Scale Inhomogeneities Research Articles

Interaction of driven ‘cold’ electron plasma wave with thermal bulk via ion spatial inhomogeneity

Abstract Using high resolution Vlasov - Poisson simulations, evolution of driven ``cold" electron plasma wave (EPW) in the presence of stationary inhomogeneous background of ions is studied. Mode coupling dynamics between ``cold'' EPW with phase velocity $v_{\phi}$ greater than thermal velocity i.e $v_{\phi} \gg v_{thermal}$ and its inhomogeneity induced sidebands is illustrated as an initial value problem. In driven cases, formation of BGK like phase space structures corresponding to sideband modes due to energy exchange from primary mode to bulk particles via wave-wave and wave-particle interactions leading to particle trapping is demonstrated for inhomogeneous plasma. Qualitative comparison studies between initial value perturbation and driven problem is presented, which examines the relative difference in energy transfer time between the interacting modes. Effect of variation in background ion inhomogeneity amplitude as well as ion inhomogeneity scale length on the driven EPWs is reported.

Cosmological foundations revisited with Pantheon+

Abstract We reanalyse the Pantheon+ supernova catalogue to compare a cosmology with non-FLRW evolution, the timescape cosmology, with the standard ΛCDM cosmology. To this end, we analyse the Pantheon+ for a geometric comparison between the two models. We construct a covariance matrix to be as independent of cosmology as possible, including independence from the FLRW geometry and peculiar velocity with respect to FLRW average evolution. This framework goes far beyond most other definitions of model independence. We introduce new statistics to refine Type Ia supernova (SNe Ia) light-curve analysis. In addition to conventional galaxy correlation functions used to define the scale of statistical homogeneity we introduce empirical statistics which enables refined analysis of the distribution biases of SNe Ia light-curve parameters βc and $\alpha {x_{\lower2pt\hbox{$\scriptstyle 1$}}}$. For lower redshifts, the Bayesian analysis highlights important features attributable to the increased number of low-redshift supernovae, the artefacts of model-dependent light-curve fitting and the cosmic structure through which we observe supernovae. This indicates the need for cosmology-independent data reduction to conduct a stronger investigation of the emergence of statistical homogeneity and to compare alternative cosmologies in light of recent challenges to the standard model. Dark energy is generally invoked as a place-holder for new physics. For the first time, we find evidence that the timescape cosmology may provide a better overall fit than ΛCDM and that its phenomenology may help disentangle other astrophysical puzzles. Our from-first-principles reanalysis of Pantheon+ supports future deeper studies between the interplay of matter and nonlinear spacetime geometry in a data-driven setting.

Mechanisms of electromagnetic field control on mineral scaling in brackish water reverse osmosis: Combined homogenous and heterogeneous nucleation

Electromagnetic field (EMF) treatment has emerged as a promising approach for scaling control due to its cost-effectiveness, simplicity, and low energy consumption. However, there is a limited understanding of the mechanisms by which applied EMF impacts mineral scaling in reverse osmosis (RO) systems. This has led to inconclusive and varied results and uncertainties regarding its effectiveness. This study elucidates the impacts of EMF on homogenous and heterogeneous nucleation and membrane performance during RO desalination of different feedwaters. Our results reveal that EMF exhibits greater efficacy in treating near-saturated water (SI∼0), especially when coupled with extended hydraulic flushing (HF). For saturated brackish water desalination, heterogeneous scaling predominantly occurs on membrane surfaces, with the effectiveness of EMF in inhibiting scaling primarily attributed to the hydration effect. In supersaturated solutions, EMF promotes bulk precipitation due to the magnetohydrodynamic effect, quickly blocking membrane pores. Thus, when the saturation reaches a certain high level during RO desalination, magnetohydrodynamic EMF effects can accelerate flux decline caused by homogeneous scaling. This work provides an efficient method for predicting EMF efficiency, emphasizing the importance of saturation conditions and HF cleaning duration in determining membrane performance, suggesting these show promise for improving undersaturated or near-saturated feedwater desalination via RO.

