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One of the classical ways to describe the dynamics of nonlinear systems is to analyze theur Fourier spectra. For periodic and quasiperiodic processes the Fourier spectrum consists purely of discrete delta-functions. On the contrary, the spectrum of a chaotic motion is marked by the presence of the continuous component. In this work, we describe the peculiar, neither regular nor completely chaotic state with so called singular-continuous power spectrum. Our investigations concern various cases from most different fields, where one meets the singular continuous (fractal) spectra. The examples include both the physical processes which can be reduced to iterated discrete mappings or even symbolic sequences, and the processes whose description is based on the ordinary or partial differential equations.
We have recently reported the phenomenon of doubly stochastic resonance [Phys. Rev. Lett. 85, 227 (2000)], a synthesis of noise-induced transition and stochastic resonance. The essential feature of this phenomenon is that multiplicative noise induces a bimodality and additive noise causes stochastic resonance behavior in the induced structure. In the present paper we outline possible applications of this effect and design a simple lattice of electronic circuits for the experimental realization of doubly stochastic resonance.
Contents: 1 Introduction 2 Main result 3 Construction of the asymptotic solutions 3.1 Derivation of the equations for the profiles 3.2 Exsistence of the principal profile 3.3 Determination of Usub(2) and the remaining profiles 4 Stability of the samll global solutions. Justification of One Phase Nonlinear Geometric Optics for the Kirchhoff-type equations 4.1 Stability of the global solutions to the Kirchhoff-type symmetric hyperbolic systems 4.2 The nonlinear system of ordinary differential equations with the parameter 4.3 Some energies estimates 4.4 The dependence of the solution W(t, ξ) on the function s(t) 4.5 The oscillatory integrals of the bilinear forms of the solutions 4.6 Estimates for the basic bilinear form Γsub(s)(t) 4.7 Contraction mapping 4.8 Stability of the global solution 4.9 Justification of One Phase Nonlinear Geometric Optics for the Kirchhoff-type equations
It is shown that bounded solutions to semilinear elliptic Fuchsian equations obey complete asymptoic expansions in terms of powers and logarithms in the distance to the boundary. For that purpose, Schuze's notion of asymptotic type for conormal asymptotics close to a conical point is refined. This in turn allows to perform explicit calculations on asymptotic types - modulo the resolution of the spectral problem for determining the singular exponents in the asmptotic expansions.
We report on deep multi-color imaging (R5sigma = 26) of the Chandra Deep Field South, obtained with the Wide Field Imager (WFI) at the MPG/ESO 2.2 m telescope on La Silla as part of the multi-color survey COMBO-17. As a result we present a catalogue of 63 501 objects in a field measuring 31farcm5 x 30arcmin with astrometry and BVR photometry. A sample of 37 variable objects is selected from two-epoch photometry. We try to give interpretations based on color and variation amplitude.
Asymptotic algebras
(2001)
Asymptotic algebras
(2001)
Ventricular tachycardia or fibrillation (VT) as fatal cardiac arrhythmias are the main factors triggering sudden cardiac death. The objective of this recurrence quantification analysis approach is to find early signs of sustained VT in patients with an implanted cardioverter-defibrillator (ICD). These devices are able to safeguard patients by returning their hearts to a normal rhythm via strong defibrillatory shocks; additionally, they are able to store at least 1000 beat-to-beat intervals immediately before the onset of a life-threatening arrhythmia. We study the
European monetary union and exchange rate dynamics : new approaches and application to the Euro
(2001)
Phytoplankton dynamics in a shallow eutrophic lake were investigated over a 3-year period with respect to environmental forces which drive species composition and diversity. Diversity was calculated on the basis of species as well as on the basis of their functional properties (the C-R-S-concept). Stratification and water column mixing had a strong impact on phytoplankton composition. Application of a similarity-diversity model revealed that a high diversity was a transient non-stable state, whereas drastic changes or long-lasting stable environmental conditions are characterized by low diversity. This effect was more pronounced when the diversity was calculated on the basis of the phytoplankton species functional properties. Thus, this functional approach supports the intermediate disturbance hypothesis from field data.
