Heterogeneous Media Research Articles

Double-diffusive convection with gravitationally unstable temperature and concentration gradients in homogeneous and heterogeneous porous media

Double-diffusive convection with gravitationally unstable temperature and concentration gradients in homogeneous and heterogeneous porous media

Presolar Grains as Probes of Supernova Nucleosynthesis.

We provide an overview of the isotopic signatures of presolar supernova grains, specifically focusing on 44Ti-containing grains with robustly inferred supernova origins and their implications for nucleosynthesis and mixing mechanisms in supernovae. Recent technique advancements have enabled the differentiation between radiogenic (from 44Ti decay) and nonradiogenic 44Ca excesses in presolar grains, made possible by enhanced spatial resolution of Ca-Ti isotope analyses with the Cameca NanoSIMS (Nano-scale Secondary Ion Mass Spectrometer) instrument. Within the context of presolar supernova grain data, we discuss (i) the production of 44Ti in supernovae and the impact of interstellar medium heterogeneities on the galactic chemical evolution of 44Ca/40Ca, (ii) the nucleosynthesis processes of neutron bursts and explosive H-burning in Type II supernovae, and (iii) challenges in identifying the progenitor supernovae for 54Cr-rich presolar nanospinel grains. Drawing on constraints and insights derived from presolar supernova grain data, we also provide an overview of our current understanding of the roles played by various supernova types- including Type II, Type Ia, and electron capture supernovae- in accounting for the diverse array of nucleosynthetic isotopic variations identified in bulk meteorites and meteoritic components. We briefly overview the potential mechanisms that have been proposed to explain these nucleosynthetic variations by describing the transport and distribution of presolar dust carriers in the protoplanetary disk. We highlight existing controversies in the interpretation of presolar grain data and meteoritic nucleosynthetic isotopic variations, while also outlining potential directions for future research.

An Effective Discontinuous Galerkin Method for Solving Acoustic Wave Equations in Heterogeneous Media

Abstract A discontinuous Galerkin (DG) method is introduced for solving 2D and 3D first-order velocity-pressure acoustic wave propagation problems in heterogeneous media. First, acoustic equations are reformulated into a first-order hyperbolic system, which can be integrated into the framework of the DG method. Then, we introduce an effective numerical flux in DG spatial discretization, which preserves physical laws on both sides of interfaces with discontinuous material parameters. It is compared with both the classic Lax-Friedrichs flux and the exact upwind flux, with the latter derived from solving the Riemann problem and satisfying the Rankine-Hugoniot condition. The comparison reveals that while our flux is formally similar to the classic local Lax-Friedrichs flux, its numerical behavior is analogous to the exact upwind flux. The primary advantage of this method lies in its simplicity and straightforward computation yet can maintain physical continuity conditions near interfaces with discontinuous material parameters. Several numerical experiments of acoustic wave propagation in 2D and 3D heterogeneous media are carried out, illustrating the effectiveness of this method.

Unveiling nanomechanical and pore-structural evolution of bio-precipitate arrays in heterogeneous granular media

Biologically induced reactions in granular media (geomaterials) often rely on precipitates from enzymes or microbes to promote the formation of mineral precipitate crystals in its pores. However, there is a major knowledge gap in understanding the hypotheses behind the mechanisms of how, where, and when these biomineralization reactions influence the microbial or enzymatic precipitate growth in heterogeneous granular media, and its impact on its material properties at the pore scale. In this regard, we propose to identify the complex spatio-temporal mechanisms controlling enzymatic (EP) and microbial (MP) precipitates, the temporal distribution patterns (arrays) in heterogeneous granular media (rocks), and quantify the resultant alterations in its nanomechanical signatures due to enzymatic- or microbial-induced reactions. The rock material specimens were incubated with enzymes and microbial species followed by quantitatively analyzing their modified nanomechanical properties (Young's modulus, E; fracture toughness, KIC; hardness, H) and pore volume in addition to characterizing the nano-to-micro-structure. Analysis of the results reveals that bio-precipitates can occlude the nano-and-micro-pores in specimens with reduced pore volume (MP:12.4 %; EP:48.8 %), thereby yielding beneficial nanomechanical alterations (MP: +21.2 % H, +16 % E, +41.3 % KIC; EP: +38.5 % H, +17 % E, +22.2 % KIC) depending on distinct conditions of the bio-precipitated reactions. Looking forward, this work provides a blueprint for the rational design of inherently-heterogeneous granular media with further enhanced biomimicry toward more innovative and environmentally friendly solutions in natural and built infrastructure.

