Mathematical Model for Analysis of Near and Far Field Characteristics based on Equivalent Transformation

Author(s):  
A.V. Bashkirov ◽  
I.V. Ostroumov ◽  
V.V. Glotov ◽  
T.S. Glotova ◽  
S.N. Panychev ◽  
...  
2020 ◽  
Vol 49 (12) ◽  
pp. 118-137
Author(s):  
王拯洲 Zheng-zhou WANG ◽  
王力 Li WANG ◽  
谭萌 Meng TAN ◽  
段亚轩 Ya-xuan DUAN ◽  
王伟 Wei WANG ◽  
...  

2008 ◽  
Vol 399 ◽  
pp. 177-182
Author(s):  
Eduard Marius Craciun ◽  
Tomasz Sadowski

In this paper we study the behaviour of a Mode I crack in a pre-stressed wood composite material. A mathematical model is associated to the mechanical problem. Starting from the boundary, constitutive and far field conditions we obtain the representation of the incremental displacement, stress and strain fields using two complex potentials. Using numerical analysis we determine the critical value, which causes crack propagation and the direction of crack propagation in a particular case of a Pine wood composite.


PLoS ONE ◽  
2020 ◽  
Vol 15 (11) ◽  
pp. e0242011
Author(s):  
Jinzhang Jia ◽  
Bin Li ◽  
Dinglin Ke ◽  
Yumo Wu ◽  
Dan Zhao ◽  
...  

A ventilation network feature graph can directly and quantitatively represent the features of a ventilation network. To ensure the stability of airflow in a mine and improve ventilation system analysis, we propose a new algorithm to draw ventilation network feature graphs. The independent path method serves as the algorithm’s main frame, and an improved adaptive genetic algorithm is embedded so that the graph may be drawn better. A mathematical model based on the node adjacency matrix method for unidirectional circuit discrimination is constructed as the drawing algorithm may not be valid in such cases. By modifying the edge-seeking strategy, the improved depth-first search algorithm can be used to determine all of the paths in the ventilation network with unidirectional circuits, and the equivalent transformation method of network topology relations is used to draw the ventilation network feature graph. Through the analysis of the topological relation of a ventilation network, a simplified mathematical model is constructed, and network simplification technology makes the drawing concise and hierarchical. The rapid and intuitive drawing of the ventilation network feature graphs is significant for optimization of the ventilation system and day-to-day management.


2020 ◽  
Vol 49 (12) ◽  
pp. 118-137
Author(s):  
王拯洲 Zheng-zhou WANG ◽  
王力 Li WANG ◽  
谭萌 Meng TAN ◽  
段亚轩 Ya-xuan DUAN ◽  
王伟 Wei WANG ◽  
...  

2006 ◽  
Vol 306-308 ◽  
pp. 1229-1234 ◽  
Author(s):  
Hua Rui Liu ◽  
Jung Ju Lee

This paper is concerned with developing a mathematical model to describe the scattering of a plane wave obliquely incident on a piezoelectric hexagonal 6mm cylinder in a fluid. The mode is based on the normal-mode expansion method. Far-field form functions are obtained. The sensitivities of Rayleigh, Whispering Gallery, and guided wave resonances to perturbations in elastic and piezoelectric constants are discussed. The resonance scattering theory can be used for characterizing the sample in both transverse and axial directions.


Author(s):  
N. Bonnet ◽  
M. Troyon ◽  
P. Gallion

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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