Variable ventilation ages in the equatorial Indian Ocean thermocline during the LGM

Variations of atmospheric CO₂ during the Pleistocene ice-ages have been associated with changes in the drawdown of carbon into the deep-sea. Modelling studies suggest that about one third of the glacial carbon drawdown may not be associated to the deep ocean, but to the thermocline or intermediate ocean. However, the carbon storage capacity of thermocline waters is still poorly constrained. Here we present paired ²³⁰Th/U and ¹⁴C measurements on scleractinian cold-water corals retrieved from ~ 450 m water depth off the Maldives in the Indian Ocean. Based on these measurements we calculate ∆¹⁴C, ∆∆¹⁴C and Benthic-Atmosphere (B_atm) ages in order to understand the ventilation dynamics of the equatorial Indian Ocean thermocline during the Last Glacial Maximum (LGM). Our results demonstrate a radiocarbon depleted thermocline as low as -250 to -345‰ (∆∆¹⁴C), corresponding to ~ 500-2100 years (B_atm) old waters at the LGM compared to ~ 380 years today. More broadly, we show that thermocline ventilation ages are one order of magnitude more variable than previously thought. Such a radiocarbon depleted thermocline can at least partly be explained by variable abyssal upwelling of deep-water masses with elevated respired carbon concentrations. Our results therefore have implications for radiocarbon-only based age models and imply that upper thermocline waters as shallow as 400 m depth can also contribute to some of the glacial carbon drawdown.

Spiral defect chaos in an advection-reaction-diffusion system

This paper comprises numerical and theoretical studies of spatiotemporal patterns in advection-reaction-diffusion systems in which the chemical species interact with the hydrodynamic fluid. Due to the interplay between the two, we obtained the spiral defect chaos in the activator-inhibitor-type model. We formulated the generalized Swift-Hohenberg-type model for this system. Then the evolution of fractal boundaries due to the effect of the strong nonlinearity at the interface of the two chemical species is studied numerically. The purpose of the present paper is to point out that spiral defect chaos, observed in model equations of the extended Swift-Hohenberg equation for low Prandtl number convection, may actually be obtained also in certain advection-reaction-diffusion systems.

Generalized vortex model for the inverse cascade of two-dimensional turbulence

We generalize Kirchhoff's point vortex model of two-dimensional fluid motion to a rotor model which exhibits an inverse cascade by the formation of rotor clusters. A rotor is composed of two vortices with like-signed circulations glued together by an overdamped spring. The model is motivated by a treatment of the vorticity equation representing the vorticity field as a superposition of vortices with elliptic Gaussian shapes of variable widths, augmented by a suitable forcing mechanism. The rotor model opens up the way to discuss the energy transport in the inverse cascade on the basis of dynamical systems theory.

Instabilities of localized structures in dissipative systems with delayed feedback

We report on a novel behavior of solitary localized structures in a real Swift-Hohenberg equation subjected to a delayed feedback. We shall show that variation in the product of the delay time and the feedback strength leads to nontrivial instabilities resulting in the formation of oscillons, soliton rings, labyrinth patterns, or moving structures. We provide a bifurcation analysis of the delayed system and derive a system of order parameter equations explicitly describing the temporal behavior of the localized structure in the vicinity of the bifurcation point. We demonstrate that a normal form of the bifurcation, responsible for the emergence of moving solitary structures, can be obtained and show that spontaneous motion to the lowest order occurs without change of the shape.

Langevin description of superdiffusive Lévy processes

The description of diffusion processes is possible in different frameworks such as random walks or Fokker-Planck or Langevin equations. Whereas for classical diffusion the equivalence of these methods is well established, in the case of anomalous diffusion it often remains an open problem. In this paper we aim to bring three approaches describing anomalous superdiffusive behavior to a common footing. While each method clearly has its advantages it is crucial to understand how those methods relate and complement each other. In particular, by using the method of subordination, we show how the Langevin equation can describe anomalous diffusion exhibited by Lévy-walk-type models and further show the equivalence of the random walk models and the generalized Kramers-Fokker-Planck equation. As a result a synergetic and complementary description of anomalous diffusion is obtained which provides a much more flexible tool for applications in real-world systems.