Acoustic and soliton propagation using fully-discrete energy preserving partially implicit scheme in homogeneous and heterogeneous mediums

This study presents an energy preserving partially implicit scheme for the simulation of wave propagation in homogeneous and heterogeneous mediums. Despite its implicit nature, the developed scheme does not require any explicit numerical or analytical inversion of the coefficient matrix. Theoretical analysis and numerical experiments are performed to validate the energy preserving properties of the fully-discrete scheme. Convergence analysis is also performed to assess the rate of convergence of the developed scheme. The efficiency and accuracy of the developed scheme are validated by numerical solutions of wave propagation in layered heterogeneous mediums. Furthermore, simulations of soliton propagation following nonlinear sine-Gordon and Klein-Gordon equations in homogeneous and heterogeneous mediums are discussed. Numerical solutions are also compared with the results available in the literature. The present method accurately resolves the physical characteristics of the chosen problems, competing well with existing multi-stage time-integration methods. Moreover, it has significantly lower computational complexity than the four-stage, fourth-order Runge-Kutta-Nyström method.

A one-field fluid/meso-structure coupling approach for multiscale transport in heterogeneous porous media

Modeling transport phenomena within heterogeneous porous media poses considerable challenges, particularly on account of the complexity of the involved geometries combined with nonlinear transport interactions. In the present study, a novel one-field modeling approach for multiscale fluid–solid interactions is proposed that does not need any a priori information on permeability. This approach implicitly considers the existence of multiscale structures through a penalization function that encompasses merely one single effective parameter. The definition, determination, as well as the response of the effective parameter to influencing factors are elaborated in detail. It is demonstrated that this approach is effective in representing properly the heterogeneity of solids. The method has been successfully applied to both nonlinear porous media flows and Darcian transport problems, exhibiting comparable accuracy but substantial computational savings as opposed to pore-scale simulations. It leads to more accurate interphase mass transfer predictions and lower computational cost in comparison with the Darcy–Brinkmann–Stokes approach. Overall, this method appears to be highly effective in forecasting realistic, industrial-scale porous media transport problems.

Modeling a pure qP wave in attenuative transverse isotropic media using a complex-valued fractional viscoacoustic wave equation

Seismic anisotropy, characterized by direction-dependent seismic velocity and attenuation, is a fundamental property of the earth, widely observed in field and laboratory measurements. This anisotropy significantly influences seismic wavefield attributes, such as amplitude, phase, and traveltime. Accurate quantification of anisotropy-related seismic wave propagation is essential for global- and regional-scale studies in seismology, such as imaging and inversion. Because the elastic assumption of the earth requires contending with S waves, which are often weak in our seismic recording, we derive a new general complex-valued spatial fractional Laplacian (SFL) viscoacoustic anisotropic pure quasi-P (qP) wave equation (WE) in attenuative transverse isotropic (A-TI) media under the acoustic assumption and use the fixed-order SFL operator to quantify seismic wave propagation in heterogeneous media. Our WE accurately captures anisotropic effects in seismic velocity and attenuation, even in strongly attenuative and anisotropic environments. It also describes the decoupled energy attenuation and velocity dispersion behaviors of the frequency-independent quality factor Q, beneficial for seismic imaging and inversion. Compared with existing viscoacoustic anisotropic pure qP WEs in A-TI media, our WE simplifies computational complexity and is easy to implement, as it decomposes into a complex-valued scalar operator and two differential operators. The evaluated dispersion curves further confirm the accuracy of our approach. Numerical examples in complex geologic settings demonstrate the new equation’s precision, stability, and efficiency in modeling seismic wave propagation.

