Observation of optical gyromagnetic properties in a magneto-plasmonic metamaterial

Metamaterials with artificial optical properties have attracted significant research interest. In particular, artificial magnetic resonances in non-unity permeability tensor at optical frequencies in metamaterials have been reported. However, only non-unity diagonal elements of the permeability tensor have been demonstrated to date. A gyromagnetic permeability tensor with non-zero off-diagonal elements has not been observed at the optical frequencies. Here we report the observation of gyromagnetic properties in the near-infrared wavelength range in a magneto-plasmonic metamaterial. The non-zero off-diagonal permeability tensor element causes the transverse magneto-optical Kerr effect (TMOKE) under s-polarized incidence that otherwise vanishes if the permeability tensor is not gyromagnetic. By retrieving the permeability tensor elements from reflection, transmission, and TMOKE spectra, we show that the effective off-diagonal permeability tensor elements reach the 10-3 level at the resonance wavelength (~900 nm) of the split-ring resonators that is at least two orders of magnitude higher than that of magneto-optical materials at the same wavelength. The artificial gyromagnetic permeability is attributed to the change in the local electric field direction modulated by the split-ring resonators. Our study demonstrates the possibility of engineering the permeability and permittivity tensors in metamaterials at arbitrary frequencies, thereby promising a variety of applications of next-generation nonreciprocal photonic devices, magneto-plasmonic sensors, and active metamaterials.

A FEM-Based Optimization Method for Driving Frequency of Contactless Magnetoelastic Torque Sensors in Steel Shafts

This paper presents a novel finite element method (FEM) of optimization for driving frequency in magneto-mechanical systems using contactless magnetoelastic torque sensors. The optimization technique is based on the generalization of the axial and shear stress dependence of the magnetic permeability tensor. This generalization creates a new possibility for the determination of the torque dependence of a permeability tensor based on measurements of the axial stress on the magnetization curve. Such a possibility of quantitative description of torque dependence of a magnetic permeability tensor has never before been presented. Results from the FEM-based modeling method were validated against a real magnetoelastic torque sensor. The sensitivity characteristics of the model and the real sensor show a maximum using a driving current of similar frequency. Consequently, the proposed method demonstrates the novel possibility of optimizing magnetoelastic sensors for automotive and industrial applications.

Influences of Coal Properties on the Principal Permeability Tensor during Primary Coalbed Methane Recovery: A Parametric Study

Coal permeability is intrinsically anisotropic because of the cleat structure of coal. Therefore, coal permeability can be denoted by a second-order tensor under three-dimensional conditions. Our previous paper proposed an analytical model of the principal permeability tensor of coal during primary coalbed methane (CBM) recovery. Based on this model, 18 modeling cases were considered in the present study to evaluate how the principal permeabilities were influenced by representative coal properties (the areal porosity, the internal swelling ratio, and the Young modulus) during primary CBM recovery. The modeling results show that with regard to the influences of the areal porosity on the principal permeabilities, an increase in cleat porosity reduces the sensitivity of each principal permeability to pore pressure change. The magnitudes of the principal permeabilities are positively proportional to the internal swelling ratio. The principal permeabilities thus tend to monotonically increase with a depletion in the pore pressure when the internal swelling ratio increases. Because the internal swelling ratio represents the extent of gas-sorption-induced matrix deformation, an increase in the internal swelling ratio increases desorption-induced matrix shrinkage and thus induces an increase in permeability. The principal permeabilities are positively proportional to the isotropic principal Young moduli and the synchronously changing anisotropic principal Young moduli. On the other hand, the principal Young modulus within the plane of isotropy influences the principal permeabilities within this plane in diverse patterns depending on both the dip angle of the coalbed and the pitch angle of the cleat sets. The principal permeability perpendicular to the plane of isotropy is positively proportional to this principal Young modulus, and this correlation pattern is independent of both the dip angle and pitch angle.

Can fill-and-spill subsurface flow be represented by a moisture-dependent anisotropic permeability tensor in Richards equation-based models with coarse spatial resolution?

<p>Subsurface structural heterogeneity can route soil water through the vadose zone in complex ways that are difficult to observe or model in detail. The fill-and-spill hypothesis, which was developed to explain observations from field experiments at the hillslope scale, suggests that lateral flow at the soil-bedrock interface (or other permeability contrasts) is only activated once depressions in the microtopography of that interface become saturated and connect laterally. To reproduce this fill-and-spill phenomenon, a Richards equation-based numerical model would require a discretization of this morphology at a fine scale. A coarse representation smooths the interface eliminating the essential local storage-excess threshold behavior. However, the accuracy and abundance of field measurements rarely provide the data that would be needed to do this, and the fine discretization creates a high computational burden.</p><p>Here we explore the potential of an upscaled representation of the fill-and-spill mechanism based on parameterization of a permeability tensor with saturation-dependent anisotropy. By increasing empirical lateral hydraulic conductivity as they approach saturation, this anisotropy could reproduce how the fill-and-spill causes saturated patches at the permeability contrast to connect along preferential flow paths. Such a process representation could be incorporated into a Richards equation-based model enabling it to reproduce the fill-and-spill phenomenon even with a coarse spatial resolution.</p><p>We tested this idea using ParFlow to model virtual hillslopes with synthetic rugged internal topography. We then investigated the effective permeability tensor over an averaging volume that encloses the interface. By parameterizing the anisotropy of an interface block under changing moisture variables, we may be able to generate predictions of how the fine-scale fill-and-spill processes integrate to the hillslope and catchment scale.</p>

Equivalent Permeability Distribution for Fractured Porous Rocks: The Influence of Fracture Network Properties

Equivalent fracture models are widely used for simulations of groundwater exploitation, geothermal reservoir production, and solute transport in groundwater systems. Equivalent permeability has a great impact on such processes. In this study, equivalent permeability distributions are investigated based on a state-of-the-art numerical upscaling method (i.e., the multiple boundary method) for fractured porous rocks. An ensemble of discrete fracture models is created based on power law length distributions. The equivalent permeability is upscaled from discrete fracture models based on the multiple boundary method. The results show that the statistical distributions of equivalent permeability tensor components are highly related to fracture geometry and differ from each other. For the histograms of the equivalent permeability, the shapes of k x x and k y y change from a power law-like distribution to a lognormal-like distribution when the fracture length and the number of fractures increase. For the off-diagonal component k x y , it is a normal-like distribution and its range expands when the fracture length and the number of fractures increase. The mean of diagonal equivalent permeability tensor components increases linearly with the fracture density. The analysis helps in generating stochastic equivalent permeability models in fractured porous rocks and reduces uncertainties when applying equivalent fracture models.

Generalization of the Model of Magnetoelastic Effect: 3D Mechanical Stress Dependence of Magnetic Permeability Tensor in Soft Magnetic Materials

This paper presents a new solution enabling modeling of the mechanical stress tensor dependence of the 3D relative permeability tensor of isotropic material only on the basis of knowledge of the axial stress dependence characteristics. For the proposed model, the concept of principal stresses is utilized. In such a case, the sophisticated system of axial and shear stresses may be reduced to the set of axial stresses in a rotated coordination axes system. As a result, the proposed solution generalizes the explanation of the shape of magnetoelastic characteristics as well as radically extending possibility of the application of the finite elements methods (FEM) to describe sophisticated magnetoelastic systems.