Anomalous Mass Research Articles

Application of horizontal gravity-gradient stack for estimation of surface layer density in mountainous areas

The author proposes a new approach for analysing datasets of the differential curvature of a gravity-gradient tensor for density evaluation of the surface layer without a prior density assumption. The method, called the horizontal gravity-gradient stack–moving window correlation (HGGS-MWC) method, is based on a successive MWCs between the acquired data and the data of differential curvature responses of the surface layer calculated based on a digital elevation model. For improving the correlation, a HGGS processing method was devised and patented. It is applied to both datasets before the MWC processing. A point-source differential curvature response has the characteristic of forming a peculiar and symmetrical shape of a quadrant and distributing peaks and troughs over an underlying anomalous mass. These peaks and troughs are near or far away from their centre depending on the depth of the anomalous mass. This enables one to design a filter to enhance the responses of the surface layer. In addition, the HGGS processing affects both the contraction of the gravitational response and the attenuation of responses from deeper subsurface layers. The HGGS-MWC method leads to the production of values of the mass surface roughness ratio (MSR) in the wavenumber domain that are inherent to the measuring plane of surveys and determines the phase relation between the mass of the surface layer and the surface roughness. The MSR is a good indicator of whether a mass surplus or deficit relative to the regional average mass exists under a convex surface layer. Application to the observed datasets was performed in the area where serious landslides were triggered by the 2008 Iwate-Miyagi inland earthquake. Based on a flight height of 150 m, the mass variations of the surface layer, which is down to 300 m below the surface, are properly evaluated by analysing the wavelengths in the data mainly within the range of 270–650 m and perceivably up to 1,650 m. The specific areas can be delineated where low-density deposits, such as possible volcanic ashes and pumices associated with high water content, sit on high mountains with steep slopes. The information is useful for disaster prevention by playing a role in selecting potential areas for conducting further precise surveys. Regional density variations whose wavelengths are longer than 1,650 m remain unsolved and are an issue for future studies. With the issue solved, the results for the density distribution of the surface layer obtained by the HGGS-MWC method will serve for terrain corrections of the vertical gravity-gradient data and gravity data as well.

Single-step insertion of M-Nx moieties in commercial carbon for sustainable bifunctional electrocatalysis: Mapping insertion capacity, mass loss, and carbon reconstruction

Atomically dispersed earth-abundant metals in N-doped carbon (M-N-Cs) have emerged as a new class of electroactive materials that can match not only the performance of the precious metals but can catalyze both the cathodic and the anodic reactions due to their bifunctional behaviour. This inspires the development of simpler strategies for scale-up production since the existing ones rely on precursors whose commercial viability is not yet ascertained. Herein, we demonstrate the insertion prospects of M-Nx (M = Fe, Co, Ni) moieties, the electrocatalytic centers in the M-N-Cs, into commercial carbon to establish that a single-step heating of the inexpensive precursors is sufficient to generate bifunctional electrocatalysts for oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) with efficiencies that bypass the majority of the known catalysts. Further importantly, we quantify both the ORR and OER trends and the metal insertion limits for each metal while maintaining an atomic dispersion, without the formation of surface migration-induced clustering, because such clustering is inevitable in the existing processes to necessitate an extra acid-leaching step to remove them. We further quantify and explain for each metal a negative mass balance originating from anomalous mass loss of both metal and carbon content, and a massive reconstruction of the carbon backbone catalyzed by the very metal, an event documented for the first time though it ought to be associated with other M-N-C syntheses too. The study establishes an incredibly simple and inexpensive strategy for the realization of M-N-Cs and outlines the parameters to be considered during mass-production.

The eastern limit of ‘Kunlun-Pamir-Karakoram Anomaly’ reflected by changes in glacier area and surface elevation

AbstractUnder global warming, many glaciers worldwide are receding. However, recent studies have suggested the extension of the Karakoram Anomaly, a region of anomalous glacier mass gain, into the western Kunlun and eastern Pamir mountains. However, the eastern limit of this anomaly in the Kunlun Mountains is unclear. This study, using changes in glacier area and surface elevation, estimates the eastern limit of the Kunlun-Pamir-Karakoram anomaly at ~85°E. Over the past 50 years, glaciers west of 85°E in the Kunlun Mountains decreased in area from 8401 to 7945 km2 at a rate of −0.12 ± 0.07% a−1, showed a reduction in the rate of retreat through time and have recently gained mass, with surface elevation changes of 0.15 ± 0.35 m a−1 over the period of 2000–2013. Glaciers east of 85°E have experienced greater rates of area change (−61 ± 12 km2 and −0.43 ± 0.13% a−1) over the past 50 years, accelerated area loss in recent years and elevation change rate of −0.51 ± 0.18 m a−1 between 2000 and 2013. These patterns of elevation and area change are consistent with regional increases in summer temperature in the eastern Kunlun Mountains and slight cooling in the western Kunlun Mountains.

