Spectral Theorem of Many-Body Green's Functions When Complex Eigenvalues Appear

In this paper, an extended spectral theorem is given, which enables one to calculate the correlation functions when complex eigenvalues appear. To do so, a Fourier transformation with a complex argument is utilized. We treat all the Matsbara frequencies, including Fermionic and Bosonic frequencies, on an equal footing. It is pointed out that when complex eigenvalues appear, the dissipation of a system cannot simply be ascribed to the pure imaginary part of the Green function. Therefore, the use of the name fluctuation-dissipation theorem should be careful.

Matrix Roots and Embedding Conditions for Three-State Discrete-Time Markov Chains with Complex Eigenvalues

The present paper examines matrix root properties and embedding conditions for discrete-time Markov chains with three states and a transition matrix having complex eigenvalues.Necessary as well as sufficient conditions for the existence of an m-th stochastic root of the transition matrix are investigated.Matrix roots are expressed in analytical form based on the spectral decomposition of the transition matrix,and properties of these matrix roots are proved.

Complex eigenvalues and group velocities of normal modes in shallow water with a lossy bottom

For the stratified shallow water with a lossy bottom, the distribution and asymptotic behavior of mode eigenvalues in the complex plane are discussed on the basis of the Pekeris cut. The analysis shows that even in the shallow water with a low-speed lossy bottom there may be the proper modes which satisfy the radiation condition at infinite depth. It is also shown that when the ratio between the densities of the seawater and seabottom is close to one, there exist only a finite number of improper modes . An iterative method for evaluating the complex eigenvalues and group velocities of normal modes is presented and some numerical results are given.

Ag-coated Long-period Fiber Grating

Based on coupled-mode theo ry , the eigenvalue equation of five-layered long-period fiber grating(LPFG) sens or with Ag film and gas-sensitive film overlays are firstly studied. The probl em of resolving complex eigenvalue equation on five-layered LPFG is analyzed, a nd the method of resolution is also given. Then the eigenvalue equation of three -layered metal cladding LPFG is analyzed, and the complex transcendental equati on is also discussed. The computing result shows that the coupling between the l ow-order EH modes and the core mode is much stronger than that between the low -order HE modes and the core mode.

Modeling and Experimental Study for Automotive Dry Clutch Sliding Noise

Automotive dry clutches have been found to produce a low frequency sliding noise in many applications,which challenges the ride comfort of vehicles.In order to study this clutch sliding noise,a detailed finite element model including both a pressure plate assembly and a driven plate assembly was developed.Based on this model,a complex eigenvalue analysis is performed in this research.The effect of several major factors on the clutch sliding noise,such as the coefficient of friction,the clamping force,the geometric imperfection of the friction plate,and the thermal deformation of the pressure plate,were investigated numerically.A vehicle road test with clutch sliding noise was conducted for several different conditions.The leading frequencies of the clutch sliding noise in the testing were obtained and compared with the frequencies predicted by the numerical model.The simulation results show the same tendency as the road test.It is found that the clutch sliding noise can be reduced by decreasing the coefficient of friction.With the presence of the surface bumping of the friction plate,the propensity of the clutch sliding noise greatly increases and the corresponding squeal frequencies fall into the range lower than 1 kHz.With the consideration of the thermally introduced deformation of the clutch pressure plate,the possibility of clutch sliding noise is significantly reduced.It is concluded that the model with the incorporation of the thermal deformation of the pressure plate is more effective for the frequency prediction of clutch sliding noise.