Smooth Regions Research Articles

A Consistent and Well‐Balanced Hybrid Weighted Essentially Non‐Oscillatory Scheme for Shallow Water Equations on Unstructured Meshes

ABSTRACTIn this article, a type of high‐order consistent and well‐balanced hybrid weighted essentially non‐oscillatory (WENO) scheme is proposed for shallow water equations with flat or non‐flat bottom on unstructured triangular meshes. The hybrid scheme presents a new consistent discretization format on the flux and the source term with the goal of obtaining a hybridization of the high‐order WENO scheme and linear scheme. According to the modified multi‐resolution analysis approach, we can select the more robust and accurate WENO reconstruction in the vicinity of discontinuities, and the less expensive linear reconstruction in the smooth regions. As a result, the suggested hybrid WENO scheme can acquire the capacity of saving the computing time cost while maintaining the excellent numerical features of the original WENO scheme. Eventually, some extensive and classical two‐dimensional numerical examples, including a tidal bore of an estuary with an irregular computation area are provided to validate the performance of this hybrid WENO scheme on triangular meshes in terms of accuracy order, exact conservation property, shock‐capturing, good resolution, and computational efficiency.

Robust 3D multi‐material hydrodynamics using discontinuous Galerkin methods

AbstractA high‐order discontinuous Galerkin (DG) method is presented for nonequilibrium multi‐material () flow with sharp interfaces. Material interfaces are reconstructed using the algebraic THINC approach, resulting in a sharp interface resolution. The system assumes stiff velocity relaxation and pressure nonequilibrium. The presented DG method uses Dubiner's orthogonal basis functions on tetrahedral elements. This results in a unique combination of sharp multimaterial interfaces and high‐order accurate solutions in smooth single‐material regions. A novel shock indicator based on the interface conservation condition is introduced to mark regions with discontinuities. Slope limiting techniques are applied only in these regions so that nonphysical oscillations are eliminated while maintaining high‐order accuracy in smooth regions. A local projection is applied on the limited solution to ensure discrete closure law preservation. The effectiveness of this novel limiting strategy is demonstrated for complex three‐dimensional multi‐material problems, where robustness of the method is critical. The presented numerical problems demonstrate that more accurate and efficient multi‐material solutions can be obtained by the DG method, as compared to second‐order finite volume methods.

A new high-order RKDG method based on the TENO-THINC scheme for shock-capturing

In recent years, Runge-Kutta Discontinuous Galerkin (RKDG) methods have gained substantial attention in solving hyperbolic conservation laws, attributed to their high-order accuracy and adaptability to unstructured meshes. However, standard RKDG methods cannot capture discontinuities without oscillation unless they are supplemented with troubled cell indicators and limiters. Existing indicators, such as the total variation bounded (TVB) minmod indicator and the KXRCF indicator, typically depend on a critical parameter tied to the equation's solution, necessitating tuning for different cases. In terms of limiters, the popular limiters even fail to guarantee the high-order property in the smooth regions. The advent of Weighted Essentially Non-Oscillatory (WENO) schemes prompts the implementation of WENO limiters for RKDG methods, preserving high-order properties. However, WENO-family schemes exhibit significant numerical dissipation, potentially smearing small-scale flow structures. In this work, the Targeted Essentially Non-Oscillatory (TENO) indicator [1] is utilized, which leverages the nonlinear weighting strategy of the TENO scheme to separate high-wavenumber physical fluctuations and genuine discontinuities from smooth regions with a unified set of parameters. For troubled cells, a novel limiter is proposed for structured meshes, which combines a TENO scheme for resolving high-wavenumber physical fluctuations and a novel non-polynomial Tangent of Hyperbola for the INterface Capturing (THINC) scheme for resolving genuine discontinuities with extremely low numerical dissipation. Furthermore, the shifting between the TENO and THINC schemes is based on a new boundary variation diminishing (BVD) strategy, which only relies on compact neighborhoods and is significantly simpler than its predecessors. Meanwhile, a new strategy is proposed to ensure the consistency of the new limiter applied for 1D and 2D cases. A set of 1D and 2D benchmark cases including strong shockwaves and a broad range of flow length scales is simulated with uniform meshes for 1D cases and structured quadrilateral meshes for 2D cases to demonstrate the performance of the new numerical scheme. The indicator does not activate any limiters in the accuracy test cases to ensure the high-order property of the whole numerical scheme. Other cases with discontinuities demonstrate the low-dissipation properties of the new limiter in comparison to the simple WENO limiter.

