Passive two-plateau relaxation from Tricomi confluent hypergeometric kernels
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911588831723520 |
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| author | Tudela-Pi, Marc Colombaro, Ivano |
| author_facet | Tudela-Pi, Marc Colombaro, Ivano |
| contents | Anomalous relaxation with memory spectra arises in disordered solids, soft matter, biological tissues and electrochemical interfaces. Fractional-order models capture broad power-law behaviour efficiently, but they can obscure spectral structure and are not always convenient for passive realisation or finite-dimensional simulation. We introduce a non-fractional passive framework based on the Tricomi confluent hypergeometric function, combined with a bounded Moebius normalisation that enforces prescribed low-frequency and high-frequency plateaux while preserving a broad dispersive transition. The resulting family contains the Debye and Cole-Cole responses as exact subcases, while extending them to asymmetric two-plateau dispersive laws with independently tunable low- and high-frequency exponents. For an admissible parameter range, we prove that the bounded block admits a Stieltjes representation with nonnegative spectral density, implying complete monotonicity, passivity, causality and compatibility with standard circuit and state-space descriptions. Building on this structure, we derive a passive Gauss-Stieltjes discretisation leading to Foster-type rational approximations and first-order state-space realisations with positive poles and residues. Numerical experiments show convergence of these finite-dimensional approximations across moderate-memory and long-tail regimes, enabling passive reduced-order representations of broad-memory responses. The framework is then validated on broadband dielectric data and battery electrochemical impedance spectra. In tissues, multi-block Tricomi mixtures improve complex-domain fitting accuracy relative to classical Cole-Cole baselines while preserving interpretable modal structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11464 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Passive two-plateau relaxation from Tricomi confluent hypergeometric kernels Tudela-Pi, Marc Colombaro, Ivano Mathematical Physics Adaptation and Self-Organizing Systems Anomalous relaxation with memory spectra arises in disordered solids, soft matter, biological tissues and electrochemical interfaces. Fractional-order models capture broad power-law behaviour efficiently, but they can obscure spectral structure and are not always convenient for passive realisation or finite-dimensional simulation. We introduce a non-fractional passive framework based on the Tricomi confluent hypergeometric function, combined with a bounded Moebius normalisation that enforces prescribed low-frequency and high-frequency plateaux while preserving a broad dispersive transition. The resulting family contains the Debye and Cole-Cole responses as exact subcases, while extending them to asymmetric two-plateau dispersive laws with independently tunable low- and high-frequency exponents. For an admissible parameter range, we prove that the bounded block admits a Stieltjes representation with nonnegative spectral density, implying complete monotonicity, passivity, causality and compatibility with standard circuit and state-space descriptions. Building on this structure, we derive a passive Gauss-Stieltjes discretisation leading to Foster-type rational approximations and first-order state-space realisations with positive poles and residues. Numerical experiments show convergence of these finite-dimensional approximations across moderate-memory and long-tail regimes, enabling passive reduced-order representations of broad-memory responses. The framework is then validated on broadband dielectric data and battery electrochemical impedance spectra. In tissues, multi-block Tricomi mixtures improve complex-domain fitting accuracy relative to classical Cole-Cole baselines while preserving interpretable modal structure. |
| title | Passive two-plateau relaxation from Tricomi confluent hypergeometric kernels |
| topic | Mathematical Physics Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2604.11464 |