Modification of the electronic oscillation spectrum in metallic clusters, caused by the presence of a large spatial scale of inhomogeneity

This work presents a theoretical analysis of the oscillations of a system of degenerate electrons in metallic submicron clusters, taking into account the presence of a large-scale spatial inhomogeneity caused by quantum shell effects. The analysis was carried out in a model formulation in which the large-scale effect was taken into account by the presence of an effective external field acting on the electrons. Two approaches to the description of electron dynamics were considered: kinetic and hydrodynamic. The results obtained within these approaches are in good qualitative and quantitative agreement with each other and demonstrate that for certain cluster sizes, a spectrum of oscillations of the electronic system appears with frequencies differing by the value Δω ∼ ω0/R20 and localized in the vicinity of plasmon frequency ω0 (R0, radius of cluster). The impact of the large-scale effect on the processes of light and electron scattering by metal clusters is estimated. It is shown that maxima appear in the absorption spectrum of the electromagnetic waves, and they turn out to be shifted from the plasmon frequency by value Δω ∼ ω0/R20. Within the framework of the Born approximation, it is shown that a maximum at kR0 ∼ 4π appears in the cross section of elastic scattering of electrons on a metal cluster. The results obtained are important from the point of view of interpreting experiments on plasmonic structures, in particular, on metal films.

Deep Learning Based 3D Resolution Recovery for Breakthrough Imaging of Electrochemical Energy Devices

Many energy materials can only be understood within the context of the (often sealed) devices they make up. Batteries and fuel cells contain intricate mixtures of materials with features and arrangements that span across many orders of magnitude in size and operate under non-ambient conditions. In these devices, the microstructures of the constituent materials and how they are arranged with respect to each other is directly linked to the device performance and degradation behaviors. Complicating matters, opening the devices for inspection and analysis can irreversibly alter the very microstructures in question and can pose safety hazards to researchers if not done correctly. Furthermore, critical material and device properties such as tortuosity or ion transport pathways can only be accurately quantified in 3D. As such, observing microstructures and their evolution in 3D and in their native state is essential for developing a robust understanding of how to engineer new battery and fuel cell materials and architectures with improved performance.X-ray microscopy (XRM) provides a unique method for observing these microstructures in 3D at high resolutions without needing to open them. However, microscopy techniques like XRM make tradeoffs between FOV and resolution, which can pose challenges for strongly multiscale systems like batteries and fuel cells. For example, if images are acquired at high enough resolution to observe critical features like electrode particle sizes in lithium-ion batteries or gas diffusion layer fiber weaves, catalyst distributions, and microporous layer cracks in polymer electrolyte fuel cells, the field of view of that image is restricted to a small local region of the sample. This means that broader defect distributions or larger scale inhomogeneities will be missed. Additionally, for quantitative analysis applications, this means that statistical relevance will be sacrificed because of the limited analysis volume at the appropriate resolution. And for computational modelling efforts, device level phenomena will not be captured well due to the restricted field of view.Advances in modern AI-based resolution recovery methods combined with the non-destructive multiscale imaging capabilities of X-ray microscopy have allowed researchers to overcome this dependency between resolution and field of view to produce 3D images with both high resolution and large field of view. We present here examples of applying these methods to applications in lithium-ion battery and polymer electrolyte fuel cell research [1].[1] Wang, Y.D., Meyer, Q., Tang, K. et al. Large-scale physically accurate modelling of real proton exchange membrane fuel cell with deep learning. Nat Commun 14, 745 (2023).

Intermittent cluster dynamics and temporal fractional diffusion in a bulk metallic glass

Glassy solids evolve towards lower-energy structural states by physical aging. This can be characterized by structural relaxation times, the assessment of which is essential for understanding the glass’ time-dependent property changes. Conducted over short times, a continuous increase of relaxation times with time is seen, suggesting a time-dependent dissipative transport mechanism. By focusing on micro-structural rearrangements at the atomic-scale, we demonstrate the emergence of sub-diffusive anomalous transport and therefore temporal fractional diffusion in a metallic glass, which we track via coherent x-ray scattering conducted over more than 300,000 s. At the longest probed decorrelation times, a transition from classical stretched exponential to a power-law behavior occurs, which in concert with atomistic simulations reveals collective and intermittent atomic motion. Our observations give a physical basis for classical stretched exponential relaxation behavior, uncover a new power-law governed collective transport regime for metallic glasses at long and practically relevant time-scales, and demonstrate a rich and highly non-monotonous aging response in a glassy solid, thereby challenging the common framework of homogeneous aging and atomic scale diffusion.

