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AIM: To assess the retinal function in patients with dense cataracts in resource poor settings in Kinshasa, DR Congo. METHODS: In a tertiary eye care center, the Purkinje entoptic test was performed as part of the ophthalmological examination in 98 eyes in patients with cataract, using a penlight. Totally 92 cataract patients including 86 patients suffered from unilateral and 6 from bilateral cataracts were included in the study. The investigator asked the patients about their perception of the vascular pattern most commonly described as a leafless or dead tree. Visual acuity≥6/60 was considered an indication of good visual function and visual acuity

Rayleigh–Bénard convection, i.e. the flow of a fluid between two parallel plates that is driven by a temperature gradient, is an idealised set-up to study thermal convection. Of special interest are the statistics of the turbulent temperature field, which we are investigating and comparing for three different geometries, namely convection with periodic horizontal boundary conditions in three and two dimensions as well as convection in a cylindrical vessel, in order to determine the similarities and differences. To this end, we derive an exact evolution equation for the temperature probability density function. Unclosed terms are expressed as conditional averages of velocities and heat diffusion, which are estimated from direct numerical simulations. This framework lets us identify the average behaviour of a fluid particle by revealing the mean evolution of a fluid with different temperatures in different parts of the convection cell. We connect the statistics to the dynamics of Rayleigh–Bénard convection, giving deeper insights into the temperature statistics and transport mechanisms. We find that the average behaviour is described by closed cycles in phase space that reconstruct the typical Rayleigh–Bénard cycle of fluid heating up at the bottom, rising up to the top plate, cooling down and falling again. The detailed behaviour shows subtle differences between the three cases.

We investigate the unfolding pathway of a cytosine-rich DNA structure via molecular dynamics simulations. By the study of the essential dynamics, we are able to identify a hidden complexity in the description of the dynamics in terms of the first two eigenvectors which are used as collective variables. This complexity can be mainly explained by non-Gaussian fluctuations due to contributions arising from the disregarded set of eigenvectors. We introduce the local non-Gaussian parameter as a tool for the detection of hidden complexities. The usage of this parameter allows a fast and reliable investigation for the determination of the important minimal number of eigenvectors which is needed for a sufficient description of molecular unfolding motion.

We are interested in the stability of two-dimensional localized structures in reaction-diffusion systems subjected to a delayed feedback. We show that the presence of the delay can induce complex behavior of the localized structures, including, e.g., spontaneous motion or breathing of the localized objects. In the case of spontaneous motion, the corresponding order parameter equation for the position of the localized structure is derived. In addition, numerical simulations are carried out showing good agreement with the analytical predictions.

In glaucoma surgery, fibrotic processes occur, leading to impairment of liquid outflow. Activated fibroblasts are responsible for postoperative scarring. The transforming growth factor-β (TGF-β) pathway plays a key role in fibroblast function, differentiation and proliferation. The aim of this study was the characterization of the fibrotic potential of two subtypes of primary human ocular fibroblasts and the attempt to inhibit fibrotic processes specifically, without impairing cell viability. For fibrosis inhibition we focused on the small molecule pirfenidone, which has been shown to prevent pulmonary fibrosis by the decrease of the expression of TGF-β1, TGF-β2 and TGF-β3 cytokines. For in vitro examinations, isolated human primary fibroblasts from Tenon capsule and human intraconal orbital fat tissues were used. These fibroblast subpopulations were analyzed in terms of the expression of matrix components responsible for postoperative scarring. We concentrated on the expression of collagen I, III, VI and fibronectin. Additionally, we analyzed the expression of α-smooth muscle actin, which serves as a marker for fibrosis and indicates transformation of fibroblasts into myofibroblasts. Gene expression was analyzed by rtPCR and synthesized proteins were examined by immunofluorescence and Western blot methods. Proliferation of fibroblasts under different culture conditions was assessed using BrdU assay. TGF-β1 induced a significant increase of cell proliferation in both cell types. Also the expression of some fibrotic markers was elevated. In contrast, pirfenidone decreased cell proliferation and matrix synthesis in both fibroblast subpopulations. Pirfenidone slightly attenuated TGF-β1 induced expression of fibronectin and α-smooth muscle actin in fibroblast cultures, without impairing cell viability. To summarize, manipulation of the TGF-β signaling pathway by pirfenidone represents a specific antifibrotic approach with no toxic side effects in two human orbital fibroblast subtypes. We presume that pirfenidone is a promising candidate for the treatment of fibrosis following glaucoma surgery.