In the middle of the 19th century the question whether expanding civilization and industrialization had an effect on climate was discussed intensely worldwide. It was feared that increasing deforestation would lead to continuous decrease in rainfall. This first scientific discussion about climate change as the result of human intervention was strongly influenced by the research Alexander von Humboldt and Jean-Baptiste Boussingault had undertaken when they investigated the falling water levels of Lake Valencia in Venezuela. This essay aims to clarify the question whether Alexander von Humboldt can be counted among the leading figures of modern environmentalism on account of this research as is being claimed by Richard H. Grove in his influential book Green Imperialism. Colonial Expansion, Tropical Island Edens and Origins of Environmentalism, 1600-1860 (1995).
Volcano seismology
(2001)
In the roughly 20 years of its existence as an observational science, gravitational lensing has established itself as a valuable tool in many astrophysical fields. In the introduction of this review we briefly present the basics of lensing. Then it is shown that the two propagation effects, lensing and scintillation, have a number of properties in common. In the main part various lensing phenomena are discussed with emphasis on recent observations.
Microlensing of Quasars
(2001)
Microlens-induced variability in multiple quasars can be used to study two cosmological issues of great interest, the size and brightness profile of quasars on one hand, and the distribution of compact (dark) matter along the line of sight on the other. Here a summary is given of recent theoretical progress as well as observational evidence for quasar microlensing, plus a discussion of desired observations and required theoretical studies.
Quasar Microlensing
(2001)
Cosmological microlensing
(2001)
The filtration rate of Daphnia galeata was determined in in situ experiments in Bautzen Reservoir and in laboratory experiments, where daphnids were exposed to filtrates that previously contained either natural phytoplankton or cultured eukaryotic algae (Scenedesmus obliquus or Asterionella formosa), respectively. Individual filtration rate (FR) was measured using fluorescent beads, taking into account ingested beads in the gut only. Compared to heated control treatments (100°C), dissolved compounds released by the nutritious cultured algae during the preconditioning phase or by the natural phytoplankton assemblages from Bautzen Reservoir strongly reduced the filtration rate of D. galeata (down to 60 %). Heating deactivated these dissolved compounds. A significant correlation was found between primary production measured in situ and the reduction of FR in the filtrate of reservoir water, indicating that extra- cellular products released during photosynthesis triggered the reduction of the filtration rate. The ratio of ingested to collected beads was used to quantify the proportion of food, which was not only collected but passed the mouth of D. galeata. The ratio of ingestion to collection was compared between filtered and unfiltered reservoir water both media identical with respect to the concentration of dissolved compounds, whereas other factors (e. g. food concentration, temperature, filtration rate) were different. The changes in this ratio between filtered and unfiltered reservoir water suggest that D. galeata is capable of a chemosensory control of the ingestion behaviour by detecting external metabolites.
The factors that determine the efficiency of energy transfer in aquatic food webs have been investigated for many decades. The plant-animal interface is the most variable and least predictable of all levels in the food web. In order to study determinants of food quality in a large lake and to test the recently proposed central importance of the long-chained eicosapentaenoic acid (EPA) at the pelagic producer-grazer interface, we tested the importance of polyunsaturated fatty acids (PUFAs) at the pelagic producerconsumer interface by correlating sestonic food parameters with somatic growth rates of a clone of Daphnia galeata. Daphnia growth rates were obtained from standardized laboratory experiments spanning one season with Daphnia feeding on natural seston from Lake Constance, a large pre-alpine lake. Somatic growth rates were fitted to sestonic parameters by using a saturation function. A moderate amount of variation was explained when the model included the elemental parameters carbon (r2 = 0.6) and nitrogen (r2 = 0.71). A tighter fit was obtained when sestonic phosphorus was incorporated (r2 = 0.86). The nonlinear regression with EPA was relatively weak (r2 = 0.77), whereas the highest degree of variance was explained by three C18-PUFAs. The best (r2 = 0.95), and only significant, correlation of Daphnia's growth was found with the C18-PUFA α-linolenic acid (α-LA; C18:3n-3). This correlation was weakest in late August when C:P values increased to 300, suggesting that mineral and PUFA-limitation of Daphnia's growth changed seasonally. Sestonic phosphorus and some PUFAs showed not only tight correlations with growth, but also with sestonic α-LA content. We computed Monte Carlo simulations to test whether the observed effects of α-LA on growth could be accounted for by EPA, phosphorus, or one of the two C18-PUFAs, stearidonic acid (C18:4n-3) and linoleic acid (C18:2n-6). With >99 % probability, the correlation of growth with α-LA could not be explained by any of these parameters. In order to test for EPA limitation of Daphnia's growth, in parallel with experiments on pure seston, growth was determined on seston supplemented with chemostat-grown, P-limited Stephanodiscus hantzschii, which is rich in EPA. Although supplementation increased the EPA content 80-800x, no significant changes in the nonlinear regression of the growth rates with α-LA were found, indicating that growth of Daphnia on pure seston was not EPA limited. This indicates that the two fatty acids, EPA and α-LA, were not mutually substitutable biochemical resources and points to different physiological functions of these two PUFAs. These results support the PUFA-limitation hypothesis for sestonic C:P < 300 but are contrary to the hypothesis of a general importance of EPA, since no evidence for EPA limitation was found. It is suggested that the resource ratios of EPA and α-LA rather than the absolute concentrations determine which of the two resources is limiting growth.
