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Shakedown analysis of two dimensional structures by an edge-based smoothed finite element method
(2010)
In this paper we propose a stochastic programming method to analyse limit and shakedown of structures under uncertainty condition of strength. Based on the duality theory, the shakedown load multiplier formulated by the kinematic theorem is proved actually to be the dual form of the shakedown load multiplier formulated by static theorem. In this investigation a dual chance constrained programming algorithm is developed to calculate simultaneously both the upper and lower bounds of the plastic collapse limit and the shakedown limit. The edge-based smoothed finite element method (ES-FEM) with three-node linear triangular elements is used for structural analysis.
Structural design analyses are conducted with the aim of verifying the exclusion of ratchetting. To this end it is important to make a clear distinction between the shakedown range and the ratchetting range. The performed experiment comprised a hollow tension specimen which was subjected to alternating axial forces, superimposed with constant moments. First, a series of uniaxial tests has been carried out in order to calibrate a bounded kinematic hardening rule. The load parameters have been selected on the basis of previous shakedown analyses with the PERMAS code using a kinematic hardening material model. It is shown that this shakedown analysis gives reasonable agreement between the experimental and the numerical results. A linear and a nonlinear kinematic hardening model of two-surface plasticity are compared in material shakedown analysis.
Treatment of posttraumatic osteoarthritis of the radial column of the elbow joint remains a challenging yet common issue.
While partial joint replacement leads to high revision rates, radial head excision has shown to severely increase joint instability. Shortening osteotomy of the radius could be an option to decrease the contact pressure of the radiohumeral joint and thereby pain levels without causing valgus instability. Hence, the aim of this biomechanical study was to evaluate the effects of radial shortening on axial load distribution and valgus stability of the elbow joint.
We present an electromechanically coupled Finite Element model for cardiac tissue. It bases on the mechanical model for cardiac tissue of Hunter et al. that we couple to the McAllister-Noble-Tsien electrophysiological model of purkinje fibre cells. The corresponding system of ordinary differential equations is implemented on the level of the constitutive equations in a geometrically and physically nonlinear version of the so-called edge-based smoothed FEM for plates. Mechanical material parameters are determined from our own pressure-deflection experimental setup. The main purpose of the model is to further examine the experimental results not only on mechanical but also on electrophysiological level down to ion channel gates. Moreover, we present first drug treatment simulations and validate the model with respect to the experiments.
Following the successful PHILAE landing with ESA's ROSETTA probe and the launch of the MINERVA rovers and the Mobile Asteroid Surface Scout, MASCOT, aboard the JAXA space probe, HAYABUSA2, to asteroid (162173) Ryugu, small landers have found increasing interest. Integrated at the instrument level in their mothership they support small solar system body studies. With efficient capabilities, resource-friendly design and inherent robustness they are an attractive exploration mission element. We discuss advantages and constraints of small sub-spacecraft, focusing on emerging areas of activity such as asteroid diversity studies, planetary defence, and asteroid mining, on the background of our projects PHILAE, MASCOT, MASCOT2, the JAXA-DLR Solar Power Sail Lander Design Study, and others. The GOSSAMER-1 solar sail deployment concept also involves independent separable sub-spacecraft operating synchronized to deploy the sail. Small spacecraft require big changes in the way we do things and occasionally a little more effort than would be anticipated based on a traditional large spacecraft approach. In a Constraints-Driven Engineering environment we apply Concurrent Design and Engineering (CD/CE), Concurrent Assembly, Integration and Verification (CAIV) and Model-Based Systems Engineering (MBSE). Near-term solar sails will likely be small spacecraft which we expect to harmonize well with nano-scale separable instrument payload packages.
