arXiv subjects

Maria P. Beccar-Varela

Publications and source records attributed to Maria P. Beccar-Varela.

4 recordsLinked to original sources

arXiv2026

Persistence without Multifractality in Tropical Atlantic SST Indices: Scaling-Range Artefacts and a Reappraisal of the ENSO Association

We investigate the scaling properties of three weekly tropical Atlantic sea-surface-temperature indices (SAT, TSA and the interhemispheric gradient TASI) over 1981--2025 using multifractal detrended fluctuation analysis and its sign-preserving cross-correlation extension. Exponents are estimated over $s\in[18,100]$ weeks, bounded by $s_{\min}\gtrsim6(m+1)$ for second-order detrending and a crossover near 100 weeks. On these scales all three indices are strongly persistent and locally non-stationary ($h(2)=1.32$--$1.35$). Comparison with shuffled and phase-randomised surrogates shows that none of the indices are multifractal within record resolution. SAT ($Δh=0.077$) and TASI ($Δh=0.054$) are fully consistent with both null models. Although TSA yields a larger width ($Δh=0.217$), its increasing $h(q)$ implies the unphysical condition $f(α)>1$, indicating a crossover rather than a multiplicative cascade. At the available record length ($N\approx2300$), apparent multifractal widths are not identifiable because confidence intervals overlap and rankings remain sensitive to analysis choices. The increments are only mildly leptokurtic, excluding heavy tails as the source of the apparent widths. Pairwise couplings reveal strong positive cross-correlations between the regional indices and anticorrelation of the gradient with both, all described by a single cross-scaling exponent, consistent with monofractal behaviour. A lagged analysis further shows that the previously reported TASI--ENSO association disappears after surrogate testing accounting for multiple lags. These results substantially revise downward previous estimates of multifractal strength in tropical Atlantic SST and show that reported widths should not be interpreted without verifying both the sign of $h'(q)$ and the stability of the scaling range.

physics.ao-ph↗

arXiv2026

Multifractal Signatures of Hamiltonian Chaos in Hyperion's Rotational Dynamics

The chaotic rotation of Saturn's moon Hyperion is a paradigmatic example of Hamiltonian chaos in a natural system. Although its tumbling motion is well established theoretically, identifying a robust observational signature of chaos from sparse and noisy astronomical time series remains a major challenge, making phase-space reconstruction techniques impractical under realistic conditions. In this work, we show that multifractal detrended fluctuation analysis (MFDFA) provides an effective alternative for detecting chaotic dynamics directly from photometric observations. Using historical ground-based light curves and synthetic datasets, we demonstrate that the intermittency associated with chaotic tumbling produces a broad multifractal singularity spectrum. While multifractality is a known feature of Hamiltonian chaos, we show that it can serve as a practical observational diagnostic when traditional chaos indicators fail because of sparse sampling. In particular, the multifractal spectrum remains detectable after realistic observational filtering and distinguishes chaotic tumbling from aliased regular rotation. By contrast, regular resonant rotation exhibits a significantly narrower spectrum, approaching the monofractal behavior expected for uncorrelated noise. For the observational data, we measure a broad spectral width consistent with the synthetic chaotic model, statistically distinct from surrogate datasets, and robust against finite time-series length. These results establish multifractal scaling as a viable observational signature of Hamiltonian chaos in sparse astronomical datasets, bridging nonlinear dynamics and planetary photometry.

astro-ph.EP↗

arXiv2026

Multifractal Complexity of the Chandler Wobble and Its Anomalous Disappearance (2015--2020): A MFDFA Study

The Chandler wobble (CW) -- the $\sim$433-day free nutation of Earth's rotation pole -- experienced an anomalous near-disappearance between 2015 and 2020, followed by a re-excitation with an approximately $180^{\circ}$ phase reversal. Using Multifractal Detrended Fluctuation Analysis (MFDFA) applied to more than six decades (1962--2024) of daily IERS EOP C04 polar motion data, this study provides the first multifractal characterisation of the CW and its recent anomaly. Global MFDFA shows that the residual polar motion components and the CW amplitude are genuine multifractal processes with strongly $q$-dependent generalised Hurst exponents and broad singularity spectra. Surrogate-data tests with shuffled and phase-randomised ensembles demonstrate that this multifractality originates from the combined action of long-range temporal correlations and heavy-tailed excitation statistics. A sliding-window analysis reveals a pronounced collapse in long-range persistence and multifractal spectral width of the geometric polar motion signal several years before and during the 2015--2020 amplitude minimum, indicating a genuine dynamical regime change rather than a simple suppression of oscillation amplitude. In contrast, the amplitude- and phase-related variables retain broad multifractal spectra and stable scaling exponents across all epochs, revealing a dynamical decoupling between the geometry of the CW and the multiscale structure of its amplitude and phase fluctuations. These findings highlight the CW amplitude as an exceptionally multifractal integrator of geophysical excitation and suggest that multifractal metrics may provide early-warning indicators of major transitions in Earth rotation dynamics.

cond-mat.stat-mech↗

arXiv2026

Resolving Spurious Multifractality in Discrete Systems: A Finite-Size Scaling Protocol for MFDFA in the 2D Ising Model

Multifractal Detrended Fluctuation Analysis (MFDFA) has emerged as a standard tool for characterizing scale invariance in complex systems, yet its application to discrete spin models is frequently marred by reports of ``spurious multifractality'' that contradict established theory. In this work, we resolve this controversy by establishing a rigorous protocol for the analysis of discrete lattice snapshots. Using the 2D Ising model as a benchmark, we demonstrate that the previously reported broad singularity spectra \cite{Ludescher2011} are finite-size artifacts dominated by lattice discreteness effects in the negative moment regime ($q<0$). By restricting the analysis to positive moments and performing a systematic Finite-Size Scaling (FSS) analysis, we show that the spectral width collapses to zero ($Δα\to 0$) in the thermodynamic limit. The method accurately recovers the monofractal exponent of the Ising universality class ($α\approx H \approx 0.875$), consistent with Conformal Field Theory. To validate the discriminatory power of this protocol, we contrast these findings with the Random Bond Ising Model (RBIM), showing that quenched disorder induces a genuine, broad multifractal spectrum ($Δα\approx 0.23$) that survives scaling. Furthermore, we propose a theoretical interpretation where the MFDFA polynomial detrending functions as a phenomenological Renormalization Group filter, suppressing analytic background fields (irrelevant operators) to isolate the singular critical behavior. These results define a robust methodology for distinguishing between clean and disorder-dominated criticality in finite systems.

cond-mat.stat-mech↗