[IOL multifocality combined with the compensation for corneal spherical aberration: a new concept of presbyopia correcting IOL]

Further developments in the field of intraocular lenses have resulted in improvements of multifocal lenses (MIOL) which enable spectacle-free vision at near and far distance under most conditions. In our prospective study we investigated a new aberration-corrected MIOL, whereby 31 eyes of 19 patients, aged between 40 and 81 years, received a Tecnis ZMB00 MIOL (Abbott Medical Optics). Postoperative visual results were documented. Patients were enrolled if they were at least 40 years old and if they were scheduled for cataract surgery or presbyobic lens exchange. Exclusion criteria were any other visually relevant pathologies and a corneal astigmatism of 1.5 D or more. After 6 months, 94.7 % of the patients had a binocular uncorrected distance vision of 0.1 LogMAR or better, 67.7 % of eyes could read Jaeger 1+ (0.0 LogMAR) and 93.6 % could read Jaeger 1 (0.1 LogMAR) or better. There was no correlation between the power of the implanted lens and the postoperative distance or near vision or between IOL power and best-corrected distance vision. The aspheric diffractive multifocal IOL Tecnis ZMB00 provides a restoration of far and near visual function after cataract surgery or presbyopia correction. The correction provided by the IOL is predictable and independent from the optical power of the IOL implanted. The combination of diffractive multifocality and compensation for corneal spherical aberration is an effective alternative for cataract surgery and presbyopia correction.

Statistical analysis of global wind dynamics in vigorous Rayleigh-Bénard convection

Experimental and numerical studies of thermal convection have shown that sufficiently vigorous convective flows exhibit a large-scale thermal wind component sweeping along small-scale thermal boundary layer instabilities. A characteristic feature of these flows is an intermittent behavior in the form of irregular reversals in the orientation of the large-scale circulation. There have been several attempts toward a better understanding and description of the phenomenon of flow reversals, but so far most of these models are based on a statistical analysis of few-point measurements or on simplified theoretical assumptions. The analysis of long-term data sets (>5×10(5) turnover times τ(t)=d/u(rms)) obtained by numerical simulations of turbulent two-dimensional Rayleigh-Bénard convection allows us to get a more comprehensive view of the spatio-temporal flow behavior. By means of a global statistical analysis of the characteristic spatial modes of the flow we extract information about the stability of dominant large-scale modes as well as the reversal paths in state subspace. We examine probability density functions and drift vector fields of two-dimensional state subspaces spanned by different large-scale spatial modes. This also provides information about the coexistence of dominant modes.

Different methods to estimate the Einstein-Markov coherence length in turbulence

We study the Markov property of experimental velocity data of different homogeneous isotropic turbulent flows. In particular, we examine the stochastic "cascade" process of nested velocity increments ξ(r):=u(x+r)-u(x) as a function of scale r for different nesting structures. It was found in previous work that, for a certain nesting structure, the stochastic process of ξ(r) has the Markov property for step sizes larger than the so-called Einstein-Markov coherence length l(EM), which is of the order of magnitude of the Taylor microscale λ [Phys. Lett. A 359, 335 (2006)]. We now show that, if a reasonable definition of the effective step size of the process is applied, this result holds independently of the nesting structure. Furthermore, we analyze the stochastic process of the velocity u as a function of the spatial position x. Although this process does not have the exact Markov property, a characteristic length scale l(u(x))≈l(EM) can be identified on the basis of a statistical test for the Markov property. Using a method based on the matrix of transition probabilities, we examine the significance of the non-Markovian character of the velocity u(x) for the statistical properties of turbulence.

MEGAPOLI: concept of multi-scale modelling of megacity impact on air quality and climate

Abstract. The EU FP7 Project MEGAPOLI: "Megacities: Emissions, urban, regional and Global Atmospheric POLlution and climate effects, and Integrated tools for assessment and mitigation" (http://megapoli.info) brings together leading European research groups, state-of-the-art scientific tools and key players from non-European countries to investigate the interactions among megacities, air quality and climate. MEGAPOLI bridges the spatial and temporal scales that connect local emissions, air quality and weather with global atmospheric chemistry and climate. The suggested concept of multi-scale integrated modelling of megacity impact on air quality and climate and vice versa is discussed in the paper. It requires considering different spatial and temporal dimensions: time scales from seconds and hours (to understand the interaction mechanisms) up to years and decades (to consider the climate effects); spatial resolutions: with model down- and up-scaling from street- to global-scale; and two-way interactions between meteorological and chemical processes.

