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Beamspace multiple-input multiple-output (B-MIMO) provides a promising solution for reducing the number of required expensive radio frequency (RF) chains without obvious performance loss. However, the high computational complexities of beam selection algorithms prohibits their practical applications in 5G millimeter wave (mmWave) massive MIMO communication systems. Reviewing existing beam selection procedures and using the matrix perturbation theory, the complexity reduction on beam selection for beamspace MIMO is considered in this letter. Two beam selection algorithms, one for B-MIMO systems with classic zero-forcing (ZF) precoder and the other for the systems with QR precoder are proposed. Theoretical analyses and numerical simulations all show that the proposed beam selection algorithms possess a much lower complexity than conventional ones.

The rapid growth of maritime transportation and its regularization have imposed an increasing demand for developing a global maritime surveillance capacity. The existing cooperative maritime traffic monitoring relies on the shipborne automatic identification system (AIS), which is now confronting severe security threats due to the vulnerabilities of AIS at both the implementation and protocol levesl. In this article, the possibility of passive AIS signal localization using low Earth orbit satellite constellations is investigated, which provides a more reliable vessel position determination. To this end, the article first presents an overview on two categories of passive localization methods. Realizations of these methods on the satellite-based AIS emitter position determination are then demonstrated and compared. To evaluate the system performance, the lower bound for the localization error is also derived. Focusing on the system realization, some general design considerations and localization accuracy optimization are further discussed.

The increasingly popular characteristic mode analysis (CMA) techniques in the free-space have been well-established, while the half-space counterpart is less concerned. In this communication, we consider the CMA for half-space platforms such as vehicles on the ground and ships on the sea surface, which is also commonly mounted with antennas. To overcome the difficulty of CMA’s application on electrically large targets, the half-space multilevel fast multipole algorithm is integrated into the eigensolver. Numerical results of half-space CMA for realistic platforms from FM-band to ${L}$ -band are presented to validate the accuracy and the robustness of the proposed method. It has been shown that this communication can be used as a legitimate CMA tool for the antenna design and integration on half-space platforms.

In ferromagnetic materials, spin up and down electrons can carry different heat currents. This spin-dependent energy excitation mode (‘spin energy mode’) occurs only when spin up and down energy distribution functions are different. In superconductors, heat is carried by quasiparticle excitations and the spin energy mode can be excited by spin-polarised current injection. In the presence of a finite Zeeman magnetic field, the spin energy mode surprisingly leads to a charge imbalance (different numbers of hole- and electron-like quasiparticles) at the superconducting gap edge. By performing spin-resolved spectroscopy of the out-of-equilibrium quasiparticle populations in a mescoscopic superconductor, we reveal that their distribution functions are non-Fermi–Dirac. In addition, our spectroscopic technique allows us to observe a charge imbalance, localised in energy to the gap edge and thus unambiguously identify the spin energy mode. Our results agree well with theory and shed light on energy transport in superconducting spintronics., In systems where the spin states have different energy distributions, the different spin populations can carry different heat currents, in what is known as the spin-energy mode. Here, using spin-resolved spectroscopy, the authors demonstrate the existence of a spin-energy mode in a superconductor.

The scattering center (SC) model provides a concise, explicit description of the object electromagnetic characteristics, significantly improves the efficiency of radar signal simulations, and plays an important role in model-based automatic target recognition. The existing models are mainly developed for conducting objects, and few are developed for dielectric ones. The SC models of dielectric objects are essentially different from those of their conducting counterparts due to the different scattering mechanisms. In this article, the backscattering mechanisms of canonical dielectric structures are studied, and their corresponding SC models are proposed. More importantly, the parametric SC models of the composite objects of canonical structures are first presented. These SC models are validated by comparing the radar cross section (RCS), the time–frequency representation (TFR), and the high-resolution range profile (HRRP) from the SC model with the results of the full-wave numerical method.

In this communication, the asymptotic expressions for Sommerfeld integrals (SIs) over an impedance plane are studied, since the impedance boundary condition (IBC) is a widely used simplification of many discontinuous interfaces. Based on the single image representation of SI, it is found that the far-field asymptotics of SIs can be written in forms of the well-known Fresnel integrals. A simple high-order approximation to the SI is derived, the accuracy and convergence behavior are numerically investigated. The behavior difference for SIs associated with different polarizations in some special cases is also analyzed.

