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Nordau, Max
(2004)
We study the effects of mutual and external chaotic phase synchronization in ensembles of bursting oscillators. These oscillators (used for modeling neuronal dynamics) are essentially multiple time scale systems. We show that a transition to mutual phase synchronization takes place on the bursting time scale of globally coupled oscillators, while on the spiking time scale, they behave asynchronously. We also demonstrate the effect of the onset of external chaotic phase synchronization of the bursting behavior in the studied ensemble by a periodic driving applied to one arbitrarily taken neuron. We also propose an explanation of the mechanism behind this effect. We infer that the demonstrated phenomenon can be used efficiently for controlling bursting activity in neural ensembles
We study phase synchronization effects of chaotic oscillators with a type-I intermittency behavior. The external and mutual locking of the average length of the laminar stage for coupled discrete and continuous in time systems is shown and the mechanism of this synchronization is explained. We demonstrate that this phenomenon can be described by using results of the parametric resonance theory and that this correspondence enables one to predict and derive all zones of synchronization
Zimzum
(2004)
We derive a slip rate for a thrust at the central Qilian Shan mountain front by combining structural investigations, satellite imagery, topographic profiling, luminescence dating, and Be-10 exposure dating. The seismically active Zhangye thrust transects late Pleistocene alluvial fan deposits and forms a prominent north facing scarp. The fault consists of two segments that differ in orientation, scarp height, and age. A series of loess-covered terraces records the uplift history of the western thrust segment. Loess accumulation on all terraces started at 8.5 +/- 1.5 kyr and postdates terrace formation. Gravels from the highest terrace yielded a Be-10 exposure age of 90 +/- 11 kyr, which dates the onset of faulting. With a displacement of 55-60 m derived from fault scarp profiles, this yields a vertical slip rate of 0.64 +/- 0.08 mm yr(-1). Along the eastern thrust segment, three Be-10 ages from the uplifted alluvial fan constrain that faulting started at similar to31 +/- 5 kyr. Together with a displacement of 25-30 m this leads to a vertical faulting rate of 0.88 +/- 0.16 mm yr(-1). A dip estimate of 40degrees to 60degrees for the fault plane combined with lower and upper limits of similar to0.6 and similar to0.9 mm yr(-1) for the vertical slip rate gives minimum and maximum horizontal shortening rates of 0.4 and 1.1 mm yr(-1) across the Zhangye thrust. Our results are consistent with geologic and GPS constraints, which suggest that NNE directed shortening across the northeastern Tibetan Plateau is distributed on several active faults with a total shortening rate of 4 to 10 mm yr(-1)
[1] The development of topography within and erosional removal of material from an orogen exerts a primary control on its structure. We develop a model that describes the temporal development of a frontally accreting, critically growing Coulomb wedge whose topography is largely limited by bedrock fluvial incision. We present general results for arbitrary initial critical wedge geometries and investigate the temporal development of a critical wedge with no initial topography. Increasing rock erodibility and/or precipitation, decreasing mass flux accreting to the wedge front, increasing wedge sole-out depth, decreasing wedge and basal decollement overpressure, and increasing basal decollement friction lead to narrow wedges. Large power law exponent values cause the wedge geometry to quickly reach a condition in which all material accreted to the front of the wedge is removed by erosion. We apply our model to the Aconcagua fold-and-thrust belt in the central Andes of Argentina where wedge development over time is well constrained. We solve for the erosional coefficient K that is required to recreate the field-constrained wedge growth history, and these values are within the range of independently determined values in analogous rock types. Using qualitative observations of rock erodibilities within the wedge, we speculate that power law exponents of 1/3 less than or equal to m less than or equal to 0.4 and 2/3 less than or equal to n less than or equal to 1 characterize the erosional growth of the Aconcagua fold-and-thrust belt. This general model may be used to understand the development of mountain belts where orogenic wedges grow as they deform at their Coulomb failure limit