Possible Causes of Anomalous Glacier Mass Balance in the Western Kunlun Mountains

AbstractUnder current global warming, most glaciers on the Tibetan Plateau have shown significant mass loss during 2000–2019. However, the average glacier mass balance in the western Kunlun Mountains (WKM) was positive during this period. The causes of these opposing average status and the temporal glacier mass changes over the last several decades in the WKM continue to be the subject of active debate. The long‐term mass balance of the Guliya Ice Cap (Guliya) in the WKM during 1970–2019 was reconstructed using an energy and mass balance model and calibrated ERA5 data, which was calibrated and validated by in situ measurements and geodetic mass balances. Guliya showed a positive mean mass balance during 2000–2019 because annual snowfall was larger than low ablation‐season meltwater caused by low air temperature (T a ). At interannual scales, annual mass balances were equally controlled by ablation‐season precipitation and T a during 1970–2019. From 1970s–1990s to 1990s–2010s, most Tibetan glaciers showed decreased mass balance due to increased ablation season T a , while the WKM glaciers experienced increased mass balance due to increased ablation‐season precipitation related to changes in the Silk Road Pattern. However, during 2000–2019, the annual mass balance of Guliya followed a decreasing trend due to increasing ablation‐season T a . The positive mass balance of the WKM glaciers will cease under future warming due to annual snowfall decreasing below ablation‐season meltwater. These changes will threaten lives and livelihoods in the Tarim Basin, whilst also jeopardizing ice core‐derived climate histories from the WKM glaciers.

Many-body Green's function approaches to the doped Fröhlich solid: Exact solutions and anomalous mass enhancement

In polar semiconductors and insulators, the Fr\"ohlich interaction between electrons and long-wavelength longitudinal optical phonons induces a many-body renormalization of the carrier effective masses and the appearence of characteristic phonon sidebands in the spectral function, commonly dubbed 'polaron satellites'. The simplest model that captures these effects is the Fr\"ohlich model, whereby electrons in a parabolic band interact with a dispersionless longitudinal optical phonon. The Fr\"ohlich model has been employed in a number of seminal papers, from early perturbation-theory approaches to modern diagrammatic Monte Carlo calculations. One limitation of this model is that it focuses on undoped systems, thus ignoring carrier screening and Pauli blocking effects that are present in real experiments on doped samples. To overcome this limitation, we here extend the Fr\"ohlich model to the case of doped systems, and we provide exact solutions for the electron spectral function, mass enhancement, and polaron satellites. We perform the analysis using two approaches, namely Dyson's equation with the Fan-Migdal self-energy, and the second-order cumulant expansion. We find that these two approaches provide qualitatively different results. In particular, the Dyson's approach yields better quasiparticle masses and worse satellites, while the cumulant approach provides better satellite structures, at the price of worse quasiparticle masses. Both approaches yield an anomalous enhancement of the electron effective mass at finite doping levels, which in turn leads to a breakdown of the quasiparticle picture in a significant portion of the phase diagram.

Combined Compact and Smooth Inversion for Gravity and Gravity Gradiometry Data

3-D inversion for gravity data is of great significance in geophysical quantitative interpretation. However, due to the complexity of the density distribution on the subsurface and nonuniqueness of inverse problems, the classical inversion still has many shortages. The smooth constrained inversion results in redundant structures, whereas the results of the compact inversion are too focused, and excessively rely on the choice of target density parameters. In view of the above issues, we develop a 3-D combined compact and smooth inversion for gravity and gravity gradient data. The objective function is built by the combination of the minimization of field source volume and the misfit between observed and predicted data. The prior information is treated as the “target density” in the inversion process. Furthermore, in order to solve the problem of overreliance on “target density,” we improve a 3-D gravity inversion algorithm where the model constraints include the combination of compact and smooth factors. Model tests show the method can better recover the source distribution when the parameter of target density is not given. Also, we make a comparative analysis of the inversion results of different gradient components and conclude that the inversion results of the gradient data <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$g_{xy}$ </tex-math></inline-formula> are better than those of other gradient components. Finally, we apply the method to the real gravity data. The inferred results of the anomalous rock mass are consistent with the previous geologic knowledge.

