scholarly journals Primitive model electrolytes in the near and far field: Decay lengths from DFT and simulations

2021 ◽  
Vol 154 (12) ◽  
pp. 124504
Author(s):  
P. Cats ◽  
R. Evans ◽  
A. Härtel ◽  
R. van Roij
Keyword(s):  
Far Field ◽  
Primitive Model ◽  
Field Decay

scholarly journals Analysis of an atomistic model for anti-plane fracture

2019 ◽  
Vol 29 (13) ◽  
pp. 2469-2521
Author(s):  
Maciej Buze ◽  
Thomas Hudson ◽  
Christoph Ortner
Keyword(s):  
Pair Potential ◽  
Square Lattice ◽  
Far Field ◽  
Decay Estimates ◽  
Nearest Neighbour ◽  
Stability Of Solutions ◽  
Local Uniqueness ◽  
Field Decay ◽  
Interatomic Pair Potential ◽  
Crack Defect

We develop a model for an anti-plane crack defect posed on a square lattice under an interatomic pair-potential with nearest-neighbour interactions. In particular, we establish existence, local uniqueness and stability of solutions for small loading parameters and further prove qualitatively sharp far-field decay estimates. The latter requires establishing decay estimates for the corresponding lattice Green’s function, which are of independent interest.

scholarly journals Global well-posedness to the Cauchy problem of 2D inhomogeneous incompressible magnetic Bénard equations with large initial data and vacuum

2021 ◽  
Vol 6 (11) ◽  
pp. 12085-12103
Author(s):  
Zhongying Liu ◽  
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Initial Density ◽  
Well Posedness ◽  
Far Field ◽  
Large Initial Data ◽  
Global Strong Solution ◽  
Vacuum States ◽  
The Cauchy Problem ◽  
Field Decay

<abstract><p>In this paper, we are concerned with the Cauchy problem of inhomogeneous incompressible magnetic Bénard equations with vacuum as far-field density in $ \Bbb R^2 $. We prove that if the initial density and magnetic field decay not too slowly at infinity, the system admits a unique global strong solution. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states and even has compact support. Moreover, we extend the result of [16, 17] to the global one.</p></abstract>

Emergence of bi-cluster flocking for the Cucker–Smale model

2016 ◽  
Vol 26 (06) ◽  
pp. 1191-1218 ◽  
Author(s):  
Junghee Cho ◽  
Seung-Yeal Ha ◽  
Feimin Huang ◽  
Chunyin Jin ◽  
Dongnam Ko
Keyword(s):  
Lower Bound ◽  
Asymptotic Convergence ◽  
Far Field ◽  
Differential Inequalities ◽  
Local Velocity ◽  
Velocity Fluctuations ◽  
Spatial Fluctuations ◽  
The Difference ◽  
Field Decay ◽  
Velocity Averages

We present the mathematical analysis of bi-cluster flocking phenomenon for the short-ranged Cucker–Smale model with some well-prepared initial data. For this, we derive a system of differential inequalities for the functionals measuring the local spatial and velocity fluctuations and differences of local velocity averages, and then estimate the upper bound of spatial fluctuations and the lower bound of the difference between local velocity averages. We explicitly present an admissible class of initial configurations leading to the asymptotic emergence of bi-cluster flocking phenomenon. Unlike global flocking (a mono-cluster flocking configuration in velocity), where the convergence rate is always exponential, the asymptotic convergence to bi-cluster flocking configurations is affected by the far-field decay rate of communication weights so that it can be algebraic.

Possible applications of fraunhofer holography in high resolution electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 222-223 ◽  
Author(s):  
N. Bonnet ◽  
M. Troyon ◽  
P. Gallion
Keyword(s):  
Electron Microscopy ◽  
High Resolution ◽  
Transfer Function ◽  
Radiation Damage ◽  
High Resolution Electron Microscopy ◽  
Far Field ◽  
Field Region ◽  
Crystalline Materials ◽  
Resolution Electron ◽  
The Ideal

Two main problems in high resolution electron microscopy are first, the existence of gaps in the transfer function, and then the difficulty to find complex amplitude of the diffracted wawe from registered intensity. The solution of this second problem is in most cases only intended by the realization of several micrographs in different conditions (defocusing distance, illuminating angle, complementary objective apertures…) which can lead to severe problems of contamination or radiation damage for certain specimens.Fraunhofer holography can in principle solve both problems stated above (1,2). The microscope objective is strongly defocused (far-field region) so that the two diffracted beams do not interfere. The ideal transfer function after reconstruction is then unity and the twin image do not overlap on the reconstructed one.We show some applications of the method and results of preliminary tests.Possible application to the study of cavitiesSmall voids (or gas-filled bubbles) created by irradiation in crystalline materials can be observed near the Scherzer focus, but it is then difficult to extract other informations than the approximated size.

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