[1] Orogenic structure appears to be partially controlled by the addition to and removal of material from the mountain belt by tectonic accretion and geomorphic erosion, respectively. We developed a coupled erosion-deformation model for orogenic wedges that are in erosional steady state and deform at their Coulomb failure limit. Erosional steady state is reached when all material introduced into the wedge is removed by erosion that is limited by the rate at which rivers erode through bedrock. We found that the ultimate form of a wedge is controlled by the wedge mechanical properties, sole-out depth of the basal decollement, erosional exponents, basin geometry, and the ratio of the added material flux to the erosional constant. As this latter ratio is increased, wedge width and surface slopes increase. We applied these models to the Taiwan and Himalayan orogenic wedges and found that despite a higher flux of material entering the former, the inferred ratio was larger for the latter. Calculated values for the erodibility of each wedge showed at least an order of magnitude lower value for the Himalaya relative to Taiwan. These values are consistent with the lower precipitation regime in the Himalaya relative to Taiwan and the exposure of crystalline rocks within the Himalayan orogenic wedge. Independently determined rock erodibility estimates are consistent with the accretionary wedge sediments and metasediments and the crystalline and high-grade metamorphic rocks exposed within Taiwan and the Himalaya, respectively. Therefore differences in rock type and climate apparently lead to key differences in the erosion and hence orogenic structure of these two mountain belts
A fault scaling law suggests that, over eight orders of magnitude, fault length L is linearly related to maximum displacement D. Individual faults may therefore retain a constant ratio of D/L as they grow. If erosion is minor compared with tectonic uplift, the length and along-strike relief of young mountain ranges should thus reflect fault growth. Topographic profiles along the crests of mountain ranges in the actively deforming foreland of north-east Tibet exhibit a characteristic shape with maximum height near their centre and decreasing elevation toward the tips. We interpret the along-strike relief of these ranges to reflect the slip distribution on high-angle reverse faults. A geometric model illustrates that the lateral propagation rate of such mountain ranges may be deciphered if their length- to-height ratio has remained constant. As an application of the model, we reconstruct the growth of the Heli Shan using a long-term uplift rate of similar to1.3 mm yr(-1) derived from Ne-21 and Be-10 exposure dating
We argue that there is a crucial difference between determiner and adverbial quantification. Following Herburger [2000] and von Fintel [1994], we assume that determiner quantifiers quantify over individuals and adverbial quantifiers over eventualities. While it is usually assumed that the semantics of sentences with determiner quantifiers and those with adverbial quantifiers basically come out the same, we will show by way of new data that quantification over events is more restricted than quantification over individuals. This is because eventualities in contrast to individuals have to be located in time which is done using contextual information according to a pragmatic resolution strategy. If the contextual information and the tense information given in the respective sentence contradict each other, the sentence is uninterpretable. We conclude that this is the reason why in these cases adverbial quantification, i.e. quantification over eventualities, is impossible whereas quantification over individuals is fine.
Being one of the fundamental phenomena in nonlinear science, synchronization of oscillations has permanently remained an object of intensive research. Development of many asymptotic methods and numerical simulations has allowed an understanding and explanation of various phenomena of self-synchronization. But even in the classical case of coupled van der Pol oscillators a full description of all possible dynamical regimes, their mutual transitions and characteristics is still lacking. We present here a study of the phenomenon of mutual synchronization for two non-scalar- coupled non-identical limit-cycle oscillators and analyze phase, frequency and amplitude characteristics of synchronization regimes. A series of bifurcation diagrams that we obtain exhibit various regions of qualitatively different behavior. Among them we find mono-, bi- and multistability regions, beating and "oscillation death" ones; also a region, where one of the oscillators dominates the other one is observed. The frequency characteristics that we obtain reveal three qualitatively different types of synchronization: (i) on the mean frequency (the in-phase synchronization), (ii) with a shift from the mean frequency caused by a conservative coupling term (the anti-phase synchronization), and (iii) on the frequency of one of the oscillators (when one oscillator dominates the other). (C) 2003 Elsevier B.V. All rights reserved
E-Government : von der Portalisierung zur umfassenden Neugestaltung öffentlicher Leistungserbringung
(2004)
Cafeteria-Systeme
(2004)
Partizipation
(2004)
Making diversity work
(2004)
