Infusion pasteurization of skim milk: Effects of different time-temperature combinations

Infusion pasteurization technology was used in different time-temperature combinations for heat treatment of skim milk and compared to untreated skim milk and a standard pasteurization treatment. Aerobic count of microorganisms and activity of alkaline phosphatase showed that all infusion-pasteurized samples had received proper pasteurization. There were no difference in the size of casein micelles, but differences were seen in activity of the enzyme xanthine oxidase. The results indicate possible differences in properties of infusion-pasteurized skim milk compared to standard pasteurized skim milk

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]

Dynamical properties of chemical systems near Hopf bifurcation points

In this paper, we numerically investigate local properties of dynamical systems close to a Hopf bifurcation instability. We focus on chemical systems and present an approach based on the theory of normal forms for determining numerical estimates of the limit cycle that branches off at the Hopf bifurcation point. For several numerically ill-conditioned examples taken from chemical kinetics, we compare our results with those obtained by using traditional approaches where an approximation of the limit cycle is restricted to the center subspace spanned by critical eigenvectors, and show that inclusion of higher-order terms in the normal form expansion of the limit cycle provides a significant improvement of the limit cycle estimates. This result also provides an accurate initial estimate for subsequent numerical continuation of the limit cycle

Finite Wavelength Instabilities in a Slow Mode Coupled Complex Ginzburg-Landau Equation

In this Letter, we discuss the effect of slow real modes in reaction-diffusion systems close to a supercritical Hopf bifurcation. The spatiotemporal effects of the slow mode cannot be captured by traditional descriptions in terms of a single complex Ginzburg-Landau equation (CGLE). We show that the slow mode coupling to the CGLE introduces a novel set of finite wavelength instabilities not present in the CGLE. For spiral waves, these instabilities highly affect the location of regions for convective and absolute instability. These new instability boundaries are consistent with transitions to spatiotemporal chaos found by simulation of the corresponding coupled amplitude equations

Geographic Variation of Cirques on Iceland: Factors Influencing Cirque Morphology

Cirques are one of the most common glacial landforms in alpine settings. They also provide important paleoclimate information (e.g. Meierding 1984; Evans 2006). The purpose of this study is to fill in gaps in the climate record of Iceland by conducting a quantitative analysis of cirques in three regions in Iceland: Tröllaskagi, the East Fjords, and Vestfirðir. Iceland, located in the center of the North Atlantic Ocean, contains many small glaciers, in addition to large ice caps. The glaciers on Iceland are particularly sensitive to variations in oceanic and atmospheric circulation (Andresen et al. 2005; Geirsdóttir et al., 2009; Ólafsdóttir et al. 2010). Iceland thus provides an excellent case study to examine factors influencing glacial landforms such as cirques. (excerpt

Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems

Approximate Bayesian computation methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper we discuss and apply an approximate Bayesian computation (ABC) method based on sequential Monte Carlo (SMC) to estimate parameters of dynamical models. We show that ABC SMC gives information about the inferability of parameters and model sensitivity to changes in parameters, and tends to perform better than other ABC approaches. The algorithm is applied to several well known biological systems, for which parameters and their credible intervals are inferred. Moreover, we develop ABC SMC as a tool for model selection; given a range of different mathematical descriptions, ABC SMC is able to choose the best model using the standard Bayesian model selection apparatus.Comment: 26 pages, 9 figure

Self-organized stable pacemakers near the onset of birhythmicity

General amplitude equations for reaction-diffusion systems near to the soft onset of birhythmicity described by a supercritical pitchfork-Hopf bifurcation are derived. Using these equations and applying singular perturbation theory, we show that stable autonomous pacemakers represent a generic kind of spatiotemporal patterns in such systems. This is verified by numerical simulations, which also show the existence of breathing and swinging pacemaker solutions. The drift of self-organized pacemakers in media with spatial parameter gradients is analytically and numerically investigated.Comment: 4 pages, 4 figure

A Bayesian conjugate gradient method (with Discussion)

A fundamental task in numerical computation is the solution of large linear systems. The conjugate gradient method is an iterative method which offers rapid convergence to the solution, particularly when an effective preconditioner is employed. However, for more challenging systems a substantial error can be present even after many iterations have been performed. The estimates obtained in this case are of little value unless further information can be provided about the numerical error. In this paper we propose a novel statistical model for this numerical error set in a Bayesian framework. Our approach is a strict generalisation of the conjugate gradient method, which is recovered as the posterior mean for a particular choice of prior. The estimates obtained are analysed with Krylov subspace methods and a contraction result for the posterior is presented. The method is then analysed in a simulation study as well as being applied to a challenging problem in medical imaging