scholarly journals A dichotomy between discrete and continuous spectrum for a class of special flows over rotations

2007 ◽  
Vol 1 (1) ◽  
pp. 107-122 ◽  
Author(s):  
Bassam Fayad ◽  
◽  
A. Windsor ◽  
Keyword(s):  
Continuous Spectrum ◽  
Discrete And Continuous Spectrum

Discrete and continuous spectrum in subwavelength imaging with wire-medium type lenses

2016 ◽  
Author(s):  
Francisco Mesa ◽  
Raul Rodriguez-Berral ◽  
George W. Hanson ◽  
Ali Forouzmand ◽  
Alexander B. Yakovlev ◽  
...  
Keyword(s):  
Continuous Spectrum ◽  
Subwavelength Imaging ◽  
Medium Type ◽  
Discrete And Continuous Spectrum

scholarly journals The Discrete and Continuous Retardation and Relaxation Spectrum Method for Viscoelastic Characterization of Warm Mix Crumb Rubber-Modified Asphalt Mixtures

Materials ◽  
2020 ◽  
Vol 13 (17) ◽  
pp. 3723 ◽  
Author(s):  
Fei Zhang ◽  
Lan Wang ◽  
Chao Li ◽  
Yongming Xing
Keyword(s):  
Continuous Spectrum ◽  
Discrete Spectrum ◽  
Creep Compliance ◽  
Relaxation Modulus ◽  
Crumb Rubber ◽  
Asphalt Mixtures ◽  
Time Range ◽  
Modified Asphalt ◽  
Dynamic Modulus Test ◽  
Discrete And Continuous Spectrum

To study the linear viscoelastic (LVE) of crumb rubber-modified asphalt mixtures before and after the warm mix additive was added methods of obtaining the discrete and continuous spectrum are presented. Besides, the relaxation modulus and creep compliance are constructed from the discrete and continuous spectrum, respectively. The discrete spectrum of asphalt mixtures can be obtained from dynamic modulus test results according to the generalized Maxwell model (GMM) and the generalized Kelvin model (GKM). Similarly, the continuous spectrum of asphalt mixtures can be obtained from the dynamic modulus test data via the inverse integral transformation. In this paper, the test procedure for all specimens was ensured to be completed in the LVE range. The results show that the discrete spectrum and the continuous spectrum have similar shapes, but the magnitude and position of the spectrum peaks is different. The continuous spectrum can be considered as the limiting case of the discrete spectrum. The relaxation modulus and creep compliance constructed by the discrete and continuous spectrum are almost indistinguishable in the reduced time range of 10−5 s–103 s. However, there are more significant errors outside the time range, and the maximum error is up to 55%.

On the Discrete and Continuous Spectrum of Acoustic-Vortical Waves

2013 ◽  
Vol 12 (7-8) ◽  
pp. 743-781 ◽  
Author(s):  
L. M. B. C. Campos ◽  
P. G. T. A. Serrão
Keyword(s):  
Continuous Spectrum ◽  
Discrete And Continuous Spectrum

COMPLETE EXACT QUANTUM STATES OF THE GENERALIZED TIME-DEPENDENT HARMONIC OSCILLATOR

2004 ◽  
Vol 18 (24) ◽  
pp. 1267-1274 ◽  
Author(s):  
I. A. PEDROSA
Keyword(s):  
General Solution ◽  
Harmonic Oscillator ◽  
Exact Solutions ◽  
Continuous Spectrum ◽  
Invariant Operator ◽  
Quantum States ◽  
Time Dependent ◽  
Quadratic Invariants ◽  
Generalized Time ◽  
Discrete And Continuous Spectrum

By making use of linear and quadratic invariants and the invariant operator formulation of Lewis and Riesenfeld, the complete exact solutions of the Schrödinger equation for the generalized time-dependent harmonic oscillator are obtained. It is shown that the general solution of the system under consideration contains both the discrete and continuous spectrum. The connection between linear and quadratic invariants and their corresponding eigenstates via time-dependent auxiliary equations is also established.

WAVE FUNCTIONS WITH DISCRETE AND WITH CONTINUOUS SPECTRUM FOR QUANTUM DAMPED HARMONIC OSCILLATOR PERTURBED BY A SINGULARITY

2004 ◽  
Vol 18 (07) ◽  
pp. 1007-1020 ◽  
Author(s):  
JEONG-RYEOL CHOI
Keyword(s):  
Harmonic Oscillator ◽  
Continuous Spectrum ◽  
Unitary Operator ◽  
Invariant Operator ◽  
Confluent Hypergeometric Function ◽  
Quantum States ◽  
Wave Functions ◽  
The Other ◽  
Damped Harmonic Oscillator ◽  
Discrete And Continuous Spectrum

The quantum states with discrete and continuous spectrum for the damped harmonic oscillator perturbed by a singularity have been investigated using invariant operator and unitary operator together. The eigenvalue of the invariant operator for ω0≤β/2 is continuous while for ω0>β/2 is discrete. The wave functions for ω0=β/2 expressed in terms of the Bessel function and for ω0<β/2 in terms of the Kummer confluent hypergeometric function. The convergence of the probability density is more rapid for over-damped harmonic oscillator than that of the other two cases due to the large damping constant.

Discrete and continuous spectrum of nitrogen-induced bound states in heavily dopedGaAs1−xNx

2001 ◽  
Vol 63 (8) ◽  
Author(s):  
Yong Zhang ◽  
A. Mascarenhas ◽  
J. F. Geisz ◽  
H. P. Xin ◽  
C. W. Tu
Keyword(s):  
Continuous Spectrum ◽  
Bound States ◽  
Discrete And Continuous Spectrum
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