A One-Dimensional Particle in a Potential Field

Author(s):  
D. M. Gitman ◽  
I. V. Tyutin ◽  
B. L. Voronov
Author(s):  
H. Seifert ◽  
W. Borchardt-Ott

AbstractThe crystallographical expectation of different behaviour of crystals with asymmetric molecules against the optical antipodes of quartz was not exactly proved up to date. The weak asymmetry of the potential field of the crystal surfaces was probably the cause. We awaited a distinct effect from a substance consisting of large complex molecules like vitamin BThe epitaxial effect is extremely selective. The orientation of the vitamin crystals was splendidly positive upon the polished L-quartz surfaces activated by etching with HF, never upon R quartz. There were found and described 18 laws of orientation of the vitamin crystals upon the faces (101̄0), (1̄1̄20), (112̄0), (101̄1), (011̄1), (0001). The laws could be formulated as one-dimensional structure analogies.The structural interpretation of the molecular kinetics, i.e. adsorption, formation of H bridges between both active groups and seed formation gave a new outlook upon the existence of small molecular matrices of very different size at the surfaces for this catalytic process which leads to the macroscopic appearance of the overranging one-dimensional analogies. The proof of a total mismatch of every matrix system with respect to the vitamin upon the R quartz is especially interesting.


2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Xiaoyu Yang ◽  
Yongbin Xie ◽  
Jianhua Dong ◽  
Guosheng Liu ◽  
Yalin Zheng

In the electroosmosis method, when the distance between the opposite electrode and the same electrode is equal, the two-dimensional effect of electroosmotic consolidation is significant, and the use of one-dimensional model will overestimate the potential gradient, making the calculated pore pressure value too large. Aiming at this problem, according to the electrode arrangement rule and the minimum composition, a punctiform electrode unit model is proposed, and electroosmotic experiments are carried out on the symmetric and asymmetric unit models. The two-dimensional electroosmotic consolidation governing equation of the punctiform electrode unit is established. The electric potential field of the electrode unit and the finite element form of the electroosmotic consolidation equation are given by the Galerkin method. The PyEcFem finite-element numerical library is developed using Python programming to calculate. The research results show the following: (1) The two-dimensional effect of the potential field distribution of the punctiform electrode unit is significant. The reduction of spacing of the same nature electrode in the symmetrical unit can make the potential distribution close to a uniform electric field. The asymmetry prevents the electric potential field distribution from being reduced to a one-dimensional model. (2) The number of anodes will affect the electroosmosis effect of the soil. The more the anodes, the better the electroosmosis reinforcement effect of the soil, and the distribution of negative excess pore water pressure will be more uniform. (3) In the early stage of electroosmosis, the more the drainage boundaries, the faster the generation of negative pore pressure, but in the middle and late stages of electroosmosis, the potential value becomes the decisive factor, and the amplitude of negative pore water pressure in asymmetric units is higher than that in symmetric units. The potential distribution will not affect the degree of consolidation but will affect the extreme pore water pressure.


2008 ◽  
Vol 516 (16) ◽  
pp. 5625-5631
Author(s):  
Chuan Li ◽  
J.H. Hsieh ◽  
Jui-Ching Cheng

2000 ◽  
Vol 265 (4) ◽  
pp. 294-296 ◽  
Author(s):  
D.M Sedrakian ◽  
A.Zh Khachatrian

1966 ◽  
Vol 25 ◽  
pp. 93-97
Author(s):  
Richard Woolley

It is now possible to determine proper motions of high-velocity objects in such a way as to obtain with some accuracy the velocity vector relevant to the Sun. If a potential field of the Galaxy is assumed, one can compute an actual orbit. A determination of the velocity of the globular clusterωCentauri has recently been completed at Greenwich, and it is found that the orbit is strongly retrograde in the Galaxy. Similar calculations may be made, though with less certainty, in the case of RR Lyrae variable stars.


1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.


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