A Comparative Analysis of Fractal and Fractionalized Thermal Non-Equilibrium Model for Chaotic Convection Saturated by Porous Medium

The convective heat transfer is one of the most important mechanism of heat transference for controlling the chaotic characteristics in porous media. A comparative study of thermal non-equilibrium model is proposed for fractal porous under the consideration of chaotic convection. A novel chaos control is focused between fractal porous and fractional porous by means of newly proposed differential and integral techniques. The sensitivity analysis for chaos expansion and uncertainty quantification for the flow in heterogeneous media have been perceived to the problem of chaotic convection through numerical simulations. In order to approximate the propagation of chaos, two types of simulations have been carried out in terms of chaotic attractors through fractal and fractional approaches. For examining a variety of chaos under the numerical simulations in which fractal domain is varied and fractional domain is fixed, fractal domain is fixed and fractional domain is varied, and both fractal as well as fractional domain are varied. Finally, it is observed that the fractional and fractal memory effects have caused by interactions between uncertain parameters and disclosed the microstructures on the permeability of porous media.

Acoustic vortex-based dynamic lens for light focusing and steering.

This study explores a technique for light manipulation using an acoustic vortex generated by a high-intensity focused ultrasound transducer. The acoustic vortex forms a ring of bubble wall near the high-pressure region, creating a lens-like structure that can effectively focus a laser beam. The effects of varying acoustic pressures and dissolved oxygen content on the focused ultrasound and vortex waveforms were tested. Results showed that the vortex waveform could enhance the laser beam peak intensity by 55.6% and reduce its full width at half maximum from 1.16 mm to 0.91 mm. Additionally, the study demonstrated the capability to dynamically steer the laser beam at angles ranging from 0° to 0.7°, achieving precise control without the need for mechanical components. This technique offers a stable, real-time, and on-demand method for light manipulation, with potential applications in various liquid environments and heterogeneous media. The study also highlights current hardware limitations and suggests future improvements for optimizing parameters and further exploring related mechanisms.

Biofilm Growth in Porous Media Well Approximated by Fractal Multirate Mass Transfer With Advective‐Diffusive Solute Exchange

AbstractBiofilm growth in porous media changes not only the hydrodynamic properties of the medium (reduction in porosity and permeability, and increase in dispersivity), but also the transport itself (breakthrough curves display increasingly fast first arrivals and long tails). These features are well reproduced by multicontinuum models (Multi‐Rate Mass Transfer, MRMT) which can be used to describe reactive transport in heterogeneous porous media and facilitate the simulation of reactions that are localized within biofilms. Here, we present a conceptual and numerical model of biochemical reactive transport with dynamic biofilm growth based on MRMT formulations. Mass exchange between mobile water and immobile biofilm aggregates is represented by a memory function, which simplifies definition of MRMT parameters. We successfully tested this model on two sets of laboratory data and found that (a) a basic model based on the growth of uniformly sized biofilm aggregates fails to reproduce laboratory tracer tests and rate of biofilm growth, while a fractal growth model, which we obtain by integrating the memory functions of biofilm aggregates with a power law distribution, does; (b) the biofilm memory function evolves as the biofilm grows; and (c) the early time portion of eluted volume tracer breakthrough curves are independent of flow rate, whereas the tail becomes heavier when the flow rate is decreased, which implies that both advection controlled and diffusion controlled mass exchange coexist in biofilms. These findings imply that porous media biofilms are essentially different from those developing in human tissues or open spaces.