Mesoscale and Submesoscale Shelf‐Ocean Exchanges Initialize an Advective Marine Heatwave

AbstractObservations and high‐resolution numerical modeling are used to investigate the dynamical processes related to the initiation of an advective Marine Heatwave in the Middle Atlantic Bight of the Northwest Atlantic continental shelf. Both the observations and the model identify two significant cross‐shelf intrusions in November 2016 and January 2017, with the latter inducing large‐magnitude water mass anomalies across the shelf. Model prognostic fields reveal the importance of the combination of cyclonic eddies or ringlets and upwelling‐favorable winds in producing the large‐distance cross‐shelf penetration and temperature/salinity anomalies. The cyclonic eddies in close proximity to the shelfbreak set up local along‐isobath pressure gradients and provide favorable conditions for the intensification of the shelfbreak front, both processes driving cross‐isobath intrusions of warm, salty offshore water onto the outer continental shelf. Subsequently, strong and persistent upwelling‐favorable winds drive a rapid, bottom intensified cross‐shelf penetration in January 2017 composed of the anomalous water mass off the shelfbreak. The along‐shelf settings including realistic representation of bathymetric features are essential in the characteristics of the cross‐shelf penetration. The results highlight the importance of smaller scale cyclonic eddies and the intricacy of the interplay between multiple processes to drive significant cross‐shelf events.

Low mass strange stars and the compact star 1E1207.4-5209 in the field correlator method

We investigate the possible existence of anomalous mass defects in the low mass region of stellar sequences of strange stars. We employ the nonperturbative equation of state derived in the framework of the field correlator method to describe the hydrostatic equilibrium of the strange matter. The large distance static $Q\overline{Q}$ potential ${V}_{1}$ and the gluon condensate ${G}_{2}$ are the main parameters of the model. We use the surface gravitational redshift measurements as a probe to determine the ratio $(\mathcal{P}/\mathcal{E}{)}_{C}$ at the center of strange stars. For ${V}_{1}=0$ and ${G}_{2}\ensuremath{\gtrsim}0.035\text{ }\text{ }{\mathrm{GeV}}^{4}$, we show that $(\mathcal{P}/\mathcal{E}{)}_{C}\ensuremath{\simeq}0.262$ and the corresponding redshift ${z}_{S}\ensuremath{\simeq}0.47$ are limiting values at the maximum mass of the highest mass stellar sequence. As a direct application of our study, we try to determine the values of ${V}_{1}$ and ${G}_{2}$ from astrophysical observations of the compact star 1E 1207.4-5209. Due to the uncertainties in the surface redshift determination, we made two attempts to obtain the model parameters. Our findings show that $(\mathcal{P}/\mathcal{E}{)}_{C}=0.07{3}_{+0.024}^{+0.029}$ at 68% confidence, ${V}_{1}=0.44\ifmmode\pm\else\textpm\fi{}0.10\text{ }\text{ }\mathrm{GeV}$ at 90% confidence and ${G}_{2}=0.008\ifmmode\pm\else\textpm\fi{}0.001\text{ }\text{ }{\mathrm{GeV}}^{4}$ at 95% confidence in the first attempt; and $(\mathcal{P}/\mathcal{E}{)}_{C}=0.087\ifmmode\pm\else\textpm\fi{}0.028$ at 71% confidence, ${V}_{1}=0.43\ifmmode\pm\else\textpm\fi{}0.085\text{ }\text{ }\mathrm{GeV}$ at 94% confidence and ${G}_{2}=0.0093\ifmmode\pm\else\textpm\fi{}0.00092\text{ }\text{ }{\mathrm{GeV}}^{4}$ at 94% confidence in the second attempt. These values of ${V}_{1}$ and ${G}_{2}$ are in reasonable agreement with the lattice and QCD sum rules calculations. As a consequence of the high values of ${V}_{1}$ and ${G}_{2}$, the anomalous mass defects of 1E 1207.4-5209 are $|{\mathrm{\ensuremath{\Delta}}}_{2}M|\ensuremath{\simeq}2.56\ifmmode\times\else\texttimes\fi{}{10}^{53}\text{ }\text{ }\mathrm{erg}$ in the first attempt and $|{\mathrm{\ensuremath{\Delta}}}_{2}M|\ensuremath{\simeq}2.94\ifmmode\times\else\texttimes\fi{}{10}^{53}\text{ }\text{ }\mathrm{erg}$ in the second attempt.

