Nonrandom Mixing Research Articles

Negative binomial approach: A useful application for the study of Echinococcus granulosus

Cystic Echinococcosis is a parasitic disease caused by the larvae of Echinococcus granulosus. The transmission of E. granulosus is affected by environmental changes and anthropogenic factors, which are in turn influenced by changes in the spatial and population dynamics of animals. The deterministic model can be extended stochastically to address the low prevalence rate, which is often observed in small mammal host populations, and to account for complex processes that reflect the highly widespread disease reservoirs and non-random mixing, such as the heterogeneous contact patterns of susceptible hosts with infectious materials. In this study, a mathematical model based on a set of differential equations that define the continuous transition between different classes was used is not regulated by host. The findings indicate that each protoscolex has an equal chance of developing into a worm and creating a dispersed population. Empirical modeling can be used to represent the frequency distribution of the number of parasites in each host using the negative binomial distribution.

Swelling Behaviors of Natural Rubber/Solvent Systems Based on the Extended Modified Double Lattice Model

AbstractSwelling experiments are conducted on nonfiller natural rubber using four solvents (toluene, cyclohexane, tetrahydrofuran (THF), and methylethylketone (MEK)) over temperatures from 10 to 70 °C. Toluene, cyclohexane, and THF, classified as effective solvents, show swelling ratios between 3 and 7, influenced by the crosslink density of the rubber. MEK, however, has a lower ratio of 1.5 to 2. Temperature has a minor impact on swelling compared to the crosslink density. The study evaluates the Extended Modified Double Lattice (EMDL) model for its mixing contribution in polymer network swelling, aiming to improve the Flory–Hüggins (FH) model. The superiority of EMDL above FH is in the boundary condition at the unvulcanized state, the former aligning its interaction energy with values from solvent activities in primary linear polymer/solvent solutions, unlike the FH model. The EMDL model also accounts for oriented interactions in polar solvents through a secondary lattice, linking specific interaction energy with solvent dipole moments. The study observes a nonlinear correlation between crosslinking density and sulfur amount, proposing a nonrandom mixing at lower sulfur concentrations. This model shows strong alignment with experimental data, suggesting that replacing the FH model's mixing contribution with the EMDL model could improve results with minimal additional complexity.

Impact of immune evasion, waning and boosting on dynamics of population mixing between a vaccinated majority and unvaccinated minority.

We previously demonstrated that when vaccines prevent infection, the dynamics of mixing between vaccinated and unvaccinated sub-populations is such that use of imperfect vaccines markedly decreases risk for vaccinated people, and for the population overall. Risks to vaccinated people accrue disproportionately from contact with unvaccinated people. In the context of the emergence of Omicron SARS-CoV-2 and evolving understanding of SARS-CoV-2 epidemiology, we updated our analysis to evaluate whether our earlier conclusions remained valid. We modified a previously published Susceptible-Infectious-Recovered (SIR) compartmental model of SARS-CoV-2 with two connected sub-populations: vaccinated and unvaccinated, with non-random mixing between groups. Our expanded model incorporates diminished vaccine efficacy for preventing infection with the emergence of Omicron SARS-CoV-2 variants, waning immunity, the impact of prior immune experience on infectivity, "hybrid" effects of infection in previously vaccinated individuals, and booster vaccination. We evaluated the dynamics of an epidemic within each subgroup and in the overall population over a 10-year time horizon. Even with vaccine efficacy as low as 20%, and in the presence of waning immunity, the incidence of COVID-19 in the vaccinated subpopulation was lower than that among the unvaccinated population across the full 10-year time horizon. The cumulative risk of infection was 3-4 fold higher among unvaccinated people than among vaccinated people, and unvaccinated people contributed to infection risk among vaccinated individuals at twice the rate that would have been expected based on the frequency of contacts. These findings were robust across a range of assumptions around the rate of waning immunity, the impact of "hybrid immunity", frequency of boosting, and the impact of prior infection on infectivity in unvaccinated people. Although the emergence of the Omicron variants of SARS-CoV-2 has diminished the protective effects of vaccination against infection with SARS-CoV-2, updating our earlier model to incorporate loss of immunity, diminished vaccine efficacy and a longer time horizon, does not qualitatively change our earlier conclusions. Vaccination against SARS-CoV-2 continues to diminish the risk of infection among vaccinated people and in the population as a whole. By contrast, the risk of infection among vaccinated people accrues disproportionately from contact with unvaccinated people.

