Nonrandom Mixing Research Articles

Appropriateness of the Darroch Estimator for Monitoring Adult Chum Salmon on the Middle Yukon River, Alaska

AbstractFrom 1996 to 1999, a Darroch two‐sample stratified capture–recapture experiment was conducted on adult chum salmon Oncorhynchus keta in the Yukon River, Alaska. Annual release of marked chum salmon ranged from 8,527 to 18,631 fish. At the recovery site, 15,581–45,232 fish were examined for marks annually. The percentage of tagged fish among those examined for marks ranged from 2.8% to 6.4%. Abundance estimates ranged from 189,742 (SE = 6,967) to 654,296 (SE = 21,921) fish during the four study years. Weekly estimates ranged from 6,796 to 126,268 fish. The assumption of a closed population was evaluated in light of life history and other data. One closure violation due to sample starting and ending dates was mitigated using migration times. We used statistical analysis and modeling to evaluate assumptions of (1) equal probability of capture, (2) equal probability of movement, and (3) random mixing of fish. Logistic regression suggested that the probability of recapture was not independent of length and gender in 8 of 32 weeks among years. Modeling changes in the probabilities of movement and capture indicated that differences in movement would cause little bias in population estimates relative to differences in capture. However, length‐ and gender‐stratified and unstratified population estimates showed little difference (e.g., in 1997: length‐stratified estimate = 351,138 fish, gender‐stratified estimate = 333,842 fish, unstratified estimate = 333,057 fish). Three explanations were offered for these results: violations were due to changes in the probability of movement, statistical tests were overly sensitive, or the estimator was robust to the assumption violations. Probability of recapture was related to bank orientation (i.e., nonrandom mixing) only in 1999. Annual estimates during the study documented a decline in the spawning population. Weekly estimates indicated that run timing was inconsistent among years. The estimates compared favorably with other assessments of the run. We concluded that the Darroch estimator was reasonably applied to data collected via fish wheels for this population.

Molecular thermodynamics approach for phase behaviors of solid polymer electrolytes/salt system in lithium secondary battery on the nonrandom mixing effect: Applicability of the group-contribution method

A new group-contribution model based on the lattice model is developed to interpret phase behaviors of solid polymer electrolyte/salt systems on the nonrandom mixing effect. The model includes the combinatorial energy contribution that is responsible for the revised Flory–Huggins entropy of mixing, the van der Waals energy contribution from dispersion, and the polar force and the specific energy contribution from hydrogen bonding. Lattice model gives a starting point for a theoretical description of thermodynamic properties of polymer solution systems. The proposed model in this study improves the configurational energy of mixing and correlates energy of mixing term including the effect of nonrandom mixing on the configurational thermodynamic properties of a binary mixture with experimental data. Our results show that good agreement is obtained upon comparison with experimental data of various PEO and salt systems in the interested ranges.

Assessing the effects of human mixing patterns on human immunodeficiency virus-1 interhost phylogenetics through social network simulation.

Geneticists seeking to understand HIV-1 evolution among human hosts generally assume that hosts represent a panmictic population. Social science research demonstrates that the network patterns over which HIV-1 spreads are highly nonrandom, but the effect of these patterns on the genetic diversity of HIV-1 and other sexually transmitted pathogens has yet to be thoroughly examined. In addition, interhost phylogenetic models rarely account explicitly for genetic diversity arising from intrahost dynamics. This study outlines a graph-theoretic framework (exponential random graph modeling, ERGM) for the estimation, inference, and simulation of dynamic partnership networks. This approach is used to simulate HIV-1 transmission and evolution under eight mixing patterns resembling those observed in empirical human populations, while simultaneously incorporating intrahost viral diversity. Models of parametric growth fit panmictic populations well, yielding estimates of total viral effective population on the order of the product of infected host size and intrahost effective viral population size. Populations exhibiting patterns of nonrandom mixing differ more widely in estimates of effective population size they yield, however, and reconstructions of population dynamics can exhibit severe errors if panmixis is assumed. I discuss implications for HIV-1 phylogenetics and the potential for ERGM to provide a general framework for addressing these issues.

