arXiv subjects

Fernando Alonso-Marroquin

Publications and source records attributed to Fernando Alonso-Marroquin.

At least 19 recordsLinked to original sources

arXiv2026

Residual Saturation under Pressure-Controlled Drainage

Here, pressure-controlled drainage is formulated as bond percolation with trapping on the pore-network graph, establishing a direct connection between percolation theory and pressure--saturation relations. In two dimensions, the deviation of the residual saturation from its non-vanishing thermodynamic limit obeys a finite-size scaling law with exponent $\delta \approx 0.25$, independent of microscopic details of the lattice. In three dimensions, finite-size corrections decay more rapidly ($\delta \approx 0.75$), while the asymptotic residual saturation remains finite and depends on coordination number. This extends the standard invasion-percolation picture beyond the breakthrough state, where the invading cluster is fractal and the invaded-phase saturation vanishes in the infinite-size limit.

cond-mat.stat-mech↗

arXiv2026

Stationarity-constrained representative volume elements for image-based homogenization of granular microstructures

We present an image-based workflow for representative elementary volume (REV) sizing in chemically mapped granular microstructures, applied to Arabian dune-sand samples characterized by mineralogical and textural heterogeneity. The REV is treated as a finite-window convergence scale within approximately stationary material domains, rather than as a global length assigned to a non-stationary image. Full-resolution backscattered-electron (BSE) gray-level maps are screened by local mean and standard-deviation compatibility to identify stationary domains. Candidate windows are sampled only inside these domains, and the representative support is selected using a persistent mean--spectral criterion requiring both the apparent-mean residual and the low-wavenumber covariance-spectrum residual to remain within tolerance over the non-reference tail. Ensemble reproducibility is used as an auxiliary check. Applied to seven full-resolution BSE images of dune-sand microstructures, the strict stationary-domain criterion gives $(L_{\rm REV}=1536~\mathrm{pixels})$, corresponding to $(\ell_{\rm REV}\approx2.01~\mathrm{mm})$ for a BSE pixel size of $(1.31~\mu\mathrm{m})$. Property-level homogenization on QEMSCAN-derived numerical maps independently supports this millimetre-scale estimate: the converted support is $(L_{\rm REV}^{\rm prop}=201.2)$ pixels and is snapped to the nearest tested size, $(L_{\rm REV}^{\rm prop}=204)$ pixels $(\ell_{\rm REV}^{\rm prop}=2.04~\mathrm{mm})$. This length lies in the large-window regime of the apparent conductivity, stiffness, and directional Young-modulus curves. The workflow provides a reproducible route for REV sizing while making explicit its dependence on stationarity, image field, window sequence, and target observable.

cond-mat.mtrl-sci↗

arXiv2026

Nonisothermal global-pressure exactness in fractured multiphase flow with aperture feedback

Global-pressure formulations recast multiphase Darcy flow in terms of a single pressure driving the total flux. Their exact equivalence to phase-pressure formulations holds only when the constitutive data satisfy the compatibility conditions required for a total-differential structure and its generalized nonisothermal extension. Here, we derive the exactness criterion for temperature-dependent mobilities and capillary pressures. We show that equivalence depends on whether the mobility-weighted capillary contribution is path independent in the saturation--temperature domain, so that it can be absorbed into a scalar global pressure. This yields the classical compatibility conditions within the saturation sector and a distinct mixed saturation--temperature condition that arises only in nonisothermal settings. We then incorporate this structure into a reduced matrix--fracture model with heat transport, matrix--fracture thermal exchange, and evolving aperture. Numerical benchmarks recover the three regimes predicted by the theory: globally exact, exact on each fixed-temperature slice but not on the full saturation--temperature domain, and fully nonexact. In fractured systems, thermal forcing alone can drive transitions between these regimes, while aperture evolution changes the path through state space. When saturation-sector exactness is lost, a least-squares projection on fixed-temperature slices extracts the nearest gradient component of the mobility-weighted capillary field. This yields a conservative slice-wise scalar-pressure surrogate and a quantitative projection residual. The residual separates saturation-sector nonintegrability from the mixed saturation--temperature incompatibility that controls genuinely nonisothermal loss of exactness. The framework links nonisothermal exactness theory, fractured-flow dynamics, and conservative reduced closure in a global-pressure formulation.

