Mathematical Model For Migration Research Articles

Geoinformation modeling of radioactive contamination of territories on the example of mines of the “ShidGSK” mining and processing plant

The aim of the study was to model the territorial distribution and statistical assessment of migration through the trophic chain of naturally occurring radionuclides released into the environment as a result of uranium ore mining. Statistical, geoinformation and experimental research methods were used in the study. Interpolation of the results of volumetric activity of natural radionuclides in environmental components and development of spatial models of their territorial distribution were performed using the ArcGIS software; statistical processing of modelling results and development of mathematical models of migration of natural radionuclides between environmental components were performed using ArcGIS Geostatistical Analyst software. The paper substantiates the choice of the method of geostatistical modelling of the territorial distribution of volumetric activity of natural radionuclides 234U, 238U, 210Po, 210Pb, 226Ra in soils and plants, which allows modelling the values of probabilistic indicators of radioecological contamination in the absence of a sufficient array of initial actual research results. Based on the analysis of the data obtained, the methodology of mathematical modelling of migration of natural radionuclides between soil and plant parts was further developed, which will facilitate consideration of the specifics of migration of natural radionuclides through the trophic chain and help in determining the level of radioecological hazard to the environment. The developed territorial models allow one to obtain stochastic data for their further analytical processing and visualizing radioecological hazard zones. Based on the developed models, zones of increased radioecological hazard within the existing sources of radioactive contamination were identified.

Individual‐based models of avian migration for estimating behavioural traits and predicting ecological interactions

Abstract Rapid advances in the field of movement ecology have led to increasing insight into both the population‐level abundance patterns and individual‐level behaviour of migratory species. Despite this progress, research questions that require scaling individual‐level understanding of the behaviour of migrating organisms to the population level remain difficult to investigate. To bridge this gap, we introduce a generalizable framework for training full‐annual cycle individual‐based models of migratory movements by combining information from tracking studies and species occurrence records. Focusing on migratory birds, we call this method: Models of Individual Movement of Avian Species (MIMAS). We implement MIMAS to design individual‐based models of avian migration that are trained using previously published weekly occurrence maps and fit via Approximate Bayesian Computation. MIMAS models leverage individual‐ and population‐level information to faithfully represent continental‐scale migration patterns. Models can be trained successfully for species even when little existing individual‐level data is available for parameterization by relying on population‐level information. In contrast to existing mathematical models of migration, MIMAS explicitly represents and estimates behavioural attributes of migrants. MIMAS can additionally be used to simulate movement over consecutive migration seasons, and models can be easily updated or validated as new empirical data on migratory behaviours becomes available. MIMAS can be applied to a variety of research questions that require representing individual movement at large scales. We demonstrate three applied uses for MIMAS: estimating population‐specific migratory phenology, predicting the spatial patterns and magnitude of ectoparasite dispersal by migrants, and simulating the spread of a pathogen across the annual cycle of a migrant species. Currently, MIMAS can easily be used to build models for hundreds of migratory landbird species but can also be adapted in the future to build models of other types of migratory animals.

Laboratory Experiment on Formation of MICP Horizontal Seepage-Reducing Body in Confined Aquifer for Deep Excavation

