Other Nonlinear Dispersive Models

2009 ◽  
pp. 1-20
Author(s):  
Felipe Linares ◽  
Gustavo Ponce
Keyword(s):  
Dispersive Models

Estimation and geologic interpretation of regolith chargeability and superparamagnetic susceptibility in airborne electromagnetic data

Geophysics ◽  
2020 ◽  
Vol 85 (5) ◽  
pp. E153-E162 ◽  
Author(s):  
James Macnae ◽  
Tim Munday ◽  
Camilla Soerensen
Keyword(s):  
Magnetic Permeability ◽  
Thin Sheet ◽  
Secondary Field ◽  
Conductivity Model ◽  
Electromagnetic Data ◽  
Delay Times ◽  
Airborne Electromagnetic ◽  
Geologic Interpretation ◽  
Airborne Electromagnetic Data ◽  
Dispersive Models

All available inversion software for airborne electromagnetic (AEM) data can at a minimum fit a nondispersive conductivity model to the observed inductive secondary field responses, whether operating in the time or frequency domain. Quasistatic inductive responses are essentially controlled by the induction number, the product of frequency with conductivity and magnetic permeability. Recent research has permitted the conductivity model to be dispersive, commonly using a single Cole-Cole parameterization of the induced polarization (IP) effect; but this parameterization slows down and destabilizes any inversion, and it does not account for the need for dual or multiple Cole-Cole responses. Little has been published on inverting AEM data affected by frequency-dependent magnetic permeability, or superparamagnetism (SPM), usually characterized by a Chikazumi model. Because the IP and SPM effects are small and are usually only obvious at late delay times, the aim of our research is to determine if these IP and SPM effects can be fitted and stripped from the AEM data after being approximated with simple dispersive models. We are able to successfully automate a thin-sheet model to do this stripping. Stripped data then can be inverted using a nondispersive conductivity model. The IP and SPM parameters fitted independently to each independent measured decay to provide stripping are proven to be spatially coherent, and they are geologically sensible. The results are found to enhance interpretation of the regolith geology, particularly the nature and distribution of transported materials that are not afforded by mapping conductivity/conductance alone.

scholarly journals Dispersive models describing mosquitoes’ population dynamics

2016 ◽  
Vol 738 ◽  
pp. 012065 ◽  
Author(s):  
W M S Yamashita ◽  
L T Takahashi ◽  
G Chapiro
Keyword(s):  
Population Dynamics ◽  
Dispersive Models

Unified integro-differential equation for efficient dispersive FDTD simulations

2017 ◽  
Vol 36 (4) ◽  
pp. 1089-1105 ◽  
Author(s):  
Omar Ramadan
Keyword(s):  
Differential Equation ◽  
Time Domain ◽  
Stability Limit ◽  
Model Parameters ◽  
Time Step ◽  
Content Type ◽  
Integro Differential Equation ◽  
Dispersive Model ◽  
Fdtd Simulations ◽  
Dispersive Models

Purpose The purpose of this paper is to derive a unified formulation for incorporating different dispersive models into the explicit and implicit finite difference time domain (FDTD) simulations. Design/methodology/approach In this paper, dispersive integro-differential equation (IDE) FDTD formulation is presented. The resultant IDE is written in the discrete time domain by applying the trapezoidal recursive convolution and central finite differences schemes. In addition, unconditionally stable implicit split-step (SS) FDTD implementation is also discussed. Findings It is found that the time step stability limit of the explicit IDE-FDTD formulation maintains the conventional Courant–Friedrichs–Lewy (CFL) constraint but with additional stability limits related to the dispersive model parameters. In addition, the CFL stability limit can be removed by incorporating the implicit SS scheme into the IDE-FDTD formulation, but this is traded for degradation in the accuracy of the formulation. Research limitations/implications The stability of the explicit FDTD scheme is bounded not only by the CFL limit but also by additional condition related to the dispersive material parameters. In addition, it is observed that implicit JE-IDE FDTD implementation decreases as the time step exceeds the CFL limit. Practical implications Based on the presented formulation, a single dispersive FDTD code can be written for implementing different dispersive models such as Debye, Drude, Lorentz, critical point and the quadratic complex rational function. Originality/value The proposed formulation not only unifies the FDTD implementation of the frequently used dispersive models with the minimal storage requirements but also can be incorporated with the implicit SS scheme to remove the CFL time step stability constraint.

scholarly journals DISPERSIVE EFFECTIVE MODELS FOR WAVES IN HETEROGENEOUS MEDIA

2011 ◽  
Vol 21 (09) ◽  
pp. 1871-1899 ◽  
Author(s):  
AGNES LAMACZ
Keyword(s):  
Heterogeneous Media ◽  
Variable Coefficients ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Smooth Functions ◽  
Long Time ◽  
Constant Coefficients ◽  
The One ◽  
Effective Models ◽  
Dispersive Models

We study the long-time behavior of waves in a strongly heterogeneous medium, starting from the one-dimensional scalar wave equation with variable coefficients. We assume that the coefficients are periodic with period ε and ε > 0 is a small length parameter. Our main result concerns homogenization and consists in the rigorous derivation of two different dispersive models. The first is a fourth-order equation with constant coefficients including powers of ε. In the second model, the ε-dependence is completely avoided by considering a third-order linearized Korteweg–de Vries equation. Our result is that both simplified models describe the long-time behavior well. An essential tool in our analysis is an adaption operator which modifies smooth functions according to the periodic structure of the medium.

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