Graphene ribbons, which may be fabricated by a wide variety of experimental techniques such as chemical processing, unzipping or etching of carbon nanotubes, molecular precursors, ion implantation,...

A flexible and efficient Hierarchical LU ( $\mathcal{H}$ -LU)-based preconditioner ( $\mathcal{H}$ -LU-P) is presented for the hybrid finite element-boundary integral (FE-BI) multilevel fast multipole algorithm for solving three-dimensional scattering by inhomogeneous objects. The formulation of FE-BI is first approximated by using locally approximated integral operators for the BI part to construct a finite element method-absorbing boundary condition (FEM-ABC) based preconditioning matrix. Then, the preconditioning matrix equation is solved by the nested dissection accelerated $\mathcal{H}$ -LU-based fast direct solver. A semi-geometric clustering strategy is proposed to simplify the cluster tree-building procedure in representing the preconditioning matrix in the $\mathcal{H}$ -matrix form. Numerical results demonstrate that the $\mathcal{H}$ -LU-P outperforms other alternative preconditioners, based on multifrontal approach. The scattering by a large and complex aircraft model with a radome on its nose section is calculated, showing the capability and efficiency of the preconditioner.

We report fabrication and measurements of hexagonal boron nitride (h-BN)/chemical vapor deposition (CVD) graphene/h-BN heterostructure devices without using expensive, time-consuming electron-beam lithography and toxic carbon tetrafluoride or sulfur tetrafluoride etching. We use efficient transfer of h-BN/CVD graphene by polypropylene carbonate onto a pre-prepared metal contacts/h-BN/SiO2 substrate. In this case, CVD-graphene is suspended from the h-BN substrate which allows efficient gas annealing process for improving the device mobility. Interestingly, we find that the top h-BN capping layer could enhance the carrier interference effect in CVD graphene, a great advantage for low-cost graphene-based interference-type electronic devices.

In this paper, we present a flexible and efficient ternary parallelization approach for the multilevel fast multipole algorithm (MLFMA) for the solution of extremely large 3-D scattering problems with over 10 billion unknowns. In the ternary parallelization approach, a binary clustering tree of all the message passing interface (MPI) processes is built first. Then, the MLFMA tree is categorized into plane wave partitioning, hierarchical-structure partitioning, and box partitioning (BP) levels via a top–down approach to match the process clustering tree. Compared with the bottom–up approach, interprocess communications in the far interaction are reduced. An inner-group transition level is designed for switching partitions on the intermediate level between the hierarchical-structure partitioning and BP levels. The ternary strategy can realize as high parallel efficiency as the hierarchical partitioning strategy while maintaining flexibility in selecting the total number of processes. An auxiliary-tree-based parallel mesh refinement technique and a hybrid octree storage strategy are designed to facilitate the realization of fast full-wave simulation on a scale of over 10 billion unknowns with the ternary MLFMA. The accuracy of the solutions is validated by comparing the radar cross sections (RCSs) of a sphere of diameter 3042 wavelengths with 10 773 415 728 unknowns via the MLFMA and the Mie series, which is the largest number of unknowns to be computed via full wave numerical methods to date. Furthermore, the solutions for complicated objects, namely a ship and an aircraft model, both of which have maximum lengths that exceed 10 000 wavelengths and over 10 billion unknowns, are presented.

The integral equation method is one of the most successful computational models for microwave devices or integrated circuits in planar layered media. However, the efficient and accurate evaluation of the associated Green’s function consisting of Sommerfeld integrals (SIs) is still a remaining challenge. To mitigate this difficulty, this work proposes a spatial domain rational function fitting technique (RFFT) for SIs so that the approximation accuracy is controllable. In conjunction with an adaptive sampling strategy, the proposed RFFT minimizes the orders of rational functions, and the resultant SI evaluation efficiency is optimized. In addition, we investigate the semi-analytical singularity treatment for the rational expression of SIs in method of moment (MoM) implementation. Extensive simulation of representative planar devices validates the correctness of the proposed method and demonstrates its superior performance over conventional SI approximation methods.

Owing to the revolutions in satellite constellation networking and the development of microelectronics, the terahertz band has become an attractive solution for inter-satellite communication links for its promising high date rate. For the accurate estimation of propagation characteristics of THz signals in space, this letter presents a deterministic channel estimation approach. Due to the existence of thermal multilayer insulation (MLI) blankets covering the satellite, the scattering mechanism from the satellite platform at the THz band is complicated and difficult to estimate. In this work, a simplified procedure to model the MLI surface and the physical optics approximation to calculate its scattering are presented. Mento-Carlo simulations are performed to evaluate the impact of the rough MLI surface in channel impulse response and other propagation characteristics.