Extracting strong measurement noise from stochastic time series: applications to empirical data

It is a big challenge in the analysis of experimental data to disentangle the unavoidable measurement noise from the intrinsic dynamical noise. Here we present a general operational method to extract measurement noise from stochastic time series even in the case when the amplitudes of measurement noise and uncontaminated signal are of the same order of magnitude. Our approach is based on a recently developed method for a nonparametric reconstruction of Langevin processes. Minimizing a proper non-negative function, the procedure is able to correctly extract strong measurement noise and to estimate drift and diffusion coefficients in the Langevin equation describing the evolution of the original uncorrupted signal. As input, the algorithm uses only the two first conditional moments extracted directly from the stochastic series and is therefore suitable for a broad panoply of different signals. To demonstrate the power of the method, we apply the algorithm to synthetic as well as climatological measurement data, namely, the daily North Atlantic Oscillation index, shedding light on the discussion of the nature of its underlying physical processes.

Physics of brain dynamics: Fokker-Planck analysis reveals changes in EEG delta and theta activity during anaesthesia

We use drift and diffusion coefficients to reveal interactions between different oscillatory processes underlying a complex signal and apply the method to EEG delta and theta frequencies in the brain. By analysis of data recorded from rats during anaesthesia we consider the stability and basins of attraction of fixed points in the phase portrait of the deterministic part of the retrieved stochastic process. We show that different classes of dynamics are associated with deep and light anaesthesia, and we demonstrate that the predominant directionality of the interaction is such that theta drives delta.

Physics of brain dynamics: Fokker-Planck analysis reveals changes in EEG delta and theta activity during anaesthesia

We use drift and diffusion coefficients to reveal interactions between different oscillatory processes underlying a complex signal and apply the method to EEG delta and theta frequencies in the brain. By analysis of data recorded from rats during anaesthesia we consider the stability and basins of attraction of fixed points in the phase portrait of the deterministic part of the retrieved stochastic process. We show that different classes of dynamics are associated with deep and light anaesthesia, and we demonstrate that the predominant directionality of the interaction is such that theta drives delta.

Anomalous diffusion in a field of randomly distributed scatterers

We consider the motion of particles which are scattered by randomly distributed obstacles. In between scattering events the particles move uniformly. The governing master equation is obtained by mapping the problem onto a master equation which was previously devised for the description of anomalous diffusion of particles with inertia [R. Friedrich, Phys. Rev. Lett. 96, 230601 (2006)]. We show that for a scale-free distance distribution of scatterers a time-fractional master equation arises. The corresponding diffusion equation which exhibits a power-law diffusion coefficient is solved in d dimensions via the method of subordination.

Exact relation between Eulerian and Lagrangian velocity increment statistics

We present a formal connection between Lagrangian and Eulerian velocity increment distributions which is applicable to a wide range of turbulent systems ranging from turbulence in incompressible fluids to magnetohydrodynamic turbulence. For the case of the inverse cascade regime of two-dimensional turbulence we numerically estimate the transition probabilities involved in this connection. In this context we are able to directly identify the processes leading to strongly non-Gaussian statistics for the Lagrangian velocity increments.

Continuous-time random walks with internal dynamics and subdiffusive reaction-diffusion equations

We formulate the generalized master equation for a class of continuous-time random walks in the presence of a prescribed deterministic evolution between successive transitions. This formulation is exemplified by means of an advection-diffusion and a jump-diffusion scheme. Based on this master equation, we also derive reaction-diffusion equations for subdiffusive chemical species, using a mean-field approximation.

Lagrangian statistics in forced two-dimensional turbulence

We report on simulations of two-dimensional turbulence in the inverse energy cascade regime. Focusing on the statistics of Lagrangian tracer particles, scaling behavior of the probability density functions of velocity fluctuations is investigated. The results are compared to the three-dimensional case. In particular an analysis in terms of compensated cumulants reveals the transition from a strong non-Gaussian behavior with large tails to Gaussianity. The reported computation of correlation functions for the acceleration components sheds light on the underlying dynamics of the tracer particles.

