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Über dieses Buch

All of us are confronted with complex phenomena occurring in daily life and in the living and inanimate nature surrounding us. Our scientific curiosity strives to unravel the mechanisms at work to create such complexity. Among various approaches to solve this problem, the field of synergetics, developed by Hermann Haken, has proven very successful as a general and interdisciplinary concept for describing and explaining complex phenomena that appear in systems under non-equilibrium conditions. These comprise dynamical states in evolving systems, spatial structure-forming processes, synchronization of states and regulatory mechanisms, and many other examples. The encompassing concepts have been applied to many disciplines, like physics, chemistry, biology, and beyond those also from synergetics to information theory, brain science, economics, and others.

Starting from basic methods of complexity research and synergetics, this volume contains thirty contributions on complex systems that exhibit spontaneous pattern formation far from thermal equilibrium. Written by international experts and young researchers assembled under one roof, this volume reflects state of the art research from a variety of scientific fields and disciplines where complexity theory and synergetics are important or even indispensable tools today and in the future.





About Self-organization of Information and Synergetics

The self-organization of information belongs to the basic topics of Haken’s synergetics. The basic statement of this paper is following Eigen and Haken-Krell that information is a product of evolution and: there is no information processing without life, and there is no life without information processing. The origin of information processing is based on the self-organization of life. In our view, information is not a physical quantity but its transfer is always related to transfer of a universal physical quantity, the entropy. Information cannot be reduced to physics alone, it is basically a non-physical term and bound to the evolution of life. Information-processing systems exist only in the context of life and its descendants: animal behaviour, human sociology, science, technology etc.
Werner Ebeling, Rainer Feistel

Some Aspects of Synergetics. From Laser Light to Cognition

While the study of the selforganized formation of spatial, temporal or even functional structures has a long history in individual scientific disciplines, ranging from physics over medicine till economy, the goal of synergetics is to unearth the underlying principles of selforganization. The explicit example of a physical device, the laser, allows the development and illustration of general concepts such as order parameters, the slaving principle and circular causality. I show how these concepts and the related mathematical approach can be applied to brain processes connected with visual perception. At the level of order parameters, hysteresis in perception and ambivalent figures are dealt with. A bridge between this phenomenological level and that of real neurons is provided by the Synergetic Computer based on the analogy between pattern formation and pattern recognition. A more recently established link with information theory is outlined,—including a brief discussion of Shannon-, pragmatic and semantic information.
Hermann Haken



Dynamical Systems with Time-Varying Delay: Dissipative and More Dissipative Systems

We investigate the dynamical properties of time-delay systems with time-varying delay, where we focus on the influence of the functional structure of the delay. Two universality classes of systems with time-varying delays are presented which lead to fundamental differences in the dynamics of the related systems, as for example the scaling behavior of the Lyapunov spectrum. The classification is connected to the well-known existence or non-existence of topological conjugacies of circle maps to constant rotations. It is independent of the specific delay system.
David Müller, Andreas Otto, Günter Radons

Markov Property of Velocity Increments in Burgers Turbulence

We investigate the intermittency properties of a turbulent flow without pressure described by the Burgers equation. To this end, we make use of a phenomenogical description devised by R. Friedrich and J. Peinke [Phys. Rev. Lett. 78, 863 (1997)] that interprets the turbulent energy cascade as a Markov process in scale. The impact of Burgers-shocks on the Markov property of the velocity increments is discussed and compared to numerical simulations. Furthermore, we give a brief outlook on the use of the Markov property as a possible closure of a hierarchy of multi-increment probability density functions derived directly from the Burgers equation.
Jan Friedrich, Rainer Grauer

Beads in a Rotating Box

Granular materials contain, even though they have been an integral part of human technology since ancient times, numerous mysteries even today. Dynamic phenomena observed in such materials depend on a multitude of parameters, and a general description is still missing. Here, a simple experiment is presented that extends the diversity of these pattern forming phenomena. A flat container (Hele-Shaw cell) is filled with a mixture of granular material and slowly horizontally rotated. Depending on the height of the filling the beads either stripe-wise demix or circulate in convection rolls that are known from hydrodynamic instabilities. Irrespective of some superficial similarity to convection in other granular systems, the driving mechanism is completely different, and only partially understood. Particularly interesting are traveling wave structures where demixed stripes move periodically along the axial direction.
Frank Rietz, Ralf Stannarius

