Counting quantum states and field modes

2021 ◽  
pp. 60-66
Author(s):  
Geoffrey Brooker
Keyword(s):  
Density Of States ◽  
Fourier Expansion ◽  
Standing Waves ◽  
Travelling Wave ◽  
Quantum States ◽  
Arbitrary Volume ◽  
Wave Modes

“Counting quantum states and field modes” deals with wave modes identified as terms in a Fourier expansion made within a large arbitrary volume. Travelling-wave modes are preferred as they are eigenstates of momentum; counting modes is also made straightforward, whence the density of states. This is in contrast to a fashion that works instead with standing waves.

Use of dFRFs for Identification of Travelling Wave Modes in Rotating Disks

1998 ◽  
Vol 120 (3) ◽  
pp. 719-726 ◽  
Author(s):  
Myeong-Eop Kim ◽  
Chong-Won Lee
Keyword(s):  
Frequency Response ◽  
Frequency Response Function ◽  
Rotating Disk ◽  
Travelling Wave ◽  
Weighted Sum ◽  
Response Functions ◽  
Rotating Disks ◽  
Complex Wave ◽  
Wave Coordinates ◽  
Wave Modes

Use of the wave directional frequency response function (dFRF), which is composed of conventional frequency response functions, is proposed for identification of the forward and backward travelling wave modes of isotropic rotating disks. The driving point dFRF, which is a weighted sum of complex wave dFRFs defined in the complex wave coordinates, is also derived for separation of the forward and backward travelling wave modes in the frequency domain. Numerical examples of rotating disks are treated to demonstrate the analytical developments. Experiments with a laboratory rotating disk are also performed to verify the theoretical findings.

scholarly journals Mode selection mechanism in traveling and standing waves revealed by Min wave reconstituted in artificial cells

2022 ◽  
Author(s):  
Sakura Takada ◽  
Natsuhiko Yoshinaga ◽  
Nobuhide Doi ◽  
Kei Fujiwara
Keyword(s):  
Mode Selection ◽  
Standing Waves ◽  
Reaction Diffusion ◽  
Wave Mode ◽  
Spatiotemporal Pattern ◽  
Selection Mechanism ◽  
Artificial Cells ◽  
Pattern Formations ◽  
Selection Of ◽  
Wave Modes

Reaction-diffusion coupling (RDc) generates spatiotemporal patterns, including two dynamic wave modes: traveling and standing waves. Although mode selection plays a significant role in the spatiotemporal organization of living cell molecules, the mechanism for selecting each wave mode remains elusive. Here, we investigated a wave mode selection mechanism using Min waves reconstituted in artificial cells, emerged by the RDc of MinD and MinE. Our experiments and theoretical analysis revealed that the balance of membrane binding and dissociation from the membrane of MinD determines the mode selection of the Min wave. We successfully demonstrated that the transition of the wave modes can be regulated by controlling this balance and found hysteresis characteristics in the wave mode transition. These findings highlight a novel role of the balance between activators and inhibitors as a determinant of the mode selection of waves by RDc and depict a novel mechanism in intracellular spatiotemporal pattern formations.

Amplifying Quantum States with a Superconducting Microstrip Kinetic Inductance Travelling Wave Amplifier

2020 ◽  
Author(s):  
Samuel Goldstein ◽  
Naftali Kirsh ◽  
Elisha Svetitsky ◽  
Shimon Eliav ◽  
Nadav Katz
Keyword(s):  
Travelling Wave ◽  
Quantum States ◽  
Kinetic Inductance

Research on Aerodynamic Damping of Bladed Disk With Random Mistuning

2017 ◽  
Author(s):  
Lin Li ◽  
Xiaoping Yu ◽  
Peiyi Wang
Keyword(s):  
Travelling Waves ◽  
Elastic Stability ◽  
Travelling Wave ◽  
Wave Mode ◽  
Analysis Model ◽  
Aerodynamic Damping ◽  
Bladed Disk ◽  
Random Mistuning ◽  
Value Of It ◽  
Wave Modes

This paper presents an investigation on the aerodynamic damping of bladed disk (also called ‘blisk’) with mistuning. The study focuses mainly on the mechanism of the effect of random and intentional mistuning on the aero-elastic stability of blisk. For the purpose, aero-elastic stability equations of tuned and mistuned blisk in the frequency domain are established. NASA-Rotor37 is taken as the analysis model. In order to obtain the aerodynamic damping, the unsteady aero-elastic forces are calculated by the double channel harmonic method based on phase correction with aid of the general software CFX. Considering the stochastic characteristics of random mistuning, statistical analysis on the aerodynamic damping of mistuned blisk is performed. The effects of mistuning with different levels are compared. The mechanism of the effects of mistuning on the aero-elastic stability of blisk is found that mistuning couples the modes of different travelling waves and it concentrates the aerodynamic damping in a travelling wave-mode-family by increasing the aerodynamic damping ratios in forward travelling wave modes and decreasing the aerodynamic damping ratios in backward travelling wave modes. And the higher the mistuning level, the more obvious the trend. Furthermore, the following result is obtained: Whatever the mistuning level, in a traveling wave-mode-family, the aerodynamic damping of mistuned blisk is greater than the minimum aerodynamic damping of corresponding tuned blisk and less than the maximum value of it. Besides, the harmonic order of intentional mistuning that can be used to raise the aero-elastic stability of blisk is proposed.