A dual-scale fused hypergraph convolution-based hyperedge prediction model for predicting missing reactions in genome-scale metabolic networks.

Genome-scale metabolic models (GEMs) are powerful tools for predicting cellular metabolic and physiological states. However, there are still missing reactions in GEMs due to incomplete knowledge. Recent gaps filling methods suggest directly predicting missing responses without relying on phenotypic data. However, they do not differentiate between substrates and products when constructing the prediction models, which affects the predictive performance of the models. In this paper, we propose a hyperedge prediction model that distinguishes substrates and products based on dual-scale fused hypergraph convolution, DSHCNet, for inferring the missing reactions to effectively fill gaps in the GEM. First, we model each hyperedge as a heterogeneous complete graph and then decompose it into three subgraphs at both homogeneous and heterogeneous scales. Then we design two graph convolution-based models to, respectively, extract features of the vertices in two scales, which are then fused via the attention mechanism. Finally, the features of all vertices are further pooled to generate the representative feature of the hyperedge. The strategy of graph decomposition in DSHCNet enables the vertices to engage in message passing independently at both scales, thereby enhancing the capability of information propagation and making the obtained product and substrate features more distinguishable. The experimental results show that the average recovery rate of missing reactions obtained by DSHCNet is at least 11.7% higher than that of the state-of-the-art methods, and that the gap-filled GEMs based on our DSHCNet model achieve the best prediction performance, demonstrating the superiority of our method.

Can the angular scale of cosmic homogeneity be used as a cosmological test?

In standard cosmology, the cosmic homogeneity scale is the transition scale above which the patterns arising from non-uniformities – such as groups and clusters of galaxies, voids, and filaments – become indistinguishable from a random distribution of sources. Recently, different groups have investigated the feasibility of using such a scale as a cosmological test and arrived at different conclusions. 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Using the currently available θH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _{\ extrm{H}}$$\\end{document} measurements, we illustrate the constraints on the Ωm0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varOmega _{\ extrm{m0}}$$\\end{document}–H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_{0}$$\\end{document} plane through a MCMC analysis and show the feasibility of using the angular homogeneity scale as a new, model-independent way to constrain cosmological parameters.

MODIFICATION OF 3D BALANCE MODEL FOR BI-POLAR AGGREGATION OPERATORS VISUALISATION

Aggregation operators provide an overall assessment of an object or a process which is described with several quantitative criteria. An aggregation operator is constructed on the basis of expert knowledge and can take into account the types of criteria interdependencies, the partial order of criteria importance, the desired overall scores for distinct sets of the criteria values provided by an expert. However, in practice the aggregation operator construction process and its result appear to be difficult to perceive and understand by an expert. There is a balance model method for visualizing the aggregation operators in order to simplify evaluation of their conformity to expert preferences. This method allows visualizing an aggregation operator in an intuitively clear way as a mechanical system of weights on a rod. One limitation of the balance model method is that the weights can overlap each other on a rod which makes it difficult to perceive the aggregation result by the expert. A three-dimensional balance model overcomes this limitation but it can visualize unipolar aggregation operators only. This paper extends the existing three-dimensional balance model for bipolar aggregation operators. The extended model allows visualizing the aggregation operators of the criteria defined on bipolar scales of three different types: symmetric bipolar scales, homogeneous bivariate bipolar scales, heterogeneous bipolar scales. The model plane rotation angle constraints were updated to visualize the bipolar aggregation operators. The implementation of the extended model in the Unity game engine is presented. The application of the extended model is illustrated in a case study of the energy storage technology selection considering a trade-off between its performance and its environmental impact.