Using a soil improvement biotechnology based on microbial-induced carbonate precipitation (MICP) to form a horizontal water barrier in foundation pit dewatering can not only achieve a good dewatering control effect, but also control the cost and obtain good economic and environmental benefits. In this study, taking the Shanghai layer ⑨ sand as the research object, the solution injected into the layer ⑨ sand by MICP grouting technology includes bacterial solution (Sporosarcina pasteurii) and cementation solution (urea and CaCl2 solution). The migration mechanism of the bacterial solution and cementation solution in groundwater was analyzed through batch experiment and column test, and the mathematical model of migration was established. The dynamic adsorption characteristics of the S. pasteurii, Ca2+, and urea were obtained by dynamic adsorption test. Through isothermal adsorption test, the Freundlich isotherm was used to describe the isothermal adsorption of S. pasteurii onto fine sand, and the partition coefficient of the S. pasteurii was found to be 1.5 × 10−7 L/mg. The Langmuir isotherm can be used truly reflect the isothermal adsorption of Ca2+ onto fine sand. The distribution coefficient of the Ca2+ was 7 × 10−8 L/mg. The maximum adsorption capacity of the solute was 2404.8 mg/kg. The adsorption capacity of the urea was very small. According to the sand column test, the vertical dispersion was 11.5 cm. Due to the obvious size effect of dispersion, the sensitivity of dispersion in actual working conditions should be analyzed in a subsequent numerical simulation. The determined solute transport parameters provide support for the further study of the numerical simulation of the solute transport process of the HSRB formed by MICP grouting technology and provide a basis for further field application.

A Simple Stability Analysis for a Mathematical Model of Migration Due to Noise and Resources

This research studies a metapopulation model where each patch is considered a form of fragmentation of the environment produced by the spatio-temporal variability of anthropogenic noise. A deterministic mathematical model is proposed that describes two processes of migration between patches. The first process consists of migration due to chronic critical noise produced by an anthropogenic and biological source (self-generated acoustic signals of higher intensity, due to the Lombard effect). The second process consists of migration due to a higher level of stain occupancy. A simple and classical analysis of the local stability of the model is performed. The results indicate that no subpopulation goes extinct; in fact, a necessary condition for long-term stabilization of the size of the subpopulations is that the noise attenuation rate is higher. Moreover, as long as the noise is of low intensity the differences in the carrying capacity of each patch do not produce substantial, long-term differences in the sizes of the subpopulations. However, as the noise intensity increases, the difference in carrying capacities produce noticeable, long-term differences between subpopulation sizes. Finally, the results are corroborated by numerical simulations.

PH-taxis drives aerobic bacteria in duodenum to migrate into the pancreas with tumors

As oral or intestinal bacteria have been found in pancreatic cystic fluid and tumors, understanding bacterial migration from the duodenum into the pancreas via hepato-pancreatic duct is critical. Mathematical models of migration of aerobic bacteria from the duodenum to the pancreas with tumors were developed. Additionally, the bacterial distributions under the pH gradient and those under flow were measured in double-layer flow based microfluidic device and T-shaped cylinders. Migration of aerobic bacteria from the duodenum into pancreas is counteracted by bile and pancreatic juice flow but facilitated by pH-taxis from acidic duodenum fluid toward more favorable slightly alkaline pH in pancreatic juice. Additionally, the reduced flow velocity in cancer patients, due to compressed pancreatic duct by solid tumor, facilitates migration. Moreover, measured distribution of GFP E. coli under the pH gradient in a microfluidic device validated pH-tactic behaviors. Furthermore, Pseudomonas fluorescens in hydrochloride solution, but not in bicarbonate solution, migrated upstream against bicarbonate flow of > 20 μm/s, with an advancement at approximately 50 μm/s.

A Mathematical Model of Gas and Water Flow in a Swelling Geomaterial—Part 1. Verification with Analytical Solution

Gas generation and migration are important processes that must be considered in a safety case for a deep geological repository (DGR) for the long-term containment of radioactive waste. Expansive soils, such as bentonite-based materials, are widely considered as sealing materials. Understanding their long-term performance as barriers to mitigate gas migration is vital in the design and long-term safety assessment of a DGR. Development and the application of numerical models are key to understanding the processes involved in gas migration. This study builds upon the authors’ previous work for developing a hydro-mechanical mathematical model for migration of gas through a low-permeable geomaterial based on the theoretical framework of poromechanics through the contribution of model verification. The study first derives analytical solutions for a 1D steady-state gas flow and 1D transient gas flow problem. Using the finite element method, the model is used to simulate 1D flow through a confined cylindrical sample of near-saturated low-permeable soil under a constant volume boundary stress condition. Verification of the numerical model is performed by comparing the pore-gas pressure evolution and stress evolution to that of the results of the analytical solution. The results of the numerical model closely matched those of the analytical solutions. Future studies will attempt to improve upon the model complexity and investigate processes and material characteristics that can enhance gas migration in a nearly saturated swelling geomaterial.