Radiation of a bunch in a waveguide having areas with deeply corrugated and smooth walls

We analyze radiation from a filamentary bunch that uniformly moves in a circular waveguide and crosses the boundary between two areas: the one has a corrugated wall and another has a smooth wall. It is assumed that the corrugation period is much less than the wavelengths under consideration. However, in difference with our previous works, the corrugation depth is of the same order as the wavelength. The influence of the corrugation on the electromagnetic field is investigated using the method of the equivalent boundary conditions. At first, we study a regular corrugated waveguide. Then two cases of the waveguides with boundaries between the corrugated and smooth regions is studied: first, when the bunch flies out of the corrugated part into the smooth one, and second, when the bunch flies into the corrugated part from the smooth one. We obtain and analyze the analytical expressions for the field components in both areas and reveal the main physical peculiarities of the bunch radiation.

An improved high-order low dissipation weighted compact nonlinear scheme for compressible flow simulations

Recently, Zhang developed a low-dissipation high-order scheme that employs Fu's targeted essentially non-oscillatory approach. this method incorporates an essentially non-oscillatory-like stencil selection strategy within the framework of the weighted compact nonlinear scheme proposed by Deng. Although this new scheme, termed targeted compact nonlinear scheme (TCNS), can recover ideal weights in smooth regions, it reduces accuracy at the discontinuities by discarding less smooth sub-stencils. Acker et al. showed in a recent study that increasing the weight of less smooth sub-stencils on a relatively coarse grid can further improve the wave resolution. Luo further improved Acker's scheme to fully exploit its potential in spectral characteristics. By following this idea, the less smooth stencil weights were incorporated to overcome problems of classical TCNS and to further improve the scheme's ability to resolve high-frequency waves. Moreover, by introducing an adaptive factor, we further optimized the spectral properties to improve the TCNS. A series of standard cases were used to measure the resolution of the new method for multiscale structures and the ability to suppress nonphysical oscillations at shock waves. The new scheme was applied to three cases involving complex configurations and multiscale flows, demonstrating that its low dissipation characteristics offer advantages in solving real-life problems.

Image dejittering on the perspective of spatially-varying mixed noise removal

Jittery image is visually abnormal in jags of edge and loss of coherence. The problem of image dejittering is challenging to resolve due to the ubiquitous blur and/or noise in jittery data. In this paper, we devote to the pixel-jitter (possibly blurry) image recovery on the perspective of spatially-varying mixed noise removal. By viewing jittery image as the corruption of ideal image with outliers and spatially-varying Gaussian noise, we proposed a two-phase (including filtering and diffusing phases) image dejittering approach. In the filtering phase, outliers posed by jitters around edges are inspected by median filters. In the diffusing phase, structure tensor based anisotropic diffusion is exploited to reduce the perturbations in piecewise smooth image regions. Upon the spectral decomposition of structure tensor, the variational model in diffusing phase can be solved by some state-of-the-art optimization methods. Numerical simulations on synthetic and real jittery data demonstrate the compelling performance of the proposed approach. The Matlab source codes of the proposed approach are available at the repositories of https://github.com/WenxingZhang.

Quantum phase transitions and cat states in cavity-coupled quantum dots

We study double quantum dots coupled to a quasistatic cavity mode with high mode-volume compression allowing for strong light-matter coupling. Besides the cavity-mediated interaction, electrons in different double quantum dots interact with each other via dipole-dipole (Coulomb) interaction. There is a first-order cavity-induced ferroelectric quantum phase transition when the attractive dipolar interaction is smaller than the critical value defined by the energy splitting in DQDs and a smooth transition, otherwise. We show that, in the smooth transition region, both the ground and the first excited states of an array of double quantum dots are cat states. Such states are actively discussed as high-fidelity qubits for quantum computing, and thus our proposal provides a platform for semiconductor implementation of such qubits. We also calculate gauge-invariant observables such as the net dipole moment, the optical conductivity, and the absorption spectrum beyond the semiclassical approximation. The results are robust against cavity losses and variations of system parameters. Published by the American Physical Society 2024

Measuring and reducing the carbon footprint of fMRI preprocessing in fMRIPrep.

