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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2601.06638 |
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| _version_ | 1866918296467537920 |
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| author | Segura, Juan J. |
| author_facet | Segura, Juan J. |
| contents | Fragmentation population-balance equations (PBEs) describe how particle size distributions (PSDs) evolve under breakage and daughter fragment redistribution. From a standard self-similar fragmentation class we derive an \emph{exact conservative transport equation in log-size} for the \emph{normalized mass fraction}: a state-dependent \emph{pure-jump} master equation (nonlocal internal-coordinate mass transfer). We also give an explicit Gorini--Kossakowski--Sudarshan--Lindblad (GKSL) factorization whose diagonal sector reproduces this master equation, used here as an \emph{optional} structure-preserving operator representation and constrained parameterization for inverse modeling (rather than a computational necessity).
In a controlled small-jump regime, the nonlocal jump transport reduces to a drift--diffusion (Fokker--Planck) operator in log-size space. Under detailed-balance conditions this operator admits the standard symmetrization to a self-adjoint Schrödinger-type spectral problem, enabling compact parametric hypothesis classes for PSD shapes. We then present two inverse routes: (i) time-resolved parametric fitting of transport/spectral parameters, and (ii) a regularized steady-state inversion that reconstructs an effective potential from a measured steady PSD.
To address practical validation, we include numerical benchmarks: forward simulation of the jump transport model (CTMC discretization) and its drift--diffusion reduction, quantitative discrepancy metrics, and inverse parameter recovery on an Airy half-line synthetic benchmark under controlled multiplicative noise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06638 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Conservative Log-Size Master Equation for Fragmentation PBEs: Jump Transport, Drift--Diffusion Asymptotics, and PSD Inference Segura, Juan J. Statistical Mechanics Mathematical Physics 35Q84 (Primary) 60J75, 45K05, 47D07 (Secondary) condary) Fragmentation population-balance equations (PBEs) describe how particle size distributions (PSDs) evolve under breakage and daughter fragment redistribution. From a standard self-similar fragmentation class we derive an \emph{exact conservative transport equation in log-size} for the \emph{normalized mass fraction}: a state-dependent \emph{pure-jump} master equation (nonlocal internal-coordinate mass transfer). We also give an explicit Gorini--Kossakowski--Sudarshan--Lindblad (GKSL) factorization whose diagonal sector reproduces this master equation, used here as an \emph{optional} structure-preserving operator representation and constrained parameterization for inverse modeling (rather than a computational necessity). In a controlled small-jump regime, the nonlocal jump transport reduces to a drift--diffusion (Fokker--Planck) operator in log-size space. Under detailed-balance conditions this operator admits the standard symmetrization to a self-adjoint Schrödinger-type spectral problem, enabling compact parametric hypothesis classes for PSD shapes. We then present two inverse routes: (i) time-resolved parametric fitting of transport/spectral parameters, and (ii) a regularized steady-state inversion that reconstructs an effective potential from a measured steady PSD. To address practical validation, we include numerical benchmarks: forward simulation of the jump transport model (CTMC discretization) and its drift--diffusion reduction, quantitative discrepancy metrics, and inverse parameter recovery on an Airy half-line synthetic benchmark under controlled multiplicative noise. |
| title | A Conservative Log-Size Master Equation for Fragmentation PBEs: Jump Transport, Drift--Diffusion Asymptotics, and PSD Inference |
| topic | Statistical Mechanics Mathematical Physics 35Q84 (Primary) 60J75, 45K05, 47D07 (Secondary) condary) |
| url | https://arxiv.org/abs/2601.06638 |