The factors that determine the efficiency of energy transfer in aquatic food webs have been investigated for many decades. The plant-animal interface is the most variable and least predictable of all levels in the food web. In order to study determinants of food quality in a large lake and to test the recently proposed central importance of the long-chained eicosapentaenoic acid (EPA) at the pelagic producer-grazer interface, we tested the importance of polyunsaturated fatty acids (PUFAs) at the pelagic producer-consumer interface by correlating sestonic food parameters with somatic growth rates of a clone of Daphnia galeata. Daphnia growth rates were obtained from standardized laboratory experiments spanning one season with Daphnia feeding on natural seston from Lake Constance, a large pre-alpine lake. Somatic growth rates were fitted to sestonic parameters by using a saturation function. A moderate amount of variation was explained when the model included the elemental parameters carbon (r2 = 0.6) and nitrogen (r2 = 0.71). A tighter fit was obtained when sestonic phosphorus was incorporated (r2 = 0.86). The nonlinear regression with EPA was relatively weak (r2 = 0.77), whereas the highest degree of variance was explained by three C18-PUFAs. The best (r2 = 0.95), and only significant, correlation of Daphnia's growth was found with the C18-PUFA a-linolenic acid (a-LA; C18:3n-3). This correlation was weakest in late August when C:P values increased to 300, suggesting that mineral and PUFA- limitation of Daphnia's growth changed seasonally. Sestonic phosphorus and some PUFAs showed not only tight correlations with growth, but also with sestonic alpha-LA content. We computed Monte Carlo simulations to test whether the observed effects of alpha-LA on growth could be accounted for by EPA, phosphorus, or one of the two C18-PUFAs, stearidonic acid (C18:4n-3) and linoleic acid (C18:2n-6). With >99% probability, the correlation of growth with alpha-LA could not be explained by any of these parameters. In order to test for EPA limitation of Daphnia's growth, in parallel with experiments on pure seston, growth was determined on seston supplemented with chemostat-grown, Plimited Stephanodiscus hantzschii, which is rich in EPA. Although supplementation increased the EPA content 80-800x, no significant changes in the nonlinear regression of the growth rates with alpha-LA were found, indicating that growth of Daphnia on pure seston was not EPA limited. This indicates that the two fatty acids, EPA and alpha-LA, were not mutually substitutable biochemical resources and points to different physiological functions of these two PUFAs. These results support the PUFA-limitation hypothesis for sestonic C:P < 300 but are contrary to the hypothesis of a general importance of EPA, since no evidence for EPA limitation was found. It is suggested that the resource ratios of EPA and alpha-LA rather than the absolute concentrations determine which of the two resources is limiting growth.