Computationally expensive data processing in neuroimaging research places demands on energy consumption-and the resulting carbon emissions contribute to the climate crisis. We measured the carbon footprint of the functional magnetic resonance imaging (fMRI) preprocessing tool fMRIPrep, testing the effect of varying parameters on estimated carbon emissions and preprocessing performance. Performance was quantified using (a) statistical individual-level task activation in regions of interest and (b) mean smoothness of preprocessed data. Eight variants of fMRIPrep were run with 257 participants who had completed an fMRI stop signal task (the same data also used in the original validation of fMRIPrep). Some variants led to substantial reductions in carbon emissions without sacrificing data quality: for instance, disabling FreeSurfer surface reconstruction reduced carbon emissions by 48%. We provide six recommendations for minimising emissions without compromising performance. By varying parameters and computational resources, neuroimagers can substantially reduce the carbon footprint of their preprocessing. This is one aspect of our research carbon footprint over which neuroimagers have control and agency to act upon.

Experimental investigation of the distribution patterns of micro-scratches in abrasive waterjet cutting surface

The existence of striations, and scratches in Abrasive waterjet (AWJ) cutting surface necessitates an exploration of these features for enhancing the cutting accuracy of AWJ machining. This article investigates surface roughness and micro-scratch morphology characteristics on brass cutting surfaces. According to the variation law of surface roughness values, the cutting section can be divided into three regions: the initial region, smooth region, and rough region. Numerous micron-scale scratches were observed in the cutting section. The scratch length, width, and depth values all show an increasing trend as the cutting depth increases, with the scratch length experiencing the greatest growth and variability. The influence of position and traverse speed on scratch size was studied using variance analysis. Furthermore, the length and width of the scratches on the cutting surface are significantly influenced by their position, accounting for 89.19% and 81.13%, respectively. Traverse speed had a minor effect on scratch length and width, accounting for 0.01% and 2.64% respectively. The depth of the scratches is influenced by their position on the cutting surface at a rate of 41.12%, while traverse speed had an impact of 38.10%. Finally, a mathematical method based on standard scores was proposed to assess the quality of the cutting section based on micro-scratch dimension.

An improved method for upscaling 2D images using adaptive edge sharpening and an optimized directional anisotropic diffusion filter

Image upscaling employs various polynomial techniques, including bicubic and Lanczos, to minimize computing load for various real-time applications. Polynomial interpolation, on the other hand, results in blurring artifacts in high resolution (HR) images due to edge degradation. Many other interpolation approaches, including edge-based and dictionary learning-based schemes, result in blurring in the image’s high frequency (HF) region. As a result, a novel post-processing technique is proposed that uses the Lanczos method to upscale the low resolution (LR) image. To eliminate blur along the image’s edge, the edge component of the interpolated image is retrieved. Adaptive sharpening is used to make the edges more prominent, as predicting pixels in the high variance region is challenging. After the edge is extracted, the smooth region is filtered with an optimized directional anisotropic diffusion (ODAD) filter to preserve texture details and geometric regularity. The sharpened edge image is aggregated with the ODAD filtered image to generate an improved HR (IHR) image. The IHR is then scaled up and down to reduce blurring even further, resulting in a blurred HR image (BHR). The residual image is obtained by subtracting the BHR from the IHR images, which represent the undetected HF. Finally, the residual image and the IHR image are combined to generate the final restored image, which includes all prediction loss details. The results of the experiments show that the proposed algorithm outperforms existing methodologies, particularly in terms of visuality and parameter-wise measurement.

Neural network-based reversible data hiding for medical image

Pixel prediction is an important issue in the field of reversible data hiding. Neural networks are gradually used to improve the accuracy of pixel prediction owing to their excellent performance. However, current neural network-based pixel predictors are designed for natural images and do not consider the characteristics of medical images. Therefore, in this paper, we propose a dual-branch neural network-based reversible data hiding scheme for medical images. Detailedly, considering the characteristics of medical images, in which complex and smooth regions are more clearly distinguished, we present a clustering method to classify pixels into three classes according to their complexities, and generate masks to assist pixel prediction. Then, in the prediction stage, a dual-branch neural network-based pixel predictor is designed to extract unique and shared features, and a convolutional block attention module is used to optimize the extracted features. Finally, in the embedding stage, considering the characteristics of region of interest (ROI) and region of non-interest (NROI) in medical images, we design a class-based embedding algorithm, which can prioritize embedding data into NROI with low complexity and then sequentially into low texture complexity region and high texture complexity region of ROI. Experimental results show that our scheme can achieve better performance of pixel prediction and data embedding than existing state-of-the-art works.