Alkoxy-substituted CN-containing phenylene-vinylene-alt-phenylene-ethynylene hybrid polymers (CN-PPV-PPE), 3a, 3b, and 7a, were obtained from luminophoric dialdehydes 1 by step growth polymerization via Knoevenagel reaction as high molecular-weight materials. Corresponding CN-free polymers 3c and 7b and an ethynylene-free polymer 5 with similar side chains were synthesized for the purpose of comparison. The chemical structures of the polymers were confirmed by IR, H-1 and C-13 NMR, and elemental analysis. Thermal characterization was conducted by means of thermogravimetric analysis and differential scanning calorimetry. Morphology was investigated by means of optical microscopy and small-angle light scattering. The final morphologies are determined by the molecular characteristics (side chains volume fraction, backbone stiffness) of the studied polymers. All the CN-containing polymers 3b, 5, and 7a exhibit higher fluorescence quantum yield in solid state (50 to 60%), but lower quantum yields (12-40%) in dilute chloroform solution, in total contrast to CN-free polymers 3c, 3d, and 7b. Identical optical, E-g(opt), and electrochemical band gap energies, E- g(ec), were obtained for 3b, 3c and 3d with intrinsic self-assembly ability, whereas a discrepancy, DeltaE(g), was observed in the cases of the fully substituted polymers 5, 7a, and 7b, whose values are dependent on the level of backbone stiffness and length of the side groups combined with the presence or absence of CN units. The incorporation of CN units in 3b and 7a lowers their respective LUMO level by 220 and 350 meV compared to their corresponding CN-free counterparts 3c and 7b, suggesting an improvement of the electron-accepting strength. Polymers 3b and 7a are efficient electron acceptors suitable for photovoltaic application. The experiments indicate that 3b is a better electron acceptor when used together with M3EH-PPV, but transport properties seem to be better for 7a. With 3b, high external quantum efficiencies of up to 23%, an open circuit voltage of up to 1.52 V, and a white light energy efficiency of 0.65% could be realized in bilayer solar cell devices. LED-devices of configuration ITO/PEDOT:PSS/polymer/Ca/Al from 3b, 3c, 7a, and 7b showed low turn-on voltages between 2 and 2.5 V. The CN-free polymers 3c and 7b exhibit far better EL parameters than their corresponding CN containing counterparts 3b and 7a
Polymer solar cell devices with nanostructured blend layers have been fabricated using single- and dual- component polymer nanospheres. Starting from an electron-donating and an electron-accepting polyfluorene derivative, PFB and F8BT, dissolved in suitable organic solvents, dispersions of solid particles with mean diameters of ca. 50 nm, containing either the pure polymer components or a mixture of PFB and F8BT in each particle, were prepared with the miniemulsion process. Photovoltaic devices based on these particles have been studied with respect to the correlation between external quantum efficiency and layer composition. It is shown that the properties of devices containing a blend of single-component PFB and F8BT particles differ significantly from those of solar cells based on blend particles, even for the same layer composition. Various factors determining the quantum efficiency in both kinds of devices are identified and discussed, taking into account the spectroscopic properties of the particles. An external quantum efficiency of ca. 4% is measured for a device made from polymer blend nanoparticles containing PFB:F8BT at a weight ratio of 1:2 in each individual nanosphere. This is among the highest values reported so far for photovoltaic cells using this material combination
The delayed luminescence and phosphorescence of ladder-type methyl-poly(para-phenylene) (MeLPPP) doped with benzil at a concentration of 20% by weight has been measured. The introduction of benzil leads to a dramatic reduction of the polymer singlet emission. At the same time, a new band with maximum at 611 nm appears, corresponding to the phosphorescence of MeLPPP. The phosphorescence decay on the short time scale is close to an exponential law with a time decay of 15 ms. This indicates that benzil can efficiently sensitize the phosphorescence of the polymer. In addition, a broad and featureless emission is observed in the delayed luminescence spectra of benzil-doped MeLPPP, which is attributed to an exciplex formed between the polymer host and the dopant. We further observe that the delayed fluorescence is enhanced by the addition of benzil. It is concluded that the delayed fluorescence of benzil-doped MeLPPP is mainly due to the annihilation of triplet excitons on the polymer. Finally, efficient triplet-triplet energy transfer from the benzil-doped polymer to the red-emitting phosphorescent dye Pt(II)octaethylporphyrin is established. (C) 2004 American Institute of Physics
Materials for polymer electronics applications semiconducting polymer thin films and nanoparticles
(2004)
The paper presents two different approaches to nanostructured semiconducting polymer materials: (i) the generation of aqueous semiconducting polymer dispersions (semiconducting polymer nanospheres SPNs) and their processing into dense films and layers, and (ii) the synthesis of novel semiconducting polyfluorene-block-polyaniline (PF-b-PANI) block copolymers composed of conjugated blocks of different redox potentials which form nanosized morphologies in the solid state
Energy transfer in a ladder-type methyl-poly(para-phenylene) doped by Pt(II)octaethylporphyrin
(2004)
The luminescence of a ladder-type methyl-poly(para-phenylene) (MeLPPP) doped by platinum-porphyrin dye PtOEP covering the concentration 10(-3) to 5% by weight has been measured employing cw and transient techniques. Upon excitating into the range of absorption of the host strong phosphorescence of the dopant is observed. Possible ways of populating of the dopant triplet state are considered. It is shown that the main channel is singlet-singlet energy transfer among chromophor groups of the polymer followed by Forster-type transfer to the guest and subsequent intersystem crossing. (C) 2003 Elsevier B.V. All rights reserved
