in combination with GB hardening depending on the equivalent plastic strain at the GBs is shown to give a better agreement to DDD results. The differences in the plastic strain profiles obtained in DDD simulations by using different orientations of the central grain could not be captured. This indicates that the misorientation-dependent elastic interaction of dislocations reaching over the GBs should also be included in the continuum model.

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