Homogenization Technique Research Articles

Parental Involvement in Curricular Performance of Students at Risk

Parental involvement plays an important role in the academic performance of at-risk learners facing educational challenges. However, many parents struggle to contribute effectively due to various challenges, such as limited educational backgrounds, busy schedules, and personal commitments. This study aims to describe the parental involvement in the academic performance of at-risk learners, specifically focusing on involvement, success, and support within the school. This study uses a Mixed-methods sequential explanatory design. The study involves quantitative analysis supplemented by qualitative insights obtained through standardized questionnaires and interviews. Purposive sampling was employed to select 50 parents as respondents, while 8 participants were chosen using a homogeneous sampling technique to represent outliers. Results indicate that active parental involvement positively improves academic outcomes, including behavior, attendance, and grades. Conversely, learners with less engaged parents tend to show limited progress in their academic performance. Lack of financial resources poses significant challenges, but scholarships lessen burdens, ensuring access to education for all. This study underscores the importance of parental support beyond academics, creating helpful learning environments, and fostering strong development. Understanding parental challenges can enhance strategies to improve learners’ behavior and academic performance. Overall, parental involvement is an important factor in promoting academic success and preparing learners for future opportunities.

Study and Design of Corrugated Cardboard Trays With Microwaves by Experimental Analysis (EA) and Finite Element Methods (FEM)

ABSTRACTThe purpose of the work is to study by experimental analysis and finite element methods the mechanical response of a packaging, consisting of a corrugated cardboard container, used for the transport of fruit and vegetables. During the container design, three different configurations were selected which differ both in the choice of liner and in the type of wave. In particular, the type E, F and N microwaves were chosen. They are characterized by a lower amplitude than the high and medium waves commonly used in corrugated cardboard packaging, making it possible to reduce material consumption and, consequently, costs. In the initial phase of the study, experimental tests were performed to evaluate the mechanical strength of the liners. In addition, edge compression tests (ECTs) were performed to determine the stacking resistance of the structure. The break‐in resistance of the structures was analysed using a test conducted according to an internal standard, called strength packaging test (SPT). Subsequently, a parametric study was set up with the finite element method for the simulation of the mechanical behaviour of the three structures, using the homogenization technique. The comparison between the maximum total deformations, measured experimentally and calculated numerically, has highlighted the need to introduce corrective coefficients to improve the homogenization of the wave structure. In this way, it was possible to improve the matching of the results obtained on the structures simulated by the homogenization technique and those obtained on the corresponding real structures.

A bidomain model for the calcium dynamics in living cells

The aim of this paper is to analyze, via periodic homogenization techniques, the effective behavior of a non-linear system of coupled reaction-diffusion equations appearing in the modeling of calcium dynamics in living cells under the action of buffering proteins. We obtain, at the macroscale, a calcium bidomain model governing the evolution of the concentration of the calcium ions and of the buffers in the cytoplasm.

Assessment of effective elastic constants of U-10Mo fuel: A multiscale modeling and homogenization study

The significant microstructural changes that U-Mo fuel undergoes during operation degrades its mechanical properties and structural integrity. Microstructural evolution entails the formation, evolution, and redistribution of porosity in conjunction with grain refinement. In the present paper, we employ numerical approaches to assess the impact of the various microstructural features—grains, nanoscale intragranular fission gas bubbles, and mesoscale intergranular voids—on the degradation of elastic constants. Phase-field microstructure models are combined with the asymptotic expansion homogenization technique in order to derive the effective elastic constants as a function of porosity and fission density. The results are verified and compared against theoretical bounds. Using this approach, elastic degradation in operating nuclear fuels can be quantified when the distributions of microstructural features are known.

Effect of Cremophor RH40, Hydroxypropyl Methylcellulose, and Mixing Speed on Physicochemical Properties of Films Containing Nanostructured Lipid Carriers Loaded with Furosemide Using the Box-Behnken Design.