We present new measures of complexity and their application to event-related potential data. The new measures are based on structures of recurrence plots and makes the identification of chaos-chaos transitions possible. The application of these measures to data from single-trials of the Oddball experiment can identify laminar states therein. This offers a new way of analyzing event-related activity on a single-trial basis
Suppression of the keto-emission in polyfluorene light-emitting diodes : Experiments and models
(2004)
The spectral characteristics of polyfluorene (PF)-based light-emitting diodes (LEDs) containing a defined low concentration of either keto-defects or of the polymer poly(9.9-octylfuorene-co-benzothiadiazole) (F8BT) are preseneted. Both types of blend layers were tested in different device configurations with respect to the relative and absolute intensities of green blue emission components. It is shown that blending hole-transporting molecules into the emission layer at low concentration or incorporation of a suitable hole-transport layer reduces the green emission contribution in the electroluminescence (EL) spectrum of the PF:F8BT blend, which is similar to what is observed for the keto- containing PF layer. We conclude that the keto-defects in PF homopolymer layers mainly constitute weakly emissive electron traps, in agreement with the results of quantum-mechanical calculations
Aggregation of chromophores in the solid state commonly causes undesirable red shifts in the emission spectra and/or emission quenching. To overcome this problem, we have prepared soluble perylenetetracarboxidiimide dyes in which the chromophores are effectively shielded by polyphenylene dendrimers attached in the bay positions. Models show that attachment of the shielding units in the bay position should provide more efficient shielding than attaching them via the imide moieties. The dendrimers possess excellent film-forming properties due to alkyl substituents on their peripheries. The lack of a red shift in emission upon going from solution to the solid state indicates the dendrons suppress interaction of the emissive cores, leading to pure red-orange emission. Single-layer LEDs produce red-orange emission with relatively low efficiency especially for the higher generation dendrons, which is attributed to poor charge conduction. LEDs using blends of the dendrimers and the undendronized dye as a model compound in PVK have been investigated, and a model to extract relative charge injection rates through the dendritic scaffold from the spectral contributions in the EL spectra is developed
The presence of partially folded intermediates along the folding funnel of proteins has been suggested to be a signature of potentially aggregating systems. Many studies have concluded that metastable, highly flexible intermediates are the basic elements of the aggregation process. In a previous paper, we demonstrated how the choice between aggregation and folding behavior was influenced by hydrophobicity distribution patterning along the sequence, as quantified by recurrence quantification analysis (RQA) of the Myiazawa-Jernigan coded primary structures. In the present paper, we tried to unify the "partially folded intermediate" and "hydrophobicity/charge" models of protein aggregation verifying the ability of an empirical relation, developed for rationalizing the effect of different mutations on aggregation propensity of acyl-phosphatase and based on the combination of hydrophobicity RQA and charge descriptors, to discriminate in a statistically significant way two different protein populations: (a) proteins that fold by a process passing by partially folded intermediates and (b) proteins that do not present partially folded intermediates
Optically induced mass transport studied by scanning near-field optical- and atomic force microscopy
(2004)
Some functionalised thin organic films show a very unusual property, namely the light induced material transport. This effect enables to generate three-dimensional structures on surfaces of azobenzene containing films only caused by special optical excitation. The physical mechanisms underlying this phenomenon have not yet been fully understood, and in addition, the dimensions of structures created in that way are macroscopic because of the optical techniques and the wavelength of the used light. In order to gain deeper insight into the physical fundamentals of this phenomenon and to open possibilities for applications it is necessary to create and study structures not only in a macroscopic but also in nanometer range. We first report about experiments to generate optically induced nano structures even down to 100 nm size. The optical stimulation was therefore made by a Scanning Near-field Optical Microscope (SNOM). Secondly, physical conditions inside optically generated surface relief gratings were studied by measuring mechanical properties with high lateral resolution via pulse force mode and force distance curves of an AFM
A statistical model describing the propensity for protein aggregation is presented. Only amino-acid hydrophobicity values and calculated net charge are used for the model. The combined effects of hydrophobic patterns as computed by the signal analysis technique, recurrence quantification, plus calculated net charge were included in a function emphasizing the effect of singular hydrophobic patches which were found to be statistically significant for predicting aggregation propensity as quantified by fluorescence studies obtained from the literature. These results suggest preliminary evidence for a mesoscopic principle for protein folding/aggregation. (C) 2004 Elsevier B.V. All rights reserved