A Mathematical Model of Gas and Water Flow in a Swelling Geomaterial—Part 2. Process Simulation

Gases can potentially generate in a deep geological repository (DGR) for the long-term containment of radioactive waste. Natural and engineered barriers provide containment of the waste by mitigating contaminant migration. However, if gas pressures exceed the mechanical strength of these barriers, preferential flow pathways for both the gases and the porewater could form, providing a source of potential exposure to people and the environment. Expansive soils, such as bentonite-based materials, are widely considered as sealing materials. Understanding the long-term performance of these seals as barriers against gas migration is an important component in the design and the long-term safety assessment of a DGR. This study proposes a hydro-mechanical mathematical model for migration of gas through a low-permeable swelling geomaterial based on the theoretical framework of poromechanics. Using the finite element method, the model is used to simulate 1D flow through a confined cylindrical sample of near-saturated low-permeable soil under a constant volume boundary stress condition. The study expands upon previous work by the authors by assessing the influence of heterogeneity, the Klinkenberg “slip flow” effect, and a swelling stress on flow behavior. Based on the results, this study provides fundamental insight into a number of factors that may influence two-phase flow.

Laboratory investigations of diclofenac migration in saturated porous media – a case study

Abstract At present, concentrations of pharmaceuticals in surface and ground waters are low; however, even low concentrations of certain substances may prove very harmful. One of such pharmaceutical drugs is diclofenac, a popular non-steroidal anti-inflammatory drug (NSAID). For this reason, it is important to determine its mobility in groundwater and to estimate parameters of migration. Authors conducted column tests for two porous media: an artificial one, consisting of glass granules, and a natural one, i.e., sandur sand obtained from a site north of the city of Poznań (Poland). During the test, impulse breakthrough curves of chloride ions and diclofenac were recorded. The results were used to identify a specific sorption model and to determine values of migration parameters. Solutions of the inverse problem using optimisation methods and of equations of mathematical migration models were carried out in a MATLAB environment. Based on test results, the mobility of diclofenac is shown to be very high and comparable to that of chloride ions. The tests also revealed a slight and irreversible sorption of diclofenac on grains of both porous media.

Математическое моделирование миграции и многостадийных превращений химических веществ в подземных водах

Математическое моделирование миграции и многостадийных превращений химических веществ в подземных водах

Theoretical research on migration and settlement of dust in roadway

At present, most scholars use the mathematical model of FLUENT software to simulate migration and settlement process of dust, and tend to focus only on the graphical simulation results. For intermediate operation principle and process is not very clear, simulation results of commercial software will easily lead to distortion of simulation results. Based on this, the migration and settlement process of flowing dust in return airway of coal face has carried on the further analysis and research in this paper, and the main factors affecting the dust migration and settlement are analyzed comprehensively. At the same time, according to the law of mass conservation, a three-dimensional mathematical model of migration and settlement of flowing dust is established. The purpose is to reveal the migration and settlement law of flowing dust.

Experimental and theoretical study of polypropylene: Antioxidant migration with different food simulants and temperatures

Polypropylene is a synthetic plastic widely used in industry due to its low price and convenience. Although its wide applications, serious safety issues have been raised about toxic chemicals such as butylated hydroxytoluene (BHT) and pentaerythritol tetrakismethylene-(3,5-di-tert-butyl-4-hydroxyhydrocinnamate) (Irganox 1010) which may migrate from polypropylene packaging into foods. Here, the effects of severe processing conditions [autoclave heating (121 °C), microwave radiation (700 W), and freezer storage (−30 °C)] on migration behavior were confirmed. Mathematical models were used to estimate the migration behavior of these compounds, and the results were compared with data from real experimental analyses which were performed by high-performance liquid chromatography. Overall, the estimated values from the mathematical model were 1.5–2 times larger than the experimental values for all conditions, suggesting that the mathematical migration models provide reliable predictions of migration. Taken together, computational assessment of migration behavior may be an effective way to decrease the time and expense of food safety evaluations.

