Molecular dynamics simulations employing up to 64,000 particles are used to investigate aggregation and microheterogeneity in aqueous tert-butyl alcohol (TBA) solutions for TBA mole fractions X(t) ≤ 0.1. Four different force fields are considered. It is shown that the results obtained can be strongly dependent on the particular force field employed, and can be significantly influenced by system size. Two of the force fields considered show TBA aggregation in the concentration range X(t) ≈ 0.03 - 0.06. For these models, systems of 64,000 particles are minimally sufficient to accommodate the TBA aggregates. The structures resulting from TBA aggregation do not have a well-defined size and shape, as one might find in micellar systems, but are better described as TBA-rich and water-rich regions. All pair correlation functions exhibit long-range oscillatory behavior with wavelengths that are much larger than molecular length scales. The oscillations are not strongly damped and the correlations can easily exceed the size of the simulation cell, even for the low TBA concentrations considered here. We note that these long-range correlations pose a serious problem if one wishes to obtain certain physical properties such as Kirkwood-Buff integrals from simulation results. In contrast, two other force fields that we consider show little sign of aggregation for X(t) ≲ 0.08. In our 64,000 particle simulations all four models considered show demixing-like behavior for X(t) ≳ 0.1, although such behavior is not evident in smaller systems of 2000 particles. The meaning of the demixing-like behavior is unclear. Since real TBA-water solutions do not demix, it might be an indication that all four models we consider poorly represent the real system. Alternatively, it might be an artifact of finite system size. Possibly, the apparent demixing indicates that for X(t) ≳ 0.1, the stable TBA aggregates are simply too large to fit into the simulation cell. Our results provide a view of the possible nature of microheterogeneity in dilute TBA-water solutions, and of the associated long correlation lengths. It is clear that system size can be a very important factor in simulations of these solutions, and must be taken into account in the evaluation and development of TBA-water force fields.

a b s t r a c tIn the present paper we discuss bifurcation analysis of a modified Leslie-Gower prey-predator model in the presence of nonlinear harvesting in prey. We give a detailed mathematical analysis of the model to describe some significant results that may arise from the interaction of biological resources. The model displays a complex dynamics in the prey-predator plane. The permanence, stability and bifurcation (saddle-node bifurcation, transcritical, Hopf-Andronov and Bogdanov-Takens) of this model are discussed. We have analyzed the effect of prey harvesting and growth rate of predator on the proposed model by considering them as bifurcation parameters as they are important from the ecological point of view. The local existence and stability of the limit cycle emerging through Hopf bifurcation is given. The emergence of homoclinic loops has been shown through simulation when the limit cycle arising though Hopf bifurcation collides with a saddle point. This work reflects that the feasible upper bound of the rate of harvesting for the coexistence of the species can be guaranteed. Numerical simulations using MATLAB are carried out to demonstrate the results obtained.

Molecular dynamics simulations are employed to investigate aggregation and microheterogeneity in dilute solutions of 2-butoxyethanol (BE) in water. The BE concentration is varied from near infinite dilution to the mole fraction X(BE) = 0.04. It was found that large systems (32,000 molecules) are necessary to accommodate the BE aggregates that form in this concentration range. Simulations were performed with two different force fields, and similar results were obtained. At very low concentration, BE aggregation is not observed, but evidence is found for intramolecular hydrogen bonds (between the hydroxyl hydrogen and the ether oxygen of the same BE molecule) that form five-member ring configurations, similar to those reported in experimental studies of BE in nonaqueous solvent. Initial signs of BE association appear at X(BE) ≈ 0.005, after which aggregation occurs rapidly, with aggregates that can be described as micelle-like being fully formed at X(BE) ≈ 0.02. This concentration agrees well with many experimental studies of aggregation in BE-water solutions. Between X(BE) = 0.02 and 0.04, the aggregates appear to grow a little in size, but the basic structure remains the same. At long range, the various pair correlation functions show clear density oscillations associated with BE aggregation. This allows us to identify the length scales of the existing microheterogeneity and to estimate the size of the BE aggregates. If we assume spherical aggregates, then our estimate of the radius at X(BE) = 0.04 (~42 Å) is close to estimates obtained from light scattering and small-angle neutron scattering experiments.

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