Analytical Model of the Time Developing Turbulent Boundary Layer

We present an analytical model for the time-developing turbulent boundary layer (TD-TBL) over a flat plate. The model provides explicit formulae for the temporal behavior of the wall-shear stress and both the temporal and spatial distributions of the mean streamwise velocity, the turbulence kinetic energy and Reynolds shear stress. The resulting profiles are in good agreement with the DNS results of spatially-developing turbulent boundary layers at momentum thickness Reynolds number equal to 1430 and 2900. Our analytical model is, to the best of our knowledge, the first of its kind for TD-TBL.Comment: 5pages, 9 figs, JETP Letters, submitte

Empathes: A general code for nudged elastic band transition states search

An easy and flexible interface, Empathes (Extensible Minimum PATH EStimator), that allows to perform Nudged Elastic Band calculation for the determination of transition states is presented. The code is designed to be easily modified, in order to be associated with the user's preferred calculation software, even with those which implement composite approaches. In particular, the interfaces to Gaussian and Siesta programs are discussed in details, being the former only used for testing purpose, while the latter can be productively employed for transition states search with that commonly used density functional theory software for periodic calculations. Program summary: Program Title: Empathes CPC Library link to program files: https://doi.org/10.17632/v525mwf3cc.1 Developer's repository link: https://github.com/marberti/empathes Code Ocean capsule: https://codeocean.com/capsule/2394233 Licensing provisions: GPLv3 Programming language: Fortran 08 Nature of problem: The search for the structure of transition states through computational methods, essentially based on Density Functional Theory, is of overwhelming importance for the determination of the elementary steps forming a reaction mechanism. Allowing to develop basic knowledge, these investigations can be used to direct experimentalists towards a more efficient realization of chemical compounds synthetic processes. In cases where it is necessary to describe the reactive system through periodic calculations, which is very common in heterogeneous catalysis, this research must be done through the use of non-analytical methods. Solution method: In case of lacking of analytical procedures, the search for the transition states associated with the elementary stages that make up chemical reactions must take place through numerical methods. The Nudged Elastic Band (NEB) approach is, together with its variants, one of the most used for this purpose. In accordance with the NEB algorithm, a chain of geometric structures, generated by interpolating between the reactant and product geometries and joined by fictitious springs, is relaxed on the minimum energy path, allowing the association of the transition state to the maximum along this path. The NEB method involves the determination of molecular energies and forces acting on the nuclei of the system, which is generally carried out through a program for electronic structure calculation. The present code is a useful general interface