Non-local dispersive model for wave propagation in heterogeneous media: one-dimensional case

2002 ◽  
Vol 54 (3) ◽  
pp. 331-346 ◽  
Author(s):  
Jacob Fish ◽  
Wen Chen ◽  
Gakuji Nagai
Keyword(s):  
Wave Propagation ◽  
Heterogeneous Media ◽  
Dimensional Case ◽  
One Dimensional ◽  
Dispersive Model ◽  
Non Local

A Dispersive Model for Wave Propagation in Periodic Heterogeneous Media Based on Homogenization With Multiple Spatial and Temporal Scales

2000 ◽  
Vol 68 (2) ◽  
pp. 153-161 ◽  
Author(s):  
W. Chen ◽  
J. Fish
Keyword(s):  
Wave Propagation ◽  
Heterogeneous Media ◽  
Initial Boundary ◽  
Multiple Scale ◽  
Initial Boundary Value Problem ◽  
Higher Order ◽  
Homogenization Theory ◽  
Temporal Scales ◽  
Spatial And Temporal Scales ◽  
Dispersive Model

A dispersive model is developed for wave propagation in periodic heterogeneous media. The model is based on the higher order mathematical homogenization theory with multiple spatial and temporal scales. A fast spatial scale and a slow temporal scale are introduced to account for the rapid spatial fluctuations as well as to capture the long-term behavior of the homogenized solution. By this approach the problem of secularity, which arises in the conventional multiple-scale higher order homogenization of wave equations with oscillatory coefficients, is successfully resolved. A model initial boundary value problem is analytically solved and the results have been found to be in good agreement with a numerical solution of the source problem in a heterogeneous medium.

scholarly journals Consequences of deformation of the Heisenberg algebra

2015 ◽  
Vol 12 (02) ◽  
pp. 1550022 ◽  
Author(s):  
Mir Faizal
Keyword(s):  
Gauge Symmetry ◽  
Mechanical Systems ◽  
Heisenberg Algebra ◽  
Dimensional Case ◽  
Quantum Mechanical ◽  
Second Quantization ◽  
One Dimensional ◽  
Non Local ◽  
Quantum Mechanical Systems

In this paper, we will demonstrate that like the existence of a minimum measurable length, the existence of a maximum measurable momentum, also influence all quantum mechanical systems. Beyond the simple one-dimensional case, the existence of a maximum momentum will induce non-local corrections to the first quantized Hamiltonian. However, these non-local corrections can be effectively treated as local corrections by using the theory of harmonic extensions of functions. We will also analyze the second quantization of this deformed first quantized theory. Finally, we will analyze the gauge symmetry corresponding to this deformed theory.

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