On the density of states and extinction mean free path of waves in random media: Dispersion relations and sum rules

We establish a fundamental relationship between the averaged density of states and the extinction mean free path of wave propagating in random media. From the principle of causality and the Kramers-Kronig relations, we show that both quantities are connected by dispersion relations and are constrained by a frequency sum rule. The results are valid under very general conditions and should be helpful in the analysis of measurements of wave transport through complex systems and in the design of randomly or periodically structured materials with specific transport properties.Comment: 2 (double) figures, 8 page

Systematic Derivation of Amplitude Equations and Normal Forms for Dynamical Systems

We present a systematic approach to deriving normal forms and related amplitude equations for flows and discrete dynamics on the center manifold of a dynamical system at local bifurcations and unfoldings of these. We derive a general, explicit recurrence relation that completely determines the amplitude equation and the associated transformation from amplitudes to physical space. At any order, the relation provides explicit expressions for all the nonvanishing coefficients of the amplitude equation together with straightforward linear equations for the coefficients of the transformation. The recurrence relation therefore provides all the machinery needed to solve a given physical problem in physical terms through an amplitude equation. The new result applies to any local bifurcation of a flow or map for which all the critical eigenvalues are semisimple i.e. have Riesz index unity). The method is an efficient and rigorous alternative to more intuitive approaches in terms of multiple time scales. We illustrate the use of the method by deriving amplitude equations and associated transformations for the most common simple bifurcations in flows and iterated maps. The results are expressed in tables in a form that can be immediately applied to specific problems.Comment: 40 pages, 1 figure, 4 tables. Submitted to Chaos. Please address any correspondence by email to [email protected]

Phase chaos in the anisotropic complex Ginzburg-Landau Equation

Of the various interesting solutions found in the two-dimensional complex Ginzburg-Landau equation for anisotropic systems, the phase-chaotic states show particularly novel features. They exist in a broader parameter range than in the isotropic case, and often even broader than in one dimension. They typically represent the global attractor of the system. There exist two variants of phase chaos: a quasi-one dimensional and a two-dimensional solution. The transition to defect chaos is of intermittent type.Comment: 4 pages RevTeX, 5 figures, little changes in figures and references, typos removed, accepted as Rapid Commun. in Phys. Rev.

Propagating semantic information in biochemical network models

<p>Abstract</p> <p>Background</p> <p>To enable automatic searches, alignments, and model combination, the elements of systems biology models need to be compared and matched across models. Elements can be identified by machine-readable biological annotations, but assigning such annotations and matching non-annotated elements is tedious work and calls for automation.</p> <p>Results</p> <p>A new method called "semantic propagation" allows the comparison of model elements based not only on their own annotations, but also on annotations of surrounding elements in the network. One may either propagate feature vectors, describing the annotations of individual elements, or quantitative similarities between elements from different models. Based on semantic propagation, we align partially annotated models and find annotations for non-annotated model elements.</p> <p>Conclusions</p> <p>Semantic propagation and model alignment are included in the open-source library semanticSBML, available on sourceforge. Online services for model alignment and for annotation prediction can be used at <url>http://www.semanticsbml.org</url>.</p

Testing Biochemistry Revisited: How In Vivo Metabolism Can Be Understood from In Vitro Enzyme Kinetics

A decade ago, a team of biochemists including two of us, modeled yeast glycolysis and showed that one of the most studied biochemical pathways could not be quite understood in terms of the kinetic properties of the constituent enzymes as measured in cell extract. Moreover, when the same model was later applied to different experimental steady-state conditions, it often exhibited unrestrained metabolite accumulation