Power Grids as Synergetic Systems

In this article we study power grids from the viewpoint of Synergetics. We show that the typical behavior of self-organizing systems like phase transitions and critical fluctuations can be observed in models for the dynamics of power grids . Therefore we numerically investigate a model, where the phase and voltage dynamics are represented by Kuramoto-like equations. For the topology of the grid we use real world data from the northern Europe high voltage transmission grid.
Oliver Kamps, Katrin Schmietendorf



Nonlinear Phenomena in Heterogeneous Catalysis

The manuscript demonstrates with a few selected examples how the nonlinear phenomena can change the way in which heterogeneous reactions proceed. Firstly it is shown that the kinetic oscillations and synergetic effect can originate due to the diffusion coupling of two different catalysts . Secondly it is demonstrated that due to the nonlinearity of the system and the ability to form spatial structures two catalysts can produce the same catalytic activity as one catalyst.
Marina M. Slinko, Alexei G. Makeev, Nikolai V. Peskov

Catalytic Oxidation of CO—A Striking Example of Synergetics

Experimental Studies of Coupled Zeolite Catalyst Wafers in a Tube Reactor
The dynamics of coupled catalyst wafers in a tube reactor was studied and traced by examining the oxidation of CO on a supported palladium zeolite catalyst under normal pressure in a continuous flow of reactants. An X-type zeolite loaded with 0.05% by weight palladium was used as catalyst. The overall conversion rate exhibits a dynamic behavior with self-affine patterns of excursions to smaller conversion rates on a time scale in the order of some seconds. Similar patterns were observed for the temperature time series of the catalyst wafers. The influence of the flow rate on catalyst wafer coupling was studied. Increasing the flow rate causes decoupling of the catalyst wafers, increased frequency of maximum excursions, increasing rate of smaller excursions, increasing pattern complexity and a decrease in maximum conversion (baseline).
Peter J. Plath, Carsten Ballandis

Understanding Earth: The Self-organization Concept and Its Geological Significance; on the Example of Liesegang-Structures and Electric Fields

The existence of ordered structures in the lithosphere is a well-known and yet remarkable matter of fact. They appear as banded formations, layered and folded structures, diapirs, or cockade ores and in numerous other shapes and forms. Their size ranges from less than one centimeter up to kilometers. In many cases ordered structures develop in self-organized systems, making this concept a useful tool for better understanding complex and diverse processes in geology. In essence, self-organized systems are autonomously shaped units resulting from their inner determination under the influence of environmental conditions. It is important to recognize ordered structures and interpret them as self-organized with respect to their (external) environment and their (inner) components and properties in order to understand their genesis. Conversely, self-organized geological systems that have ordered structures contain valuable information about their genesis that is preserved within the structure. Because geological objects typically preserve only one picture for a very long time-frame, it is important to evaluate the ordered structures from the perspective of self-organization to gain access to the information. Reading this information enables us to learn more about Earth’s history and future, and to use it toward the sustainable management of global resources. For this reason, applying the self-organization concept to geology is also important for the society as a whole.
Sabine Dietrich, Karl-Heinz Jacob

Pattern Formation in Microemulsions Affected by Electric Fields

In living nature and biological morphogenesis, Turing’s mechanism plays an important role. Accordingly, patterns can be found on animal skins or in chemical reactive systems. The formation of these structures is governed by gradients of chemical reactants and ions and thus, of electric fields. Here, an electric field is applied to a chemical compartmentalized reaction (i.e., a water-in-oil microemulsion), in which Turing patterns may form. In this system, percolation can occur when the volume of water is large compared to that of the oil. Thus, water droplets generate a network of water channels. Due to the presence of ions, this formation can be manipulated by an electric field. Turing patterns show a spatial drift, caused by the electric field. The strength of the field resolves the resulting drift velocity of the patterns. Additionally, a reorientation of the patterns is induced by a gradient generated by the electric field.
Patricia Dähmlow, Stefan C. Müller

Unpinning of Spiral Waves

Spiral waves are propagating self-organized structures commonly found in excitable media. Spiral waves of electrical excitation in cardiac systems connect to some arrhythmias, such as tachycardia and fibrillations, potentially leading to sudden cardiac death so that they should be eliminated. Such waves may drift and eventually annihilate at the boundary. However, they can be stabilized, when they are pinned to obstacles, that are weakly excitable or unexcitable regions in the medium. Recently, we used the Belousov-Zhabotinsky solutions, the well-known excitable chemical systems, to study the propagation of spiral waves pinned to obstacles and applied electrical forcing to unpin them in different situations of obstacle size and excitability. We employed simulations with the Oregonator model, a realistic scheme for the Belousov-Zhabotinsky reaction , to confirm the experimental findings as well as to reveal the detailed motions of the spiral waves under some specific conditions that are difficult to be realized in the experiments.
Jiraporn Luengviriya, Malee Sutthiopad, Metinee Phantu, Porramain Porjai, Stefan C. Müller, Chaiya Luengviriya