Lagrangian particle statistics in turbulent flows from a simple vortex model

The statistics of Lagrangian particles in turbulent flows is considered in the framework of a simple vortex model. Here, the turbulent velocity field is represented by a temporal sequence of Burgers vortices of different circulation, strain, and orientation. Based on suitable assumptions about the vortices' statistical properties, the statistics of the velocity increments is derived. In particular, the origin and nature of small-scale intermittency in this model is investigated both numerically and analytically. We critically compare our results to experimental studies.

Continuous-time random walks: simulation of continuous trajectories

Continuous-time random walks have been developed as a straightforward generalization of classical random-walk processes. Some ten years ago, Fogedby introduced a continuous representation of these processes by means of a set of Langevin equations [H. C. Fogedby, Phys. Rev. E 50, 1657 (1994)]. The present work is devoted to a detailed discussion of Fogedby's model and presents its application for the robust numerical generation of sample paths of continuous time random-walk processes.

Improved estimation of Fokker-Planck equations through optimization

An improved method for the description of hierarchical complex systems by means of a Fokker-Planck equation is presented. In particular the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm for constraint problems is used to minimize the distance between the numerical solutions of the Fokker-Planck equation and the empirical probability density functions and thus to estimate properly the drift and diffusion term of the Fokker-Planck equation. The optimization routine is applied to a time series of velocity measurements obtained from a turbulent helium gas jet in order to demonstrate the benefits and to quantify the improvements of this optimization routine.

Langevin Approach to Fractional Diffusion Equations Including Inertial Effects

In recent years, several fractional generalizations of the usual Kramers-Fokker-Planck equation have been presented. Using an idea of Fogedby (Fogedby, H. C. Phys. Rev. E 1994, 50, 041103), we show how these equations are related to Langevin equations via the procedure of subordination.

Mean first passage time for a class of non-Markovian processes

We determine the probability distribution of the first passage time for a class of non-Markovian processes. This class contains, amongst others, the well-known continuous time random walk (CTRW), which is able to account for many properties of anomalous diffusion processes. In particular, we obtain the mean first passage time for CTRW processes with truncated power-law transition time distribution. Our treatment is based on the fact that the solutions of the non-Markovian master equation can be obtained via an integral transform from a Markovian Langevin process.

Markov analysis and Kramers-Moyal expansion of nonstationary stochastic processes with application to the fluctuations in the oil price

We describe a general method for analyzing a nonstationary stochastic process X(t) which, unlike many of the previous analysis methods, does not require X(t) to have any scaling feature. The method is used to study the fluctuations in the daily price of oil. It is shown that the returns time series, y(t)=ln[X(t+1)X(t)] , is a stationary and Markov process, characterized by a Markov time scale t_{M} . The coefficients of the Kramers-Moyal expansion for the probability density function P(y,tmid R:y_{0},t_{0}) are computed. P(y,tmid R:,y_{0},t_{0}) satisfies a Fokker-Planck equation, which is equivalent to a Langevin equation for y(t) that provides quantitative predictions for the oil price over times that are of the order of t_{M}. Also studied is the average frequency of positive-slope crossings, nu_{alpha};{+}=P(y_{i}>alpha,y_{i-1}<alpha) , for the returns, where T(alpha)=1nu_{alpha};{+} is the average waiting time for observing y(t)=alpha again.

Stochastic order parameter equation of isometric force production revealed by drift-diffusion estimates

We address two questions that are central to understanding human motor control variability: what kind of dynamical components contribute to motor control variability (i.e., deterministic and/or random ones), and how are those components structured? To this end, we derive a stochastic order parameter equation for isometric force production from experimental data using drift-diffusion estimates. We show that the force variability increases with the required force output because of a decrease of deterministic stability and an accompanying increase of noise intensity. A structural analysis reveals that the deterministic component consists of a linear control loop, while the random component involves a noise source that scales with force output. In addition, we present evidence for the existence of a subject-independent overall noise level of human isometric force production.

