Periodic measures of impulsive stochastic Hopfield-type lattice systems

2021 ◽  
pp. 1-17
Author(s):  
Yusen Lin ◽  
Dingshi Li
Keyword(s):  
Lattice Systems ◽  
Type Lattice

scholarly journals Spreading speeds of KPP-type lattice systems in heterogeneous media

2018 ◽  
Vol 22 (01) ◽  
pp. 1850083 ◽  
Author(s):  
Xing Liang ◽  
Tao Zhou
Keyword(s):  
Heterogeneous Media ◽  
Diffusion Rate ◽  
Reaction Diffusion ◽  
Lattice System ◽  
Reaction Diffusion Equations ◽  
Almost Periodic ◽  
Spreading Speeds ◽  
Lattice Systems ◽  
One Dimensional ◽  
Type Lattice

In this paper, we investigated spreading properties of the solutions of the Kolmogorov–Petrovsky–Piskunov–type (KPP-type) lattice system [Formula: see text] Motivated by the work in [H. Berestycki and G. Nadin, Spreading speeds for one-dimensional monostable reaction–diffusion equations, J. Math. Phys. 53(11) (2012) 115619, 23 pp.], we develop some new discrete Harnack-type estimates and homogenization techniques for the lattice system [Formula: see text] to construct two speeds [Formula: see text] such that [Formula: see text] for any [Formula: see text], and [Formula: see text] for any [Formula: see text]. These speeds are characterized by two generalized principal eigenvalues of the linearized systems of [Formula: see text]. In particular, we derive the exact spreading speed when the coefficients are random stationary ergodic or almost periodic (where [Formula: see text]). Finally, in the case where [Formula: see text] is almost periodic in [Formula: see text] and the diffusion rate [Formula: see text] is independent of [Formula: see text], we show that the spreading speeds in the positive and negative directions are identical even if [Formula: see text] is not invariant with respect to the reflection.

Direct structure images of 30° partial dislocation cores in silicon

1987 ◽  
Vol 45 ◽  
pp. 242-243
Author(s):  
J. C. Barry ◽  
H. Alexander
Keyword(s):  
Dislocation Core ◽  
Preparation Technique ◽  
Burgers Vector ◽  
Vector Type ◽  
Sample Preparation Technique ◽  
Lattice Images ◽  
Dislocation Core Structure ◽  
Type Lattice ◽  
Direct Inspection

Dislocations in silicon produced by plastic deformation are generally dissociated into partials. 60° dislocations (Burgers vector type 1/2[101]) are dissociated into 30°(Burgers vector type 1/6[211]) and 90°(Burgers vector type 1/6[112]) dislocations. The 30° partials may be either of “glide” or “shuffle” type. Lattice images of the 30° dislocation have been obtained with a JEM 100B, and with a JEM 200Cx. In the aforementioned experiments a reasonable but imperfect match was obtained with calculated images for the “glide” model. In the present experiment direct structure images of 30° dislocation cores have been obtained with a JEOL 4000EX. It is possible to deduce the 30° dislocation core structure by direct inspection of the images. Dislocations were produced by compression of single crystal Si (sample preparation technique described in Alexander et al.).

Elastic scattering from cubic lattice systems with paracrystalline distortion. II

1990 ◽  
Vol 41 (6) ◽  
pp. 3854-3856 ◽  
Author(s):  
Hideki Matsuoka ◽  
Hideaki Tanaka ◽  
Norio Iizuka ◽  
Takeji Hashimoto ◽  
Norio Ise
Keyword(s):  
Elastic Scattering ◽  
Lattice Systems ◽  
Cubic Lattice

Transition from particlelike to wavelike behavior for an electron in one-dimensional nonuniform lattice systems

2016 ◽  
Vol 94 (3) ◽  
Author(s):  
Longyan Gong ◽  
Bingjie Xue ◽  
Wenjia Li ◽  
Weiwen Cheng ◽  
Shengmei Zhao
Keyword(s):  
Lattice Systems ◽  
One Dimensional
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