Im folgenden wollen wir eine Reihe von mathematischen Modellen vorstellen, die zu zeitlich chaotischem Verhalten fuhren. Wir werden dabei verschiedene Moglichkeiten kennenlernen, wie regulare Dynamik in chaotische ubergehen kann. Das Uberraschende dabei ist, das es gar nicht so sehr auf die Form des Bewegungsgesetzes im einzelnen ankommt, sondern das die einzelnen Wege ins Chaos universellen Charakter haben.

We are interested in the stability of the localized stationary solutions of a three-component reaction-diffusion system with one activator and two inhibitors. We show that depending on control parameters, solutions in form of moving and breathing localized structures can be observed in the vicinity of the codimension-two bifurcation point. We analyze this situation performing multiple scale perturbation expansion in the vicinity of the bifurcation point and derive a set of order parameter equations, explicitly describing the dynamics of the single localized structure. Numerical simulations are carried out, showing good agreement with the analytical predictions.

This review summarizes the work conducted in the last decade on the fabrication of mesostructured patterns, which have lateral dimensions within the nano- and microscales, over a wafer-scaled size by means of dynamic self-assembly using Langmuir-Blodgett (LB) transfer or dip-coating. First, strategies to form mesostructures from a homogeneous Langmuir monolayer with controlled shape, size, and patterns alignment will be presented, followed by a detailed theoretical explanation of the pattern formation. In addition, the patterning of nanocrystals and other chemicals with LB transfer or other dynamic processes, such as dip-coating, will be summarized.

This review addresses a central question in the field of complex systems: given a fluctuating (in time or space), sequentially measured set of experimental data, how should one analyze the data, assess their underlying trends, and discover the characteristics of the fluctuations that generate the experimental traces? In recent years, significant progress has been made in addressing this question for a class of stochastic processes that can be modeled by Langevin equations, including additive as well as multiplicative fluctuations or noise. Important results have emerged from the analysis of temporal data for such diverse fields as neuroscience, cardiology, finance, economy, surface science, turbulence, seismic time series and epileptic brain dynamics, to name but a few. Furthermore, it has been recognized that a similar approach can be applied to the data that depend on a length scale, such as velocity increments in fully developed turbulent flow, or height increments that characterize rough surfaces. A basic ingredient of the approach to the analysis of fluctuating data is the presence of a Markovian property, which can be detected in real systems above a certain time or length scale. This scale is referred to as the Markov–Einstein (ME) scale, and has turned out to be a useful characteristic of complex systems. We provide a review of the operational methods that have been developed for analyzing stochastic data in time and scale. We address in detail the following issues: (i) reconstruction of stochastic evolution equations from data in terms of the Langevin equations or the corresponding Fokker–Planck equations and (ii) intermittency, cascades, and multiscale correlation functions.

We investigate the single-point probability density function of the velocity in three-dimensional stationary and decaying homogeneous isotropic turbulence. To this end, we apply the statistical framework of the Lundgren–Monin–Novikov hierarchy combined with conditional averaging, identifying the quantities that determine the shape of the probability density function. In this framework, the conditional averages of the rate of energy dissipation, the velocity diffusion and the pressure gradient with respect to velocity play a key role. Direct numerical simulations of the Navier–Stokes equation are used to complement the theoretical results and assess deviations from Gaussianity.

The modelling of the ion conduction in disordered systems is analysed from two different perspectives. First, molecular dynamics simulations are employed to extract some basic properties of the hopping dynamics. It turns out that the dynamical processes can be described to a very good approximation as vacancy hopping processes. Second, the information content of nonlinear conductivity experiments, using high electric fields, is elucidated. For this purpose the single-particle dynamics on 1D and 2D model energy landscapes is elucidated numerically and partly analytically. The approaches encompass discrete as well as continuous energy landscapes, yielding complementary results about the dynamics. The impact for the interpretation of experimental data is discussed.

The formation of regular stripe patterns during transfer of surfactant monolayers onto solid substrates is investigated. Two coupled differential equations describing the surfactant density and the height profile of the water subphase are derived within the lubrication approximation. If the transfer is carried out in the vicinity of a first order phase transition of the surfactant, the interaction with the substrate plays a key role. This effect is included in the surfactant free-energy functional via a height-dependent external field. Using transfer velocity as a control parameter, a bifurcation from a homogeneous transfer to regular stripe patterns arranged parallel to the contact line is investigated in one and two dimensions. Moreover, in the two-dimensional case, a secondary bifurcation to perpendicular stripes is observed in a certain control parameter range.

