Oxygen transport and consumption in germinating seeds

Three mathematical models were formulated to describe the oxygen con-sumption of seeds during germination. These models were fitted to measure-ment data of oxygen consumption curves for individual germinating seeds of Savoy cabbage, barley and sugar beet provided by Fytagoras. The first model builds on a logistic growth model for the increasing population of mitochondria in the embryo during growth. The other two take the anatomy and physiologi-cal properties of the seed into account. One describes the oxygen uptake during the germination phase only. An extension of this model is capable of fitting the complete oxygen consumption curve, including the initial ‘repair’ phase in which the embryonic cells recover from their dormant state before extensive cell division and growth commences. Keywords: Modelling, seed germination, cellular respiration, oxygen transpor

Continuation for thin film hydrodynamics and related scalar problems

This chapter illustrates how to apply continuation techniques in the analysis of a particular class of nonlinear kinetic equations that describe the time evolution through transport equations for a single scalar field like a densities or interface profiles of various types. We first systematically introduce these equations as gradient dynamics combining mass-conserving and nonmass-conserving fluxes followed by a discussion of nonvariational amendmends and a brief introduction to their analysis by numerical continuation. The approach is first applied to a number of common examples of variational equations, namely, Allen-Cahn- and Cahn-Hilliard-type equations including certain thin-film equations for partially wetting liquids on homogeneous and heterogeneous substrates as well as Swift-Hohenberg and Phase-Field-Crystal equations. Second we consider nonvariational examples as the Kuramoto-Sivashinsky equation, convective Allen-Cahn and Cahn-Hilliard equations and thin-film equations describing stationary sliding drops and a transversal front instability in a dip-coating. Through the different examples we illustrate how to employ the numerical tools provided by the packages auto07p and pde2path to determine steady, stationary and time-periodic solutions in one and two dimensions and the resulting bifurcation diagrams. The incorporation of boundary conditions and integral side conditions is also discussed as well as problem-specific implementation issues

Optimized structure and vibrational properties by error affected potential energy surfaces

The precise theoretical determination of the geometrical parameters of molecules at the minima of their potential energy surface and of the corresponding vibrational properties are of fundamental importance for the interpretation of vibrational spectroscopy experiments. Quantum Monte Carlo techniques are correlated electronic structure methods promising for large molecules, which are intrinsically affected by stochastic errors on both energy and force calculations, making the mentioned calculations more challenging with respect to other more traditional quantum chemistry tools. To circumvent this drawback in the present work, we formulate the general problem of evaluating the molecular equilibrium structures, the harmonic frequencies, and the anharmonic coefficients of an error affected potential energy surface. The proposed approach, based on a multidimensional fitting procedure, is illustrated together with a critical evaluation of systematic and statistical errors. We observe that the use of forces instead of energies in the fitting procedure reduces the statistical uncertainty of the vibrational parameters by 1 order of magnitude. Preliminary results based on variational Monte Carlo calculations on the water molecule demonstrate the possibility to evaluate geometrical parameters and harmonic and anharmonic coefficients at this level of theory with an affordable computational cost and a small stochastic uncertainty (<0.07% for geometries and <0.7% for vibrational properties). © 2012 American Chemical Society

Global Stability and Local Bifurcations in a Two-Fluid Model for Tokamak Plasma

International audienc

Global Stability and Local Bifurcations in a Two-Fluid Model for Tokamak

We study a two-fluid description for high and low temperature components of the electron velocity distribution in an idealized tokamak plasma evolving on a cylindrical domain, taking into account nonlinear drift effects only. We refine previous results on the laminar steady state stability and include viscosity. Taking the temperature difference as the primary parameter, we show that linear instabilities and bifurcations occur within a finite interval and for small enough viscosity only, while the steady state is globally stable for parameters sufficiently far outside the interval. We find that primary instabilities always stem from the lowest spatial harmonics for aspect ratios of poloidal versus radial extent below some value larger than 2. Moreover, we show that any codimension-one bifurcation of the laminar state is supercritical, yielding spatio-temporal oscillations in the form of traveling waves, and hence locally stable for such bifurcations destabilizing the laminar state. In the degenerate case, where the instability region in the temperature difference is a point, these solutions form an arc connecting the bifurcation points. We also provide numerical simulations to illustrate and corroborate the analysis and find additional bifurcations of the traveling waves