Exact solution of a generalized Kramers-Fokker-Planck equation retaining retardation effects

In order to describe non-Gaussian kinetics in weakly damped systems, the concept of continuous time random walks is extended to particles with finite inertia. One thus obtains a generalized Kramers-Fokker-Planck equation, which retains retardation effects, i.e., nonlocal couplings in time and space. It is shown that despite this complexity, exact solutions of this equation can be given in terms of superpositions of Gaussian distributions with varying variances. In particular, the long-time behavior of the respective low-order moments is calculated.

Anomalous diffusion of inertial, weakly damped particles

The anomalous (i.e., non-Gaussian) dynamics of particles subject to a deterministic acceleration and a series of "random kicks" is studied. Based on an extension of the concept of continuous time random walks to position-velocity space, a new fractional equation of the Kramers-Fokker-Planck type is derived. The associated collision operator necessarily involves a fractional substantial derivative, representing important nonlocal couplings in time and space. For the force-free case, a closed solution is found and discussed.

A new Puumala hantavirus subtype in rodents associated with an outbreak of Nephropathia epidemica in South-East Germany in 2004

A micro-epidemic of hantavirus infections occurred in Lower Bavaria, South-East Germany, starting in April 2004. While only three cases were registered from 2001 to 2003, a dramatically increased number of clinically apparent human hantavirus infections (n=38) was observed in 2004, plus seven additional cases by June 2005. To determine the reservoir responsible for the infections, a total of 43 rodents were trapped in Lower Bavaria. Serological and genetic investigations revealed that Puumala virus (PUUV) is dominant in the local population of bank voles. Partial PUUV S segment nucleotide sequences originating from bank voles at four different trapping sites in Lower Bavaria showed a low divergence (up to 3.1%). This is contrasted by a nucleotide sequence divergence of 14-16% to PUUV strains detected in Belgium, France, Slovakia or North-Western Germany. PUUV sequences from bank voles in Lower Bavaria represent a new PUUV subtype which seems to be responsible for the observed increase of human hantavirus infections in 2004-2005.

Theoretical analysis of destabilization resonances in time-delayed stochastic second-order dynamical systems and some implications for human motor control

A linear stochastic delay differential equation of second order is studied that can be regarded as a Kramers model with time delay. An analytical expression for the stationary probability density is derived in terms of a Gaussian distribution. In particular, the variance as a function of the time delay is computed analytically for several parameter regimes. Strikingly, in the parameter regime close to the parameter regime in which the deterministic system exhibits Hopf bifurcations, we find that the variance as a function of the time delay exhibits a sequence of pronounced peaks. These peaks are interpreted as delay-induced destabilization resonances arising from oscillatory ghost instabilities. On the basis of the obtained theoretical findings, reinterpretations of previous human motor control studies and predictions for future human motor control studies are provided.

The staphylocoagulase family of zymogen activator and adhesion proteins

Staphylocoagulase (SC) secreted by Staphylococcus aureus is a potent non-proteolytic activator of the blood coagulation zymogen prothrombin and the prototype of a newly established zymogen activator and adhesion protein (ZAAP) family. The conformationally activated SC.prothrombin complex specifically cleaves fibrinogen to fibrin, which propagates the growth of bacteria-fibrin-platelet vegetations in acute bacterial endocarditis. Our recent 2.2 A X-ray crystal structures of an active SC fragment [SC(1-325)] bound to the prothrombin zymogen catalytic domain, prethrombin 2, demonstrated that SC(1-325) represents a new type of non-proteolytic activator with a unique fold. The observed insertion of the SC(1-325) N-terminus into the 'Ile 16' cleft of prethrombin 2, which triggers the activating conformational change, provided the first unambiguous structural evidence for the 'molecular sexuality' mechanism of non-proteolytic zymogen activation. Based on the SC(1-325) fold, a new family of bifunctional zymogen activator and adhesion proteins was identified that possess N-terminal domains homologous to SC(1-325) and C-terminal domains that mediate adhesion to plasma or extracellular matrix proteins. Further investigation of the ZAAP family may lead to new insights into the mechanisms of bacterial factors that hijack zymogens of the human blood coagulation and fibrinolytic systems to promote and disseminate endocarditis and other infectious diseases.