Modelling changes in glass transition temperature in polymer matrices exposed tolow molecular weight penetrants.

Polymer matrices, when placed in contact with a fluid phase made of low molecular weight compounds, undergo a depression of their glass transition temperature (Tg) determined by the absorption of these compounds and the associated plasticization phenomena. Frequently, this effect is coupled with the mechanical action of the compressive stress exerted by the pressure of the fluid phase that, in contrast, promotes an increase in the Tg. This issue is relevant for technological and structural applications of composites with high-performance glassy polymer matrices, due to their significant impact on mechanical properties. We propose an approach to model and predict rubbery-glassy states maps of polymer-penetrant mixtures as a function of pressure and temperature based on the Gibbs-Di Marzio criterion. This criterion establishes that a 'thermodynamic' glass transition does occur when the configurational entropy of the system vanishes. Although questioned and criticized, this criterion constitutes a good practical approach to analyse changes of Tg and, in some way, reflects the idea of an 'entropy catastrophe' occurring at the glass transition. Several polymer-penetrant systems have been analysed modelling configurational entropy by means of the Non-Random Hydrogen Bond lattice fluid theory, able to cope with possible non-random mixing and occurrence of strong interactions. This article is part of the theme issue 'Ageing and durability of composite materials'.

Data-driven electron-diffraction approach reveals local short-range ordering in CrCoNi with ordering effects

The exceptional mechanical strength of medium/high-entropy alloys has been attributed to hardening in random solid solutions. Here, we evidence non-random chemical mixing in a CrCoNi alloy, resulting from short-range ordering. A data-mining approach of electron nanodiffraction enabled the study, which is assisted by neutron scattering, atom probe tomography, and diffraction simulation using first-principles theory models. Two samples, one homogenized and one heat-treated, are observed. In both samples, results reveal two types of short-range-order inside nanoclusters that minimize the Cr–Cr nearest neighbors (L12) or segregate Cr on alternating close-packed planes (L11). The L11 is predominant in the homogenized sample, while the L12 formation is promoted by heat-treatment, with the latter being accompanied by a dramatic change in dislocation-slip behavior. These findings uncover short-range order and the resulted chemical heterogeneities behind the mechanical strength in CrCoNi, providing general opportunities for atomistic-structure study in concentrated alloys for the design of strong and ductile materials.

A constitutive model for predicting the solubility of gases in water at high temperature and pressure

In the drilling and development of gas fields, gas exhibits good solubility in drilling fluids and in the formation water under high temperatures and pressures. Therefore, the prediction of the amount of dissolved gas in water plays a vital role in the development of natural gas. In this work, the principle of equal fugacity in a gas-liquid equilibrium, a non-iterative gas solubility prediction model was established. The gas-phase fugacity coefficient was calculated by the Peng-Robinson equation of state combined with the non-random mixing rule, and the liquid phase was calculated by Henry's law. The model can predict the solubility of CO2, CH4 and C2H6 in pure water at temperatures of 273–448 K and pressures of 0–100 MPa, with an error of less than 5.5%; however, the calculation accuracy for H2S was low. It is found that the effect of moisture in the gas phase of gas-liquid equilibrium cannot be ignored. Compared with the existing mixed gas solubility experimental data, this model could accurately calculate the solubility of non-polar mixed gases, such as CO2 + CH4, and CH4 + C2H6 mixture. For the mixtures containing a polar gas, the lower the polar gas content, the smaller was the prediction error of the model for the non-polar gas in the mixture. On the contrary, the higher the content of polar gas, the larger was the deviation in the prediction of non-polar gas in the mixture, but lower was the deviation in the prediction of polar gas. Finally, the ability of Krichevsky-Kasarnovsky equation to predict the solubility of pure gas was evaluated.