Physical interaction with small solar system bodies (SSSB) is the next step in planetary science, planetary in-situ resource utilization (ISRU), and planetary defense (PD). It requires a broader understanding of the surface properties of the target objects, with particular interest focused on those near Earth. Knowledge of composition, multi-scale surface structure, thermal response, and interior structure is required to design, validate and operate missions addressing these three fields. The current level of understanding is occasionally simplified into the phrase, ”If you’ve seen one asteroid, you’ve seen one asteroid”, meaning that the in-situ characterization of SSSBs has yet to cross the threshold towards a robust and stable scheme of classification. This would enable generic features in spacecraft design, particularly for ISRU and science missions. Currently, it is necessary to characterize any potential target object sufficiently by a dedicated pre-cursor mission to design the mission which then interacts with the object in a complex fashion. To open up strategic approaches, much broader in-depth characterization of potential target objects would be highly desirable. In SSSB science missions, MASCOT-like nano-landers and instrument carriers which integrate at the instrument level to their mothership have met interest. By its size, MASCOT is compatible with small interplanetary missions. The DLR-ESTEC Gossamer Roadmap Science Working Groups‘ studies identified Multiple Near-Earth asteroid (NEA) Rendezvous (MNR) as one of the space science missions only feasible with solar sail propulsion. The Solar Polar Orbiter (SPO) study showed the ability to access any inclination, theDisplaced-L1 (DL1) mission operates close to Earth, where objects of interest to PD and for ISRU reside. Other studies outline the unique capability of solar sails to provide access to all SSSB, at least within the orbit of Jupiter, and significant progress has been made to explore the performance envelope of near-term solar sails for MNR. However, it is difficult for
sailcraft to interact physically with a SSSB. We expand and extend the philosophy of the recently qualified DLR Gossamer solar sail deployment technology using efficient multiple sub-spacecraft integration to also include landers for one-way in-situ investigations and sample-return missions by synergetic integration and operation of sail and lander. The MASCOT design concept and its characteristic features have created an ideal counterpart for thisand has already been adapted to the needs of the AIM spacecraft, former part of the NASA-ESA AIDA missionDesigning the 69th International Astronautical Congress (IAC), Bremen, Germany, 1-5 October 2018. IAC-18-F1.2.3 Page 2 of 17 combined spacecraft for piggy-back launch accommodation enables low-cost massively parallel access to the NEA population.
Following the recent successful landings and occasional re-awakenings of PHILAE, the lander carried aboard ROSETTA to comet 67P/Churyumov-Gerasimenko, and the launch of the Mobile Asteroid Surface Scout, MASCOT, aboard the HAYABUSA2 space probe to asteroid (162173) Ryugu we present an overview of the characteristics and peculiarities of small spacecraft missions to small solar system bodies (SSSB). Their main purpose is planetary science which is transitioning from a ‘pure’ science of observation of the distant to one also supporting in-situ applications relevant for life on Earth. Here we focus on missions at the interface of SSSB science and planetary defence applications. We provide a brief overview of small spacecraft SSSB missions and on this background present recent missions, projects and related studies at the German Aerospace Center, DLR, that contribute to the worldwide planetary defence community. These range from Earth orbit technology demonstrators to active science missions in interplanetary space. We provide a summary of experience from recently flown missions with DLR participation as well as a number of studies. These include PHILAE, the lander of ESA’s ROSETTA comet rendezvous mission now on the surface of comet 67P/Churyumov-Gerasimenko, and the Mobile Asteroid Surface Scout, MASCOT, now in cruise to the ~1 km diameter C-type near-Earth asteroid (162173) Ryugu aboard the Japanese sample-return probe HAYABUSA2. We introduce the differences between the conventional methods employed in the design, integration and testing of large spacecraft and the new approaches developed by small spacecraft projects. We expect that the practical experience that can be gained from projects on extremely compressed timelines or with high-intensity operation phases on a newly explored small solar system body can contribute significantly to the study, preparation and realization of future planetary defence related missions. One is AIDA (Asteroid Impact & Deflection Assessment), a joint effort of ESA, JHU/APL, NASA, OCA and DLR, combining JHU/APL’s DART (Double Asteroid Redirection Test) and ESA’s AIM (Asteroid Impact Monitor) spacecraft in a mission towards near-Earth binary asteroid system (65803) Didymos. DLR is currently applying MASCOT heritage and lessons learned to the design of MASCOT2, a lander for the AIM mission to support a bistatic low frequency radar experiment with PHILAE/ROSETTA CONSERT heritage to explore the inner structure of Didymoon which is the designated impact target for DART.