Opposite anomalous synoptic patterns for potential California large wildfire spread and extinguishing in 2018 cases

The consecutive occurrence of three large wildfires in 1 year is rarely seen in northern California including the deadliest case during 8–25 November 2018 in Butte County. They happened under favorable fuel and meteorological conditions including long-term warming trends, normal summer-autumn warm-dry climate, and extreme heated air masses with strong offshore wind. The former two meteorological conditions contribute a background for large wildfires but extreme heated air masses and strong offshore winds are critical potentials for a fire spread. The relationship between extreme heated/cooled air masses and the three large wildfires was carefully examined from their starts to extinguishing. An anomaly-based synoptic analysis method is used by separating atmospheric variables into climatology and anomalies. A 3-dimensional anomalous synoptic pattern of atmospheric variables is established for the three wildfire cases in 2018. The analysis showed that one anomalous warm-air mass in the mid-to-low troposphere dynamically associated with a positive center of geopotential height (GPH) anomalies at the upper troposphere (150–300 hPa) is an anomalous synoptic pattern indicating a potential large wildfire spread, and conversely by negative anomalies when the fires were extinguished. The ECMWF model seems to be capable of predicting such anomalous temperature-pressure patterns to indicate possible fire spread and extinguishing.

Quantum confinement induced metal-insulator transition in strongly correlated quantum wells of SrVO3 superlattices

Dynamical mean-field theory (DMFT) has been employed in conjunction with density functional theory (DFT+DMFT) to investigate the metal-insulator transition (MIT) of strongly correlated $3d$ electrons due to quantum confinement. We shed new light on the microscopic mechanism of the MIT and previously reported anomalous subband mass enhancement, both of which arise as a direct consequence of the quantization of V $xz(yz)$ states in the SrVO$_3$ layers. We therefore show that quantum confinement can sensitively tune the strength of electron correlations, leading the way to applying such approaches in other correlated materials.

QCD analysis of near-threshold photon-proton production of heavy quarkonium

The near threshold photo or electroproduction of heavy vector quarkonium off the proton is studied in quantum chromodynamics. Similar to the high-energy limit, the production amplitude can be factorized in terms of gluonic Generalized Parton Distributions and the quarkonium distribution amplitude. At the threshold, the threshold kinematics has a large skewness parameter $\xi$, leading to the dominance of the spin-2 contribution over higher-spin twist-2 operators. Thus threshold production data are useful to extract the gluonic gravitational form factors, allowing studying the gluonic contributions to the quantum anomalous energy, mass radius, spin and mechanical pressure in the proton. We use the recent GlueX data on the $J/\psi$ photoproduction to illustrate the potential physics impact from the high-precision data from future JLab 12 GeV and EIC physics program.

Emergent gravity as the eraser of anomalous gauge boson masses, and QFT-GR concord

In the same base setup as Sakharov's induced gravity, we investigate emergence of gravity in effective quantum field theories (QFT), with particular emphasis on the gauge sector in which gauge bosons acquire anomalous masses in proportion to the ultraviolet cutoff $\Lambda_\wp$. Drawing on the fact that $\Lambda_\wp^2$ corrections explicitly break the gauge and Poincare symmetries, we find that it is possible to map $\Lambda_\wp^2$ to spacetime curvature as a covariance relation and we find also that this map erases the anomalous gauge boson masses. The resulting framework describes gravity by the general relativity (GR) and matter by the QFT itself with $\log\Lambda_\wp$ corrections (dimensional regularization). This QFT-GR concord predicts existence of new physics beyond the Standard Model such that the new physics can be a weakly-interacting or even a non-interacting sector comprising the dark matter, dark energy and possibly more. The concord has consequential implications for collider, astrophysical and cosmological phenomena.

Near-conformal dynamics in a chirally broken system

Composite Higgs models must exhibit very different dynamics from quantum chromodynamics (QCD) regardless whether they describe the Higgs boson as a dilatonlike state or a pseudo-Nambu-Goldstone boson. Large separation of scales and large anomalous dimensions are frequently desired by phenomenological models. Mass-split systems are well-suited for composite Higgs models because they are governed by a conformal fixed point in the ultraviolet but are chirally broken in the infrared. In this work we use lattice field theory calculations with domain wall fermions to investigate a system with four light and six heavy flavors. We demonstrate how a nearby conformal fixed point affects the properties of the four light flavors that exhibit chiral symmetry breaking in the infrared. Specifically we describe hyperscaling of dimensionful physical quantities and determine the corresponding anomalous mass dimension. We obtain $y_m=1+\gamma^*= 1.47(5)$ suggesting that $N_f=10$ lies inside the conformal window. Comparing the low energy spectrum to predictions of dilaton chiral perturbation theory, we observe excellent agreement which supports the expectation that the 4+6 mass-split system exhibits near-conformal dynamics with a relatively light $0^{++}$ isosinglet scalar.

