Effective Models for Long Time Wave Propagation in Locally Periodic Media

The research of stress wave propagation law under cracked rock has important theoretical value and practical significance. Because of the discontinuity, nonelasticity and nonlinearity of the cracks, the theoretical interpretation and mechanism research about tress wave propagation law are a great challenge to researchers for a long time. From the establishment of the research method, the determination of mathematic model of micro-cracks and the main solutions, this paper brief reviews the current development of the influence of the complicated micro-cracks on stress wave propagation law.

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Boundary element method for long-time water wave propagation over rapidly varying bottom topography

International Journal for Numerical Methods in Fluids ◽

10.1002/fld.1650141106 ◽

1992 ◽

Vol 14 (11) ◽

pp. 1347-1365 ◽

Cited By ~ 1

Author(s):

A. Nachbin ◽

G. C. Papanicolaou

Keyword(s):

Wave Propagation ◽

Boundary Element Method ◽

Boundary Element ◽

Water Wave ◽

Bottom Topography ◽

Long Time ◽

Element Method

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A method of controlling wave propagation in initially spatially periodic media

EPL (Europhysics Letters) ◽

10.1209/0295-5075/78/44001 ◽

2007 ◽

Vol 78 (4) ◽

pp. 44001 ◽

Cited By ~ 9

Author(s):

C Inserra ◽

V Tournat ◽

V Gusev

Keyword(s):

Wave Propagation ◽

Periodic Media ◽

Spatially Periodic

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Electromagnetic wave propagation and wave-vector diagram in space-time periodic media

IRE Transactions on Antennas and Propagation ◽

10.1109/tap.1972.1140230 ◽

1972 ◽

Vol 20 (4) ◽

pp. 534-536 ◽

Cited By ~ 11

Author(s):

C. Elachi

Keyword(s):

Wave Propagation ◽

Electromagnetic Wave ◽

Wave Vector ◽

Electromagnetic Wave Propagation ◽

Space Time ◽

Vector Diagram ◽

Periodic Media ◽

Time Periodic

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Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202516500627 ◽

2016 ◽

Vol 26 (14) ◽

pp. 2651-2684 ◽

Cited By ~ 5

Author(s):

Assyr Abdulle ◽

Timothée Pouchon

Keyword(s):

Wave Equation ◽

Wave Equations ◽

Heterogeneous Media ◽

Multiscale Model ◽

Bloch Wave ◽

Time Interval ◽

Numerical Homogenization ◽

Effective Equation ◽

Long Time ◽

Effective Models

A family of effective equations that capture the long time dispersive effects of wave propagation in heterogeneous media in an arbitrary large periodic spatial domain [Formula: see text] is proposed and analyzed. For a wave equation with highly oscillatory periodic spatial tensors of characteristic length [Formula: see text], we prove that the solution of any member of our family of effective equations is [Formula: see text]-close to the true oscillatory wave over a time interval of length [Formula: see text] in a norm equivalent to the [Formula: see text] norm. We show that the previously derived effective equation in [T. Dohnal, A. Lamacz and B. Schweizer, Bloch-wave homogenization on large time scales and dispersive effective wave equations, Multiscale Model. Simulat. 12 (2014) 488–513] belongs to our family of effective equations. Moreover, while Bloch wave techniques were previously used, we show that asymptotic expansion techniques give an alternative way to derive such effective equations. An algorithm to compute the tensors involved in the dispersive equation and allowing for efficient numerical homogenization methods over long time is proposed.

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