Bioterrorism. Mathematical modeling applications in homeland security.

Bioterrorism. Mathematical modeling applications in homeland security.

Mechanisms of moisture absorption by cyanate ester modified epoxy resin matrices: the clustering of water molecules

One of the important factors, which determine the concentration of moisture that a polymer will absorb, is the effect of non-random mixing whereby water-clustering is said to occur. The Flory–Huggins theory cannot predict the isotherms observed for highly polar polymers since the theory assumes complete random mixing. The complementary model of Brown [Brown GL. In: Rowland SP, editor. Water in polymers. Washington, DC: American Chemical Society; 1980. p. 441. [1]] considers the moisture distribution in polar polymers, consists of components associated with random mixing (Flory–Huggins theory) and clustering of the water molecules. Moisture sorption isotherms of cyanate ester/epoxy blends at different relative humidities have been analysed by the clustering theory of Brown [Brown GL. In: Rowland SP, editor. Water in polymers. Washington, DC: American Chemical Society; 1980. p. 441. [1]] and the dual mode sorption theory of Zimm [Zimm BH. J Chem Phys 1953;21:934. [2]]. Clustering was found to occur in cyanate ester/epoxy blends conditioned at relative humidities of 40% and higher. The Cluster size indicates that the majority of the absorbed water in a cured cyanate ester/epoxy blend was not clustered but present in monomeric form through hydrogen bonding to polar sites. It is postulated that the phenomenon of thermal spiking enhanced moisture absorption can be explained by an equilibrium between cluster formation and declustering associated with network relaxation at the spike-temperature.

Investigation of interaction parameters in mixed micelle using pulsed field gradient NMR spectroscopy

Pulsed field gradient NMR spectroscopy was used to determine the partitioning of surfactant between monomeric and micellar forms in a mixed CTAB (hexadecyltetramethylammonium bromide) and Triton X-100 [ p-(1,1,3-tetramethylbutyl)polyoxyethylene] system. In addition, potentiometric and surface tension measurements were used to determine the free concentration of ionic surfactant and the critical micelle concentration (CMC) of mixtures of n-alkyltrimethylammonium bromide ( C n TAB, n = 12 , 14, 16, 18) and Triton X-100. Regular solution theory cannot describe the behavior of the activity coefficient and the excess Gibbs free energy of mixtures of ionic and nonionic surfactants. To overcome these shortcomings, we developed a new model that combines Van Laar expressions and the theory of nonrandom mixing in mixed micelles. The Van Laar expressions contain an additional parameter, ρ, which reflects differences in the size of the components of the mixture. Nonrandom mixing theory was introduced to describe nonrandom mixing in mixed micelles. This effect was modeled by a packing parameter, P ∗ . The proposed model provided a good description of the behavior of binary surfactant mixtures. The results indicated that head group size and packing constraints are important contributors to nonideal surfactant behavior. In addition, the results showed that as the chain length of the C n TAB molecule in C n TAB/Triton X-100 mixtures was increased, the head group size parameter remained constant, but the interaction and packing parameters increased. Increase of the temperature caused an increase in the interaction parameter β and a decrease in the packing parameter ( P ∗ ) .