Battery—Determination and Forecast via Synergetics

A rechargeable battery can be considered as a complex system which is self-organizing under charging, discharging and relaxation. Depending of the type of battery and the kind of external influences, the battery is stressed in many different ways. This leads to an alteration of the internal self-organization processes which are indicative for the present internal state and the future development of the battery. To get detailed information about the State-Of-Charge (SOC) and the State-Of-Health (SOH) of such electrochemical systems we carried out on the one hand internal spatio-temporal measurements of the half-cell potentials within lead-acid batteries. By this, significant structure formation can be observed and is represented using several methods of synergetics. On the other hand, we performed external short-time measurements of the battery’s voltage with differently triggered charging and discharging currents. The response curves of repeated excitations are characteristic for the dynamic behavior of the electrochemical system providing information on the battery’s aging state. The fits of these curves are comprehended in a small set of significant parameters.
Ernst-Christoph Haß, Katharina Knicker, Uwe Sydow, Matthias Schulz, Peter J. Plath

Dynamics and Control of Spiral and Scroll Waves

Excitable systems can sustain different kinds of wave forms like target patterns, two-dimensional spiral waves or their three-dimensional counterparts, the scroll waves . The dynamics of these excitation patterns and their responses to different kinds of internal and external perturbations are being looked into. These waves interact with neighboring vortices, that could lead to either attraction or repulsion and sometimes even their merging. Thermal gradients and electric fields can be used to control the motion of spiral and scroll waves. Scroll waves anchor to unexcitable heterogeneities and external field gradients can be used to unpin them from such obstacles. Our experiments with the Belousov–Zhabotinsky reaction are explained on the basis of numerical simulations using the Barkley model.
Sumana Dutta, Nirmali Prabha Das, Dhriti Mahanta

One-Way Diffusion and Active Motion of Ionic Liquids in a Dissolution Process in Water

The dissolution dynamics of ionic liquid (IL) in ILs/water systems and at an IL/water/air interface is investigated. When a hydrophobic IL dissolves in water, it forms a droplet with a clear interface even though it is soluble to water. The transition between the two liquids remains sharp throughout the dissolution process, and it seems that the diffusion occurs unidirectionally, only outward from the droplet. The dissolution dynamics can be described as an activation process in which IL molecules escape from the droplet with a probability proportional to the surface area of the droplet. This distinctive feature of the dissolution dynamics may relate to alignment of the IL molecules at the IL/water interface. On the other hand, an active motion of water appears around the IL droplet, when hydrophobic ILs dissolve in a thin layer of water with contacting the air/water boundary .
Noriko Oikawa, Rei Kurita



Pattern Formation in Marine Systems

Pattern formation processes in marine science are very versatile, the spatial scale of these patterns ranges from cm to about a 100 km. We demonstrate three mechanisms of pattern formation in the water column as well as in the sediment of the ocean. Plankton patterns result from an intricate interplay between biological growth and transport by ocean currents. Mesoscale hydrodynamic structures like vortices can act as incubators for plankton blooms, while transport barriers in the flow can lead to a segregation of species in certain spatial regions of the ocean characterized by the dominance of a particular plankton species. Spatial patterns of chemicals and microorganisms in the sediment can emanate from a Turing instability leading to inhomogeneous distributions of nutrients and bacteria. Marine aggregates agglomerations of plankton, bacteria and inorganic substances form preferential concentrations, i.e. inhomogeneous distributions in space, which in turn influence strongly aggregation and fragmentation processes and, hence, the export of carbon from the atmosphere to the bottom of the ocean.
Ulrike Feudel

Nonlinear Behavior of a Self-Propelled Droplet Coupled with a Chemical Oscillatory Reaction

Several self-propelled objects have been investigated and used to add functionalities mimicking biological systems. One promising approach is the introduction of nonlinear chemical reactions such as the Belousov-Zhabotinsky (BZ) reaction . In this work we placed an aqueous droplet of the BZ solution into an oil phase composed of monoolein and squalane. The BZ droplet moved spontaneously, and its speed oscillated periodically in synchronization with the redox state of the aqueous solution. This finding and measurements of the interfacial tension between water and squalane reveal that the oscillatory motion of the BZ droplet originated from the oscillation of the Br2-concentration. This system has the potential to reflect the characteristics of nonlinear chemical reactions inside the aqueous droplet: not only periodical oscillation but also bifurcations , hysteresis, and responsiveness to the environment.
Nobuhiko J. Suematsu, Yoshihito Mori, Takashi Amemiya, Satoshi Nakata

