Particle-particle particle-mesh method for dipolar interactions: On error estimates and efficiency of schemes with analytical differentiation and mesh interlacing J. Chem. Phys. 135, 184110 (2011) Revisiting falloff curves of thermal unimolecular reactions J. Chem. Phys. 135, 054304 (2011) Collision limited reaction rates for arbitrarily shaped particles across the entire diffusive Knudsen number range J. Chem. Phys. 135, 054302 (2011) Simulating structural transitions by direct transition current sampling: The example of LJ38 J. Chem. Phys. 135, 034108 (2011) Optimizing transition interface sampling simulations J. Chem. Phys. 134, 244118 (2011) Additional information on J. Chem. Phys. A mechanism for the kinetic instabilities observed in the galvanostatic electro-oxidation of methanol is suggested and a model developed. The model is investigated using stoichiometric network analysis as well as concepts from algebraic geometry ͑polynomial rings and ideal theory͒ revealing the occurrence of a Hopf and a saddle-node bifurcation. These analytical solutions are confirmed by numerical integration of the system of differential equations.
Lorenz curves of bubble size distributions and their Gini coefficients characterize demixing processes. Through a systematic size classification, bubble size histograms are generated and investigated concerning their statistical entropy. It turns out that the temporal development of the entropy is preserved although characteristics of the histograms like number of size classes and modality are remarkably reduced. Examinations by Rényi dimensions show that the bubble size distributions are multifractal and provide information about the underlying structures like self-similarity.
For the description of complex dynamics of open systems, an approach is given by different concepts of majorization order structure . Discrete diffusion processes with both invariant object number and sink or source can be represented by the development of Young diagrams on lattices.As an experimental example, we investigated foam decay, dominated by sinks. The relevance of order structures for the characterization of certain processes is discussed.
We present different methods to characterise the decay of beer foam by measuring the foam heights and recording foam images as a function of time. It turns out that the foam decay does not follow a simple exponential law but a higher-order equation ln V (t) = a − bt − ct 2.5 , which can be explained as a superposition of two processes, that is, drainage and bubble rearrangement. The reorganisation of bubbles leads to the structure of an Apollonian gasket with a fractal dimension of D ≈ 1.3058. Starting from foam images, we study the temporal development of bubble size distributions and give a model for the evolution towards the equilibrium state based upon the idea of Ernst Ruch to describe irreversible processes by lattices of Young diagrams. These lattices generally involve a partial order, but one can force a total order by mapping the diagrams onto the interval [0,1] using ordering functions such as the Shannon entropy. Several entropy-like and nonentropy-like mixing functions are discussed in comparison with the Young order, each of them giving a special prejudice for understanding the process of structure formation during beer foam decay.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.