Cation diffusion and ionic conductivity in soda-lime silicate glasses

We have studied the mobilities of calcium and sodium ions in silicate glasses of compositions xNa2O (3 - x)CaO x 4SiO2 with x = 0.0, 0.1, 0.3, 1.0 and 3.0 by means of radiotracer diffusion, electrical conductivity measurements, and dynamic mechanical thermal analyses. In glasses containing sodium oxide, the Na+ ions are much more mobile than the Ca2+ ions, and are, therefore, governing the electrical conductivity. In the pure calcium silicate glass, the activation energy of Ca2+ diffusion is higher than the activation energy of the electrical conductivity. This provides strong evidence that the electrical conductivity of this glass is not determined by the migration of Ca2+ ions, but by impurity charge carriers, which are most likely Na+ ions. We sketch the composition-dependent mobilities of Na+ and Ca2+ ions in soda-lime silicate glasses with variable Na2O and CaO content. Our results indicate that the coordination environment of Ca2+ ions remains unchanged when CaO is replaced by Na2O which is consistent with recent results of molecular dynamic simulations. Moreover, our results confirm the formation of dissimilar Na-Ca pairs which lead to a non-random mixing of the cations in the glass. The formation of such pairs was recently deduced from nuclear magnetic resonance spectra of soda-lime silicate glasses.

Scattering from Polydisperse Melts

Effective isotropic pair potentials for polymer chains in a melt are derived from a phenomenological, coarse grained model of mixing on small distance scales, and the radial distribution functions of chain centers of mass and the scattering are calculated in the hypernetted chain approximation. The systems chosen for illustrative calculations are quasi-binary melts of deuterated and protonated polyethylene and polystyrene, both of which have been reported to exhibit anomalous composition dependence of neutron scattering. Quite large deviations from the Flory−Huggins picture of random spatial mixing of chains are found and the deviations decrease rather slowly with increasing molecular weights. However, nonrandom mixing gives rise to anomalous scattering of significant magnitude only if the mixture is asymmetric in particular ways. Differences in molecular weight (smaller for the deuterated polymer) and polydispersity (larger for the deuterated polymer) of about 10% are sufficient to exhibit anomalous scattering due to errors in the Flory−Huggins entropy of mixing. Smaller differences in the packing energies of the two different monomers, which are associated in the phenomenological model with composition dependent partial monomer volumes, reveal errors in the usual random phase analysis of scattering. Relative volumes of mixing deuterated and protonated polymer must range up to 1% in order to rationalize experimental anomalous scattering.

Lattice Monte Carlo Simulations of Dilute Mixed Micelles

Three-dimensional lattice-based Monte Carlo simulations of mixed amphiphile systems are investigated, and the simulated critical micelle concentrations (cmc's) are compared with the predictions of both a molecular thermodynamic theory and a regular solution theory. The head−head interactions between identical surfactant species are varied to mimic nonideal mixing and to manipulate the net attraction (or repulsion) between surfactant species. The simulations indicate that the head−head interaction affects not only the cmc but also aggregate size and structure. The simulated cmc as a function of overall surfactant composition is in reasonable agreement with the theoretical models when a fitted value for the interaction parameter, β, is used. The fitted value is in good agreement with a value estimated a priori from the lattice model for the surfactants with attractive headgroups, but there are large discrepancies for the case of repulsive headgroups. The discrepancies in the latter are caused by nonrandom mixing, that is, segregation of the two surfactants within each micelle.

Equation of state for chain-like molecules using mixing rule based on two-fluid theory

A mixing rule based on two-fluid theory is introduced to consider the non-random mixing of spices in the calculation of the properties of mixtures when an equation of state for chain-like molecules is adopted. The equation is expressed as the sum of a reference term, a perturbation term and an association term. For systems of non-associated spices, the last term is vanished. The mixing rule is used for the second term. The method can be used to correlate vapor–liquid equilibria with only one adjustable parameter. It was found that using two-fluid theory could give better results than that using one-fluid theory for asymmetrical systems or for systems with only self-association.

A note on the distribution of the number of vaccinated infected under non‐random mixing conditions

A common situation in vaccine efficacy (VE) estimation is dealing with non-randomly mixing populations, which may subject vaccinated and unvaccinated individuals to a different infection pressure. These conditions may lead to a bias in VE estimates. The derivation of the statistical distribution of the number of vaccinated and infected out of a sample of n infections in a VE trial is essential to develop estimates and their properties. For randomly mixing populations, it has been shown recently that this follows a hypergeometric distribution for ‘all/nothing’ vaccines, whereas it is a non-central hypergeometric distribution for ‘leaky’ ones. Here it is shown that these distributions still hold under non-random mixing conditions, provided that mixing preferences and contact rates are independent of vaccination status. These conditions are met when vaccine and placebo are randomized. Copyright © 2001 John Wiley & Sons, Ltd.

