Identifying the Onset of Phase Separation in Quaternary Lipid Bilayer Systems from Coarse-Grained Simulations

Understanding the (de)mixing behavior of multicomponent lipid bilayers is an important step towards unraveling the nature of spatial composition heterogeneities in cellular membranes and their role in biological function. We use coarse-grained molecular dynamics simulations to study the composition phase diagram of a quaternary mixture of phospholipids and cholesterol. This mixture is known to exhibit both uniform and coexisting phases. We compare and combine different statistical measures of membrane structure to identify the onset of phase coexistence in composition space. An important element in our approach is the dependence of composition heterogeneities on the size of the system. While homogeneous phases can be structured and display long correlation lengths, the hallmark behavior of phase coexistence is the scaling of the apparent correlation length with system size. Because the latter cannot be easily varied in simulations, our method instead uses information obtained from observation windows of different sizes to accurately distinguish phase coexistence from structured homogeneous phases. This approach is built on very general physical principles, and will be beneficial to future studies of the phase behavior of multicomponent lipid bilayers

KE-Rod Initial Velocity of Hollow Cylindrical Charge

KE-rod warhead is a kind of forward interception warhead. To control the KE-rods to disperse uniformly, the hollow cylindrical charge is applied. Initial velocity is crucial to KE-rods distribution and the coordination between the fuze and the warhead. Therefore, based on the classical Gurney formula of cylindrical charge and tabulate interlayer charge, a mathematical model for calculating the KE-rod initial velocity of hollow cylindrical charge has been deduced based on certain assumptions, of which the basis theory is energy and momentum conservation. To validate this deduced equation, high-speed photography and metal-pass target experimental methods were applied simultaneously to test the initial velocity of designed KE-rod warhead. Testing results clearly indicate that the calculated results of the derived mathematical model coincides with the experimental  results, and with the increase in hollow radius, the calculated results become much closer to the experimental results. But the calculated results of classical Gurney formula are far above the experimental results, and the relative error increases with increase in the hollow diameter. The derived mathematical model with satisfactory accuracy is applicable to calculate the KE-rod initial velocity of hollow cylindrical charge in engineering applications.Defence Science Journal, 2011, 61(1), pp.25-29, DOI:http://dx.doi.org/10.14429/dsj.61.7

Discrete Nonlinear Planar Systems and Applications to Biological Population Models

We study planar systems of difference equations and applications to biological models of species populations. Central to the analysis of this study is the idea of folding - the method of transforming systems of difference equations into higher order scalar difference equations. Two classes of second order equations are studied: quadratic fractional and exponential. We investigate the boundedness and persistence of solutions, the global stability of the positive fixed point and the occurrence of periodic solutions of the quadratic rational equations. These results are applied to a class of linear/rational systems that can be transformed into a quadratic fractional equation via folding. These results apply to systems with negative parameters, instances not commonly considered in previous studies. We also identify ranges of parameter values that provide sufficient conditions on existence of chaotic and multiple stable orbits of different periods for the planar system. We study a second order exponential difference equation with time varying parameters and obtain sufficient conditions for boundedness of solutions and global convergence to zero. For the autonomous case, we show occurrence of multistable periodic and nonperiodic orbits. For the case where parameters are periodic, we show that the nature of the solutions differs qualitatively depending on whether the period of the parameters is even or odd. The above results are applied to biological models of populations. We investigate a broad class of planar systems that arise in the study of stage-structured single species populations. In biological contexts, these results include conditions on extinction or survival of the species in some balanced form, and possible occurrence of complex and chaotic behavior. Special rational (Beverton-Holt) and exponential (Ricker) cases are considered to explore the role of inter-stage competition, restocking strategies, as well as seasonal fluctuations in the vital rates