This study aimed to examine the characteristics of H-K4M hydroxypropyl methylcellulose (HPMC) films containing nanostructured lipid carriers (NLCs) loaded with furosemide. A hot homogenization technique and an ultrasonic probe were used to prepare and reduce the size of the NLCs. Films were made using the casting technique. This study used a Box-Behnken design to evaluate the influence of three key independent variables, specifically H-K4M concentration (X1), surfactant Cremophor RH40 concentration (X2), and mixing speed (X3), on the physicochemical properties of furosemide-loaded NLCs and films. The furosemide-loaded NLCs had a particle size ranging from 54.67 to 99.13 nm, and a polydispersity index (PDI) ranging from 0.246 to 0.670. All formulations exhibited a negative zeta potential, ranging from -7.05 to -5.61 mV. The prepared films had thicknesses and weights ranging from 0.1240 to 0.2034 mm and 0.0283 to 0.0450 g, respectively. The drug content was over 85%. Film surface wettability was assessed based on the contact angle, ranging from 32.27 to 68.94°. Film tensile strength varied from 1.38 to 7.77 MPa, and their elongation at break varied from 124.19 to 170.72%. The ATR-FTIR analysis confirmed the complete incorporation of the drug in the film matrix. Therefore, the appropriate selection of values for key parameters in the synthesis of HPMC films containing drug-loaded NLCs is important in the effective development of films for medical applications.

Homogenization theory and nonlinearities in Darcy's law

The theory of homogenization of differential equations has become an open field of research in several areas of the exact sciences and has proved to be a powerful tool for understanding the global behavior of heterogeneous materials. Despite knowing that the deduction of Darcy’s law through the Navier-Stokes equations has been debated for decades, many questions remain open, mainly regarding more complex boundary conditions, cases involving multiphase flows and the numerical homogenization techniques. It is known today that Darcy’s law is presented in the form of a linear relationship only for a range of hydraulic gradient and that this range overlaps the range of laminar flow through soil voids. Therefore, it is proposed in this work to understand the loss of linearity in Darcy’s law, based on the theory of homogenization, modifying and exploring the limit results obtained by Allaire in 1991.

Influence of the CNT addition on the mechanical performance of three-phase composite plates

This work has analyzed the bending, free vibration and buckling performance of a three-phase (CNT/Polymer/Carbon fiber) composite plate as a function of the carbon fiber volume fraction and the CNT volume fraction, under several values of the plate aspect ratio (a/b) and the plate slenderness parameter (h/b), and considering the presence of defects due to the poor dispersion on the CNTs. Based on a two-steps homogenization technique, the mechanical properties of the carbon fibers reinforced –CNT enriched– polymeric matrix are computed. Then, the mechanical response of the plate is computed according to the first-order shear deformation plate theory solutions presented in Reddy’s books. The numerical results have revealed the presence, in three-phase (CNT/Polymer/Carbon fiber) composite plates, of a CNT volume fraction threshold above which the bending, free vibration and buckling performance of the plate decay with the carbon fiber volume fraction.

Evaluation of 13 Formulae for Calculated LDL-C Using Direct Homogenous Assay in a South Indian Population.

LDL cholesterol (LDL-C) is regarded as a significant therapeutic target and a known risk factor for atherosclerosis. It can be calculated using the results of the other lipid tests or tested directly. Despite its shortcomings, the Friedewald formula is most frequently utilized since it is simple and practical. Until now, several formulae have been proposed for calculating LDL-C; however, their accuracy has not been evaluated across different populations. We sought to evaluate the validity of calculated LDL-C by comparing the findings with values acquired by the direct homogeneous technique, utilizing 13 distinct formulae from the literature. This study was a retrospective observational study conducted for a year at SRIHER, Chennai, Tamil Nadu, India. From the total 25 043 patients who had their serum lipid profile tested, 16 314 participants had their fasting blood sugar and fasting lipid profile measured simultaneously, and they were chosen for the research. The de Cordova, Chen, Martin/Hopkins (initial), and Teerakanchana equations correlated well with the direct LDL-C assay. When the dataset was stratified according to triglycerides, the Chen and Martin/Hopkins initial equations had the better measurement of agreement compared to other equations. The Martin/Hopkins initial equation outperformed all the other equations when the whole dataset irrespective of the triglyceride population was considered. Our study suggests that the Martin/Hopkins initial equation outperformed all the other equations and can be used as an alternative to direct LDL-C measurement in a South Indian population.