A note on the distribution of the number of vaccinated infected under non-random mixing conditions.

A common situation in vaccine efficacy (VE) estimation is dealing with non-randomly mixing populations, which may subject vaccinated and unvaccinated individuals to a different infection pressure. These conditions may lead to a bias in VE estimates. The derivation of the statistical distribution of the number of vaccinated and infected out of a sample of n infections in a VE trial is essential to develop estimates and their properties. For randomly mixing populations, it has been shown recently that this follows a hypergeometric distribution for 'all/nothing' vaccines, whereas it is a non-central hypergeometric distribution for 'leaky' ones. Here it is shown that these distributions still hold under non-random mixing conditions, provided that mixing preferences and contact rates are independent of vaccination status. These conditions are met when vaccine and placebo are randomized.

Prediction of nonrandom mixing in lattice model with multi-references

A new lattice theory is proposed to describe nonrandom mixing behavior based on recently developed lattice model theory by Aranovich and Donohue. The present theory assumes multi-references in order to take into account interference effects on non-random mixing among pairs. The number of references was obtained from Monte Carlo simulations for monomer+hole mixtures. Monte Carlo simulation for hole [0]+monomer [1]+monomer [2] mixture shows that this theory is more accurate than Guggenheim’s quasi-chemical theory or the Aranovich-Donohue model in a wide range of temperatures and densities. Especially, even under the stringent condition of zero interaction energy parameter e12=0, the present theory predicts well the extent of nonrandom mixing. For dimer fluid the non-randomness is calculated using the surface fraction. Here three references was used as in the case of monomer fluid with chain connectivity constraints. Comparison of the theory with Monte Carlo simulation results for dimer+hole system shows a good agreement.

Mixing Properties of Two-Dimensional Lattice Solutions of Amphiphiles

Lattice Monte Carlo simulations of two-dimensional amphiphile solutions are used to examine the accuracy of the mixing properties predicted by lattice theories such as the Flory–Huggins theory, random-solution approximation, and quasichemical approximation. The internal energy, Helmholtz free energy, and entropy of mixing have been calculated from the configurational energy data obtained from the simulations, and the effect of nonrandom mixing on these properties has been determined. The quasichemical approximation predicts the entropy and Helmholtz free energy of mixing accurately for the amphiphile solution, but fails to predict the energy of mixing, due to the presence of microphase (self-aggregation) separation, which is beyond the reach of the quasichemical approximation, a mean-field theory. Helmholtz free energy of mixing is predicted accurately, and the shielding of the solvophobic segments in the microphase leads to small energies of mixing compared to the entropy of mixing.

Simulation studies of phase III clinical trials to test the efficacy of a candidate HIV-1 vaccine.

One question of particular importance in phase III HIV vaccine trials is the choice of efficacy measure (EM) to validly and precisely estimate the true vaccinal efficacy. Traditional EMs, based on hazard rate ratio (HRR) or cumulative incidence ratio (CIR) are time-sensitive to mode of vaccine action and population heterogeneities. Through Monte-Carlo simulation, the performance of HRR and CIR based EMs are examined across different trial designs and vaccine and population characteristics. A new EM based on log-spline hazard regression (HARE) is proposed. Given that vaccinal properties (mode of action, time-lag, waning) are unknown a priori, appropriate selection of EM is problematic, and HRR and CIR can be unreliable to estimate the true maximum efficacy of candidate products. Non-random sexual mixing can exacerbate biases in HRR and CIR. HARE can offer valid estimation across different modes of vaccine action and in presence of frailty effects, contrary to its traditional counterparts. Our simulation studies highlight the weaknesses of widely used EMs while offering guidelines for trial design and suggesting new avenues for statistical analysis.

