One Dimensional Wave Function for the Effective Hamiltonian of Non-Local Potential

1980 ◽  
Vol 48 (2) ◽  
pp. 669-682 ◽  
Author(s):  
L. C. Papaloucas ◽  
A. D. Jannussis
Keyword(s):  
Wave Function ◽  
Local Potential ◽  
Effective Hamiltonian ◽  
One Dimensional ◽  
Non Local ◽  
Dimensional Wave

scholarly journals Transverse Momentum Distribution of Atoms in an Interferometer

2001 ◽  
Vol 56 (1-2) ◽  
pp. 173-177 ◽  
Author(s):  
Mirijana Božić ◽  
Dušan Arsenović ◽  
Lepša Vušković
Keyword(s):  
Wave Function ◽  
Transverse Momentum ◽  
Momentum Distribution ◽  
Quantum Interference ◽  
Transverse Momentum Distribution ◽  
Wave Functions ◽  
Transverse Motion ◽  
One Dimensional ◽  
Dimensional Wave

Abstract From the stationary solution of Schrödinger's equation in an interferometer we derive the wave functions of the longitudinal and the transverse motion. The former function is a plane wave. The wave function of the transverse motion is a one dimensional wave packet representing a super­ position of components with various values of the particles transverse momentum. The particles transverse momentum distribution in an interferometer is time independent and is determined by the aperture wave function. Consequently, it is independent of the distance from the slits. As such, it is a very important characteristic of the quantum state. Experimental determination of the mo­ mentum distribution would support the particle and wave interpretation of quantum interference in a new manner.

scholarly journals Interaction of equivalence ratio fluctuations and flow fluctuations in acoustically forced swirl flames

2021 ◽  
pp. 175682772110155
Author(s):  
Vincent Kather ◽  
Finn Lückoff ◽  
Christian O. Paschereit ◽  
Kilian Oberleithner
Keyword(s):  
Equivalence Ratio ◽  
Transfer Functions ◽  
Transport Model ◽  
Mode Conversion ◽  
Fuel Injector ◽  
One Dimensional ◽  
Flow Fluctuations ◽  
Non Linear ◽  
Non Local ◽  
Acoustic Forcing

The generation and turbulent transport of temporal equivalence ratio fluctuations in a swirl combustor are experimentally investigated and compared to a one-dimensional transport model. These fluctuations are generated by acoustic perturbations at the fuel injector and play a crucial role in the feedback loop leading to thermoacoustic instabilities. The focus of this investigation lies on the interplay between fuel fluctuations and coherent vortical structures that are both affected by the acoustic forcing. To this end, optical diagnostics are applied inside the mixing duct and in the combustion chamber, housing a turbulent swirl flame. The flame was acoustically perturbed to obtain phase-averaged spatially resolved flow and equivalence ratio fluctuations, which allow the determination of flux-based local and global mixing transfer functions. Measurements show that the mode-conversion model that predicts the generation of equivalence ratio fluctuations at the injector holds for linear acoustic forcing amplitudes, but it fails for non-linear amplitudes. The global (radially integrated) transport of fuel fluctuations from the injector to the flame is reasonably well approximated by a one-dimensional transport model with an effective diffusivity that accounts for turbulent diffusion and dispersion. This approach however, fails to recover critical details of the mixing transfer function, which is caused by non-local interaction of flow and fuel fluctuations. This effect becomes even more pronounced for non-linear forcing amplitudes where strong coherent fluctuations induce a non-trivial frequency dependence of the mixing process. The mechanisms resolved in this study suggest that non-local interference of fuel fluctuations and coherent flow fluctuations is significant for the transport of global equivalence ratio fluctuations at linear acoustic amplitudes and crucial for non-linear amplitudes. To improve future predictions and facilitate a satisfactory modelling, a non-local, two-dimensional approach is necessary.

Thermally corrected solutions of the one-dimensional wave equation for the laser-induced ultrasound

2021 ◽  
Vol 130 (2) ◽  
pp. 025104
Author(s):  
Misael Ruiz-Veloz ◽  
Geminiano Martínez-Ponce ◽  
Rafael I. Fernández-Ayala ◽  
Rigoberto Castro-Beltrán ◽  
Luis Polo-Parada ◽  
...  
Keyword(s):  
Wave Equation ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave
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