Joint probability distributions for a class of non-Markovian processes

We consider joint probability distributions for the class of coupled Langevin equations introduced by Fogedby [H. C. Fogedby, Phys. Rev. E 50, 1657 (1994)]. We generalize well-known results for the single-time probability distributions to the case of N -time joint probability distributions. It is shown that these probability distribution functions can be obtained by an integral transform from distributions of a Markovian process. The integral kernel obeys a partial differential equation with fractional time derivatives reflecting the non-Markovian character of the process.

Methylation analysis of the neurofibromatosis type 1 (NF1) promoter in peripheral nerve sheath tumours

Peripheral nerve sheath tumours are hallmarks of neurofibromatosis type 1 (NF1). Development of plexiform neurofibromas to malignant peripheral nerve sheath tumours (MPNST) is common. The NF1 gene promoter harbours a hypomethylated CpG island. Thus, methylation changes may be involved in the development of different types of neurofibromas and malignant transformation. We investigated NF1-associated dermal (n=9) and plexiform neurofibromas (n=7), MPNST (n=5) and non-NF1 leucocyte samples (n=20) for their methylation pattern by bisulphite genomic sequencing. We could not find global hypermethylation in the NF1 promoter in our series. Nevertheless, site-specific methylation, involving transcription factor binding sites for SP1, CRE (-10), and AP-2, was observed. One region of the 5'-UTR (untranslated region) overlapping with a putative AP-2 binding site was methylated at 30-100% in 4/20 control samples. In conclusion, we did not find hypermethylation in NF1-associated tumours. Instead, low level methylation could parallel a global genomic hypomethylation in malignancy.

Fokker-Planck perspective on stochastic delay systems: exact solutions and data analysis of biological systems

Stochastic delay systems with additive noise are examined from the perspective of Fokker-Planck equations. For a linear system, the exact stationary probability density is derived by means of a delay Fokker-Planck equation. We show how to determine the delay equation of the linear system from experimental data, and corroborate a fundamental result previously obtained by Küchler and Mensch. We also propose a method to derive delay equations of nonlinear systems from experimental data. To this end, the theory of multivariate Fokker-Planck equations is used. The applicability of this method is demonstrated for stochastic models describing tracking and pointing movements of humans.

Noise-covered drift bifurcation of dissipative solitons in a planar gas-discharge system

The trajectories of propagating self-organized, well-localized solitary patterns (dissipative solitons) in the form of electrical current filaments are experimentally investigated in a planar quasi-two-dimensional dc gas-discharge system with high Ohmic semiconductor barrier. Earlier phenomenological models qualitatively describing the experimental observations in terms of a particle model predict a transition from stationary filaments to filaments traveling with constant finite speed due to an appropriate change of the system parameters. This prediction motivates a search for a drift bifurcation in the experimental system, but a direct comparison of experimentally recorded trajectories with theoretical predictions is impossible due to the strong influence of noise. To solve this problem, the filament dynamics is modeled using an appropriate Langevin equation, allowing for the application of a stochastic data analysis technique to separate deterministic and stochastic parts of the dynamics. Simulations carried out with the particle model demonstrate the efficiency of the method. Applying the technique to the experimentally recorded trajectories yields good agreement with the predictions of the model equations. Finally, the predicted drift bifurcation is found using the semiconductor resistivity as control parameter. In the resulting bifurcation diagram, the square of the equilibrium velocity scales linearly with the control parameter.

Statistics of Lagrangian velocities in turbulent flows

We present a generalized Fokker-Planck equation for the joint position-velocity probability distribution of a single fluid particle in a turbulent flow. Based on a simple estimate, the diffusion term is related to the two-point two-time Eulerian acceleration-acceleration correlation. Dimensional analysis yields a velocity increment probability distribution with normal scaling v approximately t(1/2). However, the statistics need not be Gaussian.

Universality of small scale turbulence

The proposed universality of small scale turbulence is investigated for a set of measurements in a cryogenic free jet with a variation of the Reynolds number (Re) from 8500 to 10(6) (max(R(lambda) approximately 1200). The traditional analysis of the statistics of velocity increments by means of structure functions or probability density functions is replaced by a new method which is based on the theory of Markov processes. It gives access to a more complete characterization by means of joint probabilities of finding velocity increments at several scales. Based on this more comprehensive method, our results are very far from a possible universal state, even for R(lambda) above 1000.