scholarly journals On Travelling Wave Modes of Axially Moving String and Beam

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Lei Lu ◽  
Xiao-Dong Yang ◽  
Wei Zhang ◽  
Siu-Kai Lai
Keyword(s):  
Travelling Wave ◽  
Axially Moving Beam ◽  
Time Varying ◽  
Axially Moving String ◽  
Moving Beam ◽  
Axially Moving Beams ◽  
Axially Moving ◽  
Wave Phenomena ◽  
Moving Speed ◽  
Wave Modes

The traditional vibrational standing-wave modes of beams and strings show static overall contour with finite number of fixed nodes. The travelling wave modes are investigated in this study of axially moving string and beam although the solutions have been obtained in the literature. The travelling wave modes show time-varying contour instead of static contour. In the model of an axially moving string, only backward travelling wave modes are found and verified by experiments. Although there are n − 1 fixed nodes in the nth order mode, similar to the vibration of traditional static strings, the presence of travelling wave phenomenon is still spotted between any two adjacent nodes. In contrast to the stationary nodes of string modes, the occurrence of galloping nodes of axially moving beams is discovered: the nodes oscillate periodically during modal motions. Both forward and backward travelling wave phenomena are detected for the axially moving beam case. It is found that the ranges of forward travelling wave modes increase with the axially moving speed. It is also concluded that backward travelling wave modes can transform to the forward travelling wave modes as the transport speed surpasses the buckling critical speed.

scholarly journals Characterization of electron density of states in laser-superposed channeling regime

2014 ◽  
Vol 33 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Vesna Berec
Keyword(s):  
Proton Beam ◽  
Electron Density ◽  
Density Of States ◽  
Coherent Control ◽  
Quantum States ◽  
Bohr Radius ◽  
Electron Density Of States ◽  
Highly Correlated ◽  
Low Dimensional

AbstractWe present low-dimensional functionalization and characterization of electron density of states using highly correlated/precisely guided proton beam trajectories and a silicon nanocrystal as a target, representing at a same time a versatile nanolaser technique capable for coherent control of atomic quantum states and for scanning the interior of an atom with resolution comparable to 10% of the Bohr radius.

Experimental and Numerical Investigations of HPC Blisks With a Focus on Travelling Waves

2010 ◽  
Author(s):  
Ulrik Strehlau ◽  
Arnold Ku¨hhorn
Keyword(s):  
Travelling Waves ◽  
Pressure Ratio ◽  
Integrated Design ◽  
Standing Waves ◽  
Travelling Wave ◽  
Experimental Investigations ◽  
Fe Model ◽  
Mode Localization ◽  
Numerical Investigations ◽  
Aero Engines

The motivation for the usage and a further development of blade integrated disk (blisk) technology is driven by a rising demand for efficient, economical and environment-friendly aero engines. In contrast to conventional bladed disks with separated blade and disk design, blisks are either manufactured from solid or disk and blades are assembled by friction welding. Due to an optimized stress distribution, the integrated design leads to potentially higher maximum rotational speeds of the HP-shaft and thus to an improved pressure ratio. This fact offers the opportunity to reduce the number of blades or even to save whole compressor stages. In order that a significant mass-reduction is achieved, which is increased since heavy blade-disk connections of the conventional design are not necessary anymore. Apart from the advantages of the integrated design, the vibration behaviour of a real blisk is more sophisticated compared to the conventional bladed disk design. Due to the very low mechanical damping, effects like mode-localization and amplitude magnification can lead to high cycle fatigue problems of such complex structures. Extensive experimental and numerical investigations are carried out considering a real rotor-stage 1 blisk of the Rolls-Royce E3E/1 demonstrator-HPC. In order to identify “blade individual frequencies” and “blade individual damping”- values, a new patented blade by blade measurement method is used, that provides FRFs characterized by an unique resonance, as known from SDOF-systems. Based on the adjusted FE-model, numerical and experimental investigations of the vibration behaviour in the frequency range of splitted double eigenvalues are carried out. In doing so the expressions “travelling wave” and “standing waves” are commonly used to characterize the eigenmodes and forced modes of vibration respectively. The splitting of eigenvalues could be proved and a novel criterion to distinguish travelling and standing waves is introduced.

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