A shock capturing artificial viscosity scheme in consistent with the compact high-order finite volume methods

This paper presents a shock capturing artificial viscosity scheme for the compact high-order finite volume methods in terms of the variational reconstructions on unstructured grids. The key for the design of the present artificial viscosity is the smoothness indicator, which is based on the concept of interfacial jump integration, measuring the discontinuities of the reconstruction polynomial and its spatial derivatives across a cell interface. Since the variational reconstruction is carried out by minimizing the functional in terms of the interfacial jump integration, the present smoothness indicator gives a discretization-consistent measurement of the smoothness of the flow fields that is sufficiently large in the region near discontinuities, and is in the same order of magnitude as the spatial truncation error of the finite volume scheme in smooth regions. These properties ensure that the newly developed artificial viscosity scheme has the problem-independent capability to suppress non-physical oscillations near discontinuities and preserve the theoretical order of accuracy for smooth flow. The shock capturing capability of the proposed artificial viscosity scheme has been demonstrated by a number of numerical examples confirming its essentially non-oscillatory and high-resolution properties. Additionally, the proposed artificial viscosity scheme exhibits higher computational efficiency than the approach based on a traditional limiter.

Sixth-order perturbed WENO interpolation-based AWENO and WCNS-E schemes for hyperbolic conservation laws

The weighted essentially non-oscillatory (WENO) interpolation-based schemes (the alternative WENO (AWENO) scheme and the explicit weighted compact nonlinear (WCNS-E) scheme) are limited to the fifth-order despite the sixth-order Taylor expansion of the numerical flux used. This order reduction is due to the fifth-order accuracy inherent in the WENO interpolation. We investigate the perturbed WENO interpolation with a free parameter and affine-invariant WENO weights to recover sixth-order accuracy in smooth regions. A cutoff function of the free parameter with a threshold, determined by approximate dispersion relation analysis, is applied to enhance the ENO property. The proposed schemes perform better in accuracy, dissipation, resolution, shock-capturing, and efficiency in 1D and 2D benchmark problems.

Spatial-frequency gradient fusion based model augmentation for high transferability adversarial attack

In recent years, deep learning has gained widespread application across diverse fields, including image classification and machine translation. Nevertheless, the emergence of adversarial examples has revealed a vulnerability of deep learning techniques to potential attacks. Despite the introduction of diverse adversarial attack methods, they are still constrained by certain limitations. Specifically, global perturbations are easily discernible by humans, resulting in poor imperceptibility. Additionally, current methods encounter limited transferability due to their reliance on attacking specific models. To address these challenges, this paper proposed a spatial-frequency gradient fusion based model augmentation for adversarial attack. First, we utilize a Gaussian convolution kernel to pinpoint regions in images that exhibit significant pixel variation, aiming to generate locally imperceptible perturbations undetectable by humans. These areas, which we consider as complex texture regions, are ideal for adding perturbations. Then, we design a perceptual similarity constraint to regulate the generation of perturbations in smooth texture regions. Subsequently, to further enhance the transferability of our method, we propose a spatial-frequency gradient fusion based model augmentation, applying random spectral transformation to shift into the frequency domain for narrowing the differences between models. Additionally, we design complex region scaling transformations in the spatial domain, aimed at capturing common features shared across models. Finally, we integrate the gradients from both the spatial and frequency domains, leveraging the strengths of both to empower attack models in effectively simulating the target model. Extensive experiments conducted on ImageNet and CIFAR-10 datasets have shown that our method attains a remarkable black-box attack success rate of up to 93.1%, with a perceptual loss reduction of approximately 8.39%, while also exhibiting stronger robustness.

Structural elucidation a complex galactosyl andglucosyl-rich pectin from the pericarp of immature fruits of Juglans mandshurica Maxim.