FEM-Circuit co-simulation of superconducting synchronous wind generators connected to a DC network using the homogenized J–A formulation of the Maxwell equations

High-temperature superconductors (HTS) are greatly appealing for the development of high efficient, and high energy density power devices. They are particularly relevant for applications requiring light and compact machines such as wind power generation. In this context, to ensure the proper design of the superconducting machines and their reliable operation in power systems, it is then important to develop models that can accurately include their physics but also can describe properly their interaction with the system. To achieve such a goal, one approach is the co-simulation. This numerical technique can bring fine geometrical and physical details of the machines through a finite element model (FEM) meanwhile dealing with the operation of the whole system that incorporates the machine and a subset of the power grid represented by an external electrical circuit. The goal of the present work is to put to use this numerical technique when superconducting components are involved. Here, a case study is proposed involving a 15 MW hybrid superconducting synchronous generator (HTS rotor and conventional stator) coupled to a direct current network via a rectifier and its associated filter. The case study related to wind power application allows grasping the technical issues when employing co-simulation dealing with HTS machines. The FEM of the generator is done in the commercial software COMSOL Multiphysics, which interacts with the circuit simulator Simulink through the built-in Functional Mock-up Unit. For the present study, a new version of the latest J–A formulation combined with homogenization technique is introduced allowing an even faster computation time compared to the T–A formulation. Distributed variables and global variables such as current density, magnetic flux density, and local losses for the former and voltage, current, electromagnetic torque, and power quality for the latter are estimated and compared for both formulations. The idea is to find the best-suited combination FEM-circuit under criteria of computational speed, accuracy, and numerical stability. Thus, it is shown that all formulations generate an error of less than 5% on the machine parameters and that the J–A formulation with first order elements stands out with a significant 4-fold reduction in computational costs.

Solid Lipid Nanoparticles: A Review of their Biomedical Applications and Preparation.

Solid lipid nanoparticles (SLNs) are gaining significant attention in the pharmaceutical industry due to their biocompatibility and biodegradability, making them a popular functional nanocarrier. SLNs are a popular nanocarrier due to their ability to bypass the spleen and liver, offer high drug stability, and improve bioavailability, sterilization, immobilization, targeted drug release, and biocompatible ingredients. This article discusses various SLN preparation techniques, including high shear homogenization, hot homogenization, cold homogenization, microemulsion-based, solvent evaporation, solvent emulsification-evaporation, supercritical fluid-based, spray drying, double emulsion, and precipitation techniques, focusing on methodological aspects. This review discusses the physicochemical behavior of SLNs, including drug loading, release, particle size, stability, cytotoxicity, and cellular uptake, and their major biomedical applications.

Super-localization of spatial network models

Spatial network models are used as a simplified discrete representation in a wide range of applications, e.g., flow in blood vessels, elasticity of fiber based materials, and pore network models of porous materials. Nevertheless, the resulting linear systems are typically large and poorly conditioned and their numerical solution is challenging. This paper proposes a numerical homogenization technique for spatial network models which is based on the super-localized orthogonal decomposition (SLOD), recently introduced for elliptic multiscale partial differential equations. It provides accurate coarse solution spaces with approximation properties independent of the smoothness of the material data. A unique selling point of the SLOD is that it constructs an almost local basis of these coarse spaces, requiring less computations on the fine scale and achieving improved sparsity on the coarse scale compared to other state-of-the-art methods. We provide an a posteriori analysis of the proposed method and numerically confirm the method’s unique localization properties. In addition, we show its applicability also for high-contrast channeled material data.

Nonlinear interfacial contact laws in multi-layer elastic-viscoelastic structural systems

Layered structures are widely used in construction, such as pavement structures consisting of multiple layers of different materials or interfaces between bricks and mortar in masonry structures, etc. In analyzing such structures, understanding the properties of the interface between two layers of materials is essential. If one layer of material contains cracks and layers exhibit viscoelastic behavior, determining the properties of the interface becomes challenging. This study proposes a constitutive mechanical law to model the behavior of the interface between a microcracked viscoelastic medium and an undamaged elastic body based on the homogenization method. The interface is modeled by a layer of zero thickness. The coupling between the homogenization technique and the Griffith’s theory is used to provide the effective behavior of the micro-cracked medium. The interface is modelled as an effective medium (EF) characterized by normal and tangential stiffnesses (CN, CT ). In this work, two viscoelastic models are considered, i.e., Burger and Modified Maxwell. The formulas of CN and CT for two cases of crack distributions (isotropic and transversely isotropic) are obtained by asymptotic techniques where the thickness of the joint tends to zero