Aiming to the efficient electromagnetic scattering analysis from multiscale targets in half-space, the discontinuous Galerkin method is considered in this work. It is found that the widely used mixed-potential integral equation requires proper modifications in order to impose current continuity and zero charge accumulation conditions on the neighboring subdomain contours. Numerical examples and comparisons are carried out to demonstrate the accuracy, versatility, and flexibility of the discontinuous Galerkin scheme in half-space scattering problems.

An exact and asymptotic expression for dyadic Green function of a vertical dipole above impedance surface is studied in this paper. Based on the single image expression for Sommerfeld integral, the vector field quantities caused by a vertical dipole placed above impedance surface are derived. In addition, the far-field asymptotic expression is presented in terms of series expansion, which provides new physical insights of the vertical dipole radiation above impedance surface.

A flexible and efficient $\mathcal{H}$-LU-based preconditioner ($\mathcal{H}$-LU-P) is presented for the hybrid finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) for solving 3D scattering by inhomogeneous objects in this paper. The formulation of FE-BI is firstly approximated by using locally approximated integral operators for the BI part to construct a FEM-ABC based precondition matrix. Then the precondition matrix equation is solved by the nested dissection (ND) accelerated $\mathcal{H}$-LU-based fast direct solver. Performance of the $\mathcal{H}$-LU-P is studied numerically for different problems, including the quasi-static problem, 2D extended and 3D extended electrodynamic problems, etc. Numerical experiments show the $\mathcal{H}$-LU-P has an O(NlogN) memory complexity and an O(Nlog2N) CPU time complexity for the quasi-static, the 2D extended lossless and the 3D extended lossy problems. For the 3D extended lossless problems, the complexity is larger due to the increasing rank of the $\mathcal{H}$-LU, but it still outperforms alternative direct solvers, such as the popular multifrontal-based solver MUMPS. Large realistic scattering problems with more than ten million unknowns are calculated, including a honeycomb structure with 8100 elements, showing the capability and efficiency of our proposed preconditioner.

Breaking wave modeling is one of the most important difficulties in the simulation of sea scattering. To explore the scattering characteristics of a more realistic model, a time-continuous breaking wave model is developed in this paper, which is based on the open-sourced package of DualSPHysics. The electromagnetic (EM) scattering of several representative frames is calculated by the two-dimensional method of moments (MoM). In this paper, the characteristics of horizontal polarization (HH) and vertical polarization (VV) scattering under different sea conditions are elucidated. Sea spikes are pinpointed when incidence illuminating at large incidence angles. It turns out that when the wave surges, the scattering of both polarizations at large incident angles increase greatly, accompanied by significant changes in the scattering characteristics, resulting in remarkable sea spikes.

In this work, the efficient evaluation of Sommerfeld integrals (SIs) above an impedance plane is addressed. Started from Weyl’s expression of SIs, using the coordinate transformation and steepest descent path approach, an exact single image representation to SIs is derived. This single image representation image eliminates oscillating and slow-decay integrand in traditional SIs, and efficient to calculate. Moreover, the far-field asymptotic behavior of SIs in this case is considered and is represented by the Fresnel-integral related function. A high-order approximation based on series expansion of Fresnel integral is provided for fast evaluation. Finally, the validity of the proposed expressions is verified by numerical examples.

Two foremost barriers to the development of fast and efficient simulation algorithms for electromagnetic problems in half-space and planar media are efficient Sommerfeld integral evaluation techniques and fast solvers. In this paper, we focus on challenging these two difficulties in the impedance boundary half-space, which is a proper model for common air-lossy media half-space. Based on the Laplace transformation, we first propose an alternative exact image representation for the Sommerfeld integral in half-space Green’s function. In addition to its fast and absolute convergence property, this new exact image version does not contain any singularities and interprets the Sommerfeld integral as an integral over real image line. Furthermore, this representation allows a rigorous fast multipole expansion (FME), and thus it can be applied to the development of fast multipole solver with controllable precision. However, this exact image representation is not valid for the all Sommerfeld integrals in half-space Green’s function. Therefore, a more generalized single mirror image representation, also exact and computationally efficient, is then presented. The strength of the mirror image is obtained through Weyl’s method and steep descent path approach. Subsequently, an approximated FME scheme for this representation is proposed and studied via numerical examples. We find this approximated FME scheme has a higher accuracy than that of previous work. Numerical results show that the proposed work provides exact and efficient evaluations for Sommerfeld integrals in impedance boundary half-space Green’s function and valuable insights into the development of fast multipole solver for half-space electromagnetic problems.