AI-powered ultrasonic thermometry for HIFU therapy in deep organ

High-intensity focused ultrasound (HIFU) is considered as an important non-invasive way for tumor ablation in deep organs. However, accurate real-time monitoring of the temperature field within HIFU focal area remains a challenge. Although ultrasound technology, compared with other approaches, is a good choice for noninvasive and real-time monitoring on the temperature distribution, traditional ultrasonic thermometry mainly relies on the backscattered signal, which is difficult for high temperature (>50 °C) measurement. Given that artificial intelligence (AI) shows significant potential for biomedical applications, we propose an AI-powered ultrasonic thermometry using an end-to-end deep neural network termed Breath-guided Multimodal Teacher-Student (BMTS), which possesses the capability to elucidate the interaction between HIFU and complex heterogeneous biological media. It has been demonstrated experimentally that two-dimension temperature distribution within HIFU focal area in deep organ can be accurately reconstructed with an average error and a frame speed of 0.8 °C and 0.37 s, respectively. Most importantly, the maximum measurable temperature for ultrasonic technology has been successfully expanded to a record value of 67 °C. This breakthrough indicates that the development of AI-powered ultrasonic thermometry is beneficial for precise HIFU therapy planning in the future.

Deep learning for characterizing fracture toughness from the nanoindentation image of a complex heterogeneous medium

Deep learning for characterizing fracture toughness from the nanoindentation image of a complex heterogeneous medium

Numerical Method for the Variable-Order Fractional Filtration Equation in Heterogeneous Media

This paper presents a study of the application of the finite element method for solving a fractional differential filtration problem in heterogeneous fractured porous media with variable orders of fractional derivatives. A numerical method for the initial-boundary value problem was constructed, and a theoretical study of the stability and convergence of the method was carried out using the method of a priori estimates. The results were confirmed through a comparative analysis of the empirical and theoretical orders of convergence based on computational experiments. Furthermore, we analyzed the effect of variable-order functions of fractional derivatives on the process of fluid flow in a heterogeneous medium, presenting new practical results in the field of modeling the fluid flow in complex media. This work is an important contribution to the numerical modeling of filtration in porous media with variable orders of fractional derivatives and may be useful for specialists in the field of hydrogeology, the oil and gas industry, and other related fields.

A Comprehensive Study on Heterogeneous Media with Spherical Cavity: The Higher-Order Fractional Triple-Phase-Lag Thermoelasticity with Local Kernels

A Comprehensive Study on Heterogeneous Media with Spherical Cavity: The Higher-Order Fractional Triple-Phase-Lag Thermoelasticity with Local Kernels

Experimental investigation of the interplay between transverse mixing and pH reaction in porous media

Abstract. pH-induced reactive transport in porous environments is a critical factor in Earth sciences, influencing a range of natural and anthropogenic processes, such as mineral dissolution and precipitation, adsorption and desorption, microbial reactions, and redox transformations. These processes, pivotal to carbon capture and storage (CCS) applications to groundwater remediation, are determined by pH transport. However, the uncertainty in these macroscopic processes’ stems from pore-scale heterogeneities and the high diffusion value of the ions and protons forming the pH range. While practical for field-scale applications, traditional macroscopic models often fail to accurately predict experimental and field results in reactive systems due to their inability to capture the details of the pore-scale pH range. This study investigates the interplay between transverse mixing and pH-driven reactions in porous media. It focuses on how porous structure and flow rate affect mixing and chemical reaction dynamics. Utilizing confocal microscopy, the research visualizes fluorescently labeled fluids, revealing variations in mixing patterns from diffusive in homogeneous to shear-driven in heterogeneous media. However, pH-driven reactions show a different pattern, with a faster reaction rate, suggesting quicker pH equilibration between co-flowing fluids than predicted by transverse dispersion or diffusion. The study highlights the unique characteristics of pH change in water, which significantly influences reactive transport in porous media.