Effect of nonlocality on the dispersion relations of mechanical metamaterials

The advent of mechanical metamaterials, with their unconventional and programmable properties, has revolutionised the field of engineering across length scales. Their design remains an area of interest to researchers requiring careful analysis of unit cells so as to achieve desired mechanical and wave dispersion behaviour. While metamaterials are known to extract their unique properties from the internal geometry of the unit cells, the contributions of the constituent materials are typically accounted for via their local material properties in the form of Young’s modulus and Poisson’s ratio. In this article, we demonstrate that material nonlocality of the constituents can also play a crucial role in modulating the nontrivial properties of metamaterials. Such nonlocality can arise from various sources, such as finer scale inhomogeneity like defects, inclusions etc. Towards this, we propose a nonlocal continuum model by upscaling a discrete potential through a stochastic gradient estimator (SGE) interpreted herein as a generalised Cauchy–Born rule. The nonlocal parameters can also be estimated from experimental data by solving an inverse problem, similar to the estimation of constitutive parameters in classical continuum mechanics. The proposed model accurately captures the dispersion behaviour at the continuum level as compared to its discrete counterpart. We further incorporate the model within the transfer matrix method to derive the dispersion relations of a metabar as a function of the constituent material nonlocality. We envisage that the present study introduces a new handle in the form of constituent material nonlocality for designing architected metamaterials with unprecedented mechanical functionalities.

Surface matters: A case study of the scale and impact of oxide surfaces via orbital polarization

Transition metal oxides (TMOs) exhibit a broad spectrum of functional electronic, magnetic, and optical properties, making them attractive for various technological applications. The scale and impact of surface defects and inhomogeneity can extend many unit cells below the surface. Overlooking this aspect of TMO surfaces can result in an incorrect interpretation of their physics and inhibit their maturation into device technology. Soft x-ray absorption spectroscopy (XAS) is a common technique for TMO studies, and different XAS acquisition modes can be used to measure different depth regimes in the sample. Here, we demonstrate a substantial disparity between the near-surface region and the “bulk” of the prototypical TMO SrVO3. By driving the system across two scenarios of orbital polarization, we illustrate how a common XAS surface-sensitive acquisition technique fails to detect the intrinsic orbital polarization. By stark contrast, a “bulk”-sensitive technique successfully captures this effect, elucidating the expected orbital occupation inversion. These results not only underscore the impact of the near-surface region on the correct interpretation of TMO fundamental physics, but further highlight the scale of surface inhomogeneity, a critical aspect of nanoscale functional devices.

Hubble diagrams in statistically homogeneous, anisotropic universes

We consider the form of Hubble diagrams that would be constructed by observers in universes that are homogeneous but anisotropic, when averaged over suitably large length-scales. This is achieved by ray-tracing in different directions on the sky in families of exact inhomogeneous cosmological solutions of Einstein's equations, in order to determine the redshifts and luminosity distances that observers in these space-times would infer for distant astrophysical objects. We compare the results of this procedure to the Hubble diagrams that would be obtained by direct use of the large-scale-averaged anisotropic cosmological models, and find that observables calculated in the averaged model closely agree with those obtained from ray-tracing in all cases where a statistical homogeneity scale exists. In contrast, we find that in cosmologies with spaces that contain no statistical homogeneity scale that Hubble diagrams inferred from the averaged cosmological model can differ considerably from those that observers in the space-time would actually construct. We hope that these results will be of use for understanding and interpreting recent observations that suggest that large-scale anisotropy may have developed in the late Universe.

A Method for Constructing the Resulting Scale for Objects Presented in Interval Estimates in Multi-Criteria Evaluation and Selection Tasks

For the tasks of multi-criteria evaluation and selection under uncertainty conditions, the most accurate is the presentation of object estimates in an interval form, which allows you to preserve the completeness of information. The correct application of the additive data aggregation mechanism in multi-criteria problems presented in various measurement scales requires that the initial estimates be transformed into the resulting homogeneous scales characterized by the same scope and number of gradations. At the same time, there is a problem of converting interval estimates into point estimates. The idea of the method for intersecting interval estimates and a large number of objects is to construct a histogram, and then equally divide the original measurement scale into segments, the numbers of which are identified with the point gradations of the resulting scale. An example of solving the problem of multi-criteria evaluation and comparison of a civil helicopter project relative to competitors in terms of tactical and technical characteristics and with interval-set sales prices is given.