Integrating social behaviour, demography and disease dynamics in network models: applications to disease management in declining wildlife populations.

The emergence and spread of infections can contribute to the decline and extinction of populations, particularly in conjunction with anthropogenic environmental change. The importance of heterogeneity in processes of transmission, resistance and tolerance is increasingly well understood in theory, but empirical studies that consider both the demographic and behavioural implications of infection are scarce. Non-random mixing of host individuals can impact the demographic thresholds that determine the amplification or attenuation of disease prevalence. Risk assessment and management of disease in threatened wildlife populations must therefore consider not just host density, but also the social structure of host populations. Here we integrate the most recent developments in epidemiological research from a demographic and social network perspective, and synthesize the latest developments in social network modelling for wildlife disease, to explore their applications to disease management in populations in decline and at risk of extinction. We use simulated examples to support our key points and reveal how disease-management strategies can and should exploit both behavioural and demographic information to prevent or control the spread of disease. Our synthesis highlights the importance of considering the combined impacts of demographic and behavioural processes in epidemics to successful disease management in a conservation context.This article is part of the theme issue ‘Linking behaviour to dynamics of populations and communities: application of novel approaches in behavioural ecology to conservation’.

Orientational effects in alkanone, alkanal or dialkyl carbonate + alkane mixtures and in alkanone + alkanone or + dialkyl carbonate systems

Interactions and structure of alkanone, or alkanal or dialkyl carbonate+alkane mixtures, or of 2-alkanone+2-alkanone, or of ketone+dialkyl carbonate systems have been investigated by means of a set of thermodynamic properties and by the application of the Flory model. The properties considered are excess molar quantities: enthalpies, HmE, volumes, VmE, or isobaric heat capacities, CpmE, and liquid-liquid equilibria. Experimental data show that alkane mixtures are characterized by rather strong dipolar interactions. In the case of systems containing ketones with the same number of C atoms and a given alkane, dipolar interactions become weaker in the sequence: aromatic>cyclic>linear. In addition, the mentioned interactions become also weaker in the order: dialkyl carbonate>linear alkanone>linear alkanal. This is an important result, as carbonates show lower effective dipole moments than the other compounds, and it suggests that the group size may be relevant when evaluating thermodynamic properties of liquid mixtures. Results on HmE from the Flory model show that orientational effects (i.e., non-random mixing) are rather similar for systems with linear, cyclic or aromatic ketones or alkanals and alkanes. In contrast, orientational effects become weaker in dialkyl carbonate+alkane mixtures. The behavior of 2-alkanone +2-alkanone systems and of mixtures of longer 2-alkanones or cyclohexanone with dialkyl carbonate is close to random mixing. Larger orientational effects are encountered in solutions of carbonates and shorter 2-alkanones.

A simple and generalized model to represent the vapor-liquid equilibria and the liquid-molar-volume of alcohol-alkane binary mixtures

A simple thermodynamic model to describe the vapor-liquid equilibria and liquid densities of alcohol-alkane type mixtures is developed. The proposed model is based on a two-parameter cubic equation of state translated in volume and the Huron-Vidal-NRTL mixing rules. Generalized expressions in terms of the critical temperature and the critical pressure of alcohols and alkanes are developed for the binary energy interaction parameters (A12, A21) and the non-random mixing constant (α12) that appears in the NRTL activity model.To obtain the generalized expressions, the homologous series concept is used as follows: in first place, four series composed by an alcohol between ethanol and 1-pentanol with some n-alkanes between butane and n-undecane are selected. For each series, it is supposed that each binary parameter (A12, A21 and α12) can be described as a linear function in terms of the ratio RTc/Pc of n-alkanes. The slope and the intercept of generalized expressions for each series are determined by minimizing the total absolute relative deviation in bubble pressure. Finally, it is found that all the slopes and the intercepts for parameters A12 and A21 can been correlated as quadratic functions in terms of the RTc/Pc ratio of alcohols. Also, it is found that for all the series, the same generalized expression can be used to get parameter α12. In total, 22 mixtures are used to develop the model. The average absolute relative deviation in bubble pressure (AADP) estimated is 1.65%. Also, the average absolute deviation in the vapor phase molar fraction (DY) is 0.007.To validate the proposed model, calculations are performed for 31 binary mixtures that include branched alcohols and branched alkanes that were not used during the development of the model. In general, predictions are adequate and results obtained are similar to those reported in literature for associating models like the Cubic-Plus-Association (CPA), the Statistical Association Fluid Theory (SAFT) and the Group Contribution Association (GCA) equations of state. The AADP for the new model is 2.80%, while the DY value is 0.009.Finally, liquid densities predictions are performed for 22 alcohol-alkane mixtures and it is found that calculated values are in good agreement with experimental data. The average absolute relative deviation calculated in liquid density is 1.16%. In total 645 densities and 1030 bubble pressures are predicted satisfactorily with the proposed model.

