Local similarity in the stable boundary layer and mixing-length approaches: consistency of concepts

In stably stratified flows vertical movement of eddies is limited by the fact that kinetic energy is converted into potential energy, leading to a buoyancy displacement scale z B . Our new mixing-length concept for turbulent transport in the stable boundary layer follows a rigid-wall analogy, in the sense that we assume that the buoyancy length scale is similar to neutral length scaling. This implies that the buoyancy length scale is: ¿ B = ¿ B z B , with ¿ B ¿ ¿, the von Karman constant. With this concept it is shown that the physical relevance of the local scaling parameter z/¿ naturally appears, and that the ¿ coefficient of the log-linear similarity functions is equal to c/¿ 2, where c is a constant close to unity. The predicted value ¿ ¿ 1/¿ 2 = 6.25 lies within the range found in observational studies. Finally, it is shown that the traditionally used inverse linear interpolation between the mixing length in the neutral and buoyancy limits is inconsistent with the classical log-linear stability functions. As an alternative, a log-linear consistent interpolation method is proposed

Statistical properties of multistep enzyme-mediated reactions

Enzyme-mediated reactions may proceed through multiple intermediate conformational states before creating a final product molecule, and one often wishes to identify such intermediate structures from observations of the product creation. In this paper, we address this problem by solving the chemical master equations for various enzymatic reactions. We devise a perturbation theory analogous to that used in quantum mechanics that allows us to determine the first () and the second (variance) cumulants of the distribution of created product molecules as a function of the substrate concentration and the kinetic rates of the intermediate processes. The mean product flux V=d/dt (or "dose-response" curve) and the Fano factor F=variance/ are both realistically measurable quantities, and while the mean flux can often appear the same for different reaction types, the Fano factor can be quite different. This suggests both qualitative and quantitative ways to discriminate between different reaction schemes, and we explore this possibility in the context of four sample multistep enzymatic reactions. We argue that measuring both the mean flux and the Fano factor can not only discriminate between reaction types, but can also provide some detailed information about the internal, unobserved kinetic rates, and this can be done without measuring single-molecule transition events.Comment: 8 pages, 3 figure

Multiplexing Biochemical Signals

Wolde, P.R. ten [Promotor

Local similarity in the stable boundary layer and mixing-length approaches: consistency of concepts

In stably stratified flows vertical movement of eddies is limited by the fact that kinetic energy is converted into potential energy, leading to a buoyancy displacement scale z B . Our new mixing-length concept for turbulent transport in the stable boundary layer follows a rigid-wall analogy, in the sense that we assume that the buoyancy length scale is similar to neutral length scaling. This implies that the buoyancy length scale is: ¿ B = ¿ B z B , with ¿ B ¿ ¿, the von Karman constant. With this concept it is shown that the physical relevance of the local scaling parameter z/¿ naturally appears, and that the ¿ coefficient of the log-linear similarity functions is equal to c/¿ 2, where c is a constant close to unity. The predicted value ¿ ¿ 1/¿ 2 = 6.25 lies within the range found in observational studies. Finally, it is shown that the traditionally used inverse linear interpolation between the mixing length in the neutral and buoyancy limits is inconsistent with the classical log-linear stability functions. As an alternative, a log-linear consistent interpolation method is proposed

Local Similarity in the Stable Boundary Layer and Mixing-Length Approaches: Consistency of Concepts

In stably stratified flows vertical movement of eddies is limited by the fact that kinetic energy is converted into potential energy, leading to a buoyancy displacement scale z B . Our new mixing-length concept for turbulent transport in the stable boundary layer follows a rigid-wall analogy, in the sense that we assume that the buoyancy length scale is similar to neutral length scaling. This implies that the buoyancy length scale is: ? B = ? B z B , with ? B ? ?, the von Karman constant. With this concept it is shown that the physical relevance of the local scaling parameter z/? naturally appears, and that the ? coefficient of the log-linear similarity functions is equal to c/? 2, where c is a constant close to unity. The predicted value ? ? 1/? 2 = 6.25 lies within the range found in observational studies. Finally, it is shown that the traditionally used inverse linear interpolation between the mixing length in the neutral and buoyancy limits is inconsistent with the classical log-linear stability functions. As an alternative, a log-linear consistent interpolation method is proposed.Department of Multi-Scale PhysicsApplied Science