Determination of phenolic compounds using recombinant tyrosinanse from Streptomyces antibioticus
(2001)
In order to broaden our understanding of the eukaryotic CO2- concentrating mechanism the occurrence and localization of a thylakoid-asssocaate carbonic anhydrase (EC 4.2.1.1) were studied in the green algae Tetraedron on minimum and Chlamydomonas noctigama. Both algae induce a CO2-concentrating mechanism when grown under limiting CO2 conditions. Using mass- spectrometric measurements of O-18 exchange from doubly labelled CO2, the presence of a thylakoid-associated carbonic anhydrase was confirmed for both species. From purified thylakoid membranes, photosystem I (PSI), photosystem II (PSII) and the light-harvesting complex of the photosynthetic apparatus were isolated by mild detergent gel. The protein fractions were identified by 77 K fluorescence spectroscopy and immunological studies. A polypeptide was found to immunoreact with an antibody raised against thylakoid carbonic anhydrase (CAH3) from Chlamydomonas reinhardtii. It was found that this polypeptide was mainly associated with PSII, although a certain proportion was also connected to light harvesting complex II. This was confirmed by activity measurements of carbonic anhydrase in isolated bands extracted from the mild detergent gel. The thylakoid carbonic anhydrase isolated from T. minimum had an isoelectric point between 5.4 and 4.8. Together the results are consistent with the hypothesis that thylakoid carbonic anhydrase resides within the lumen where it is associated with the PSII complex.
Noise-induced dynamics of a prototypical bistable system with delayed feedback is studied theoretically and numerically. For small noise and magnitude of the feedback, the problem is reduced to the analysis of the two-state model with transition rates depending on the earlier state of the system. Analytical solutions for the autocorrelation function and the power spectrum have been found. The power spectrum has a peak at the frequency corresponding to the inverse delay time, whose amplitude has a maximum at a certain noise level, thus demonstrating coherence resonance. The linear response to the external periodic force also has maxima at the frequencies corresponding to the inverse delay time and its harmonics.
Distributed optimality
(2001)
In this thesis I propose a synthesis (Distributed Optimality, DO) between Optimality Theory (OT, Prince & Smolensky, 1993) and a morphological framework in a genuine derivational tradition, namely Distributed Morphology (DM) as developed by Halle & Marantz (1993). By carrying over the apparatus of OT to DM, phenomena which are captured in DM by language-specific rules or features of lexical entries, are given a more principled account in the terms of ranked universal constraints. On the other hand, also the DM part makes two contributions, namely strong locality and impoverishment. The first gives rise to a simple formal interpretation of DO, while the latter is shown to be indispensable in any theoretically satisfying account of agreement morphology. The empirical basis of the work is given by the complex agreement morphology of genetically different languages. Theoretical focus is mainly on two areas: First, so-called direction marking which is shown to be preferably treated in terms of constraints on feature realization. Second, the effects of precedence constraints which are claimed to regulate the status of agreement affixes as prefixes or suffixes and their respective order. A universal typology for the order of agreement categories by means of OT-constraints is proposed.
Transition to Coherence in Populations of Coupled Chaotic Oscillators: A Linear Response Approach
(2001)
We consider the collective dynamics in an ensemble of globally coupled chaotic maps. The transition to the coherent state with a macroscopic mean field is analyzed in the framework of the linear response theory. The linear response function for the chaotic system is obtained using the perturbation approach to the Frobenius-Perron operator. The transition point is defined from this function by virtue of the self-excitation condition for the feedback loop. Analytical results for the coupled Bernoulli maps are confirmed by the numerics.
Subject of this work is the investigation of generic synchronization phenomena in interacting complex systems. These phenomena are observed, among all, in coupled deterministic chaotic systems. At very weak interactions between individual systems a transition to a weakly coherent behavior of the systems can take place. In coupled continuous time chaotic systems this transition manifests itself with the effect of phase synchronization, in coupled chaotic discrete time systems with the effect of non-vanishing macroscopic mean field. Transition to coherence in a chain of locally coupled oscillators described with phase equations is investigated with respect to the symmetries in the system. It is shown that the reversibility of the system caused by these symmetries results to non-trivial topological properties of trajectories so that the system constructed to be dissipative reveals in a whole parameter range quasi-Hamiltonian features, i.e. the phase volume is conserved on average and Lyapunov exponents come in symmetric pairs. Transition to coherence in an ensemble of globally coupled chaotic maps is described with the loss of stability of the disordered state. The method is to break the self-consistensy of the macroscopic field and to characterize the ensemble in analogy to an amplifier circuit with feedback with a complex linear transfer function. This theory is then generalized for several cases of theoretic interest.
