The conception of memristor is becoming increasingly prevalent due to its remarkable electronic properties. In this paper, a circuit model of the memristor using simple SPICE code is presented. An ideal closed-loop operational amplifier (OP-AMP) is applied to realize the feedback-controlled integrator, which expands the hitherto methods to solve the memristor’s modeling equations presented by HP Lab. The behaviors of the proposed memristor model in SPICE are investigated. The desired excitation source and initial condition of the doped state can both be easily tuned in the memristor model. Different pinched hysteresis loop i-v curves are presented through different stimulus like sinusoidal and square-wave voltage source.
A simple and systematic algorithm based on the perfectly matched layer (PML) method and spectral element
method (SEM) is introduced to solve the 3-D Schrodinger equation with tensor effective mass. This algorithm
extends the lead regions of a device into artificial PML media, where a modified Schrodinger equation is satisfied.
The interface between the physical and PML media has zero reflection coefficients, thus waves attenuating rapidly
into the PML region before transmitting to the contact boundary. This algorithm provides a highly effective
open boundary condition in solving quantum transport problems. The additional PML region can be designed
such that less than -100 dB incoming waves are reflected by this artificial material with the implementation
of the spectral element method. Consequently, the solution of the Schrodinger equation and thus the current
in the original device region do not deviate from the correct solution. In this algorithm, the transmitted wave
function is treated as a total wave instead of being decomposed into waveguide modes, therefore, it significantly
simplifies the problem in comparison with conventional open boundary conditions. The implementation of the
tensor effective mass provides an excellent tool to study strain effects along any arbitrary orientation. Within
this PML implementation, the spectral element method has been applied to achieve an error that exponentially
decreases with the increase of the polynomial order and sampling points. This accuracy has been demonstrated
by comparing the numerical and analytical results from waveguide examples, and its utility is illustrated by
multiple-port devices and nanotube devices.
Acoustic waves can be a viable tool for the detection and identification of land mines, unexplored ordnance and other buried objects. Design of acoustic instruments and interpretation and processing of acoustic measurements call for accurate numerical models to simulate acoustic wave propagation in a heterogeneous soil with buried objects. Compared with the traditional seismic exploration, high attenuation is unfortunately ubiquitous for shallow surface acoustic measurements because of the loose soil and the fluid in its pore space. To adequately mode such acoustic attenuation. , we propose a comprehensive multidimensional finite-difference time-domain model to simulate the acoustic wave interactions with land miens and soils based on the Biot theory for photoelastic media. For the truncation of the computational domain, w use the perfectly matched layer (PML). The method is validated by comparison with analytical solutions. Unlike the pure elastic wave model, this efficient PML-FDTD model for photoelastic media incorporates the interactions of waves and the fluid-saturated pore space. Several typical and mine detection measurements are simulated to illustrate the application.
Acoustic waves can be a viable tool for the detection and identification of land mines and unexploded ordnance. Design of acoustic instruments and interpretation and processing of acoustic measurements call for accurate numerical models to simulate acoustic wave propagation in a heterogeneous soil with buried objects. Compared with the traditional seismic exploration, high attenuation is unfortunately ubiquitous for shallow surface acoustic measurements because of the loose soil and the fluid in its pore space. To adequately model such acoustic attention, we propose a comprehensive model to simulate the acoustic wave interactions with land mines and soils based on the Biot theory for poroelastic media. The finite-difference time-domain method is then used to solve the Biot equations. For the truncation of the computational domain in the FDTD method, we extend the acoustic and elastic perfectly matched layer (PML) to poroelastic media. Numerical experiments show that, with only 10 cells of PML medium, a high attenuation of about 50 dB can be achieved for outgoing waves. The numerical model is validated by comparison with analytical solutions. Unlike the pure elastic wave mode, this efficient PML-FDTD model for poroelastic media incorporates the interactions of waves and the fluid-saturated variation with offset in three different ground media: dry sand, fully water saturated sand and partly water saturated sand. The interaction of elastic wave with a plastic mine buried in dry sand ins simulated. The results show that the surface wave is significantly influenced by the existence of a mine-like object. The diffraction of the surface wave can serve as an acoustic target signature.
We propose the hybridization of the extended Born approximation (EBA) with the conjugate-gradient fast Fourier Hankel transform (CG-FFHT) method to improve the efficiency of numerical solution of borehole induction problems in axisymmetric media. First, we use the FFHT to accelerate the EBA as a nonlinear approximation to induction problems, resulting in an algorithm with O(N log2 N) arithmetic operations, where N is the number of unknowns in the problem. This improved EBA is accurate for most formations encountered. Then, for formations with extremely high contrasts, we utilize this improved EBA as a partial preconditioner in the CG-FFHT method to solve the problem accurately with few iterations. The seamless combination of these two approaches provides an automatic way toward the efficient and accurate modeling of induction measurements in axisymmetric media.
We invert for the axisymmetric conductivity distribution from borehole electromagnetic induction measurements using a two-step linear inversion method based on a fast Fourier and Hankel transform enhanced extended Born approximation. In this method, the inverse problem is first cast as an under- determined linear least-norm problem for the induced electric current density; from the solution of this induced current density, the unknown conductivity distribution is then obtained by solving an over-determined linear problem using the newly developed, fast Fourier and Hankel transform enhanced extended Born approximation. Numerical results show that this inverse method is applicable to a very high conductivity contrast. It is a natural extension of the original two-step linear inversion method of Torres-Verdin and Habashy to axisymmetric media. In the first step, the CPU time costs O(N2). In the second step, the CPU time costs O(N log2 N) where N is the number of unknowns. Because of the fast Fourier and Hankel transform algorithm, this inverse method is actually more efficient than the conventional, brute-force first-order Born approximation.
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