Several graphene quantized Hall resistance (QHR) devices manufactured at the National Institute of Standards and Technology (NIST) were compared with GaAs QHR devices and a 100- $\Omega $ standard resistor at the National Institute for Advanced Industrial Science and Technology (AIST). Measurements of a 100- $\Omega $ resistor with graphene QHR devices agreed within 5 $\text{n}\Omega /\Omega $ of the values for a 100- $\Omega $ resistor obtained through GaAs measurements. The electron density of the graphene devices was adjusted at AIST to restore device properties such that operation was possible at low magnetic flux densities of 4–6 T. This adjustment was accomplished by a functionalization method utilized at NIST, allowing for consistent tunability of the graphene QHR devices with simple annealing. Such a method replaces older and less predictable methods for adjusting graphene for metrological suitability. The milestone results demonstrate the ease with which graphene can be used to make resistance comparison measurements among many National Metrology Institutes (NMIs).

To enhance the capability of the characteristic mode analysis (CMA) for electrically large problems, fast multipole algorithms (FMAs) are incorporated into this increasingly popular technique in antenna community. In this communication, an improvement formulation of CMA with FMAs is presented and studied. Numerical results show that the proposed formulation has a better convergence behavior than the previous formulation when it is used for electrically large antenna platforms.

We report the fabrication and measurement of top gated epitaxial graphene p-n junctions where exfoliated hexagonal boron nitride (h-BN) is used as the gate dielectric. The four-terminal longitudinal resistance across a single junction is well quantized at the von Klitzing constant $${{\boldsymbol{R}}}_{{\boldsymbol{K}}}$$ R K with a relative uncertainty of 10−7. After the exploration of numerous parameter spaces, we summarize the conditions upon which these devices could function as potential resistance standards. Furthermore, we offer designs of programmable electrical resistance standards over six orders of magnitude by using external gating.

Homogeneous, single-crystal, monolayer epitaxial graphene (EG) is the one of most promising candidates for the advancement of quantized Hall resistance (QHR) standards. A remaining challenge for the electrical characterization of EG-based quantum Hall devices as a useful tool for metrology is that they are electrically unstable when exposed to air due to the adsorption of and interaction with atmospheric molecular dopants. The resulting changes in the charge carrier density become apparent by variations in the surface conductivity, the charge carrier mobility, and may result in a transition from n-type to p-type conductivity. This work evaluates the use of Parylene C and Parylene N as passivation layers for EG. Electronic transport of EG quantum Hall devices and non-contact microwave perturbation measurements of millimeter-sized areas of EG are both performed on bare and Parylene coated samples to test the efficacy of the passivation layers. The reported results, showing a significant improvement in passivation due to Parylene deposition, suggest a method for the mass production of millimeter-scale graphene devices with stable electrical properties.

We investigate the energy relaxation of hot carriers in a CVD-grown graphene device with a top h-BN layer by driving the devices into the nonequilibrium regime. By using the magnetic field dependent conductance fluctuations of our graphene device as a self-thermometer, we can determine the effective carrier temperature Te at various driving currents I while keeping the lattice temperature TL fixed. Interestingly, it is found that Te is proportional to I, indicating little electron-phonon scattering in our device. Furthermore the average rate of energy loss per carrier Pe is proportional to (Te 2-TL 2), suggesting the heat diffusion rather than acoustic phonon processes in our system. The long energy relaxation times due to the weak electron-phonon coupling in CVD graphene capped with h-BN layer as well as in exfoliated multilayer graphene can find applications in hot carrier graphene-based devices.

A fast finite element method (FEM) is proposed for electromagnetic computation of recently developed hyperuniform disordered materials having multiscale geometry features. The main idea of our fast FEM is to construct a small dimensional local solution space to approximate the solution space of a multiscale subdomain that requires a large number of unknowns in the conventional FEM. The approximation efficiency is guaranteed by the fact that the multiscale subdomain is usually electrically small at its working frequency and is densely meshed due to the fine geometry and material features. To further reduce the size of the solution space, the interpolative decomposition approach is employed to adaptively choose the number of skeleton vectors for a given accuracy. The solution space is then used as basis functions for the multiscale subdomain instead of using conventional ones in the finite element analysis to reduce the total number of unknowns. We present some numerical examples to demonstrate the accuracy and efficiency of our method.

