Recursive Dispersion Relations in One-Dimensional Periodic Elastic Media

2008 ◽  
Vol 69 (3) ◽  
pp. 670-689 ◽  
Author(s):  
Ani P. Velo ◽  
George A. Gazonas ◽  
Erwin Bruder ◽  
Nancy Rodriguez
Keyword(s):  
Dispersion Relations ◽  
Elastic Media ◽  
One Dimensional

scholarly journals THERMAL FIELD THEORY IN A WIRE: APPLICATIONS OF THERMAL FIELD THEORY METHODS TO THE PROPAGATION OF PHOTONS IN A ONE-DIMENSIONAL PLASMA

2011 ◽  
Vol 26 (32) ◽  
pp. 5387-5402 ◽  
Author(s):  
JOSÉ F. NIEVES
Keyword(s):  
Field Theory ◽  
Thermal Field Theory ◽  
Thermal Field ◽  
Free Field ◽  
Dynamical Variable ◽  
Effective Field ◽  
Dispersion Relations ◽  
One Dimensional ◽  
Self Energy ◽  
The One

The Thermal Field Theory methods are applied to calculate the dispersion relation of the photon propagating modes in a strictly one-dimensional (1D) ideal plasma. The electrons are treated as a gas of particles that are confined to a 1D tube or wire, but are otherwise free to move, without reference to the electronic wave functions in the coordinates that are transverse to the idealized wire, or relying on any features of the electronic structure. The relevant photon dynamical variable is an effective field in which the two space coordinates that are transverse to the wire are collapsed. The appropriate expression for the photon free-field propagator in such a medium is obtained, the one-loop photon self-energy is calculated and the (longitudinal) dispersion relations are determined and studied in some detail. Analytic formulas for the dispersion relations are given for the case of a degenerate electron gas, and the results differ from the long-wavelength formula that is quoted in the literature for the strictly 1D plasma. The dispersion relations obtained resemble the linear form that is expected in realistic quasi-1D plasma systems for the entire range of the momentum, and which have been observed in this kind of system in recent experiments.

scholarly journals Predicting the Dispersion Relations of One-Dimensional Phononic Crystals by Neural Networks

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Chen-Xu Liu ◽  
Gui-Lan Yu
Keyword(s):  
Neural Networks ◽  
Prediction Accuracy ◽  
Mass Density ◽  
Back Propagation ◽  
Dispersion Relations ◽  
Phononic Crystals ◽  
Training Time ◽  
One Dimensional ◽  
Density Ratios ◽  
Parameter Prediction

Abstract In this paper, deep back propagation neural networks (DBP-NNs) and radial basis function neural networks (RBF-NNs) are employed to predict the dispersion relations (DRs) of one-dimensional (1D) phononic crystals (PCs). The data sets generated by transfer matrix method (TMM) are used to train the NNs and detect their prediction accuracy. In our work, filling fractions, mass density ratios and shear modulus ratios of PCs are considered as the input values of NNs. The results show that both the DBP-NNs and the RBF-NNs exhibit good performances in predicting the DRs of PCs. For one-parameter prediction, the RBF-NNs have shorter training time and remarkable prediction accuracy, for two- and three-parameter prediction, the DBP-NNs have more stable performance. The present work confirms the feasibility of predicting the DRs of PCs by NNs, and provides a useful reference for the application of NNs in the design of PCs and metamaterials.

scholarly journals Anisotropic behaviour and elastic moduli of average isotropic and anisotropic elastic media

2019 ◽  
Vol 1 (3) ◽  
Author(s):  
Sadriten Tleukenov
Keyword(s):  
Elastic Moduli ◽  
Periodic Structures ◽  
Elastic Media ◽  
One Dimensional ◽  
Anisotropic Behaviour ◽  
Anisotropic Elastic

Using matricant method elastic moduli of occasionally heterogeneous isotropic and anisotropic elastic media were received. Anisotropic behaviour and conditions for change in anisotropy of media associated with averaging of one-dimensional periodic structures was determined. 

Sign in / Sign up

Export Citation Format

Share Document