scholarly journals Dual-kinetic-balance approach to the Dirac equation for axially symmetric systems: Application to static and time-dependent fields

2014 ◽  
Vol 89 (1) ◽  
Author(s):  
E. B. Rozenbaum ◽  
D. A. Glazov ◽  
V. M. Shabaev ◽  
K. E. Sosnova ◽  
D. A. Telnov
Keyword(s):  
Dirac Equation ◽  
Time Dependent ◽  
Axially Symmetric ◽  
Balance Approach ◽  
Symmetric Systems

scholarly journals Dual Kinetic Balance Approach to Basis-Set Expansions for axially symmetric Dirac equation

2014 ◽  
Vol 488 (3) ◽  
pp. 032005
Author(s):  
Efim Rozenbaum ◽  
V M Shabaev ◽  
Ksenia E Sosnova ◽  
Dmitry A Telnov
Keyword(s):  
Dirac Equation ◽  
Basis Set ◽  
Axially Symmetric ◽  
Balance Approach

Wave Functions for Time-Dependent Dirac Equation under GUP

2018 ◽  
Vol 69 (4) ◽  
pp. 383 ◽  
Author(s):  
Meng-Yao Zhang ◽  
Chao-Yun Long ◽  
Zheng-Wen Long
Keyword(s):  
Dirac Equation ◽  
Wave Functions ◽  
Time Dependent

Effect of a Time-Dependent Stenosis on Flow Through a Tube

1968 ◽  
Vol 90 (2) ◽  
pp. 248-254 ◽  
Author(s):  
D. F. Young
Keyword(s):  
Stokes Equations ◽  
Flow Characteristics ◽  
Time Dependent ◽  
Arterial System ◽  
Navier Stokes ◽  
Axially Symmetric ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
Dependent Growth ◽  
Abnormal Tissue

A common occurrence in the arterial system is the narrowing of arteries due to the development of atherosclerotic plaques or other types of abnormal tissue development. As these growths project into the lumen of the artery, the flow is disturbed and there develops a potential coupling between the growth and the blood flow through the artery. A discussion of the various possible consequences of this interaction is given. It is noted that very small growths leading to mild stenotic obstructions, although not altering the gross flow characteristics significantly, may be important in triggering biological mechanisms such as intimal cell proliferation or changes in vessel caliber. An analysis of the effect of an axially symmetric, time-dependent growth into the lumen of a tube of constant cross section through which a Newtonian fluid is steadily flowing is presented. This analysis is based on a simplified model in which the convective acceleration terms in the Navier-Stokes equations are neglected. Effect of growth on pressure distribution and wall shearing stress is given and possible biological implications are discussed.

On: “Time‐Dependent Electromagnetic Fields of an Infinite, Conducting Cylinder Excited by a Long Current‐Carrying Cable” by S. K. Verma (GEOPHYSICS, April 1973, p. 369–379)

Geophysics ◽  
1974 ◽  
Vol 39 (3) ◽  
pp. 355-355
Author(s):  
Shri Krishna Singh
Keyword(s):  
Magnetic Field ◽  
Frequency Domain ◽  
Electric Current ◽  
Electromagnetic Fields ◽  
Time Domain ◽  
Static Solution ◽  
Transverse Magnetic ◽  
Time Dependent ◽  
Axially Symmetric ◽  
The Time Domain

In this paper Verma obtains a time‐domain solution by inverting the frequency‐domain solution given by Wait (1952). However, it has been recently pointed out by Singh (1973a) (see also Wait, 1973) that there is an error in the quasi‐static solution of Wait. Wait neglected the axially symmetric inducted electric current in the cylinder giving rise to a secondary transverse magnetic field outside (the n=0 term in the scattered wavefield). Singh (1973a) has shown that this term dominates. [It should be noted that Wait in his other works on the cylinder retains this term (e.g., Wait, 1959).] It is clear that this term would be dominant in the time‐domain also. This has been shown by Singh (1972, 1973b). Since the theoretical solution given by Verma in the paper under discussion is incomplete, his interpretation schemes are meaningless.

Numerical approach to solve the time-dependent Dirac equation

1999 ◽  
Vol 59 (1) ◽  
pp. 604-612 ◽  
Author(s):  
J. W. Braun ◽  
Q. Su ◽  
R. Grobe
Keyword(s):  
Dirac Equation ◽  
Numerical Approach ◽  
Time Dependent
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