High molecular weight hyaluronic acid-liposome delivery system for efficient transdermal treatment of acute and chronic skin photodamage

Photodamage is one of the most common causes of skin injury. High molecular weight hyaluronic acid (HHA) has shown immense potential in the treatment of skin photodamage by virtue of its anti-inflammatory, reparative, and antioxidative properties. However, due to its large molecular structure of HHA, HHA solution could only form a protective film on the skin surface in conventional application, failing to effectively penetrate the skin, which necessitates the development of new delivery strategies. Liposomes, with a structure similar to biological membranes, have garnered extensive attention as transdermal drug delivery carriers because of their advantages in permeability, dermal compatibility, and biosafety. Herein, we have developed a HHA-liposome transdermal system (HHL) by embedding HHA into the liposome structure using reverse evaporation, high-speed homogenization, and micro-jet techniques. The effective penetration and long-term residence of HHA in skin tissue were multidimensionally verified, and the kinetics of HHA in the skin were extensively studied. Moreover, it was demonstrated that HHL significantly strengthened the activity of human keratinocytes and effectively inhibits photo-induced cellular aging in vitro. Furthermore, a murine model of acute skin injury induced by laser ablation was established, where the transdermal system showed significant anti-inflammatory and immunosuppressive properties, promoting skin proliferation and scar repair, thereby demonstrating immense potential in accelerating skin wound healing. Meanwhile, HHL significantly ameliorated skin barrier dysfunction caused by simulated sunlight exposure, inhibited skin erythema, inflammatory responses, and oxidative stress, and promoted collagen expression in a chronic photodamage skin model. Therefore, this transdermal delivery system with biocompatibility represents a promising new strategy for the non-invasive application of HHA in skin photodamage, revealing the significant potential for clinical translation and broad application prospects. Statement of significanceThe transdermal system utilizing hyaluronic acid-based liposomes enhances skin permeability and retains high molecular weight hyaluronic acid (HHL). In vitro experiments with human keratinocytes demonstrate significant skin repair effects of HHL and its effective inhibition of cellular aging. In an acute photodamage model, HHL exhibits stronger anti-inflammatory and immunosuppressive properties, promoting skin proliferation and scar repair. In a chronic photodamage model, HHL significantly improves skin barrier dysfunction, reduces oxidative stress induced by simulated sunlight, and enhances collagen expression.

Advancing soy protein isolate-ulvan film physicochemical properties and antioxidant activities through strategic high-pressure homogenization technique

Soy protein-based films often exhibit poor properties, including limited mechanical strength, stability, and bioactivity, which hinder their extensive application in the food industry, particularly in edible packaging. To enhance the properties of soy protein-based films, we employed high-pressure homogenization (HPH) to modify the soybean protein isolate (SPI) molecules and sought to cross-link SPI with ulvan polysaccharide, which possesses distinctive bioactivities. The results confirmed that soluble ulvan polysaccharides were incorporated into the cross-linking system through hydrogen bonding. Results indicated that HPH treatment enhanced SPI's solubility and surface hydrophobicity (H0), promoting hydrogen bonding and hydrophobic interactions between SPI and ulvan, as evidenced by ζ-potential and turbidity measurements. Structural and microstructural analyses of both individual SPI and composite films, using FT-IR, XRD, CD and SEM, demonstrated a high compatibility between HPH-treated SPI and ulvan. The incorporation of ulvan reduced the films' tensile strength (TS), but higher pressure significantly improved it (p < 0.05). Post-HPH modification, the films exhibited increased contact angle and swelling capacity (p < 0.05), indicating enhanced hydrophobicity. Higher pressure treatments resulted in more opaque and yellowish films, thereby diminishing ultraviolet light transmission. Thermal stability analyses, via TGA-DSC, showed that U-HSPI films had improved thermal stability compared to pure SPI films. Moreover, ulvan inclusion boosted the antioxidant capacity of SPI films, especially after HPH treatment. Overall, this study confirms that HPH modification substantially influences the properties and activities of SPI-based films, and the complex films based on SPI and ulvan with improved physicochemical and antioxidant properties exhibit a great potential in the food packaging field.