physics.flu-dyn↗

arXiv2026

A Nonhomogeneous Porous-Medium Equation for Field Scale CO$_2$ Plume Spreading

We derive a nonlinear diffusion model for field scale CO$_2$ plume spreading from a Global Buckley--Leverett component balance. The reduced variable $u$ is the vertically averaged mobile gas phase CO$_2$ content normalized by its maximum column value; under vertical segregation, $u=h/H$, where $h$ is plume thickness and $H$ is aquifer thickness. The resulting equation is a nonhomogeneous porous medium type equation in which nonlinear lateral spreading is coupled to source/sink terms for injection, dissolution, mineral fixation, and retention. Using the nonlinear diffusivity $D_u(u)\simeq D_0u^{1-q}$, we analyze Barenblatt-type profiles with prescribed mobile mass and a capped plume constrained by $0\le u\le1$. The capped solution contains a ful-thickness core of radius $a(t)$ and a compact plume edge $R(t)$. Constant net mobile injection can sustain the core and gives square-root growth of $R(t)$, whereas shut-in or weak mobile addition causes the core to shrink and disappear. We compare these regimes with equivalent radii from time lapse seismic plume maps at Sleipner, Aquistore, and Weyburn--Midale. The data distinguish injection controlled growth, delayed layer filling, and tail dominated redistribution, but do not determine a unique nonlinear exponent. The model provides an analytical reference for interpreting plume footprint evolution while separating cumulative injected CO$_2$ from mobile gas phase CO$_2$.

physics.flu-dyn↗

arXiv2026

Representative-volume sizing in finite cylindrical computed tomography by low-wavenumber spectral convergence

Choosing a representative element volume (REV) from finite cylindrical Computed Tomography (CT) scans becomes ambiguous when a key field variable exhibits a slow axial trend, reflecting either geological variability or CT acquisition/reconstruction artifacts. In such cases, estimated statistics may vary systematically with subvolume size and position rather than converging by simple averaging. We present a practical workflow for sizing an REV under nonstationary conditions by first suppressing axial drift/trend to obtain a residual field suitable for second-order analysis, and then selecting the smallest analysis diameter for which the low-wavenumber spectral content stabilizes within a prescribed tolerance. The method is demonstrated on \textit{Thalassinoides}-bearing rocks, where branching burrow networks introduce heterogeneity at length scales comparable to laboratory core diameters, making imaging-based microstructural statistics and digital-rock estimates sensitive to subvolume choice. From segmented data, we define a scalar ``burrowsity'' field capturing burrow-related pore spaces and infills. Axial detrending, with optional normalization, mitigates acquisition drift and nonstationary trends, while covariance/spectral convergence is evaluated on nested cylinders consistent with the core geometry. Representativeness is posed as diameter convergence on nested inscribed cylinders: the two-point covariance and isotropic spectrum $\widehat{C}$ are estimated, and the smallest diameter at which the low-wavenumber plateau becomes stable is selected. Applied to a segmented \textit{Thalassinoides} core, the method gives $D_{\mathrm{REV}}\simeq 93~\mathrm{mm}$ and $H_{\mathrm{REV}}\simeq 83~\mathrm{mm}$, enabling reproducible correlation-scale reporting and connectivity-sensitive property estimation.

cond-mat.soft↗

arXiv2025

Global Buckley-Leverett theory for multicomponent flow in fractured media: Isothermal equation-of-state coupling and dynamic capillarity