We analyse the X-ray light curves of compact objects using linear and nonlinear time series analysis methods. A Power Density Spectrum (PDS) describes the overall second order properties of the observed data well. To look beyond we propose the nonlinear Q-statistic to detect an asymmetry of the time series. This allows us to find relevant time scales. This method even grants a subclassification of the known states of X-ray sources.
Proof of Chirality of J-Aggregates Spontaneously and Enantioselectivily Generated from Achiral Dyes
(2001)
Acoustic emission signals generated during high speed cutting of steel are investigated. The data are represen ted in time-folded form. Several methods from linear and nonlinear data analysis based on time- and frequency- domain are applied to the data and reveal signatures of the observed acoustic emission signal. These investiga tions are necessary for modeling the cutting process by means of differential equations.
Isolation and characterisation of ammonium transporters from the module legumen : lotus japanicus
(2001)
Let A be a determined or overdetermined elliptic differential operator on a smooth compact manifold X. Write Ssub(A)(D) for the space of solutions to thesystem Au = 0 in a domain D ⊂ X. Using reproducing kernels related to various Hilbert structures on subspaces of Ssub(A)(D) we show explicit identifications of the dual spaces. To prove the "regularity" of reproducing kernels up to the boundary of D we specify them as resolution operators of abstract Neumann problems. The matter thus reduces to a regularity theorem for the Neumann problem, a well-known example being the ∂-Neumann problem. The duality itself takes place only for those domains D which possess certain convexity properties with respect to A.
Using the incompressible magnetohydrodynamic equations, we have numerically studied the dynamo effect in electrically conducting fluids. The necessary energy input into the system was modeled either by an explicit forcing term in the Navier-Stokes equation or fully selfconsistently by thermal convection in a fluid layer heated from below. If the fluid motion is capable of dynamo action, the dynamo effect appears in the form of a phase transition or bifurcation at some critical strength of the forcing. Both the dynamo bifurcation and subsequent bifurcations that occur when the strength of the forcing is further raised were studied, including the transition to chaotic states. Special attention was paid to the helicity of the flow as well as to the symmetries of the system and symmetry breaking in the bifurcations. The magnetic field tends to be accumulated in special regions of the flow, notably in the vicinity of stagnation points or near the boundaries of convection cells.
International trade and spatial markets : trade policy from a theory of spatial pricing perspective
(2001)
Boundary value problems for pseudodifferential operators (with or without the transmission property) are characterised as a substructure of the edge pseudodifferential calculus with constant discrete asymptotics. The boundary in this case is the edge and the inner normal the model cone of local wedges. Elliptic boundary value problems for non-integer powers of the Laplace symbol belong to the examples as well as problems for the identity in the interior with a prescribed number of trace and potential conditions. Transmission operators are characterised as smoothing Mellin and Green operators with meromorphic symbols.
Contents: Introduction 1 Edge calculus with parameters 1.1 Cone asymptotics and Green symbols 1.2 Mellin edge symbols 1.3 The edge symbol algebra 1.4 Operators on a manifold with edges 2 Corner symbols and iterated asymptotics 2.1 Holomorphic corner symbols 2.2 Meromorphic corner symbols and ellipicity 2.3 Weighted corner Sobolev spaces 2.4 Iterated asymptotics 3 The edge corner algebra with trace and potential conditions 3.1 Green corner operators 3.2 Smoothing Mellin corner operators 3.3 The edge corner algebra 3.4 Ellipicity and regularity with asymptotics 3.5 Examples and remarks
Implicit power motivation predicts testosterone changes after winning or losing a domiance contest
(2001)
Social Organization
(2001)
In soils of the Rustenbug Minig Area microorganism concentration and activity of several enzymes (dehydrogenase, phosphatase, protease, amylase, cellulase, xylanase) were determined. First results indicate an increase of heavy metal resistant Microorganisms and a possible inhibition of carbohydrate degrading enzymes.