An efficient gridless semi-analytical model was developed to simulate real gas transport in shale formation with nanopores and complex fracture geometry. This model incorporates multiple physics such as gas desorption, adsorbed gas porosity, gas slippage and diffusion, residual water saturation, non-Darcy flow, choke skin, and pressure-dependent matrix permeability and fracture conductivity. Additionally, this model is easy to handle complex fracture geometry through dividing fractures into a number of segments and nodes. We verified the model against a numerical model and an analytical model for bi-wing hydraulic fractures. After validation, the impacts of all these physics on well performance were evaluated in detail through a series of case studies. The simulation results confirm that modeling of gas production from complex fracture geometry as well as modeling important physics in shale gas reservoirs is significant. This study improves our understanding of critical physics affecting gas recovery in shale gas reservoirs. This article is protected by copyright. All rights reserved.

Summary Well interference is a common phenomenon between wells observed in unconventional reservoirs, which has received significant attention. It plays an important role in well-spacing considerations. Massive hydraulic fractures are generated in horizontal wells by multistage hydraulic-fracturing treatments and result in well interference between adjacent wells. However, very little work has been completed to understand how massive fractures cause well interference. In this study, we analyzed dynamic-stress evolution and multiple-fracture propagation from two horizontal wells to improve understanding of fracture hits. We used our newly developed nonplanar hydraulic-fracturing model that couples rock deformation and fluid flow in the fracture and horizontal wellbore. Fracture propagation in a stage is controlled by stress-shadow effects and flow-rate distribution between fractures. Fracture interaction within a stage and from adjacent wells is considered through a simplified 3D displacement discontinuity method. Well interference is well communication caused by fracture hits. Because of varying stress reorientation, fractures propagate toward each other from two adjacent wells, and fracture tips always tend to converge with each other and decrease fracture distance, which promotes fracture coalescence. For plug-and-perforate completion, multiple fractures in a stage generally cannot uniformly develop. Dominant fractures with extremely long length are often generated and hit fractures from adjacent wells. Fracture hits and well interference are induced by these two mechanisms, which are affected by fracture spacing and the differential stress (DS) of reservoirs. Results show that the larger the fracturing spacing is, the smaller the likelihood is to induce fracture connection. A large DS can prevent fractures from deviating from their original paths. For a reservoir with a large DS, fracture hits can be decreased with a stagger distance of fractures between two wells. This work uses a hydraulic-fracturing model to analyze fracture geometry between two horizontal wells and offers improved understanding of fracture connection. The results of the study provide critical insights to improve well interference and to optimize well spacing and design of multiwell completion techniques.

We have performed extensive transport experiments on a 4 nm thick aluminum (Al) superconducting film grown on a GaAs substrate by molecular beam epitaxy (MBE). Nonlinear current-voltage (I-V) measurements on such a MBE-grown superconducting nanofilm show that V ∼ I 3, which is evidence for the Berezinskii-Kosterlitz-Thouless (BKT) transition, both in the low-voltage (T BKT ≈ 1.97 K) and high-voltage regions (T BKT ≈ 2.17 K). In order to further study the two regions where the I-V curves are BKT-like, our experimental data are fitted to the temperature-induced vortices/antivortices unbinding model as well as the dynamical scaling theory. It is found that the transition temperature obtained in the high-voltage region is the correct T BKT as confirmed by fitting the data to the aforementioned models. Our experimental results unequivocally show that I-V measurements alone may not allow one to determine T BKT for superconducting transition. Therefore, one should try to fit one's results to the temperature-induced vortices/antivortices unbinding model and the dynamical scaling theory to accurately determine T BKT in a two-dimensional superconductor.

The sea spikes in radar echo lead to serious interference for marine targets detection, which is aggravated at low grazing angle (LGA). To investigate the relation between sea spikes and sea surface events, a multi-physics based numerical model is established. The results confirm the strong correlation between the sea spikes and breaking waves on the sea surface. The wide-band back-scattering characteristics of sea surface evolution for different polarizations is also numerically studied.