The paper is devoted to the construction of the superstatistical description for nonequilibrium Markovian systems. It is based on Kirchhoff’s diagram technique and the assumption on the system under consideration to possess a wide variety of cycles with vanishing probability fluxes. The latter feature enables us to introduce equivalence classes called channels within which detailed balance holds individually. Then stationary probability as well as flux distributions are represented as some sums over the channels. The latter construction actually forms the superstatistical description, which, however, deals with a certain superposition of equilibrium subsystems rather than a formal expansion of the nonequilibrium steady state distribution into terms of the Boltzmann type.

We present a numerical investigation of two-dimensional decaying turbulence in the Lagrangian framework. Focusing on single particle statistics, we investigate Lagrangian trajectories in a freely evolving turbulent velocity field. The dynamical evolution of the tracer particles is strongly dominated by the emergence and evolution of coherent structures. For a statistical analysis we focus on the Lagrangian acceleration as a central quantity. For more geometrical aspects we investigate the curvature along the trajectories. We find strong signatures for the self-similar universal behavior.

In this work a method is developed for analyzing time series of periodically driven stochastic systems involving time-delayed feedback. The proposed data-analysis method yields dynamical models in terms of stochastic delay differential equations. On the basis of these dynamical models differential effects of driving forces and time-delayed feedback forces can be identified.

Obwohl Methoden zur Inaktivierung schadlicher Mikroorganismen durch Hitze sowohl bei der Behandlung von Lebensmitteln als auch im pharmazeutisch-medizinischen Bereich seit langer Zeit erfolgreich angewendet werden, sind prazise mathematische Modellierungen derartiger Prozesse erst in neuester Zeit in Entwicklung begriffen. Dies gilt insbesondere fur moglichst „schonende” Verfahren, bei denen Temperaturen und zeitliche Einwirkung gering gehalten werden sollen (Pasteurisierung, Thermisierung). Hier spielt eine quantitative Kontrolle auch uber die Phasen der Erwarmung und Abkuhlung eine Rolle. Beschrieben wird ein solches hinreichend flexibles Modell fur derartige nicht-isotherme Inaktivierungsvorgange. Es wird ein expliziter Algorithmus angegeben, der vom Anwender mittels Microsoft Excel™ implementiert werden kann.

Small scale velocity statistics are measured in different turbulent flows with Reynolds numbers up to 106. The stochastic features of the turbulent signals are investigated by means of Markov processes for the velocity increments evolving along the cascade. The analysis of the validity of the Markovian properties yields to a new small scale coherence length. This coherence length can be seen as analogue to the mean free path length of a Brownian motion as pointed out in [A. Einstein, Ann. Phys. 17 (1905) 549]. For length scales larger than this coherence length the complexity of turbulence can be treated as a Markov process. We present experimental evidence that this Markov–Einstein coherence length scales with Re 1 / 2 and show that it is closely related to the Taylor micro-scale and not to the Kolmogorov dissipation length.

We obtain the exact solution for the Burgers equation with a time dependent forcing, which depends linearly on the spatial coordinate. For the case of a stochastic time dependence an exact expression for the joint probability distribution for the velocity fields at multiple spatial points is obtained. A connection with stretched vortices in hydrodynamic flows is discussed., Comment: 10 pages

Complex, self-regulating systems such as the human heart must process inputs with a broad range of characteristics to generate physiological data and time series. Many of these physiological time series seem to be highly chaotic, represent nonstationary data, and fluctuate in an irregular and complex manner. One hypothesis is that the seemingly chaotic structure of physiological time series arises from external and intrinsic perturbations that push the system away from a homeostatic set point. An alternative hypothesis is that the fluctuations are due, at least in part, to the system's underlying dynamics. In this review, we describe new computational approaches - based on new theoretical concepts - for analyzing physiological time series. We'll show that the application of these methods could potentially lead to a novel diagnostic tool for distinguishing healthy individuals from those with congestive heart failure (CHF)

We introduce a generalization of Obukhov's model [A.M. Obukhov, Adv. Geophys. 6, 113 (1959)] for the description of the joint position-velocity statistics of a single fluid particle in fully developed turbulence. In the presented model the velocity is assumed to undergo a continuous time random walk. This takes into account long time correlations. As a consequence the evolution equation for the joint position-velocity probability distribution is a Fokker-Planck equation with a fractional time derivative. We determine the solution of this equation in the form of an integral transform and derive a relation for arbitrary single time moments. Analytical solutions for the joint probability distribution and its moments are given., Comment: 10 pages