Small Spacecraft in Planetary Defence Related Applications–Capabilities, Constraints, Challenges
(2015)
In this paper we present an overview of the characteristics and peculiarities of small spacecraft missions related to planetary defence applications. We provide a brief overview of small spacecraft missions to small solar system bodies. On this background we present recent missions and selected projects and related studies at the German Aerospace Center, DLR, that contribute to planetary defence related activities. These range from Earth orbit technology demonstrators to active science missions in interplanetary space. We provide a summary of experience from recently flown missions with DLR participation as well as a number of studies. These include PHILAE, the lander recently arrived on comet 67P/Churyumov-Gerasimenko aboard ESA’s ROSETTA comet rendezvous mission, and the Mobile Asteroid Surface Scout, MASCOT, now underway to near-Earth asteroid (162173) 1999 JU3 aboard the Japanese sample-return probe HAYABUSA-2. We introduce the differences between the conventional methods employed in the design, integration and testing of large spacecraft and the new approaches developed by small spacecraft projects. We expect that the practical experience that can be gained from projects on extremely
compressed timelines or with high-intensity operation phases on a newly explored small solar system body can contribute significantly to the study, preparation and realization of future planetary defence related missions. One is AIDA (Asteroid Impact & Deflection Assessment), a joint effort of ESA,JHU/APL, NASA, OCA and DLR, combining JHU/APL’s DART (Double Asteroid Redirection Test) and ESA’s AIM (Asteroid Impact Monitor) spacecraft in a mission towards
near-Eath binary asteroid (65803) Didymos.
Smoothed Finite Element Methods for Nonlinear Solid Mechanics Problems: 2D and 3D Case Studies
(2016)
The Smoothed Finite Element Method (SFEM) is presented as an edge-based and a facebased techniques for 2D and 3D boundary value problems, respectively. SFEMs avoid shortcomings of the standard Finite Element Method (FEM) with lower order elements such as overly stiff behavior, poor stress solution, and locking effects. Based on the idea of averaging spatially the standard strain field of the FEM over so-called smoothing domains SFEM calculates the stiffness matrix for the same number of degrees of freedom (DOFs) as those of the FEM. However, the SFEMs significantly improve accuracy and convergence even for distorted meshes and/or nearly incompressible materials.
Numerical results of the SFEMs for a cardiac tissue membrane (thin plate inflation) and an artery (tension of 3D tube) show clearly their advantageous properties in improving accuracy particularly for the distorted meshes and avoiding shear locking effects.
Soft Materials in Technology and Biology – Characteristics, Properties, and Parameter Identification
(2008)
Solar sails are large and lightweight reflective structures that are propelled by solar radiation pressure. This chapter covers their orbital and attitude dynamics and control. First, the advantages and limitations of solar sails are discussed and their history and development status is outlined. Because the dynamics of solar sails is governed by the (thermo-)optical properties of the sail film, the basic solar radiation pressure force models have to be described and compared before parameters to measure solar sail performance can be defined. The next part covers the orbital dynamics of solar sails for heliocentric motion, planetocentric motion, and motion at Lagrangian equilibrium points. Afterwards, some advanced solar radiation pressure force models are described, which allow to quantify the thrust force on solar sails of arbitrary shape, the effects of temperature, of light incidence angle, of surface roughness, and the effects of optical degradation of the sail film in the space environment. The orbital motion of a solar sail is strongly coupled to its rotational motion, so that the attitude control of these soft and flexible structures is very challenging, especially for planetocentric orbits that require fast attitude maneuvers. Finally, some potential attitude control methods are sketched and selection criteria are given.
Near-Earth asteroid 99942 Apophis provides a typical example for the evolution of asteroid orbits that lead to Earth-impacts after a close Earth-encounter that results in a resonant return. Apophis will have a close Earth-encounter in 2029 with potential very close subsequent Earth-encounters (or even an impact) in 2036 or later, depending on whether it passes through one of several so-called gravitational keyholes during its 2029-encounter. Several pre-2029-deflection scenarios to prevent Apophis from doing this have been investigated so far. Because the keyholes are less than 1 km in size, a pre-2029 kinetic impact is clearly the best option because it requires only a small change in Apophis' orbit to nudge it out of a keyhole. A single solar sail Kinetic Energy Impactor (KEI) spacecraft that impacts Apophis from a retrograde trajectory with a very high relative velocity (75-80 km/s) during one of its perihelion passages at about 0.75 AU would be a feasible option to do this. The spacecraft consists of a 160 m x 160 m, 168 kg solar sail assembly and a 150 kg impactor. Although conventional spacecraft can also achieve the required minimum deflection of 1 km for this approx. 320 m-sized object from a prograde trajectory, our solar sail KEI concept also allows the deflection of larger objects. In this paper, we also show that, even after Apophis has flown through one of the gravitational keyholes in 2029, solar sail Kinetic Energy Impactor (KEI) spacecraft are still a feasible option to prevent Apophis from impacting the Earth, but many KEIs would be required for consecutive impacts to increase the total Earth-miss distance to a safe value. In this paper, we elaborate potential pre- and post-2029 KEI impact scenarios for a launch in 2020, and investigate tradeoffs between different mission parameters.
