Acoustic Signature of Defects in SiC/Porous SiC Laminated Ceramics

1996 ◽  
Vol 458 ◽  
Author(s):  
R. Esquivel-Sirvent ◽  
C. Noguez
Keyword(s):  
Transfer Matrix ◽  
Topological Defects ◽  
Matrix Formalism ◽  
Morphological Variations ◽  
Porous Layers ◽  
Acoustic Signature ◽  
Morphological Defects ◽  
Acoustic Techniques ◽  
Porous Sic ◽  
Transfer Matrix Formalism

ABSTRACTThe sensitivity of acoustic techniques to topological and morphological variations in SiC/porous SiC laminated ceramics is studied using a transfer matrix formalism. To implement this transfer matrix technique, the mechanical properties of the SiC porous layers are characterized using the effective medium approximation of Kuster and Toksoz. We show that topological defects have a stronger acoustic signature than morphological defects. Also, we observe that there are particular frequencies at which the defects do not present any acoustic signature.

To the developement of the transfer matrix formalism

2004 ◽  
Vol 1 (6) ◽  
pp. 1549-1553
Author(s):  
I. A. Shelykh ◽  
V. K. Ivanov
Keyword(s):  
Transfer Matrix ◽  
Matrix Formalism ◽  
Transfer Matrix Formalism

Transfer Matrix of the Two-dimensional Ising Model

2020 ◽  
pp. 211-234
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Ising Model ◽  
Critical Point ◽  
Transfer Matrix ◽  
Functional Equations ◽  
Baxter Equation ◽  
Matrix Formalism ◽  
Two Dimensional ◽  
R Matrix ◽  
Transfer Matrix Formalism ◽  
Lowest Eigenvalue

This chapter deals with the exact solution of the two-dimensional Ising model as it is achieved through the transfer matrix formalism. It discusses the crucial role played by the commutative properties of the transfer matrices, which lead to a functional equation for their eigenvalues. The exact free energy of the Ising model and its critical point can be identified by means of the lowest eigenvalue. The chapter covers Baxter's approach, the Yang–Baxter equation and its relation to the Boltzmann weights, the R-matrix, and discusses activity away from the critical point, the six-vertex model, as well as functional equations and symmetries.

Basic transfer matrix formalism

1975 ◽  
Vol 26 (1) ◽  
pp. 171-180 ◽  
Author(s):  
J. Chahoud ◽  
L. Ferrari ◽  
G. Russo
Keyword(s):  
Transfer Matrix ◽  
Matrix Formalism ◽  
Transfer Matrix Formalism

scholarly journals Trace spectrum of 1D Transfer Matrices for wave propagation in layered media

2021 ◽  
Author(s):  
Joaquin Garcia-Suarez
Keyword(s):  
Wave Propagation ◽  
Transfer Matrix ◽  
Rational Design ◽  
Single Layer ◽  
Matrix Product ◽  
Matrix Formalism ◽  
Transfer Matrices ◽  
Sensitivity Studies ◽  
Media Applications ◽  
Transfer Matrix Formalism

The Transfer Matrix formalism is ubiquitous when considering wave propagation in various stratified media, applications ranging from Seismology to Quantum Mechanics. The relation between variables at two points in the laminate can be established via a matrix, termed (global) transfer matrix (product of "atomic'' single-layer matrices). As a matter of convenience, we focus on 1D phononic structures, but our derivation can be extended to other fields where the formalism applies. We present exact expressions for entries of the global propagator for N layers. When the layering corresponds to a representative repeated cell in an otherwise infinitely periodic medium, the trace of the cumulative multi-layer matrix is known to control the dispersion relation. We show how this trace has a discrete spectrum made up of distinct 2**(N-1) harmonics (not necessarily orthogonal to each other in any sense) which we characterize exactly both in terms of the periods that they contain and their amplitudes; we also show that the phase shift among harmonics is either zero or pi. This definite appraisal of the spectrum of the trace opens the path for rational design of band gaps, going beyond parametric or sensitivity studies.

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