Deep learning-based acoustic emission source localization in heterogeneous rock media without prior wave velocity information

Abstract Acoustic emission (AE) source localization is crucial for monitoring but often relies on prior information, such as wave velocity and arrival time. This study introduces a novel method for locating AE sources in rocks without such information, addressing challenges posed by heterogeneous sensor arrays. Experiments involving pencil led break (PLB) tests on sandstone cubes collected AE waveforms and their coordinates. A ResNet-50 based deep learning model was developed to correlate the time-frequency spectra of AE with PLB locations, expressed as spatial Gaussian distributions. The model, achieved a 79% prediction accuracy for AE localization in complex environments. While there is room for improvement in training data quantity and diversity, the results validate the model’s effectiveness, particularly in coal mines and tunnel engineering.

Reflection Measurement of the Scattering Mean Free Path at the Onset of Multiple Scattering.

Multiple scattering of waves presents challenges for imaging complex media but offers potential for their characterization. Its onset is actually governed by the scattering mean free path ℓ_{s} that provides crucial information on the medium microarchitecture. Here, we introduce a reflection matrix method designed to estimate this parameter from the time decay of the single scattering rate. Our method is first validated by an ultrasound experiment on a tissue-mimicking phantom before being applied invivo to a human liver. This Letter opens important perspectives for quantitative imaging of heterogeneous media with waves, whether it be for nondestructive testing, biomedical, or geophysical applications.

Heterogeneous polarization-integrated medium wave infrared HgCdTe focal plane array detector with pixel-wise Al gratings

Heterogeneous polarization-integrated medium wave infrared HgCdTe focal plane array detector with pixel-wise Al gratings

An exactly solvable model for non-Fickian transport in dynamically heterogeneous media

Abstract Diffusion, observed in various condensed phases, finds its theoretical background in Einstein’s theory of Brownian motion, characterized by the linear time-dependence of mean square displacement (MSD) denoting Fickian behavior and the Gaussian distribution of particle displacement. Nevertheless, diverse systems exhibit either non-linear, non-Fickian time-dependence of the MSD or non-Gaussian displacement distribution. Montroll and Weiss’s continuous-time random walk (CTRW) model and the stochastic diffusivity (SD) model have provided insights into anomalous diffusion phenomena and Fickian-yet-non-Gaussian transport in dynamically heterogeneous environments, respectively. Building upon these approaches, Song et al developed a generalized transport equation with an environment-dependent diffusion kernel, providing a quantitative explanation for non-Fickian MSD and non-Gaussian displacement distribution. Based on the generalized transport equation, this study introduces an exactly solvable model for a non-Gaussian displacement distribution, accommodating arbitrary time profiles in its MSD, including both Fickian and non-Fickian behaviors. Our findings confirm the model’s capability in describing such transport processes. Furthermore, the proposed model unifies the CTRW model under fast environmental fluctuations and the SD model under Fickian time dependencies, making it suitable for understanding tracer particle motion within explicit solvent or complex media.

Cobalt Tetracationic 3,4-Pyridinoporphyrazine for Direct CO2 to Methanol Conversion Escaping the CO Intermediate Pathway.

Molecular catalysts offer a unique opportunity to implement different chemical functionalities to steer the efficiency and selectivity for the CO2 reduction for instance. Metalloporphyrins and metallophthalocyanines are under high scrutiny since their most classic derivatives the tetraphenylporphyrin (TPP) and parent phthalocyanine (Pc), have been used as the molecular platform to install, hydrogen bonds donors, proton relays, cationic fragments, incorporation in MOFs and COFs, to enhance the catalytic power of these catalysts. Herein, we examine the electrocatalytic properties of the tetramethyl cobalt (II) tetrapyridinoporphyrazine (CoTmTPyPz) for the reduction of CO2 in heterogeneous medium when adsorbed on carbon nanotubes (CNT) at a carbon paper (CP) electrode. Unlike reported electrocatalysis with cobalt based phthalocyanine where CO was advocated as the two electron and two protons reduced intermediate on the way to the formation of methanol, we found here that CoTmTPyPz does not reduce CO to methanol. Henceforth, ruling out a mechanistic pathway where CO is a reaction intermediate.