Solar Sail Kinetic Energy Impactor Trajectory Optimization for an Asteroid-Deflection Mission
(2007)
Solar sails enable missions to the outer solar system and beyond, although the solar
radiation pressure decreases with the square of solar distance. For such missions, the solar sail may gain a large amount of energy by first making one or more close approaches to the sun. Within this paper, optimal trajectories for solar sail missions to the outer planets and into near interstellar space (200 AU) are presented. Thereby, it is shown that even near/medium-term solar sails with relatively moderate performance allow reasonable transfer times to the boundaries of the solar system.
Solar Sail Trajectory Optimization for Intercepting, Impacting, and Deflecting Near-Earth Asteroids
(2005)
Solar sailcraft of the first generation technology development / Seboldt, Wolfgang ; Dachwald, Bernd
(2003)
Solar Sails for Near- and Medium-Term Scientific Deep Space Missions / W. Sebolt ; B. Dachwald
(2005)
Solar sails are propelled in space by reflecting solar photons off large mirroring surfaces, thereby transforming the momentum of the photons into a propulsive force. This innovative concept for low-thrust space propulsion works without any propellant and thus provides a wide range of opportunities for highenergy low-cost missions. Offering an efficient way of propulsion, solar sailcraft could close a gap in transportation options for highly demanding exploration missions within our solar system and even beyond. On December 17th, 1999, a significant step was made towards the realization of this technology: a lightweight solar sail structure with an area of 20 m × 20 m was successfully deployed on ground in a large facility at the German Aerospace Center (DLR) at Cologne. The deployment from a package of 60 cm × 60 cm × 65 cm with a total mass of less than 35 kg was achieved using four extremely light-weight carbon fiber reinforced plastics (CFRP) booms with a specific mass of 100 g/m. The paper briefly reviews the basic principles of solar sails as well as the technical concept and its realization in the ground demonstration experiment, performed in close cooperation between DLR and ESA. Next possible steps are outlined. They could comprise the in-orbit demonstration of the sail deployment on the upper stage of a low-cost rocket and the verification of the propulsion concept by an autonomous and free flying solar sail in the frame of a scientific mission. It is expected that the present design could be extended to sail sizes of about (40 m)2 up to even (70 m)2 without significant mass penalty. With these areas, the maximum achievable thrust at 1 AU would range between 10 and 40 mN – comparable to some electric thrusters. Such prototype sails with a mass between 50 and 150 kg plus a micro-spacecraft of 50 to 250 kg would have a maximum acceleration in the order of 0.1 mm/s2 at 1 AU, corresponding to a maximum ∆V-capability of about 3 km/s per year. Two near/medium-term mission examples to a near-Earth asteroid (NEA) will be discussed: a rendezvous mission
and a sample return mission.
20 years after the successful ground deployment test of a (20 m) 2 solar sail at DLR Cologne, and in the light of the upcoming U.S. NEAscout mission, we provide an overview of the progress made since in our mission and hardware design studies as well as the hardware built in the course of our solar sail technology development. We outline the most likely and most efficient routes to develop solar sails for useful missions in science and applications, based on our developed `now-term' and near-term hardware as well as the many practical and managerial lessons learned from the DLR-ESTEC Gossamer Roadmap. Mission types directly applicable to planetary defense include single and Multiple NEA Rendezvous ((M)NR) for precursor, monitoring and follow-up scenarios as well as sail-propelled head-on retrograde kinetic impactors (RKI) for mitigation. Other mission types such as the Displaced L1 (DL1) space weather advance warning and monitoring or Solar Polar Orbiter (SPO) types demonstrate the capability of near-term solar sails to achieve asteroid rendezvous in any kind of orbit, from Earth-coorbital to extremely inclined and even retrograde orbits. Some of these mission types such as SPO, (M)NR and RKI include separable payloads. For one-way access to the asteroid surface, nanolanders like MASCOT are an ideal match for solar sails in micro-spacecraft format, i.e. in launch configurations compatible with ESPA and ASAP secondary payload platforms. Larger landers similar to the JAXA-DLR study of a Jupiter Trojan asteroid lander for the OKEANOS mission can shuttle from the sail to the asteroids visited and enable multiple NEA sample-return missions. The high impact velocities and re-try capability achieved by the RKI mission type on a final orbit identical to the target asteroid's but retrograde to its motion enables small spacecraft size impactors to carry sufficient kinetic energy for deflection.