Recursive system identification for coefficient estimation of continuous-time fractional order systems

Fractional-order calculus has already proven to be effective in order to model diffusive phenomena, such as heat transfer or anomalous mass transfer. This has led to developments of fractional-order transfer function models and, as a consequence, system identification algorithms have been developed to identify the parameters for this type of structures. However, it may be necessary to perform real-time system identification in which the parameters evolve over time while more and more data is acquired. Extensions to recursive identification algorithms are presented for fractional-order transfer functions. Two methods are proposed for recursive estimation of the coefficients of continuous-time fractional order systems: the recursive least squares with state variable filters and the prediction-error method. These two methods are compared with different signal to noise ratio levels through Monte Carlo simulations.

An Investigation into Brain Tumor Segmentation Techniques

A tumor is an anomalous mass in the brain which can be cancerous. Such anomalous growth within this restricted space or inside the covering skull can cause problems. Detecting brain tumors from images of medical modalities like CT scan or MRI involves segmentation (Division into parts) for analysis and can be a challenging task. Accurate segmentation of brain images is very essential for proper diagnosis of tumor and non-tumor areas for clinical analysis. This paper details on segmentation algorithms for brain images, advantages, disadvantages and a comparison of the algorithms

An Investigation into Brain Tumor Segmentation Techniques

A tumor is an anomalous mass in the brain which can be cancerous. Such anomalous growth within this restricted space or inside the covering skull can cause problems. Detecting brain tumors from images of medical modalities like CT scan or MRI involves segmentation (Division into parts) for analysis and can be a challenging task. Accurate segmentation of brain images is very essential for proper diagnosis of tumor and non-tumor areas for clinical analysis. This paper details on segmentation algorithms for brain images, advantages, disadvantages and a comparison of the algorithms

Simultaneously recovering both domain and varying density in inverse gravimetry by efficient level-set methods

<p style="text-indent:20px;">We develop new efficient algorithms for a class of inverse problems of gravimetry to recover an anomalous volume mass distribution (measure) in the sense that we design fast local level-set methods to simultaneously reconstruct both unknown domain and varying density of the anomalous measure from modulus of gravity force rather than from gravity force itself. The equivalent-source principle of gravitational potential forces us to consider only measures of the form <inline-formula><tex-math id="M1">\begin{document}$ \mu = f\,\chi_{D} $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M2">\begin{document}$ f $\end{document}</tex-math></inline-formula> is a density function and <inline-formula><tex-math id="M3">\begin{document}$ D $\end{document}</tex-math></inline-formula> is a domain inside a closed set in <inline-formula><tex-math id="M4">\begin{document}$ \bf{R}^n $\end{document}</tex-math></inline-formula>. Accordingly, various constraints are imposed upon both the density function and the domain so that well-posedness theories can be developed for the corresponding inverse problems, such as the domain inverse problem, the density inverse problem, and the domain-density inverse problem. Starting from uniqueness theorems for the domain-density inverse problem, we derive a new gradient from the misfit functional to enforce the directional-independence constraint of the density function and we further introduce a new labeling function into the level-set method to enforce the geometrical constraint of the corresponding domain; consequently, we are able to recover simultaneously both unknown domain and varying density from given modulus of gravity force. Our fast level-set method is built upon localizing the level-set evolution around a narrow band near the zero level-set and upon accelerating numerical modeling by novel low-rank matrix multiplication. Numerical results demonstrate that uniqueness theorems are crucial for solving the inverse problem of gravimetry and will be impactful on gravity prospecting. To the best of our knowledge, our inversion algorithm is the first of such for the domain-density inverse problem since it is based upon the conditional well-posedness theory of the inverse problem.

