arXiv subjects

Juan J. Segura

Publications and source records attributed to Juan J. Segura.

5 recordsLinked to original sources

arXiv2026

Geostatistics from Elliptic Boundary-Value Problems: Green Operators, Transmission Conditions, and Schur Complements

Classical geostatistics encodes spatial dependence by prescribing variograms or covariance kernels on Euclidean domains, whereas the SPDE--GMRF paradigm specifies Gaussian fields through an elliptic precision operator whose inverse is the corresponding Green operator. We develop an operator-based formulation of Gaussian spatial random fields on bounded domains and manifolds with internal interfaces, treating boundary and transmission conditions as explicit components of the statistical model. Starting from coercive quadratic energy functionals, variational theory yields a precise precision--covariance correspondence and shows that variograms are derived quadratic functionals of the Green operator, hence depend on boundary conditions and domain geometry. Conditioning and kriging follow from standard Gaussian update identities in both covariance and precision form, with hard constraints represented equivalently by exact interpolation constraints or by distributional source terms. Interfaces are modelled via surface penalty terms; taking variations produces flux-jump transmission conditions and induces controlled attenuation of cross-interface covariance. Finally, boundary-driven prediction and domain reduction are formulated through Dirichlet-to-Neumann operators and Schur complements, providing an operator language for upscaling, change of support, and subdomain-to-boundary mappings. Throughout, we use tools standard in spatial statistics and elliptic PDE theory to keep boundary and interface effects explicit in covariance modeling and prediction.

stat.ME↗

arXiv2026

Computable Structuralism: A Categorical Rewrite Calculus of Mythic Variants

Structural approaches to myth and narrative are compelling in close reading but hard to compare across traditions, media, and scale. We propose a formal framework that renders Lévi-Straussian transformation as mathematics while remaining readable as narrative analysis. Variants, superhero continuities, and franchise arcs are modeled as typed rewrite programs on a coupled two-register state $(X,Y)$, abstracting an everyday/social channel and a symbolic/legitimation channel. The canonical formula becomes coherence data: a natural transformation $η:U\Rightarrow V$ between update endofunctors, where $U$ updates each register in place and $V$ performs a swap+inversion. Context is internalized by operator choice, turning naturality into a corpus-facing type check: failures diagnose mis-specified oppositions or illegal transport; successes witness coherent structural models. Order effects are summarized by a five-value invariant (Key). We apply the method to 80 narratives (20 folktales, 20 religious myths, 20 superheroes, 20 franchises), each encoded as $(a,b,x,y)$ with a Key. 59/80 (74\%) explicitly name a normative constraint in $y$ (law, taboo, contract, prophecy), supporting the two-register abstraction. The result is a testable bridge between structural anthropology and cultural analytics: stories remain interpretable yet become transportable objects for computation, comparison, and falsifiable constraints on transformation.

cs.SI↗

arXiv2026

A Conservative Log-Size Master Equation for Fragmentation PBEs: Jump Transport, Drift--Diffusion Asymptotics, and PSD Inference

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.

cond-mat.stat-mech↗

arXiv2026

From Columns to Heaps: Dimensionless Similarity with PSD-Distributed Damköhler Numbers and Dual-Porosity Flow

This work develops a unified, dimensionless framework for comparing geometrically similar reacting porous-flow systems across scale, with emphasis on hydrometallurgical heap leaching, when particle size distribution (PSD) and intraparticle pore structure differ. Under dynamic similarity, the dimensionless liquid residence-time distribution (RTD) is identical, but differences in PSD and internal porosity break microscopic similarity. Using the shrinking-core model (SCM), the analysis shows how a PSD in particle diameter maps to a distribution of particle-scale Damköhler numbers that governs heap-averaged conversion. Explicit PSD to Damköhler transformations are derived for (i) external film control, (ii) intraparticle diffusion control, and (iii) mixed control via additive rates. Dual-porosity hydrology relevant to sedimentary or strongly stratified ores is then incorporated by coupling SCM kinetics to mobile and immobile liquid domains, introducing additional dimensionless groups that describe interporosity exchange. Two numerical examples map a lognormal PSD into film- and diffusion-controlled Damköhler distributions and compare column/heap conversion for different PSDs. A practical workflow is outlined for hydrometallurgical column-test interpretation, combining tracer RTD calibration with PSD-aware kinetic fitting in dimensionless time. The framework clarifies why diffusion-controlled leaching is far more sensitive to PSD tails and dual-porosity structure than film-controlled leaching, and it identifies the compact set of dimensionless groups that must be matched to ensure similarity between laboratory columns and industrial heaps.

physics.flu-dyn↗

arXiv2026

Comminution as a Non-Hermitian Quantum Field Theory: Log-Size Jump Generators, Branching Embeddings, and the Airy Solvable Sector

Pure-breakage population balance equations (PBEs) give the standard deterministic description of fragmentation and comminution. They predict mean particle size distributions, but they do not determine fluctuations, size-size correlations, or universality under coarse-graining. We develop a field-theoretic framework anchored in the PBE kernel inputs (selection rate and daughter distribution) and compatible with the stochastic Doi-Peliti approach. From homogeneous kernels we derive an exact Markov jump generator in log-size for a mass-weighted (tagged-mass) distribution, with a jump law that is a probability density fixed by the daughter distribution. The generator is generically non-self-adjoint, admits a Lindblad embedding, and has a second-quantized extension. The deterministic PBE appears as the one-body sector, while multi-point correlators encode finite-population fluctuations. We also give a binary-fragmentation embedding whose mean-field limit reproduces the PBE but whose higher correlators capture multiplicative cascade noise. For a linear Airy-type kernel, long-wavelength coarse-graining yields an effective Airy operator as a solvable quadratic sector about a stationary profile, producing explicit mode-sum formulas for equal-time connected two-point correlations. Overall, the framework separates what is fixed by kernel data from what requires additional stochastic modeling and links comminution kernels to universality classes.

math-ph↗