The scientific interest for near-Earth asteroids as well as the interest in potentially hazardous asteroids from the perspective of planetary defense led the space community to focus on near-Earth asteroid mission studies. A multiple near-Earth asteroid rendezvous mission with close-up observations of several objects can help to improve the characterization of these asteroids. This work explores the design of a solar-sail spacecraft for such a mission, focusing on the search of possible sequences of encounters and the trajectory optimization. This is done in two sequential steps: a sequence search by means of a simplified trajectory model and a set of heuristic rules based on astrodynamics, and a subsequent optimization phase. A shape-based approach for solar sailing has been developed and is used for the first phase. The effectiveness of the proposed approach is demonstrated through a fully optimized multiple near-Earth asteroid rendezvous mission. The results show that it is possible to visit five near-Earth asteroids within 10 years with near-term solar-sail technology.
Recently, the SHARP Corporation, Japan, has developed the world’s first "Plasma Cluster Ions (PCI)" air purification technology using plasma discharge to generate cluster ions. The new plasma cluster device releases positive and negative ions into the air, which are able to decompose and deactivate harmful airborne substances by chemical reactions. Because cluster ions consist of positive and negative ions that normally exist in the natural world, they are completely harmless and safe to humans. The amount of ozone generated by cluster ions is less than 0.01 ppm, which is significantly less than the 0.05-ppm standard for industrial operations and consumer electronics. This amount, thus, has no harming effects whatsoever on the human body. But particular properties and chemical processes in PCI treatment are still under study. It has been shown that PCI in most cases show strongly pronounced irreversible killing effects in respect of airborne microflora due to free-radical induced reactions and can be considered as a potent technology to disinfect both home, medical and industrial appliances.
At the present time, one of the most serious environmental problems of Central Asia and South Kazakhstan is the ongoing large-scale deterioration of principal urban tree populations. Several major centers of massive spread of invasive plant pests have been found in urban dendroflora of this region. The degree of damage of seven most wide-spread aboriginal tree species was found to range from 21.4±1.1 to 85.4±1.8%. In particular, the integrity of the native communities of sycamore (Platanus spp.), willow (Salix spp.), poplar (Populus spp.) and elm (Ulmus spp.) is highly endangered. Our taxonomic analysis of the most dangerous tree pests of the region has revealed them as neobiontic xylophilous insects such as Cossus cossus L. (Order: Lepidoptera L.) Monochamus urussovi Fisch., Monochamus sutor L., Acanthocinus aedelis L. and Ñetonia aureate L. (Order: Coleoptera L.). We relate the origin of this threatening trend with the import of industrial wood in the mid 90s of the last century that was associated with high degree of the constructional work in the region. Because of the absence of efficient natural predators of the pest species, the application of microbiological methods of the pest control and limitation is suggested.
When confining pressure is low or absent, extensional fractures are typical, with fractures occurring on unloaded planes in rock. These “paradox” fractures can be explained by a phenomenological extension strain failure criterion. In the past, a simple empirical criterion for fracture initiation in brittle rock has been developed. But this criterion makes unrealistic strength predictions in biaxial compression and tension. A new extension strain criterion overcomes this limitation by adding a weighted principal shear component. The weight is chosen, such that the enriched extension strain criterion represents the same failure surface as the Mohr–Coulomb (MC) criterion. Thus, the MC criterion has been derived as an extension strain criterion predicting failure modes, which are unexpected in the understanding of the failure of cohesive-frictional materials. In progressive damage of rock, the most likely fracture direction is orthogonal to the maximum extension strain. The enriched extension strain criterion is proposed as a threshold surface for crack initiation CI and crack damage CD and as a failure surface at peak P. Examples show that the enriched extension strain criterion predicts much lower volumes of damaged rock mass compared to the simple extension strain criterion.
