Accurate prediction of CO2–brine relative permeability is essential for evaluating CO2 migration and storage performance in saline aquifers. However, conventional empirical models rely heavily on fitted parameters, while existing fractal models generally provide limited descriptions of the effects of pore pressure and displacement rate on two-phase flow. To address these limitations, a pore-scale-based fractal relative permeability model is developed by coupling two-phase flow theory, fractal pore-size distribution, and numerical integration. The main innovation lies in incorporating pressure-dependent CO2 viscosity and a variable immobile water-film thickness governed by pore radius, driving pressure gradient, and brine viscosity into the effective flow radius. Compared with conventional models employing fixed water-film thickness or neglecting injection-condition effects, the proposed formulation provides a physically based representation of the responses of CO2–brine relative permeability to pore pressure and displacement rate. The model is evaluated using six displacement experiments conducted on four sandstone cores. The coefficients of determination (R2) range from 0.957 to 0.998 for the brine phase and from 0.869 to 0.955 for the CO2 phase, demonstrating good agreement between predictions and measurements. Sensitivity analyses indicate that increasing absolute permeability generally enhances the relative permeabilities of both phases. Increasing pore pressure from 10 to 55 MPa and displacement rate from 1 to 5.5 mL·min−1 generally increases two-phase relative permeability and maximum CO2 saturation while reducing residual brine saturation. The proposed model provides a physically informed approach for characterizing CO2–brine two-phase flow under varying injection conditions and supports relative permeability prediction for CO2 storage in water-wet sandstone saline aquifers.
Fractal analysis has become a frequently used technique in sensory physiology for the evaluation of signal complexity, with potential applications ranging from the analysis of retinal vascular architecture to the quantification of changes in electroencephalographic recordings. Features such as fractal dimension and lacunarity may be able to detect discrete changes in both one-dimensional and two-dimensional signals associated with numerous physiological processes and disease development. However, their interpretation and translational potential are constrained by various limitations. In this concise review, we critically explore current applications of fractal analysis across major sensory domains and focus on the challenges that limit reproducibility and biological interpretation. We particularly focus on the biological ambiguity of fractal dimension and related measures, the non-equivalence of commonly used fractal metrics, acquisition-related variability, small datasets, and insufficient technical validation. Finally, we discuss issues related to the integration of fractal metrics into contemporary machine learning models, including challenges related to generalizability, overfitting, and poor explainability.
This article is devoted to the derivation of new inequalities within the theory of fractal–fractional calculus. Its principal contribution is the construction of a new auxiliary identity of fractal–fractional type. By exploiting this identity, we establish a variety of Bullen–Simpson-type inequalities associated with functions whose local fractional derivatives possess generalized harmonic convexity. Moreover, by employing the generalized Hölder and power mean inequalities, we derive supplementary bounds that further enhance the scope of the analysis. The accuracy of the theoretical developments is illustrated through a representative example, together with graphical visualizations that substantiate the consistency of the proposed results. Finally, an application to certain special fractal means is presented in order to demonstrate the effectiveness and practical relevance of the obtained inequalities.
Detrended fluctuation analysis (DFA) and its multifractal extension (MF-DFA) estimate scaling exponents from a fixed segmentation of the data. On a nonstationary series, however, a segment that crosses a transition of the local Hurst function H(t) mixes two scaling regimes and biases the estimate. We propose a local Hurst-guided segmentation for MF-DFA that leaves the classical fluctuation function and polynomial detrending unchanged and adapts only the grouping of the observations to H(t): a rolling DFA curve is estimated, its transitions are located by CUSUM or PELT, and the multifractal spectrum is estimated separately within each detected regime, with a boundary inset that discards observations of uncertain regime membership. When H(t) is constant the procedure reduces to standard MF-DFA. We prove that regime mixing induces a spurious multifractal width in global MF-DFA, and we bound the error that a misplaced transition propagates into the state-level h(q) and show that a boundary inset of the order of the detection error removes it. Simulations use multifractional Brownian motion with stepwise and continuously varying Hurst functions. The segmented estimators recover the state spectra and remove the spurious multifractal width that global MF-DFA attributes to the series as a whole. An application to the daily S&P 500 index over 1999–2026 completes the study.
This paper studies the scale-dependent co-movements of monthly changes in U.S. unemployment, inflation, and the federal funds rate from July 1954 to May 2026 using contemporaneous, lagged, and asymmetric Multifractal Detrended Cross-Correlation Analysis (MF-DCCA). Significance is assessed against 200 Iterative Amplitude Adjusted Fourier Transform (IAAFT) surrogates for every pair, lag, and trend regime, and the lead–lag patterns are compared with a linear VAR benchmark. The generalized cross-Hurst exponent Hxy(q) varies with the moment order q: the cross-scaling of small co-fluctuations (q<0) is largely compatible with the surrogate null, whereas that of moderate and large co-fluctuations departs from it at horizons of up to 12 months. The lead–lag cross-persistence between policy-rate changes and unemployment, and from policy-rate changes to inflation, is approximately invariant across horizons of 1 to 12 months, whereas for unemployment and inflation, and from inflation to policy-rate changes, the cross-persistence of large co-fluctuations increases with the horizon, most robustly from inflation to unemployment. The VAR finds linear predictability only in the first group, most robustly from policy-rate changes to inflation. The asymmetric analysis shows that joint scaling depends on the phase of the guiding series, with markedly higher cross-persistence of inflation with unemployment in high-inflation phases, a pattern that is robust to the detrending order, whereas the asymmetries involving the policy rate are less robust and the asymmetric estimates at extreme moment orders are sensitive to the estimation settings. These results are descriptive rather than structural and complement conventional macroeconometric evidence.