Generalizing the Network Scale-Up Method: A New Estimator for the Size of Hidden Populations.

The network scale-up method enables researchers to estimate the size of hidden populations, such as drug injectors and sex workers, using sampled social network data. The basic scale-up estimator offers advantages over other size estimation techniques, but it depends on problematic modeling assumptions. We propose a new generalized scale-up estimator that can be used in settings with non-random social mixing and imperfect awareness about membership in the hidden population. Further, the new estimator can be used when data are collected via complex sample designs and from incomplete sampling frames. However, the generalized scale-up estimator also requires data from two samples: one from the frame population and one from the hidden population. In some situations these data from the hidden population can be collected by adding a small number of questions to already planned studies. For other situations, we develop interpretable adjustment factors that can be applied to the basic scale-up estimator. We conclude with practical recommendations for the design and analysis of future studies.

The effect of heterogeneity in uptake of the measles, mumps, and rubella vaccine on the potential for outbreaks of measles: a modelling study

Vaccination programmes to prevent outbreaks after introductions of infectious people aim to maintain the average number of secondary infections per infectious person at one or less. We aimed to assess heterogeneity in vaccine uptake and other characteristics that, together with non-random mixing, could increase this number and to evaluate strategies that could mitigate their impact. Because most US children attend elementary school in their own neighbourhoods, surveys of children entering elementary school (age 5 years before Sept 1) allow assessment of spatial heterogeneity in the proportion of children immune to vaccine-preventable diseases. We used data from a 2008 school-entry survey by the Immunization Division of the California Department of Public Health to obtain school addresses; numbers of students enrolled; proportions of enrolled students who had received one or two doses of the measles, mumps, and rubella (MMR) vaccine; and proportions with medical or personal-belief exemptions. Using a mixing model suitable for spatially-stratified populations, we projected the expected numbers of secondary infections per infectious person for measles, mumps, and rubella. We also mapped contributions to this number for measles in San Diego County's 638 elementary schools and its largest district, comprising 200 schools (31%). We then modelled the effect on measles' realised reproduction number (RV) of the following plausible interventions: vaccinating all children with personal-belief exemptions, increasing uptake by 10% to 50% in all low-immunity schools (<90% of students immune) or in only influential (effective daily contact rates >3 or contacts inter-school >30%) low-immunity schools, and increasing private school uptake to the public school average. In 2008, 39 132 children began elementary school in San Diego County, CA, USA. At entry to school, 97% had received at least one dose of the MMR vaccine, with 2·5% having personal-belief exemptions. We note substantial heterogeneity in immunity throughout the county. Although the average population immunities for measles, mumps, and rubella (92%, 87%, 92%) were similar to the population-immunity thresholds in homogeneous, randomly-mixing populations (91%, 88%, 76%), after accounting for heterogeneity and non-random mixing, the basic reproduction numbers increased by 70%, meaning that introduced pathogens could cause outbreaks. The impact of our modelled interventions ranged from negligible to a nearly complete reduction in the outbreak potential of measles. The most effective intervention to lower the realised reproduction number (RV 3·39) was raising immunity by 50% in 114 schools with low immunity (RV 1·02), but raising immunity by this level in only influential, low-immunity schools also was effective (RV 2·02). The effectiveness of vaccinating the 972 children with personal-belief exemptions was similar to that of targeting all low-immunity schools (RV 1·11). Targeting only private schools had little effect. Our findings suggest that increasing vaccine uptake could prevent outbreaks such as that of measles in San Diego in 2008. Vaccinating children with personal-belief exemptions was one of the most effective interventions that we modelled, but further research on mixing in heterogeneous populations is needed. None.