A glucosyl-rich pectin, JMMP-3 (Mw, 2.572 × 104g/mol, O-methyl % = 3.62%), was isolated and purified from the pericarp of the immature fruit of Juglans mandshurica Maxim. (QingLongYi). The structure of JMMP-3 was studied systematically by infrared spectroscopy, monosaccharide compositions, methylation analysis, partial acid hydrolysis, and 1/2D-NMR. The backbone of JMMP-3 possessed a smooth region (→ 4GalA1 →) and a hairy region (→ 4GalA1 → 2Rha1 →) with a molar ratio of 2: 5. The substitution of four characteristic side chains (R1-R4) occurs at C-4 of → 2,4)-α-Rhap-(1→, where R1 is composed of → 5)-α-Araf-(1→, R2 is composed of → 4)-β-Galp-(1 → and β-Galp-(1→, R3 is composed of α-Glcp-(1→, →4)-α-Glcp-(1 → and → 4,6)-α-Glcp-(1→, and R4 is composed of → 5)-α-Araf-(1→, β-Galp-(1→, → 4)-β-Galp-(1→, → 3,4)-β-Galp-(1→, → 4,6)-β-Galp-(1 → and → 2,4)-β-Galp-(1 → . In addition, the antitumor activity of JMMP-3 on HepG2 cells was preliminarily investigated.

A resolution-enhanced seventh-order weighted essentially non-oscillatory scheme based on non-polynomial reconstructions for solving hyperbolic conservation laws

In high-resolution numerical simulations of flows characterized by both multiscale turbulence and discontinuities, the conflict between spectral characteristics and stability becomes increasingly pronounced as the order of accuracy improves. To address this challenge, we proposed a novel seventh-order weighted essentially non-oscillatory scheme (WENO-K7). This scheme utilizes non-polynomial reconstructions by incorporating kriging interpolation and Gaussian exponential function. Then, a hyper-parameter associated with the Gaussian function is adaptively optimized to achieve higher convergence orders on sub-stencils, reducing numerical errors on global stencils. Additionally, a criterion based on monotone interpolations is devised to automatically identify problematic hyper-parameters, facilitating the transition from non-polynomial to polynomial reconstructions near discontinuities and preserving the essentially non-oscillatory property. Compared to the conventional seventh-order WENO-Z7 scheme, WENO-K7 scheme exhibits smaller computational error and reduced numerical dissipation in smooth regions while maintaining non-oscillatory and high-resolution capabilities around discontinuities. Results from various one- and two-dimensional benchmark cases demonstrate that the proposed WENO-K7 scheme outperforms the widely used WENO-Z7 scheme with only a 12% increase in computational cost. Moreover, the WENO-K7 scheme shares the same sub-stencils as the WENO-Z7 scheme, making it easily applicable to other variants of seventh-order WENO schemes and enhancing their spectral characteristics.

A block-spectral adaptive H-/p-refinement strategy for shock-dominated problems

An adaptive H-/p-refinement strategy using a novel sensor is devised and tested in a block-spectral compressible Euler code equipped with adaptive-mesh refinement (AMR) and high-order flux-reconstruction numerics. At each Gauss quadrature point (or solution point) within each spectral block (or mesh element) the discrete velocity jump ΔU = ∂U/∂y1Δy1+∂V/∂y2Δy2+∂W/∂y3Δy3 is calculated and normalized by the local speed of sound, a. The grid spacing, Δxi, is calculated in each direction as the distance between auxiliary Gauss-Lobatto points, staggered relative to the solution points. The polynomial order is increased from p=0 to p=pmax in regions of weak compression, (ΔU/a)crit<ΔU/a<0 and kept at p=pmax in regions of flow expansion ΔU/a≥0, while staying at the H=0 base mesh level. Regions experiencing strong compressions, i.e. ΔU/a<(ΔU/a)crit, are H-refined up to H=Hmax where Hmax is applied at the location of maximum compression, ΔU/a=min(ΔU/a) in the domain, while keeping p=0 to guarantee robustness and monotonicity of the solution in the H refined region. The critical value of (ΔU/a)crit= -0.06 is found to effectively separate smooth and non-smooth solution regions, supported by a 1D detonation initiation test case in ideal gas and a shock-to-detonation transition in high explosives. Using this value, the Sod shock tube, Shu-Osher problem, double Mach reflection and a 2D detonation in a high-explosive are simulated with the proposed adaptive H-/p-refinement. In the Sod shock tube case, p-refinement resolves the (weak) contact discontinuity while H-refinement enhances the grid resolution in the shock exploiting the monotonicity of the p=0 reconstruction. For the Shu-Osher problem, p-refinement captures the small-scale oscillations trailing the shock that would be otherwise attenuated, while H-refinement triggered by the ΔU-sensor appropriately tracks the shock. In the double Mach reflection problem, H-refinement confines the numerical diffusion around the reflected shock while p-refinement recaptures many physical features trailing the shock. Finally, in the 2D high-explosive detonation case, H-refinement follows the leading shock and resolves the curvature of the detonation wave, while p-refinement adds resolution to the trailing reaction zone. Finally, the proposed methodology is tested in a detonation-wave propagation test case in high-explosives with numerical predictions comparing favorably against experiments.