All parameters describing the charge carrier dynamics in a poly(phenylene vinylene)-based photorefractive (PR) composite relevant to PR grating dynamics were determined using photoconductivity studies under various illumination conditions. In particular, the values of the coefficients for trap filling and recombination of charges with ionized sensitizer molecules could be extracted independently. It is concluded that the PR growth time without preillumination is mostly determined by the competition between deep trap filling and recombination with ionized sensitizer molecules. Further, the pronounced increase in PR speed upon homogeneous preillumination (gating) as reported recently is quantitatively explained by deep trap filling
We demonstrate efficient single-layer polymer phosphorescent light-emitting devices based on a green-emitting iridium complex and a polymer host co-doped with electron-transporting and hole-transporting molecules. These devices can be operated at relatively low voltages, resulting in a power conversion efficiency of up to 24 lm/W at luminous efficiencies exceeding 30 cd/A. The overall performances of these devices suggest that efficient electrophosphorescent devices with acceptable operating voltages can be achieved in very simple device structures fabricated by spin coating. (C) 2004 American Institute of Physics
A commercially available Ir complex has been employed for the preparation of highly efficient (see Figure) single-layer phosphorescent polymer light,emitting diodes by use of appropriate thermal treatment and proper adjustment of the layer composition. These devices exhibit essentially no dependence of the driving field on the concentration of the Ir complex, suggesting that the build-up of space-charge in the layer is insignificant
The optical, structural, and electrical properties of thin layers made from poly(3-hexylthiophene) (P3HT) samples of different molecular weights are presented. As reported in a previous paper by Kline et al., Adv. Mater 2003, 15, 1519, the mobilities of these layers are a strong function of the molecular weight, with the largest mobility found for the largest molecular weight. Atomic force microscopy studies reveal a complex polycrystalline morphology which changes considerably upon annealing. X-ray studies show the occurrence of a layered phase for all P3HT fractions, especially after annealing at 1.50 degreesC . However, there is no clear correlation between the differences in the transport properties and the data from structural investigations. In order to reveal the processes limiting the mobility in these layers, the transistor properties were investigated as a function of temperature. The mobility decreases continuously with increasing temperatures; with the same trend pronounced thermochromic effects of the P3HT films occur. Apparently, the polymer chains adopt a more twisted, disordered conformation at higher temperatures, leading to interchain transport barriers. We conclude that the backbone conformation of the majority of the bulk material rather than the crystallinity of the layer is the most crucial parameter controlling the charge transport in these P3HT layers. This interpretation is supported by the significant blue-shift of the solid-state absorption spectra with decreasing molecular weight, which is indicative of a larger distortion of the P3HT backbone in the low-molecular weight P3HT layers
The spatial variability of landscape features such as topography, soils and vegetation defines the spatial pattern of hydrological state variables like soil moisture. Spatial variability thereby controls the functional behaviour of the landscape in terms of its runoff response. A consequence of spatial variability is that exchange processes between landscape patches can occur at various spatial scales ranging from the plot to the basin scale. In semi-arid areas, the lateral redistribution of surface runoff between adjacent landscape patches is an important process. For applications to large river basins of 10(4)-10(5) km(2) in size, a multi-scale landscape discretization scheme is presented in this paper. The landscape is sub-divided into modelling units within a hierarchy of spatial scale levels. By delineating areas characterized by a typical toposequence, organised and random variability of landscape characteristics is captured in the model. Using runoff-runon relationships with transition frequencies based on areal fractions of modelling units, lateral surface and subsurface water fluxes between modelling units at the hillslope scale are represented. Thus, the new approach allows for a manageable description of interactions between fine-scale landscape features for inclusion in coarse-scale models. Model applications for the State of Ceara (148,000 km(2)) in the north- east of Brazil demonstrate the importance of taking into account landscape variability and interactions between landscape patches in a semi-arid environment. Using mean landscape characteristics leads to a considerable underestimation of infiltration-excess surface runoff and total simulated runoff. Re-infiltration of surface runoff and lateral redistribution processes between landscape patches cause a reduction of runoff volumes at the basin scale and contribute to the amplification of variations in runoff volumes relative to variations in rainfall volumes for semi-arid areas. (C) 2004 Elsevier B.V. All rights reserved