A Hybrid PIV/Optical Flow Method for Incompressible Turbulent Flows

We present novel velocimetry algorithms based on the hybridization of correlation-based Particle Image Velocimetry (PIV) and a combination of Lucas–Kanade and Liu–Shen optical flow (OpF) methods. An efficient Aparapi/OpenCL implementation of those methods is also provided in the accompanying open-source QuickLabPIV-ng tool enabled with a Graphical User Interface (GUI). Two different options of hybridization were developed and tested: OpF as a last step, after correlation-based PIV, and OpF as a substitute for sub-pixel interpolation. Hybridization increases the spatial resolution of PIV, enabling the characterization of small turbulent scales and the computation of key turbulence parameters such as the rate of dissipation of turbulent kinetic energy. The method was evaluated using both synthetic and real databases, representing flows that exhibit a variety of locally isotropic homogeneous turbulent scales. The proposed hybrid PIV-OpF results in a 3-fold increase in the PIV density for synthetic images. The analysis of power spectral density functions and auto-correlation demonstrated the impact of PIV image quality on the accuracy of the method and its ability to extend the turbulence range. We discuss the challenges posed by optical noise and tracer density in the quality of the vector map density.

Mitigating the corrosion of AISI 301LN steel in molten carbonate salts by doping with alumina nanoparticles for thermal energy storage applications

Molten carbonate salt nanofluids have become an excellent strategy to enhance the power generation efficiency of the next-generation concentrated solar power (CSP) technology due to their excellent thermophysical properties at high temperatures. The corrosion behaviour in contact with salt nanofluids is one of the main issues to address for implementing cost-effective steels as construction materials for CSP. In the present work, the effects of molten salt nanofluids with Al2O3 nanoparticles (<50 nm and 1.0 wt%) on the corrosion behaviour of AISI 301LN stainless steel have been investigated. Corrosion tests were carried out in a static molten salt mixture of Li2CO3–Na2CO3–K2CO3 at 600 °C for 1000 h. Complementary electron microscopy, microanalysis and optical characterization techniques and micromechanical tests were carried out to study the oxide scales formed after corrosion tests in salt nanofluids and base salt of reference. Results evidenced that doping nanoparticles in molten salts significantly decreased the corrosion rate by ∼50%, compared with a base salt. Incorporating nanoparticles into the oxide scale, forming a nanostructure of reticulated Al2O3 nanoparticles generated a more homogeneous and dense oxide scale, increasing its hardness about 30% and enhancing its effectiveness as a protective barrier.

Numerical simulation of the electromagnetic wave reflection from 2D random semi-infinite strongly scattering media

Light scattering in disordered media plays an important role in several areas of applied science from biophysics to astronomy. In this paper using a two-dimensional system as an example we study approaches to calculate the scattering properties of semi-infinite densely packed media with high contrast and wavelength scale inhomogeneities. We develop two methods by combining the Fourier Modal Method and the super-cell approach. Our work demonstrates the ability to obtain ensemble averaged solutions to the Maxwell's equations in complex media, while the demonstrated numerical convergence on the size parameters of the system supports the consistency of the approaches considered.

