General theory of instabilities for patterns with sharp interfaces in reaction-diffusion systems

An asymptotic method for finding instabilities of arbitrary $d$-dimensional large-amplitude patterns in a wide class of reaction-diffusion systems is presented. The complete stability analysis of 2- and 3-dimensional localized patterns is carried out. It is shown that in the considered class of systems the criteria for different types of instabilities are universal. The specific nonlinearities enter the criteria only via three numerical constants of order one. The performed analysis explains the self-organization scenarios observed in the recent experiments and numerical simulations of some concrete reaction-diffusion systems.Comment: 21 pages (RevTeX), 8 figures (Postscript). To appear in Phys. Rev. E (April 1st, 1996

Low activities of digestive enzymes in the guts of herbivorous grouse (Aves: Tetraoninae)

Avian herbivores face the exceptional challenge of digesting recalcitrant plant material while under the selective pressure to reduce gut mass as an adaptation for fight. One mechanism by which avian herbivores may overcome this challenge is to maintain high activities of intestinal enzymes that facilitate the digestion and absorption of nutrients. However, previous studies in herbivorous animals provide equivocal evidence as to how activities of digestive enzymes may be adapted to herbivorous diets. For example, “rate-maximizing” herbivores generally exhibit rapid digesta transit times and high activities of digestive enzymes. Conversely, “yield-maximizing” herbivores utilize long gut retention times and express lower activities of digestive enzymes. Here, we investigated the activities of digestive enzymes (maltase, sucrase, aminopeptidase-N) in the guts of herbivorous grouse (Aves: Tetraoninae) and compared them to activities measured in several other avian species. We found that several grouse species exhibit activities of enzymes that are dramatically lower than those measured in other birds. We propose that grouse may use a “yield-maximizing” strategy of digestion, which is characterized by relatively long gut retention times and generally lower enzyme activities. These low activities of intestinal digestive enzyme could have ecological and evolutionary consequences, as grouse regularly consume plants with compounds known to inhibit digestive enzymes. However, more comprehensive studies on passage rates, digestibility, and microbial contributions will be necessary to understand the full process of digestion in herbivorous birds.acceptedVersio

Breathing Current Domains in Globally Coupled Electrochemical Systems: A Comparison with a Semiconductor Model

Spatio-temporal bifurcations and complex dynamics in globally coupled intrinsically bistable electrochemical systems with an S-shaped current-voltage characteristic under galvanostatic control are studied theoretically on a one-dimensional domain. The results are compared with the dynamics and the bifurcation scenarios occurring in a closely related model which describes pattern formation in semiconductors. Under galvanostatic control both systems are unstable with respect to the formation of stationary large amplitude current domains. The current domains as well as the homogeneous steady state exhibit oscillatory instabilities for slow dynamics of the potential drop across the double layer, or across the semiconductor device, respectively. The interplay of the different instabilities leads to complex spatio-temporal behavior. We find breathing current domains and chaotic spatio-temporal dynamics in the electrochemical system. Comparing these findings with the results obtained earlier for the semiconductor system, we outline bifurcation scenarios leading to complex dynamics in globally coupled bistable systems with subcritical spatial bifurcations.Comment: 13 pages, 11 figures, 70 references, RevTex4 accepted by PRE http://pre.aps.or

An adjoint method for the assimilation of statistical characteristics into eddy-resolving ocean models

The study investigates perspectives of the parameter estimation problem with the adjoint method in eddy-resolving models. Sensitivity to initial conditions resulting from the chaotic nature of this type of model limits the direct application of the adjoint method by predictability. Prolonging the period of assimilation is accompanied by the appearance of an increasing number of secondary minima of the cost function that prevents the convergence of this method. In the framework of the Lorenz model it is shown that averaged quantities are suitable for describing invariant properties, and that secondary minima are for this type of data transformed into stochastic deviations. An adjoint method suitable for the assimilation of statistical characteristics of data and applicable on time scales beyond the predictability limit is presented. The approach assumes a greater predictability for averaged quantities. The adjoint to a prognostic model for statistical moments is employed for calculating cost function gradients that ignore the fine structure resulting from secondary minima. Coarse resolution versions of eddy-resolving models are used for this purpose. Identical twin experiments are performed with a quasigeostrophic model to evaluate the performance and limitations of this approach in improving models by estimating parameters. The wind stress curl is estimated from a simulated mean stream function. A very simple parameterization scheme for the assimilation of second-order moments is shown to permit the estimation of gradients that perform efficiently in minimizing cost functions

The common VWF single nucleotide variants c.2365A>G and c.2385T>C modify VWF biosynthesis and clearance

Thrombosis and Hemostasi