Adiabatic Decoupling and Time-Dependent Born-Oppenheimer Theory

We reconsider the time-dependent Born-Oppenheimer theory with the goal to carefully separate between the adiabatic decoupling of a given group of energy bands from their orthogonal subspace and the semiclassics within the energy bands. Band crossings are allowed and our results are local in the sense that they hold up to the first time when a band crossing is encountered. The adiabatic decoupling leads to an effective Schroedinger equation for the nuclei, including contributions from the Berry connection.Comment: Revised version. 19 pages, 2 figure

Space-Adiabatic Perturbation Theory

We study approximate solutions to the Schr\"odinger equation i\epsi\partial\psi_t(x)/\partial t = H(x,-i\epsi\nabla_x) \psi_t(x) with the Hamiltonian given as the Weyl quantization of the symbol $H(q,p)$ taking values in the space of bounded operators on the Hilbert space \Hi_{\rm f} of fast ``internal'' degrees of freedom. By assumption $H(q,p)$ has an isolated energy band. Using a method of Nenciu and Sordoni \cite{NS} we prove that interband transitions are suppressed to any order in \epsi. As a consequence, associated to that energy band there exists a subspace of L^2(\mathbb{R}^d,\Hi _{\rm f}) almost invariant under the unitary time evolution. We develop a systematic perturbation scheme for the computation of effective Hamiltonians which govern approximately the intraband time evolution. As examples for the general perturbation scheme we discuss the Dirac and Born-Oppenheimer type Hamiltonians and we reconsider also the time-adiabatic theory.Comment: 49 page

Condensation in the zero range process: stationary and dynamical properties

The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between particles. We rigorously prove that for the stationary probability measure there is a background phase at some critical density and for large system size essentially all excess particles accumulate at a single, randomly located site. Using random walk arguments supported by Monte Carlo simulations, we also study the dynamics of the clustering process with particular attention to the difference between symmetric and asymmetric jump rates. For the late stage of the clustering we derive an effective master equation, governing the occupation number at clustering sites.Comment: 22 pages, 4 figures, to appear in J. Stat. Phys.; improvement of presentation and content of Theorem 2, added reference

Contact angle of sessile drops in Lennard-Jones systems

Molecular dynamics simulation is used for studying the contact angle of nanoscale sessile drops on a planar solid wall in a system interacting via the truncated and shifted Lennard-Jones potential. The entire range between total wetting and dewetting is investigated by varying the solid--fluid dispersive interaction energy. The temperature is varied between the triple point and the critical temperature. A correlation is obtained for the contact angle in dependence of the temperature and the dispersive interaction energy. Size effects are studied by varying the number of fluid particles at otherwise constant conditions, using up to 150 000 particles. For particle numbers below 10 000, a decrease of the contact angle is found. This is attributed to a dependence of the solid-liquid surface tension on the droplet size. A convergence to a constant contact angle is observed for larger system sizes. The influence of the wall model is studied by varying the density of the wall. The effective solid-fluid dispersive interaction energy at a contact angle of 90 degrees is found to be independent of temperature and to decrease linearly with the solid density. A correlation is developed which describes the contact angle as a function of the dispersive interaction, the temperature and the solid density. The density profile of the sessile drop and the surrounding vapor phase is described by a correlation combining a sigmoidal function and an oscillation term

Propulsion Mechanisms for Leidenfrost Solids on Ratchets

We propose a model for the propulsion of Leidenfrost solids on ratchets based on viscous drag due to the flow of evaporating vapor. The model assumes pressure-driven flow described by the Navier-Stokes equations and is mainly studied in lubrication approximation. A scaling expression is derived for the dependence of the propulsive force on geometric parameters of the ratchet surface and properties of the sublimating solid. We show that the model results as well as the scaling law compare favorably with experiments and are able to reproduce the experimentally observed scaling with the size of the solid

Integration Deficits of IT Controlling – Historical Background, Analysis of Integration Potentials and Method Integration

The paper is based on the thesis that IT controlling suffers from two integration deficits with regard to its methods base: On the one hand, this is a lack of synchronization between research on IT controlling methods and developments in practice; on the other hand, a lack of integration of IT controlling methods with methods of business and information systems engineering (BISE). Based on this assumption, the paper investigates historical developments in IT controlling research and practice to derive theses about the present state of method integration. The analysis finds indications for further potential for method integration and identifies these potentials. Requirements towards method integration are derived from an analysis of the identified integration potentials and two examples illustrate how to realize further integration

Digital Innovation Champions: Which Champions drive the Usage of Digital Innovation Management Systems and its Impact on New Product Development Performance

Managers and researchers lack an understanding of how specific new product development (NPD) software champions, i.e. digital innovation champions, function. This is particularly the case for digital innovation management systems (DIMS). Innovation, R&D, and IT managers and top management all might take distinct roles that influence the usage of such software. These distinct roles suggest the need for more detailed investigations of 1) which champions drive the usage of DIMS, 2) if they enhance distinct NPD applications, and 3) the links to NPD performance. This study addresses this need by developing and analyzing hypotheses for the role of digital innovation champions for DIMS usage. Therefore, the authors use unique survey data from managers together with objective patent and revenue data. The results reveal that executives as digital innovation champions encourage the usage and NPD performance of DIMS, whereas, IT and R&D managers can even hinder these outcomes