NUMERICAL THREE-DIMENSIONAL MODEL OF ULTRASONIC COAGULATION OF AEROSOL PARTICLES IN VORTEX ACOUSTIC STREAMING

Separation of highly dispersed systems with huge liquid-gas or liquid-solid interfaces is relevant for practical tasks of gas purification from the most highly dispersed and difficult-to-detect dispersed fraction PM2.5, and separation of nanoparticles (including their small agglomerates) in fine chemical technology processes. One of the most effective ways to separate highly dispersed systems with a large interface surface is to combine each of the closed subsurfaces (surfaces of individual dispersed particles) under the influence of hydrodynamic effects in the gas phase, arising both near the interface surfaces and at a considerable distance from them, due to the superposition of ultrasonic vibrations. Since the efficiency of ultrasonic coagulation decreases with a large distance between closed subsurfaces from each other in PM2.5 aerosol and the small size of these surfaces, it is necessary to create conditions for the emergence of new nonlinear effects that contribute to the local compaction of the dispersed fraction. In a resonant and significantly inhomogeneous ultrasonic field (with a scale of inhomogeneity on the order of the wavelength), vortex acoustic flows arise, which, due to inertial forces, locally compact the dispersed phase in the form of an increase in the concentration of aerosol particles. A numerical model of ultrasonic coagulation of PM2.5 aerosol particles in three-dimensional (3D) vortex acoustic streaming is proposed in this paper. The model is designed to identify the possibility of increasing the efficiency of ultrasonic coagulation in 3D streaming by virtue of the following mechanisms: (1) local increase in concentration caused by the inertial transfer of particles to the periphery of 3D vortices in the gas phase; (2) increase in the frequency of particle collisions due to 3D turbulent disturbances in ultrasonic fields; and (3) increase in productivity and ensuring uninterrupted implementation of the process in a flow mode owing to transfer of particles between the streamlines of the main vortices initiated by ultrasonic vibrations. The listed mechanisms for increasing the efficiency of coagulation in 3D streaming are taken into consideration by introducing two stream functions, considering turbulent chaotic disturbances of the flow resulting in dispersion of particle velocities. It was possible to establish based on numerical analysis of the model using the example of PM2.5 that laminar vortex flows begin to influence at sound pressure level from 160-165 dB, and turbulent disturbances make an additional contribution in the range of sound pressure levels from 140-170 dB. At the same time, as a result of 3D turbulent disturbances, the efficiency of coagulation reaches almost 100&amp;#37; at a sound pressure level 5 dB lower than with laminar flows (sound pressure amplitude, 3 times lower).

Fluorescent-tagged antiscalants as a tool of homogeneous membrane scaling mitigation and inhibition mechanism investigation in electrodialysis processing of solutions prone to calcium sulfate precipitation

Fluorescent-tagged antiscalants as a tool of homogeneous membrane scaling mitigation and inhibition mechanism investigation in electrodialysis processing of solutions prone to calcium sulfate precipitation

Multicriteria ranking and selection in rank gradations of objects measured in different types of scales

To solve multi-criteria applied problems related to the construction of ratings of organizations, the choice of effective objects (alternatives, solutions), the initial data of which are presented in different types (quantitative, ordinal) measurement scales, the use of a generalized criterion in the form of an additive convolution of particular criteria is incorrect. In this regard, methods for narrowing the initial set of objects, as well as methods for constructing the resulting ranking (Kemeny-Snell medians), have become widespread. However, if the initial estimates of objects are transformed into the resulting homogeneous scale i.e., if there is a scale with the same scope of criteria, then the use of an additive aggregation mechanism in this case will be correct. An ordinal rank scale can serve as such a resultant scale. The paper substantiates a method in which the results of the transformation of quantitative (point) estimates of objects in the gradation of the rank scale when solving multi-criteria problems will be invariant for any quantitative transformations of the original scales. The preservation of the ordering of objects according to generalized estimates in the form of the sum of ranks according to equally important criteria is proved. At the same time, object orderings based on relationships with the k-th order of strict preference are also preserved. Illustrative examples are given.

Surface oxidation behavior of spark plasma sintered AlCrCuFeMnWx high entropy alloys at an elevated isothermal temperature

The high-temperature surface oxidation behavior of high-entropy alloys (HEAs) with compositions of AlCrCuFeMnWx (x = 0, 0.05, 0.1, and 0.5) was studied at 800 °C as an isothermal temperature for 50 h. The high entropy alloys (HEAs) were synthesized by mechanical alloying (MA) followed by spark plasma sintering (SPS). This study focused on the effect of oxidation resistance properties with different elevated temperatures on the high entropy alloy over the surfaces. The XRD and Raman analysis confirmed the formation of various oxides like Al2O3, Cr2O3, Fe2O3, and CrO2 mainly. The HEAs follow the single-stage parabolic law at 800 °C. To achieve better resistance against the heat, rather than adding more amount of refractory elements. Consequently, AlCrCuFeMnWx HEAs showed excellent oxidation resistance at elevated temperatures in a specific amount of tungsten. Different values of mass gain, loss, and complex oxidation kinetics were observed for the varying W-containing HEAs. These alloys formed inhomogeneous oxide scales possessing different regions with porous oxide layers and some areas revealed thin oxide scales due to the formation of discontinuous Mn, Cr, and Al-rich scales evidence found through the SEM images. It is noted that complicated oxides formed considerably more frequently on the W0 alloy than on other alloys, indicating that the addition of tungsten in the presence of Cr may inhibit the growth of certain types of multiphasic oxides and prevent spallation.