Nonlinear oscillator metamaterial model: numerical and experimental verification.

We verify numerically and experimentally the accuracy of an analytical model used to derive the effective nonlinear susceptibilities of a varactor-loaded split ring resonator (VLSRR) magnetic medium. For the numerical validation, a nonlinear oscillator model for the effective magnetization of the metamaterial is applied in conjunction with Maxwell equations and the two sets of equations solved numerically in the time-domain. The computed second harmonic generation (SHG) from a slab of a nonlinear material is then compared with the analytical model. The computed SHG is in excellent agreement with that predicted by the analytical model, both in terms of magnitude and spectral characteristics. Moreover, experimental measurements of the power transmitted through a fabricated VLSRR metamaterial at several power levels are also in agreement with the model, illustrating that the effective medium techniques associated with metamaterials can accurately be transitioned to nonlinear systems.

Improving the lens design and performance of a contemporary electromagnetic shock wave lithotripter.

The efficiency of shock wave lithotripsy (SWL), a noninvasive first-line therapy for millions of nephrolithiasis patients, has not improved substantially in the past two decades, especially in regard to stone clearance. Here, we report a new acoustic lens design for a contemporary electromagnetic (EM) shock wave lithotripter, based on recently acquired knowledge of the key lithotripter field characteristics that correlate with efficient and safe SWL. The new lens design addresses concomitantly three fundamental drawbacks in EM lithotripters, namely, narrow focal width, nonidealized pulse profile, and significant misalignment in acoustic focus and cavitation activities with the target stone at high output settings. Key design features and performance of the new lens were evaluated using model calculations and experimental measurements against the original lens under comparable acoustic pulse energy (E+) of 40 mJ. The -6-dB focal width of the new lens was enhanced from 7.4 to 11 mm at this energy level, and peak pressure (41 MPa) and maximum cavitation activity were both realigned to be within 5 mm of the lithotripter focus. Stone comminution produced by the new lens was either statistically improved or similar to that of the original lens under various in vitro test conditions and was significantly improved in vivo in a swine model (89% vs. 54%, P = 0.01), and tissue injury was minimal using a clinical treatment protocol. The general principle and associated techniques described in this work can be applied to design improvement of all EM lithotripters.

Efficient Computation of Electromagnetic Waves in Hydrocarbon Exploration Using the Improved Numerical Mode Matching (NMM) Method

In this study, we developed and improved the numerical mode matching (NMM) method which has previously been shown to be a fast and robust semi-analytical solver to investigate the propagation of electromagnetic (EM) waves in an isotropic layered medium. The applicable models, such as cylindrical waveguide, optical fiber, and borehole with earth geological formation, are generally modeled as an axisymmetric structure which is an orthogonal-plano-cylindrically layered (OPCL) medium consisting of materials stratified planarly and layered concentrically in the orthogonal directions.

In this report, several important improvements have been made to extend applications of this efficient solver to the anisotropic OCPL medium. The formulas for anisotropic media with three different diagonal elements in the cylindrical coordinate system are deduced to expand its application to more general materials. The perfectly matched layer (PML) is incorporated along the radial direction as an absorbing boundary condition (ABC) to make the NMM method more accurate and efficient for wave diffusion problems in unbounded media and applicable to scattering problems with lossless media. We manipulate the weak form of Maxwell's equations and impose the correct boundary conditions at the cylindrical axis to solve the singularity problem which is ignored by all previous researchers. The spectral element method (SEM) is introduced to more efficiently compute the eigenmodes of higher accuracy with less unknowns, achieving a faster mode matching procedure between different horizontal layers. We also prove the relationship of the field between opposite mode indices for different types of excitations, which can reduce the computational time by half. The formulas for computing EM fields excited by an electric or magnetic dipole located at any position with an arbitrary orientation are deduced. And the excitation are generalized to line and surface current sources which can extend the application of NMM to the simulations of controlled source electromagnetic techniques. Numerical simulations have demonstrated the efficiency and accuracy of this method.

Finally, the improved numerical mode matching (NMM) method is introduced to efficiently compute the electromagnetic response of the induction tool from orthogonal transverse hydraulic fractures in open or cased boreholes in hydrocarbon exploration. The hydraulic fracture is modeled as a slim circular disk which is symmetric with respect to the borehole axis and filled with electrically conductive or magnetic proppant. The NMM solver is first validated by comparing the normalized secondary field with experimental measurements and a commercial software. Then we analyze quantitatively the induction response sensitivity of the fracture with different parameters, such as length, conductivity and permeability of the filled proppant, to evaluate the effectiveness of the induction logging tool for fracture detection and mapping. Casings with different thicknesses, conductivities and permeabilities are modeled together with the fractures in boreholes to investigate their effects for fracture detection. It reveals that the normalized secondary field will not be weakened at low frequencies, ensuring the induction tool is still applicable for fracture detection, though the attenuation of electromagnetic field through the casing is significant. A hybrid approach combining the NMM method and BCGS-FFT solver based integral equation has been proposed to efficiently simulate the open or cased borehole with tilted fractures which is a non-axisymmetric model.

Modeling non-harmonic behavior of materials from experimental inelastic neutron scattering and thermal expansion measurements

Based on thermodynamic principles, we derive expressions quantifying the non-harmonic vibrational behavior of materials, which are rigorous yet easily evaluated from experimentally available data for the thermal expansion coefficient and the phonon density of states. These experimentally- derived quantities are valuable to benchmark first-principles theoretical predictions of harmonic and non-harmonic thermal behaviors using perturbation theory, ab initio molecular-dynamics, or Monte-Carlo simulations. We illustrate this analysis by computing the harmonic, dilational, and anharmonic contributions to the entropy, internal energy, and free energy of elemental aluminum and the ordered compound FeSi over a wide range of temperature. Results agree well with previous data in the literature and provide an efficient approach to estimate anharmonic effects in materials.