Liquid–liquid equilibria of binary polymer solutions with specific interactions

In our previous study, we proposed a new expression for the configurational energy of mixing taking into account non-random mixing effect and chain-length dependence of the polymer. But our model can not predict lower critical solution temperature (LCST) behaviours of liquid–liquid equilibria for binary polymer solutions. In this study, we extend our previous model to describe LCST behaviours of binary polymer solutions by employing a secondary lattice concept as a perturbation term to account for oriented interactions (or specific interactions).

The Mover-Stayer Model for the HIV/AIDS Epidemic in Action

Short- and medium-term projections of the HIV/AIDS epidemic indicators are of great interest to those evaluating the needs for health care and prevention interventions. We developed a simulation procedure to obtain forecasts of the HIV/AIDS epidemic and used it to estimate the characteristic regional parameters of the epidemic in Italy. The simulation procedure is based on a hybrid compartmental model, in which the epidemic evolves via nonrandom mixing patterns. Because of its structure, the model is suitable for policy making; in particular, for evaluating prevention campaigns, alternate forms of health care for people with AIDS, and drug supply needs. The model will also be used to estimate the number of intravenous drug users in Italy and the number of AIDS cases not reported or reported with a delay to the Italian surveillance system.

Molecular mechanisms for disparate miscibilities of poly(propylene) and head-to-head poly(propylene) with other polyolefins

Recent experiments find large differences in binary blend miscibilities between poly(propylene) in its ordinary and head-to-head forms with poly(ethylene propylene). This miscibility variation cannot be understood from simple Flory–Huggins (FH) theory but can readily be explained with the lattice cluster theory (LCT), a generalization of FH theory that accounts for nonrandom mixing, monomer structure, and chain semiflexibility in a systematic manner. Calculations are also presented of miscibility trends for poly(propylene)/poly(ethylene butylene) blends, one of which has yet to be studied. Experiments for this system should provide a nontrivial test of the LCT predictions.

A Theoretical Model for the Association Probabilities of Saturated Phospholipids from Two-Component Bilayer Lipid Membranes

The non-random mixing of biomembrane components, especially saturated phospholipids, exhibits important consequences in molecular biology. Particularly, the distribution of lipids within natural and model membranes is strongly determined by the selective association processes. These processes of phospholipids take place due to the cooperative modes in multiparticle systems as well as the specific lipid-lipid interactions both in the hydrophobic core and in the region of the polar headgroups. We demonstrated that the investigation of the selective association processes of saturated phospholipids might contribute to the insight of the lipid domains appearance inside the bilayer membranes. The association probabilities of like-pairs and cross-pairs from a binary mixture of saturated phospholipids were tested for both parallel and anti-parallel alignments of the polar headgroups. The present model confirms the experimental evidence for saturated phospholipids to have a high tendency for association in parallel configuration of the electric dipole moments of the polar headgroups whether the cross-sectional area of the polar headgroup is in an usual range of 25-55 A2. There are three major lipid domains in a binary mixture of saturated phospholipids: (i) lipid domains in non-mixed phase of the first mixture component, in parallel alignment of the polar headgroups; (ii) lipid domains in non-mixed phase of the second mixture component, in anti-parallel alignment of the polar headgroups; (iii) lipid domains in mixed phase. We think that the selective association processes of phospholipids are neither exclusively, nor only involved in promoting the lipid domains appearance through bilayer phospholipid membranes.

Chain length dependence of liquid—liquid equilibria of binary polymer solutions

The proposed model in our previous study 1 improves the mathematical approximation defect and gives a new expression for the configurational energy of mixing using the fractional form rather than the algebraic form with second-order approximation for the configurational energy of non-random mixing 2. In this study, we introduce new universal constants to take into account the chain length dependence of a polymer in a solvent. Our proposed model shows a slight discrepancy when compared with experimental data and gives a better understanding of phase equilibria dependence on the chain length of the polymer.