DEVELOPMENT OF THE MONITORING RESEARCH OF GROUNDWATER CONTAMINATED BY PETROLEUM PRODUCTS

A retrospective review of the groundwater monitoring development in the world and particularly in Ukraine is presented here. The need to intensive study of the changes in the drinking groundwater quality in the 50-ies of the last century has been associated with an increase in water consumption and increasing a reset of untreated waste water. However, it took another 10-15 years until the world drew attention to the spilled oil as a specific pollutant of underground hydrosphere. Among articles dealing with the groundwater pollution problem, different publications have appeared which show examples of mapping of oil-contaminated sites, the implementation of specific monitoring, qualitative description of the formation of multi-phase accumulations of petroleum in the pore space, the mathematical migration models, etc. In the methodological recommendations for hydrogeological research of contaminated areas, which were used in the Soviet Union, oil pollution was referred, as a rule, only in connection with the migration of dissolved petroleum hydrocarbons. The same trend has been kept in Ukraine, at least until the mid 90s. In the 80-90 years in Ukraine the cases of detection of previously hidden in the ground the lost petroleum accumulations have become more common. The article gives examples of contaminated sites, in the study of which IGS NAS Ukraine participated. In the department of protection of groundwater IGS NAS Ukraine, the general concept of contaminated geological environment monitoring, methods and ways of solving monitoring tasks in various stages of research were formulated; the principle of risk assessment of an oil product pollution of natural and economic objects and creation around potential contamination source of warning zone and the location of observation posts in it was proposed.

Six open questions about the migration of engineered nano-objects from polymer-based food-contact materials: a review

ABSTRACTThe use of nanomaterials in food-contact applications has created enormous interest in recent years. The potential migration of engineered nano-objects (ENOs) from food-contact materials (FCMs) is one of the most important concerns regarding potential human exposure to ENOs and health risks. Current research focusing on FCMs has often reached inconsistency regarding migration of ENOs. The scope of this critical review is to give a concise overview of the most relevant aspects of the subject, and to identify and discuss the major open questions in relation to migration of ENOs from FCMs. This includes the very fundamental questions whether ENOs can migrate from FCMs at all and what the potential release mechanisms of ENOs could be. The inconsistency of findings from experimental studies is highlighted based on the example of silver nanoparticle migration from polymer-based FCMs. Challenges in the detection and characterisation of ENOs in migration studies and the suitability of the most frequently used analytical techniques are discussed. Further, this review questions the suitability of standard food simulants and migration test conditions for FCMs as well as of conventional mathematical migration models. Considerations regarding the risk for consumers associated with migrating ENOs from FCMs are discussed.

Migration Kinetics of Ethylene Glycol Monomer from Pet Bottles into Acidic Food Simulant: Effects of Nanoparticle Presence and Matrix Morphology