Two single-incision mini-slings used for treating urinary incontinence in women are compared with respect to the stresses they produce in their surrounding tissue. In an earlier paper we experimentally observed that these implants produce considerably different stress distributions in a muscle tissue equivalent. Here we perform 2D finite element analyses to compare the shear stresses and normal stresses in the tissue equivalent for the two meshes and to investigate their failure behavior. The results clearly show that the Gynecare TVT fails for increasing loads in a zipper-like manner because it gradually debonds from the surrounding tissue. Contrary to that, the tissue at the ends of the DynaMesh-SIS direct may rupture but only at higher loads. The simulation results are in good agreement with the experimental observations thus the computational model helps to interpret the experimental results and provides a tool for qualitative evaluation of mesh implants.
Patients after coarctation repair still have an increased risk of cardiovascular or cerebrovascular events. This has been explained by the persisting hypertension and alterations in the peripheral vessels. However, involvement of the central vessels such as the retinal arteries is virtually unknown. A total of 34 patients after coarctation repair (22 men and 12 women; 23 to 58 years old, age range 0 to 32 years at surgical repair) and 34 nonhypertensive controls underwent structural and functional retinal vessel analysis. Using structural analysis, the vessel diameters were measured. Using functional analysis, the endothelium-dependent vessel dilation in response to flicker light stimulation was assessed. In the patients after coarctation repair, the retinal arteriolar diameter was significantly reduced compared to that of the controls (median 182 μm, first to third quartile 171 to 197; vs 197 μm, first to third quartile 193 to 206; p <0.001). These findings were independent of the peripheral blood pressure and age at intervention. No differences were found for venules. The functional analysis findings were not different between the patients and controls (maximum dilation 3.5%, first to third quartile 2.1% to 4.5% vs 3.6%, first to third quartile 2.2% to 4.3%; p = 0.81), indicating preserved autoregulative mechanisms. In conclusion, the retinal artery diameter is reduced in patients after coarctation repair, independent of their current blood pressure level and age at intervention. As a structural marker of chronic vessel damage associated with past, current, or future hypertension, retinal arteriolar narrowing has been linked to stroke incidence. These results indicate an involvement of cerebral microcirculation in aortic coarctation, despite timely repair, and might contribute to explain the increased rate of cerebrovascular events in such patients.
Biodiversity and the coexistence of species have puzzled and fascinated biologists since decades and is a hotspot in todays’ natural sciences. Preserving this biodiversity is a great challenge as habitats and environments underlying tremendous changes like climate change and the loss of natural habitats, which are mainly due to anthropogenic influences. The coexistence of numerous species even in homogeneous environments is a stunning feature of natural communities and has been summarized under the term ‘paradox of plankton’. Up to now, there are several mechanisms discussed, which may contribute to local and global diversity of organisms. Several interspecific trade offs have been identified maintaining the coexistence of species like their abilities regarding competition and predator avoidance, their capability to disperse in space and time, and their ability to exploit variable resources. Further, micro-evolutionary dynamics supporting the coexistence of species have been added to our knowledge, and deriving from theoretical deterministic models, non-linear dynamics which describe the temporal fluctuation of abundances of organisms. Whereas competition and predation seem to be clue structural elements within interacting organisms, the intrinsic dynamic behavior – by means of temporal changes in abundance - plays an important role regarding coexistence within a community. The present work sheds light on different factors affecting the coexistence of species using experimental microbial model systems consisting of a bacterivorous ciliate as the predator and two bacteria strains as prey organism. Additionally, another experimental setup consisting of two up to five bacteria species competing for one limiting resource was investigated. Highly controllable chemostat systems were established to exclude extrinsic disturbances. According to theoretical analyses I was able to show - experimentally and theoretically - that phenotypic plasticity of one species within a microbial one-predator-two-prey food web enlarges the range of possible coexistence of all species under different dynamic conditions, compared to a food web without phenotypic plasticity. This was accompanied by non-linear (chaotic) population dynamics within all experimental systems showing phenotypic plasticity. The experiments on the interplay of competition, predation and invasion showed that all aspects have an influence on species coexistence. Under undisturbed controlled conditions all aspects were analyzed in detail and in combination. Populations showed oscillations which were shown by quasi-chaotic attractors in phase space diagrams. Competition experiments with two up to five bacteria species competing for one limiting resource showed that all organisms were able to coexist which was mediated by species oscillations entering a regime of chaos. Besides that fact it was found, that the productivity (biomass) as well as the total cell numbers – under the same nutrition supply – increased by an increasing number of species in the experimental systems. Up to now, the occurrence of non-linear dynamics in well controlled experimental studies has been recognized several times and this phenomenon seemed to be more common in natural systems than generally assumed.