Approximation of Groundwater - Surface Water - Interactions in a Mesoscale Lowland River Catchment
(2004)
Probleme, Grenzen und Herausforderungen der hydrologischen Modellierung: Wasserhaushalt und Abfluss
(2004)
Given an algebra of pseudo-differential operators on a manifold, an elliptic element is said to be a reduction of orders, if it induces isomorphisms of Sobolev spaces with a corresponding shift of smoothness. Reductions of orders on a manifold with boundary refer to boundary value problems. We employ specific smooth symbols of arbitrary real orders and with parameters, and we show that the associated operators induce isomorphisms between Sobolev spaces on a given manifold with boundary. Such operators for integer orders have the transmission property and belong to the calculus of Boutet de Monvel [1], cf. also [9]. In general, they fit to the algebra of boundary value problems without the transmission property in the sense of [17] and [24]. Order reducing elements of the present kind are useful for constructing parametrices of mixed elliptic problems. We show that order reducing symbols have the Volterra property and are parabolic of anisotropy 1; analogous relations are formulated for arbitrary anisotropies. We then investigate parameter-dependent operators, apply a kernel cut-off construction with respect to the parameter and show that corresponding holomorphic operator-valued Mellin symbols reduce orders in weighted Sobolev spaces on a cone with boundary. We finally construct order reducing operators on a compact manifold with conical singularities and boundary
Mixed elliptic problems for differential operators A in a domain Q with smooth boundary Y are studied in the form Au = f in Omega, T+/-u = g+/- on Y+/-, where Y+/- subset of Y are manifolds with a common boundary Z, such that Y- boolean OR Y+ = Y and Y- boolean AND Y+ = z, with boundary conditions T+/- on Y+/- (with smooth coefficients up to Z from the respective side) satisfying the Shapiro-Lopatinskij condition. We consider such problems in standard Sobolev spaces and characterise natural extra conditions on the interface Z with an analogue of Shapiro-Lopatinskij ellipticity for an associated transmission problem on the boundary; then the extended operator is Fredholm. The transmission operators on the boundary with respect to Z belong to a complete pseudo-differential calculus, a modification of the algebra of boundary value problems without the transmission property. We construct parametrices of elliptic elements in that calculus, and we obtain parametrices of the original mixed problems under additional conditions on the interface. We consider the Zaremba problem and other mixed problems for the Laplace operator, determine the number of extra conditions and calculate the index of associated Fredholm operators. (C) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Simple water balance modelling of surface reservoir systems in a large data-scarce semiarid region
(2004)
Water resources in dryland areas are often provided by numerous surface reservoirs. As a basis for securing future water supply, the dynamics of reservoir systems need to be simulated for large river basins, accounting for environmental change and an increasing water demand. For the State of Ceara in semiarid Northeast Brazil, with several thousands of reservoirs, a simple deterministic water balance model is presented. Within a cascade-type approach, the reservoirs are grouped into six classes according to storage capacity, rules for flow routing between reservoirs of different size are defined, and water withdrawal and return flow due to human water use is accounted for. While large uncertainties in model applications exist, particularly in terms of reservoir operation rules, model validation against observed reservoir storage volumes shows that the approach is a reasonable simplification to assess surface water availability in large river basins. The results demonstrate the large impact of reservoir storage on downstream flow and stress the need for a coupled simulation of runoff generation, network redistribution and water use
Parametrices of elliptic boundary value problems for differential operators belong to an algebra of pseudodifferential operators with the transmission property at the boundary. However, generically, smooth symbols on a manifold with boundary do not have this property, and several interesting applications require a corresponding more general calculus. We introduce here a new algebra of boundary value problems that contains Shapiro-Lopatinskij elliptic as well as global projection conditions; the latter ones are necessary, if an analogue of the Atiyah-Bott obstruction does not vanish. We show that every elliptic operator admits (up to a stabilisation) elliptic conditions of that kind. Corresponding boundary value problems are then Fredholm in adequate scales of spaces. Moreover, we construct parametrices in the calculus. (C) 2003 Elsevier Inc. All rights reserved