AbstractIn this study, migration of ethylene glycol from polyethylene terephthalate (PET) bottles (neat PET and PET nanocomposites) into acidic food simulant is investigated. Nanocomposite pellets were prepared by melt blending of PET and TiO2 nanoparticles. The stretch blow molding machine was used to make the preforms and bottles from neat PET and nanocomposites. DSC analyses showed that the presence of nanoparticles at 3 wt % noticeably affected the crystallization temperature, Tc, and the final degree of crystallinity of PET. The incorporation of nanoparticles in the PET matrix leads to a substantial decrease of water vapor permeability. Nanoparticles also decreased the diffusivity of migrants due to the higher degree of crystallinity. The acetic acid samples were stored at 45C for 15 days. Gas chromatography analysis demonstrated that the migration of ethylene glycol from nanocomposite bottles was less than the neat PET. The polymer‐specific parameters (AP values) from mathematical migration models were derived from the experimental data. The diffusion coefficients (DP) based on Piringer's model showed a considerable difference between DP of nanocomposites and neat PET. It was concluded that the migration of monomers from food contact materials considerably depends on the structure of the manufactured packaging plastic.Practical ApplicationsPolyethylene terephthalate (PET) nanocomposite pellets containing 3% wt TiO2 nanoparticles were prepared by melt blending and PET bottles were made by injection stretch blow molding. The results showed that incorporation of TiO2 nano‐fillers in PET matrix considerably increased crystallinity and rigidity of PET packaging material and decreased the amorphous region in the polymer matrix. TiO2 nanoparticles with uniform distribution in the polymer matrix created a tortuous path, leading to reduce in monomer migration from packaging material into food simulant. Mathematical model used in this study was a practical tool for better understanding of migration process. Improved barrier properties and lower monomer migration from PET bottles into food could increase the application of PET nanocomposites in food packaging.

Multibarrier system preventing migration of radionuclides from radioactive waste repository

Abstract Safety of radioactive waste repositories operation is associated with a multibarrier system designed and constructed to isolate and contain the waste from the biosphere. Each of radioactive waste repositories is equipped with system of barriers, which reduces the possibility of release of radionuclides from the storage site. Safety systems may differ from each other depending on the type of repository. They consist of the natural geological barrier provided by host rocks of the repository and its surroundings, and an engineered barrier system (EBS). The EBS may itself comprise a variety of sub-systems or components, such as waste forms, canisters, buffers, backfills, seals and plugs. The EBS plays a major role in providing the required disposal system performance. It is assumed that the metal canisters and system of barriers adequately isolate waste from the biosphere. The evaluation of the multibarrier system is carried out after detailed tests to determine its parameters, and after analysis including mathematical modeling of migration of contaminants. To provide an assurance of safety of radioactive waste repository multibarrier system, detailed long term safety assessments are developed. Usually they comprise modeling of EBS stability, corrosion rate and radionuclide migration in near field in geosphere and biosphere. The principal goal of radionuclide migration modeling is assessment of the radionuclides release paths and rate from the repository, radionuclides concentration in geosphere in time and human exposure to ionizing radiation

Mathematical modeling of lymphocyte kinetics reveals true residence times in and preferential migration of lymphocytes via ovine lymph nodes (CAM4P.157)

Abstract There are many published values of lymphocyte residence times in lymph nodes of various mammals such as mice, rats, and sheep. Yet, most of these estimates have been obtained semiquantitatively, without the use of mathematical modeling, which raises a question about assumptions underlying such estimates. We developed a novel mathematical model for migration of lymphocytes in the whole body which takes into account the known biological details of how lymphocyte enter and exit major lymphoid tissues. We applied this novel mathematical model to experimental data on cannulation of different ovine lymph nodes (LNs). In particular, we predicted that in sheep, recirculatory lymphocytes spend on average 3 hours in the spleen and 20 hours in LNs with a distribution of residence times in LNs following a skewed gamma (lognormal-like) distribution. This is in contrast which a recent suggestion that the distribution of residence times of naïve T cells in murine LNs is exponential. We also found that lymphocytes isolated from the prescapular LN have a two-fold increased entrance rate into the prescapular LN as opposed to the intestinal LN. Importantly, the data could not be explained by preferential retention of cells in a specific LN. Taking together, our work illustrates the power of mathematical modeling in predicting the kinetics of lymphocyte migration in sheep and provides quantitative estimates of lymphocyte residence times in major ovine lymphoid tissues.