We present an isothermal Global Buckley--Leverett framework for multicomponent, multiphase flow in porous and fractured media that retains the interpretability of classical Buckley--Leverett while incorporating essential physics: equation of state-based phase behavior, multicomponent Maxwell--Stefan diffusion, dynamic capillarity, stress-sensitive permeability, and non-Darcy fracture flow. The formulation yields a single global-pressure equation driving the total Darcy flux and an exact fractional-flow decomposition of phase velocities with buoyancy and capillary drifts; inertial effects enter as per-phase damping that renormalizes mobilities. Crucially, the combination of Maxwell--Stefan diffusion and dynamic capillarity renders transport pseudo-parabolic, resolving the loss of strict hyperbolicity that plagues three-phase Buckley--Leverett and ensuring a well-posed initial-value problem. In practice, each time step solves the scalar global-pressure equation, reconstructs phase fluxes via the split, and advances strictly conservative component balances; axisymmetric (cylindrical) forms for radial injection with vertical buoyancy are provided. The model reduces exactly to classical Buckley--Leverett when added physics are disabled, making it a practical backbone for carbon storage, geothermal exchange, and contaminant transport in fractured, compositionally complex reservoirs.

physics.flu-dyn↗

arXiv2025

Capillarity in Stationary Random Granular Media: Distribution-Aware Screening and Quantitative Supercell Sizing

We develop a quantitative framework to determine the minimal periodic supercell required for representative simulations of capillarity-screened Darcy flow in stationary random, polydisperse granular media. The microstructure is characterized by two-point statistics (covariance and spectral density) that govern finite-size fluctuations. Capillarity is modeled as a screened, modified-Helmholtz problem with phase-dependent transport under periodic boundary conditions; periodic homogenization yields an apparent conductivity, an apparent screening parameter, and a macroscopic capillary decay length. Because screening imparts a spatial low-pass response, we introduce a distribution-aware treatment of polydispersity consisting of a capillarity-weighted volume fraction and a screened analogue of the integral range that preserves variance units and recovers classical descriptors in the appropriate limits. These descriptors lead to two sizing rules: (i) a length criterion on the shortest cell edge controlled by a microstructural correlation length, the macroscopic decay length, and a high quantile of grain size; and (ii) a volume criterion that links the target coefficient of variation to the screened integral range and the phase contrast. The framework couples statistical microstructure information to capillary response and yields reproducible, distribution-aware supercell selection for image-based finite-element or fast-Fourier-transform solvers. The resulting criteria are therefore intended for representativity of the coarse-grained screened response, rather than for isolated nonlinear pore-scale events.

cond-mat.soft↗

arXiv2025

Topological Invariants in the Pore Morphology Method

This study introduces a pore morphology algorithm that emphasizes the central role of topology in multiphase flow through porous media. Analysis of drainage in lattice-based pore networks identifies two key quantities, the percolation threshold and residual saturation, as topological invariants. These descriptors, which are based solely on connectivity rather than geometric details, capture the essential structure of the network. The percolation threshold is interpreted as a topological phase transition, marking the transition from global connectivity of the defending fluid to isolated clusters of trapped fluid. The universality of scaling exponents across different lattice geometries reveals the existence of topological universality classes, where systems with equivalent connectivity display identical critical behavior. This topological framework underscores the robustness of the identified invariants and provides a general basis for upscaling pore-scale processes in complex media.

cond-mat.stat-mech↗

arXiv2025

Stylized Facts of High-Frequency Bitcoin Time Series

This paper analyses the high-frequency intraday Bitcoin dataset from 2019 to 2022. During this time frame, the Bitcoin market index exhibited two distinct periods, 2019-20 and 2021-22, characterized by an abrupt change in volatility. The Bitcoin price returns for both periods can be described by an anomalous diffusion process, transitioning from subdiffusion for short intervals to weak superdiffusion over longer time intervals. The characteristic features related to this anomalous behavior studied in the present paper include heavy tails, which can be described using a $q$-Gaussian distribution and correlations. When we sample the autocorrelation of absolute returns, we observe a power-law relationship, indicating time dependence in both periods initially. The ensemble autocorrelation of the returns decays rapidly. We fitted the autocorrelation with a power law to capture the decay and found that the second period experienced a slightly higher decay rate. The further study involves the analysis of endogenous effects within the Bitcoin time series, which are examined through detrending analysis. We found that both periods are multifractal and present self-similarity in the detrended probability density function (PDF). The Hurst exponent over short time intervals shifts from less than 0.5 ($\sim$ 0.42) in Period 1 to closer to 0.5 in Period 2 ($\sim$ 0.49), indicating that the market has gained efficiency over time.