Entropic effects, shape, and size of mixed micelles formed by copolymers with complex architectures

The entropic effects in the comicellization behavior of amphiphilic AB copolymers differing in the chain size of solvophilic A parts were studied by means of molecular dynamics simulations. In particular, mixtures of miktoarm star copolymers differing in the molecular weight of solvophilic arms were investigated. We found that the critical micelle concentration values show a positive deviation from the analytical predictions of the molecular theory of comicellization for chemically identical copolymers. This can be attributed to the effective interactions between copolymers originated from the arm size asymmetry. The effective interactions induce a very small decrease in the aggregation number of preferential micelles triggering the nonrandom mixing between the solvophilic moieties in the corona. Additionally, in order to specify how the chain architecture affects the size distribution and the shape of mixed micelles we studied star-shaped, H-shaped, and homo-linked-rings-linear mixtures. In the first case the individual constituents form micelles with preferential and wide aggregation numbers and in the latter case the individual constituents form wormlike and spherical micelles.

Lipid bilayers: clusters, domains and phases.

In the present chapter we discuss the complex mixing behaviour of plasma membrane lipids. To do so, we first introduce the plasma membrane and membrane mixtures often used to model its complexity. We then discuss the nature of lipid phase behaviour in bilayers and the distinction between these phases and other manifestations of non-random mixing found in one-phase mixtures, such as clusters, micelles and microemulsions. Finally, we demonstrate the applicability of Gibbs phase diagrams to the study of increasingly complex model membrane systems, with a focus on phase coexistence, morphology and their implications for the cell plasma membrane.

Entropic effects in mixed micelles formed by star/linear and star/star AB copolymers

The entropic effects in the comicellization behavior of amphiphilic AB copolymers differing in chain architecture of solvophilic A or solvophobic B parts are studied by means of molecular dynamics simulations. In particular, we studied linear/star and star/star copolymer mixtures. The properties of interest were the critical micelle concentration, the mean aggregation number, the shape of the micelle, which is expressed by the shape anisotropy, the thickness of the corona, and the solvophobic core radius. We found that the critical micelle concentration values for linear/star and copolymer mixtures show a positive deviation from the analytical predictions of the molecular theory of comicellization for chemically identical copolymers. This could be attributed to the effective interactions between copolymers originated from the architectural asymmetry. The effective interactions induce a small decrease in the aggregation number of preferential micelles in linear/star mixtures triggering the nonrandom mixing between the solvophilic moieties in the corona for all mixtures. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015, 53, 442–452

Non-ideal mixing behaviour of hydrogen bonding in mixtures of protic ionic liquids.

Ionic liquids (ILs) attract interest in science and technology as a result of their unique properties. Binary and ternary mixtures of ILs significantly increase the number of possible cation/anion combinations, resulting in targeted physical and chemical properties. In this work, we study the mixing behaviour of two protic ILs: triethyl ammonium methylsulfonate [Et3 NH][CH3 SO3 ] and triethylammonium triflate [Et3 NH][CF3 SO3 ]. We find a characteristic deviation from ideal mixing by means of low-frequency infrared spectroscopy. By using molecular dynamics simulations, we explain this behaviour as being the result of different strengths of anion/cation hydrogen bonding. This non-ideality of non-random H-bond mixing is also reflected in macroscopic properties such as the viscosity. Mixing suitable ILs may, thus, result in new ILs with targeted physical properties.