Monolayer epitaxial graphene (EG) has been shown to have clearly superior properties for the development of quantized Hall resistance (QHR) standards. One major difficulty with QHR devices based on EG is that their electrical properties drift slowly over time if the device is stored in air due to adsorption of atmospheric molecular dopants. The crucial parameter for device stability is the charge carrier density, which helps determine the magnetic flux density required for precise QHR measurements. This work presents one solution to this problem of instability in air by functionalizing the surface of EG devices with chromium tricarbonyl -Cr(CO)(3). Observations of carrier density stability in air over the course of one year are reported, as well as the ability to tune the carrier density by annealing the devices. For low temperature annealing, the presence of Cr(CO)(3) stabilizes the electrical properties and allows for the reversible tuning of the carrier density in millimeter-scale graphene devices close to the Dirac point. Precision measurements in the quantum Hall regime show no detrimental effect on the carrier mobility.

The breaking waves on the sea-surface account for the sea-spikes in radar echo and lead to excessive false detections. To study the back-scattering characteristics of breaking waves in more detail, the realistic breaking wave sequential are numerically modeled by solving the govern fluid equations. Meanwhile, the back-scattering of breaking waves from different directions and polarizations are calculated by using the full-wave finite element method. It is found that the super events in sea-spikes are associated with some specific stages in the breaking cycle. The back-scattering characteristics of breaking waves compared with those of the wedge model are also investigated to justify the validity of wedge model approximation.

We have performed detailed transport measurements on a 3 nm thick (as-grown) Al film on GaAs prepared by molecular beam epitaxy (MBE). Such an epitaxial film grown on a GaAs substrate shows the Berezinskii-Kosterlitz-Thouless (BKT) transition, a topological transition in two dimensions. Our experimental data shows that the MBE-grown Al nanofilm is an ideal system for probing interesting physical phenomena such as the BKT transition and superconductivity. The increased superconductor transition temperature (~2.4 K) compared to that of bulk Al (1.2 K), together with the ultrathin film quality, may be advantageous for future superconductor-based quantum devices and quantum information technology.

The breaking wave is the primary factor causing complicated scattering characteristics of the sea surface. In this work, the electromagnetic scattering of breaking waves is analyzed from multiphysics point of view. The development of a canonical plunging breaking waves in deep-water is numerically simulated by solving the non-linear hydrodynamic equation. Meantime, the scattering of the developing breaking waves for different polarizations at different times are simulated using 2D finite element method. Numerical results reveal the scattering characteristics of breaking waves at different stages in the breaking process and under different polarizations.

We report the growth of large-area monolayer graphene on the centimeter scale using an optimized growth process allowing for reproducibility and morphology improvements. Magneto-transport measurements on graphene quantum Hall effect devices demonstrate the applicability for high-current quantum resistance metrology.

We report the performance of a quantum standard based on epitaxial graphene maintained in a 5 T table-top cryocooler system. The $v=2$ resistance plateau, with a value of ${R}_{\mathbf{K}-{90}/2}$ , is used to scale to ${1}\ \text{k}{\Omega}$ using a binary cryogenic current comparator (BCCC) bridge. The preliminary uncertainties achieved with the BCCC are like those obtained in state-of-the-art measurements using GaAs-based devices. This quantum standard requires no liquid He and can operate continuously, allowing year-round accessibility to traceable resistance measurements.

We report the fabrication and measurement of top gated epitaxial graphene p-n junctions where exfoliated hexgonal boron nitride (hBN) is used as the gate dielectric. The four terminal longitudinal resistance across a single junction is well quantized at $R_{\text{K} -90}(=25812.807\ \Omega)$ with a relative uncertainty of 10−7. Our work opens the possibility to realize programmable electrical resistance standards using external gating.

Two graphene quantized Hall resistance (QHR) devices made at the National Institute of Standards and Technology (NIST) were hand carried to the National Institute for Advanced Industrial Science and Technology (AIST) and compared to a $\mathbf{GaAs}$ QHR device and a $\pmb{100 \ \Omega}$ standard resistor. Measurement of the $\pmb{100\ \Omega}$ resistor with the graphene QHR devices agreed within $\pmb{5}\ \mathbf{x}\ \pmb{10^{-9}}$ of the $\pmb{100\ \Omega}$ resistor $\mathbf{GaAs}$ measurements. After the initial measurements, the carrier density of the graphene devices was adjusted at AIST to restore the device properties to operate at low magnetic fields of 4 T to 6 T.