q-fin.ST↗

arXiv2025

Capillary Pressure-Saturation relation derived from the Pore Morphology Method

A computationally efficient method to calculate the capillary pressure-saturation relations of immiscible multiphase flow on two-dimensional pore morphologies is presented here. The method is an extension of the Pore Morphology Method that includes wetting angle and trapped mechanism of the displaced fluid, and calculation of material properties by density functional theory. After validating the method with micro-chip fluid injection experiments, the method is used to relate pore morphology to capillary pressure-saturation relation using square-lattice pore morphologies. Because the method uses only morphological binary operations, it is more efficient than well-established high-resolution voxel dynamics methods such as Lattice Boltzmann Methods and Level-set computational fluid dynamics. Apart from pore morphology, only the material parameters related to contact angle (wettability) and interfacial tension are required to connect the pore-saturation relation and pore throat distribution. We investigate the effect on interfacial tension, wettability, sample size, and pore throat distribution on entry pressure and residual saturation.

cond-mat.soft↗

arXiv2024

Closed-form solutions for the Salpeter equation

We propose integral representations and analytical solutions for the propagator of the $1+1$ dimensional Salpeter Hamiltonian, describing a relativistic quantum particle with no spin. We explore the exact Green function and an exact solution for a given initial condition, and also find the asymptotic solutions in some limiting cases. The analytical extension of the Hamiltonian in the complex plane allows us to formulate the equivalent stochastic problem, namely the Bäumer equation. This equation describes \textit{relativistic} stochastic processes with time-changing anomalous diffusion. This Bäumer propagator corresponds to the Green function of a relativistic diffusion process that interpolates between Cauchy distributions for small times and Gaussian diffusion for large times, providing a framework for stochastic processes where anomalous diffusion is time-dependent.

quant-ph↗

arXiv2023

Variable order porous media equations: Application on modeling the S&P500 and Bitcoin price return

This article reveals a specific category of solutions for the $1+1$ Variable Order (VO) nonlinear fractional Fokker-Planck equations. These solutions are formulated using VO $q$-Gaussian functions, granting them significant versatility in their application to various real-world systems, such as financial economy areas spanning from conventional stock markets to cryptocurrencies. The VO $q$-Gaussian functions provide a more robust expression for the distribution function of price returns in real-world systems. Additionally, we analyzed the temporal evolution of the anomalous characteristic exponents derived from our study, which are associated with the long-range memory in time series data and autocorrelation patterns.

cond-mat.stat-mech↗

arXiv2020

Local and Non-local Fractional Porous Media Equations

Recently it was observed that the probability distribution of the price return in S\&P500 can be modeled by $q$-Gaussian distributions, where various phases (weak, strong super diffusion and normal diffusion) are separated by different fitting parameters (Phys Rev. E 99, 062313, 2019). Here we analyze the fractional extensions of the porous media equation and show that all of them admit solutions in terms of generalized $q$-Gaussian functions. Three kinds of "fractionalization" are considered: \textit{local}, referring to the situation where the fractional derivatives for both space and time are local; \textit{non-local}, where both space and time fractional derivatives are non-local; and \textit{mixed}, where one derivative is local, and another is non-local. Although, for the \textit{local} and \textit{non-local} cases we find $q$-Gaussian solutions , they differ in the number of free parameters. This makes differences to the quality of fitting to the real data. We test the results for the S\&P 500 price return and found that the local and non-local schemes fit the data better than the classic porous media equation.

cond-mat.stat-mech↗

arXiv2020

Stationarity of the detrended price return in stock markets

This paper proposes a governing equation for stock market indexes that accounts for non-stationary effects. This is a linear Fokker-Planck equation (FPE) that describes the time evolution of the probability distribution function (PDF) of the price return. By applying Ito's lemma, this FPE is associated with a stochastic differential equation (SDE) that models the time evolution of the price return in a fashion different from the classical Black-Scholes equation. Both FPE and SDE equations account for a deterministic part or trend, and a stationary, stochastic part as a q-Gaussian noise. The model is validated using the S\&P500 index's data. After removing the trend from the index, we show that the detrended part is stationary by evaluating the Hurst exponent of the multifractal time series, its power spectrum, and its autocorrelation.