An open-source 3D FE quench simulation tool for no-insulation HTS pancake coils

A new module, Pancake3D, of the open-source finite element quench simulator (FiQuS) has been developed in order to perform transient simulations of no-insulation (NI) high-temperature superconducting pancake coils in three-dimensions. FiQuS/Pancake3D can perform magnetodynamic or coupled magneto-thermal simulations. Thanks to the use of thin shell approximations, an H→−ϕ formulation, and anisotropic homogenization techniques, each turn can be resolved on the mesh level in an efficient and robust manner. FiQuS/Pancake3D relies on pre-formulated finite-element (FE) formulations and numerical approaches that are programmatically adjusted based on a text input file. In this paper, the functionalities and capabilities of FiQuS/Pancake3D are presented. The challenges of FE simulation of NI coils and how FiQuS/Pancake3D addresses them are explained. To highlight the functionalities, the results of a magneto-thermal analysis of a double pancake coil with 40 turns per pancake with local degradation of the critical current density are conducted and discussed. Furthermore, a parameter sweep of the size of this local degradation is presented. All FiQuS input files for reproducing the simulations are provided.

Evaluation of PEGylation efficacy of curcumin-loaded nanoemulsions using complementary methods to assess protein interactions and physicochemical properties

Nanoemulsions (NEs) are frequently used in the food, cosmetics and pharmaceutical industries to deliver nutraceuticals, pharmaceutical or cosmetic active ingredients. When administering NEs parenterally, various stabilisers are added to prevent rapid plasma clearance and to successfully deliver the active ingredient to the target site. For this purpose, PEGylation is often used to prolong the circulation time of the droplets. However, the problem is to determine the optimal concentration of the PEGylating agent – the PEGylation efficacy – that ensures adequate surface protection. This is a particular challenge when the active ingredient is incorporated into the stabilising layer, where any changes could disrupt the stability of the droplet. For this reason, we aimed to determine the optimal concentration of PEG2000-DSPE for surface protection of curcumin-loaded NEs for parenteral administration using electron paramagnetic resonance (EPR) spectroscopy. NEs were prepared using the high pressure homogenisation technique with 0.1 %, 0.3 % or 0.6 % of the PEGylated phospholipid. A droplet size of approximately 100 nm and polydispersity index below 0.25 indicated suitability for parenteral application. EPR analysis showed that PEG2000-DSPE had a stabilising effect on selected NEs, which was most pronounced in the part of the stabilising layer closest to the aqueous phase. To confirm these results, protein interaction studies were carried out using dynamic light scattering, UV–Vis spectroscopy, atomic force microscopy and release studies from protein-enriched media – bovine serum albumin (BSA) or foetal bovine serum (FBS) in phosphate-buffered saline. These analyses confirmed that the addition of PEG2000-DSPE reduced protein binding to the droplets as a function of concentration, with 0.3 % providing the best protection for the droplets. Our conclusions from the EPR spectroscopy study demonstrate the usefulness of EPR in determining the optimal concentrations of PEGylating agents for surface coverage and its usefulness in the formulation development phase.

Structural analysis of small-scale 3D printed composite tidal turbine blades

The existing research literature lacks comprehensive investigations into assessing the structural performance of marine renewable energy conversion devices, particularly 3D printed turbine blades, which often rely solely on computational modelling without experimental validation methods and/or established mechanical characterization techniques. This leads to significant uncertainty regarding the performance of 3D printed turbine blades manufactured by additive manufacturing technology. This study aims to fill this gap by proposing a procedure for evaluating the structural integrity of commercial small-scale tidal turbine blade (5 KW) manufactured using fused filament fabrication 3D printing with a linear infill pattern. This is achieved by developing a combined experimental, hydrodynamic, and finite element approach with the view to inspect the micro-mechanical properties of representative volume elements of 3D printed microstructures using homogenization technique. The results of mechanical testing and hydrodynamic modelling are used to create a finite element model of the 3D printed blade, allowing for stress and failure analysis. Findings indicate that while integrating 3D printed materials into blade design via 3D printing technology is feasible, the choice of materials is limited to high stiffness composite filaments. Finally, experimental validation of numerical results, particularly full field strain distribution maps obtained by digital image correlation technique for flexural testing and laboratory-scale 3D printed blade, confirms the accuracy of the finite element results. Finite element-based homogenization techniques provide valuable insights into potential failure modes in 3D printed tidal turbine blades. However, the expedited calculation of orthotropic properties through finite element analysis proves to be a faster mechanical characterization method compared to experimental approaches. The proposed methodology in this study facilitates quicker iterative design of 3D printed blades, thereby reducing the need for repeated experiments and ultimately lowering manufacturing costs.