Line-Based High-Order Hybrid Scheme on Unstructured Grids for Compressible Flows

This study explores the use of line-based finite difference techniques on unstructured grids employing high-order stencils for practical aerodynamic applications. The primary focus is on finite-difference explicit and compact spatial discretization up to sixth order. Problems studied include compressible flows containing discontinuities, which necessitated the use of a hybrid finite difference–finite volume approach, where the former is shown to be effective and accurate for smooth regions, while the latter is robust in capturing discontinuities and shocks. To differentiate between discontinuous and smooth zones, two distinct shock indicators are used, one based on pressure gradients and the other on the divergence of velocity. To achieve faster convergence, spatial discretization is applied with line-based alternating direction implicit (ADI) time integration. A key focus of this work is to demonstrate the proposed methodology in flow scenarios relevant to aircraft applications that also test various aspects of the methodology. Consequently, the cases studied are isentropic vortex convection, standing normal shock, transonic NACA0012 airfoil, supersonic cylinder, unsteady flow past tandem circular cylinders, and supersonic flow past a forward-facing step. Comparisons were also done against an existing line-based finite-volume technique for unstructured grids that employed Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) and fifth-order Weighted Essentially NonOscillatory (WENO5) spatial reconstruction schemes. It is observed that the hybrid finite difference–finite volume approach performed well with excellent agreement against available results, sometimes with far fewer degrees of freedom. Furthermore, the implicit ADI scheme is effective over unstructured grids and provides a three-time speed-up over the traditional Runge–Kutta fourth-order scheme.

Optimized reversible data hiding technique based on multidirectional prediction error histogram and fluctuation-based adaptation

Reversible Data Hiding Techniques (RDH) play an increasingly pivotal role in the field of cybersecurity. Overlooking the properties of the carrier image and neglecting the influence of texture can lead to undesirable distortions and irreversible data hiding. In this paper, a novel block-based RDH technique is proposed that harnesses the relative correlation between multidirectional prediction error histograms (MPEH) and pixel fluctuation values to mitigate undesirable distortions and enable RDH, thereby ensuring heightened security and efficiency in the distribution process and improving the robustness of the block-based RDH technique. The proposed technique uses a combination of pixel fluctuation and local complexity measures to determine the best embedding locations within smooth regions based on the cumulative peak regions of the MPEH with the lowest fluctuation values. Similarly, during the extraction process, the same optimal embedding locations are identified within smooth regions. The multidirectional prediction error histograms are then used to accurately extract the hidden data from the pixels with lower fluctuation values. Overall, the experimental results highlight the effectiveness and superiority of the proposed technique in various aspects of data embedding and extraction, and demonstrate that the proposed technique outperforms other state-of-the-art RDH techniques in terms of embedding capacity, image quality, and robustness against attacks. The average Peak Signal-to-Noise Ratio (PSNR) achieved with an embedding capacity ranging from 0.5×104 bits to 5×104 bits is 52.72 dB. Additionally, there are no errors in retrieving the carrier image and secret data.

Composite nanofilms of graphene and nickel: Fabrication, cw linear and nonlinear optical properties

In this study, the preparation of graphene-nickel composite nanofilms and their linear and linear optical properties under cw regime were investigated. The films were fabricated on glass and c-Si substrates in two steps by electron beam evaporation. The surface morphology of the films showed distinctive features with smooth and rough regions related to the formation of pristine and wrinkled graphene. The complex permittivity functions of the films were calculated using Maxwell-Garnett Theory. The nonlinear optical absorption coefficient and refractive index were calculated based on the open and closed aperture z-scan measurements. Enhanced nonlinear optical properties compared to the pure nickel film were obtained. The enhancement is explained in terms of the participation of the graphene’s π-electrons in the d-band plasmonic oscillation.