q-fin.ST↗

arXiv2020

Methods for forecasting the effect of exogenous risk on stock markets

Markets are subjected to both endogenous and exogenous risks that have caused disruptions to financial and economic markets around the globe, leading eventually to fast stock market declines. In the past, markets have recovered after any economic disruption. On this basis, we focus on the outbreak of COVID-19 as a case study of an exogenous risk and analyze its impact on the Standard and Poor's 500 (S\&P500) index. We assumed that the S\&P500 index reaches a minimum before rising again in the not-too-distant future. Here we present two cases to forecast the S\&P500 index. The first case uses an estimation of expected deaths released on 02/04/2020 by the University of Washington. For the second case, it is assumed that the peak number of deaths will occur 2-months since the first confirmed case occurred in the USA. The decline and recovery in the index were estimated for the following three months after the initial point of the predicted trend. The forecast is a projection of a prediction with stochastic fluctuations described by $q$-gaussian diffusion process with three spatio-temporal regimes. Our forecast was made on the premise that any market response can be decomposed into an overall deterministic trend and a stochastic term. The prediction was based on the deterministic part and for this case study is approximated by the extrapolation of the S\&P500 data trend in the initial stages of the outbreak. The stochastic fluctuations have the same structure as the one derived from the past 24 years. A reasonable forecast was achieved with 85\% of accuracy.

q-fin.ST↗

arXiv2020

A Simulation Method for Particle Fragmentation Based on Energy Landscape

We propose a method for the simulation of particle fragmentation based on the calculation of the energy landscape inside the particle. The landscape of strain energy is calculated in terms of internal stress using the principles of damage and fracture mechanics. Numerical calculation of the landscape s ridges is used to determine the breakage criterion as well as the shape of the postbreakage fragments. This method provides a physical-based understanding of the breakage effect in granular material.

cond-mat.soft↗

arXiv2019

A Boundary-Spheropolygon Element Method for Stress Determination and Breakage Modelling of Particles

We present a boundary-spheropolygon element method (BSEM), that combines the boundary integral method (BIM) and the spheropolygon-based discrete element method (SEM). The interaction between particles is simulated via the SEM, and the sub-particle stress (stress inside the grains) is calculated by BIM. The framework of BSEM is presented. Then the accuracy and efficiency of the method are analysed by comparison with both analytical solutions and a well-established finite element method (ABAQUS). The results demonstrate that BSEM could efficiently provide instant sub-particle stress for irregular particles with an optimized compromise between computational time and accuracy. The effect of particles aspect ratio, coordination number and heterogeneity on the sub-particle stress are discussed through parametric studies. Key conclusions on particle breakage are derived based on the analysis of the distribution of the sub-particle tensile stress. The simulation results suggest that BSEM could overcome most of the disadvantages of existing numerical methods and must be used for advanced simulations of particle breakage

cond-mat.soft↗

arXiv2018

Closed-form solutions for the Lévy-stable distribution

The Lévy-stable distribution is the attractor of distributions which hold power laws with infinite variance. This distribution has been used in a variety of research areas, for example in economics it is used to model financial market fluctuations and in statistical mechanics as a numerical solution of fractional kinetic equations of anomalous transport. This function does not have an explicit expression and no uniform solution has been proposed yet. This paper presents a uniform analytical approximation for the Lévy-stable distribution based on matching power series expansions. For this solution, the trans-stable function is defined as an auxiliary function which removes the numerical issues of the calculations of the Lévy-stable. Then, the uniform solution is proposed as a result of an asymptotic matching between two types of approximations called "the inner solution" and "the outer solution". Finally, the results of analytical approximation are compared to the numerical results of the Lévy-stable distribution function, making this uniform solution valid to be applied as an analytical approximation.

cond-mat.stat-mech↗