Autism Sports Education: Transforming Lives of Families

It is very important to integrate individuals with autism into social life in order to minimize the effects of autism, which is a developmental problem that lasts for a long time and needs to be lived together and is increasing numerically every day. In this context, 14 parents of individuals with autism participated in the research conducted to determine the effect of the Sports Education Project for People with Autism (SEPA), which was carried out in cooperation with Gazi University, on the daily lives of autistic individuals and their families. In the research, the phenomenology design, which is among the qualitative research methods, was utilized. Using homogeneous sampling technique, focus group interviews were conducted with 14 parents who had been attending the SEPA for 4 months without interruption. In general, the participants found the impact of SEPA on their daily lives to be positive; in terms of parents, they stated that it allowed them to share problems with other parents and increase solidarity, thus allowing them to socialize, contributed positively to family interactions and made them feel happier. In terms of their children, they stated that they contributed positively to their physical and social development and that this situation facilitated their children's daily lives. The findings obtained support that projects such as the Children with Autism Education Project will contribute positively to the life processes of individuals with autism and their families. It is recommended that studies in this direction be expanded.

Size effects of voids on the mechanical properties of 3D printed parts

Although the effects of additive manufacturing process parameters on the mechanical properties of 3D printed parts have been numerically investigated in the literature, less attention has been paid on the size effects of voids between deposited filaments. This study fills this gap by developing a methodology based on a combined finite element (FE) and design of experiment (DoE) technique. The development of FE methodology is based on micro-mechanical analysis of representative volume element (RVE) of 3D printed parts to predict the effective orthotropic properties. To account for the size effects of inter-bead voids, the RVE includes contribution of the multiple parameters of layer heights, layer widths and overlapping regions. To study the main and interaction effects of the above input parameters on the stiffness properties of 3D printed parts, a structured approach based on full factorial design is used. Although the size effects of voids on the constituents of elastic moduli of RVE were investigated, the main focus in the present work is to develop a regression model to predict the stiffness properties. The FE stress analysis of the RVE conducted in this study provides an insight about the potential failure modes such as delamination and filament debonding that may occur in load bearing 3D printed parts. For a case study, the results of FE-based homogenization technique in terms of stiffness properties are validated against the experimental data via three-point bending and Iosipescu shear tests which were conducted in conjunction with digital image correlation technique. The combined numerical and statistical approach proposed in this study provides a swift iterative design of 3D printed parts prior to the time-consuming computation modelling, contributing to reduce the number of tests and manufacturing costs.

Effect of phase exchange kinetics on Taylor dispersion of chemically reactive solutes in an oscillatory magnetohydrodynamics flow between two parallel plates

The study of kinetic sorptive effects on the transport phenomena of reactive solute has numerous real-world applications, including in the industrial and environmental sectors. These kinds of investigations become more realistic when an oscillatory pressure gradient with both the reversible and irreversible reactions at the channel walls is considered in a magnetohydrodynamics flow. In the past, Ng and Yip [J. Fluid Mech. 446, 321–345 (2001)] studied the effect of sorptive phase exchange at boundaries on the solute transport phenomena in an open-channel flow using Mei's multiple-scale homogenization technique. They considered fluid flows without magnetic field and boundary absorption. This work uses the above-mentioned method to investigate the phase exchange kinetics of Taylor dispersion phenomena in a two-dimensional magnetohydrodynamics fluid flowing through a parallel channel. The paper discusses how various parameters and dimensionless numbers, such as the Hartmann, oscillatory Reynolds, and Damkohler, affect the flow velocity, transport coefficient, multi-dimensional concentration distributions, and transverse variation rate. Due to the strong magnetic field, the flow velocity and Taylor dispersivity are adversely affected and conspicuously reduced. Additionally, for large Damkohler numbers, the total dispersion coefficient and the Taylor dispersion coefficient both decrease. However, the longitudinal concentration distribution rises with the Hartmann number and partition coefficient. It is worth noting that in the presence of unequal boundary absorption, there is no occurrence of transverse symmetry in solute concentration at any given time. Controlling various processes of tracer dispersion in environmental systems, especially water purification and the chemical industry, may benefit from these intriguing findings.