Computer modelling of haematopoietic stem cells migration

A mathematical model for migration of haematopoietic stem cells towards their niche in the bone marrow has been proposed in the literature. It consists of a chemotaxis system of partial differential equations with nonhomogeneous boundary conditions and an additional ordinary differential equation on a part of the computational boundary. The aim of the current work is to extend appropriately a second order positivity preserving central upwind scheme, originally proposed for a chemotaxis system with zero-flux boundary conditions and to apply it for the numerical solution of the considered problem. This paper introduces a first glance of such modification and outlines open questions in the handling of the nonlinear boundary conditions in a way that preserves the positivity of the solution. The presented numerical tests illustrate the need of the development of new specialized schemes for more complex chemotaxis systems.

Modelling and Mathematical Analysis of the Glass Eel Migration in the Adour River Estuary

In this paper we are interested in a mathematical model of migration of grass eels in an estuary. We first revisit a previous model proposed by O. Arino and based on a degenerate convection-diffusion equation of parabolic-hyperbolic type with time-varying subdomains. Then, we propose an adapted mathematical framework for this model, we prove a result of existence of a weak solution and we propose some numerical simulations.

ANALYSIS OF MATHEMATICAL MODELS TO DESCRIBE THE MIGRATION OF ADDITIVES FROM PACKAGING PLASTICS TO FOODS

ABSTRACTThe mathematical modeling of migration of additives from plastics to food simulants was studied using experimental data published in the literature, following two routes: the conventional approach using the solution of Fick's 2nd law, and a kinetic model based on the Weibull distribution function. The objective of this comparison was to permit using a mathematically simpler model equally able to describe migration data, and that could have a generally wider applicability by describing situations more complex than those that simple diffusional phenomena can describe. The relationship between the parameters of the two models was analyzed by regression of data generated by Fick's law using the Weibull model. The results show that the time constant parameter is related to the diffusion coefficient and the material thickness. It depends on temperature and on the molecular weight of the migrant in a similar manner to the diffusion coefficient. The activation energy presented values from 72 to 125 kJ/mol. The shape parameter is a function of the contribution of the mass transfer resistance at the interface. It was independent of temperature and of the migrant, assuming a global constant value of 0.67, for the systems and conditions studied. The results indicate that the Weibull model can be used to describe and analyze the migration of additives from plastics to foods with a meaning of the parameters in terms of the underlying physical phenomena.PRACTICAL APPLICATIONSThe Weibull model can be used to describe the migration from packaging to foods with the advantage of significant simplicity of calculation compared to Fick's 2nd law. The model can be applied in packaging systems with mass transfer processes more complex than those that simple diffusional phenomena can describe. In the migration of components from paper‐based materials (instead of plastics) into solid foods, mass transfer occurs in a heterogeneous medium of paper fibers and air. Migration curves commonly present an initial lag phase for heavier migrants. The sigmoidal‐shape of the migration curves are not adequately described by the established models based in Fick's 2nd law solutions, and the Weibull model is a good alternative. Additionally, this simple model can potentially be used in probabilistic approaches for exposure assessments of consumers to migrants originating from packaging materials.

Study on Transformation Rules of Diesel Fuels Contaminated Aquifer

Study on migration and transformation rules of diesel fuels pollution by using two-dimensional plexiglass tank to simulate underground aquifers. Through regular monitoring of the sampling ports in total petroleum hydrocarbon content of the water to determine the diesel fuels in the medium sand aquifer in the migration process, and compute out parameters of diesel fuels pollution in the medium sand aquifer in the mathematical model of migration. This prediction of diesel fuels pollution in the migration of sand media. The results showed: the highest values of different sampling ports used by the time its location is closely related to distance to sources, the concentration rose to the highest value used in a short time. The sampling ports far away from the pollution spilling place rose to the highest value of concentration used in a long time. After diesel fuels leaked 40 d later, the simulation of pollutants reached the bottom slot, and diesel fuels can be calculated transfered with a speed of 1cm•d-1, and then after 20 d more, TPH can be moved to simulate the water tank side pollution of the aquifer region.