Kinetic Theory Estimates for the Kolmogorov-Sinai Entropy and the Largest Lyapunov Exponents for Dilute, Hard-Ball Gases and for Dilute, Random Lorentz Gases

The kinetic theory of gases provides methods for calculating Lyapunov exponents and other quantities, such as Kolmogorov-Sinai entropies, that characterize the chaotic behavior of hard-ball gases. Here we illustrate the use of these methods for calculating the Kolmogorov-Sinai entropy, and the largest positive Lyapunov exponent, for dilute hard-ball gases in equilibrium. The calculation of the largest Lyapunov exponent makes interesting connections with the theory of propagation of hydrodynamic fronts. Calculations are also presented for the Lyapunov spectrum of dilute, random Lorentz gases in two and three dimensions, which are considerably simpler than the corresponding calculations for hard-ball gases. The article concludes with a brief discussion of some interesting open problems.Comment: 41 pages (REVTEX); 7 figs., 4 of which are included in LaTeX source. (Fig.7 doesn't print well on some printers) This revised paper will appear in "Hard Ball Systems and the Lorentz Gas", D. Szasz ed., Encyclopaedia of Mathematical Sciences, Springe

Optimization of the composition of crop collections for ex situ conservation

Many crop genetic resources collections have been established without a clearly defined conservation goal or mandate, which has resulted in collections of considerable size, unbalanced composition and high levels of duplication. Attempts to improve the composition of collections are hampered by the fact that conceptual views to optimize collection composition are very rare. An optimization strategy is proposed herein, which largely builds on the concepts of core collection and core selection. The proposed strategy relies on hierarchically structuring the crop gene pool and assigning a relative importance to each of its different components. Comparison of the resulting optimized distribution of the number of accessions with the actual distribution allows identification of under- and over-representation within a collection. Application of this strategy is illustrated by an example using potato. The proposed optimization strategy is applicable not only to individual genebanks, but also to consortia of cooperating genebanks, which makes it relevant for ongoing activities within projects that aim at sharing responsibilities among institutions on the basis of rational conservation, such as a European genebank integrated system and the global cacao genetic resources network CacaoNet

Variable-mesh method of solving differential equations

Multistep predictor-corrector method for numerical solution of ordinary differential equations retains high local accuracy and convergence properties. In addition, the method was developed in a form conducive to the generation of effective criteria for the selection of subsequent step sizes in step-by-step solution of differential equations

Charge regulation and ionic screening of patchy surfaces

The properties of surfaces with charge-regulated patches are studied using non-linear Poisson-Boltzmann theory. Using a mode expansion to solve the non-linear problem efficiently, we reveal the charging behaviour of Debye-length sized patches. We find that patches charge up to higher charge densities if their size is relatively small and if the patches are well separated. The numerical results are used to construct a basic analytical model which predicts the average surface charge density on surfaces with patchy chargeable groups.Comment: 9 figure

Front propagation techniques to calculate the largest Lyapunov exponent of dilute hard disk gases

A kinetic approach is adopted to describe the exponential growth of a small deviation of the initial phase space point, measured by the largest Lyapunov exponent, for a dilute system of hard disks, both in equilibrium and in a uniform shear flow. We derive a generalized Boltzmann equation for an extended one-particle distribution that includes deviations from the reference phase space point. The equation is valid for very low densities n, and requires an unusual expansion in powers of 1/|ln n|. It reproduces and extends results from the earlier, more heuristic clock model and may be interpreted as describing a front propagating into an unstable state. The asymptotic speed of propagation of the front is proportional to the largest Lyapunov exponent of the system. Its value may be found by applying the standard front speed selection mechanism for pulled fronts to the case at hand. For the equilibrium case, an explicit expression for the largest Lyapunov exponent is given and for sheared systems we give explicit expressions that may be evaluated numerically to obtain the shear rate dependence of the largest Lyapunov exponent.Comment: 26 pages REVTeX, 1 eps figure. Added remarks, a reference and corrected some typo