The Modulation of Daily Southern Africa Precipitation by El Niño–Southern Oscillation across the Summertime Wet Season

AbstractThe spatiotemporal evolution of daily southern Africa precipitation characteristics, and associated atmospheric circulation, related to El Niño and La Niña is examined across the region’s November–April wet season. Precipitation characteristics are examined in terms of monthly changes in daily average precipitation, the number of precipitation days, and the number of heavy precipitation days in three independently constructed estimates of observed precipitation during 1983–2018. Mechanisms related to precipitation changes, including contributions from mass divergence, water vapor transports, and transient eddies, are diagnosed using the atmospheric moisture budget based on the ERA5 reanalysis. El Niño is related to precipitation anomalies that build during December–March, the core of the rainy season, culminating in significantly below average values stretching across a semiarid region from central Mozambique to southeastern Angola. A broad anticyclone centered over Botswana drives these precipitation anomalies primarily through anomalous mass divergence, with moisture advection and transient eddies playing secondary roles. La Niña is related to significantly above average daily precipitation characteristics over all Africa south of 20°S in February and much less so during the other five months. February precipitation anomalies are primarily driven through mass divergence due to a strong anomalous cyclonic circulation, whereas a similar circulation is more diffuse during the other months. The spatiotemporal evolutions of anomalies in daily precipitation characteristics across southern Africa related to El Niño and La Niña are not equal and opposite. The robustness of an asymmetric evolution, which could have implications for subseasonal forecasts, needs to be confirmed with analysis of additional empirical data and established with climate model experimentation.

Crustal structure beneath the volcanic field in the Tihamat Plains, Saudi Arabia: An integrated model constrained by gravity modelling and receiver function results

• Structure of rift-related volcanic rocks in Tihamat Plains is constrained by gravity and receiver function results. • Two-layered-crustal-structure is envisaged in the Tihamat Plains, Saudi Arabia. • Moho uplift and magma underplating in the lower crust are visualized. The Tertiary Tihamat-Asir-Volcanic-Zone (TAVZ) in the Tihamat Plains (TP) at the Arabian Shield margin north of the southern Red Sea is largely obscured by Quaternary alluvium and salt deposits, but partly exposed. We integrate available gravity data in the TP which is represented by three semi-circular Bouguer Anomaly (B.A.) highs with peak values of 30 mgal, situated at distances of ~ 50 km. This feature suggests prevailing anomalous crustal masses under the TP and were investigated using: (i) Digital Elevation Model (DEM); (ii) radially averaged spectral estimates on the causative source body depths within the crust; (iii) tilt-angle derivatives with horizontal derivatives of the tilt-angle values; and (iv) a theta map to define the edge of the continental crust in offshore Jizan. 2D gravity models for two traverses, the Mansiyah-Baysh Traverse (MBT) and Suq-Al-Ahad Traverse (SAAT), were constructed across the TAVZ, constrained by Receiver Function (REF) results from ten broadband seismic stations. Additional constraints for gravity interpretation come from the physical properties derived from REF results for the upper and lower crust. Our integrated crustal model infers a zone of Moho uplift approximately ~ 40 km wide, with vertical relief of 10–12 km at depths of ~ 37–45 km, where the average density of the crust is appreciably higher. Gravity models indicate a large volcanic field beneath the TP extending along the coast of the Red Sea. We find that crustal modification is an outcome of crust–mantle interaction owing to an elevated thermal regime under the TP.

From the anomalous diffusion impedance to the closed-form, infinite-series and integral formulations of the voltammetric response of thin-film insertion materials under restricted diffusion conditions. A modelling contribution based on the anomalous mass transfer function

Abstract The voltammetric response of one-step reversible electrochemical reactions (involving dissolved redox species) to a linear potential ramp can be modelled using the calculation method proposed in our previous work (J. Electroanal. Chem. 818 (2018) 84) provided that the mass transfer function for the species involved in the electrochemical reaction is known in closed form under one-dimensional mass transport conditions. The above approach applies in this short communication to the direct insertion reaction in thin-film planar materials under both anomalous and spatially restricted (confined) diffusion conditions. The Faradaic current is obtained first as an alternating infinite series well suited to formal analysis, and then as an integral formulation well suited to numerical computation. Finally, closed-form expressions of the voltammograms are derived at very low or very high values of the potential sweep rate, respectively. Two anomalous diffusion models taken from the electrochemical literature are investigated and compared, based on their voltammetric responses. The voltammetric peak coordinates obtained from the best model are thoroughly examined, and closed-form approximations are proposed for the voltammetric peak current and potential at very low or very high potential sweep rates. A zone diagram is plotted to illustrate the conditions for observation of those limiting situations. Finally, following a referee's request, an alternative modelling approach is proposed in Appendix, which does not require the use of scientific computation software. This approach involves both the Integral Equation method formalism and numerical inversion of Laplace transform.