Buffalo milk fat globules and their biological membrane: in situ structural investigations

Milk fat globules and their surrounding biological membrane (the MFGM) are not well understood despite the importance of these milk components in human nutrition and the role of fat globules in determining the properties of dairy products. The objectives of this study were to investigate these unique colloidal assemblies and the microstructure of the MFGM in buffalo milk, which is the second largest global source of dairy products. In-situ structural investigations were performed at room temperature using confocal microscopy with multiple fluorescent probes (Nile Red, Rh-DOPE, the lectin WGA-488). Microscopic observations showed cytoplasmic crescents around fat globules and the heterogeneous distribution of glycosylated molecules and polar lipids with the occurrence of lipid domains. The lipid domains in the buffalo MFGM appear to form by the segregation of lipids with a high phase transition temperature (e.g. sphingomyelin and saturated phosphatidylcholine molecular species) and cholesterol resulting in a gel phase or a Lo phase forming circular domains. The structure of the buffalo MFGM results from a non-random mixing of components, consistent with observations for other species. Structural heterogeneities of the MFGM could affect the processability of buffalo fat globules and the bioavailability of milk lipids.

A new approach to study interaction parameters in cyanobiphenyl liquid crystal binary systems

The phase transition of heptylcyanobiphenyl 7CB and pentylcyanobiphenyl 5CB liquid crystals was investigated using the differential scanning calorimetry DSC technique. Then, the phase transition of different compositions of 7CB/5CB binary mixture was studied to determine the eutectic point. The phase diagram of mentioned binary system in 7CB mole fraction of 0.45 at T=273.45K is in good agreement with that of predicted from Schroder–van Laar equation. The thermodynamic excess functions and interaction parameters were calculated to describe the phase transition physically using the non-random mixing for the first time. The P∗ randomicity parameter was used to describe the phase transitions of C–N and N–I in which a small amount of P∗ shows a non-random identity of C–N phase transition. Contrarily, the P∗ is greater in N–I phase transition showing a random mixing process.

Mixed micellization of gemini and conventional surfactant in aqueous solution: A lattice Monte Carlo simulation

In the current study, we have investigated the micellization of pure gemini surfactants and a mixture of gemini and conventional surfactants using a 3D lattice Monte Carlo simulation method. For the pure gemini surfactant system, the effects of tail length on CMC and aggregation number were studied, and the simulation results were found to be in excellent agreement with the experimental results. For a mixture of gemini and conventional surfactants, variations in the mixed CMC, interaction parameter β, and excess Gibbs free energy GE with composition revealed synergism in micelle formation. Simulation results were compared to estimations made using regular solution theory to determine the applicability of this theory for non-ideal mixed surfactant systems. A large discrepancy was observed between the behavior of parameters such as the activity coefficients fi and the excess Gibbs free energy GE and the expected behavior of these parameters as predicted by regular solution theory. Therefore, we have used the modified version of regular solution theory. This three parameter model contains two parameters in addition to the interaction parameters: the size parameter, ρ, which reflects differences in the size of components, and the packing parameter, P*, which reflects nonrandom mixing in mixed micelles. The proposed model provides a good description of the behavior of gemini and conventional surfactant mixtures. The results indicated that as the chain length of gemini surfactants in mixture is increased, the size parameter remains constant while the interaction and packing parameters increase.

Impact of degree mixing pattern on consensus formation in social networks

The consensus formation process in a social network is affected by a number of factors. This paper studies how the degree mixing pattern of a social network affects the consensus formation process. A social network of more than 50,000 nodes was sampled from the online social services website Twitter. Nodes in the Twitter user network are grouped by their in-degrees and out-degrees. A degree mixing correlation is proposed to measure the randomness of the mixing pattern for each degree group. The DeGroot model is used to simulate the consensus formation processes in the network. Simulation suggests that the non-random degree mixing pattern of social networks can slow down the rate of consensus.

분자의 논랜덤 분포가 기체의 상태방정식에 미치는 영향

Using the free volume of van der Waals equation, Carnahan-Starling equation for hard spheres, Wilson equa- tion for nonrandom mixing of solution, NRTL equation and our equation, several new equations of states for pure gases are derived. Using these equations, compressibility factors for pure gases are calculated and compared with Nelson-Obert gen- eralized compressibility factor charts. The equation of states using the concept of molecular nonrandom distribution gave better results than those of molecular random distribution. This shows that the molecular nonrandom distribution makes considerable effect on the equation of states.