All About Cells

Investigating the longterm behaviour of cells in the lymph nodes releasing an activating substance into an intercellular space is a demanding task for mathematical modelling and numerical simulations of reaction-diffusion systems coupled with ordinary differential equations on unstructred 3D grids. To explore the vast amount of computed spatio-temporal data the visualization has to be fast and concise. Persistent homology in discrete Morse theory is a mighty tool for meaningful data reduction. Isosurfaces at characteristic thresholds can be extracted from the data without missing the crucial changes in the topology of the manifold. Visualization results are presented for single and multiple cells with details on the topological concept and computational efforts of the preprocessing steps.
Lisa Kolb, Susanne Krömker

Propagation and Aggregation of Motile Cells of Escherichia coli Pattern

A concentric pulse by motile cells of Escherichia coli (E. coli) propagates and the cells aggregate to form self-organized patterns. We summarize experimental and numerical results on the self-organized pattern formation of E. coli to elucidate some aspects of its mechanism. Our presentation includes experiments on E. coli patterns, as well as numerical simulations on the basis of a reaction-diffusion-chemotaxis model. We find good agreement for one-dimensional propagating fronts in observation and simulation. However, corresponding results for two-dimensional circular bacterial clusters have still not been obtained.
Tatsunari Sakurai, Tohru Tsujikawa, Daisuke Umeno

From Synchronised to Desynchronised Glycolytic Oscillations in Individual Yeast Cells

The cell density dependence of the glycolytic oscillations of intact yeast cells of the strain Saccharomyces carlsbergensis was investigated at both the levels of cell populations and of individual cells. On the collective, macroscopic population level the oscillation amplitudes gradually decreased with decreasing cell densities and below the critical density the collective dynamics became quiescent. However, single cells kept their oscillatory behaviour for low and very low cell densities even when cells were far away and isolated from each other. The lower the cell density of a population, the more the glycolytic oscillations of the individual cells became independent from that of their neighbours. This leads to a broadening of the distribution of oscillation frequencies in low-density populations, and also to a loss of entrainment among the individual cells.
André Weber, Yury Prokazov, Werner Zuschratter, Marcus J. B. Hauser



Financial Market Models

The dynamics of financial markets are discussed. After a brief introduction of the price formation process, we review the statistical features (also known as “stylized facts”) of stock return time series, which exhibit fat tails and intermittent periods of higher or lower volatility. Several models aimed at understanding the mechanisms that lead to these seemingly ubiquitous features of financial markets are then reviewed. Those models have largely been developed within the Econophysics community but we emphasize here that they all contain elements consistent with a Synergetic approach.
Lisa Borland

Structural Change in (Economic) Time Series

Methods for detecting structural changes, or change points, in time series data are widely used in many fields of science and engineering. This chapter sketches some basic methods for the analysis of structural changes in time series data. The exposition is confined to retrospective methods for univariate time series. Several recent methods for dating structural changes are compared using a time series of oil prices spanning more than 60 years. The methods broadly agree for the first part of the series up to the mid-1980s, for which changes are associated with major historical events, but provide somewhat different solutions thereafter, reflecting a gradual increase in oil prices that is not well described by a step function. As a further illustration, 1990s data on the volatility of the Hang Seng stock market index are reanalyzed.
Christian Kleiber

Brain and Coordination Dynamics


Coarse-Graining to Investigate Cerebral Cortex Dynamics

The Case for Experimental Simplification of Biological Phenomena
Advances in multi-channel/multi-detector recordings and data analysis over the last decades have led to an explosion in the exploration of complex neural dynamics in mammalian cortex. Powerful methods have been applied to investigate such dynamics, including connectivity measures (correlation, causality, resting state synchrony, etc.), spatiotemporal pattern analyses, and finite-element modelling based on model neurons. These methods were initially applied to data from simple experimental models such as invertebrate neurons/ganglia/tecta, cell cultures, and organotypic slice preparations. Advances in the field have triggered the expanded use of such measures on more complex data, for example to mammalian ex vivo preparations, anesthetized preparations, and mammalian awake behaving preparations. With the increasing surgical, behavioral, and physiological complexity of the preparations themselves, less invasive measurement methods such as optical recordings, massively implanted arrays, or fMRI and other electromagnetic methods must be used to ensure robustness; however, these measures tend to feature lower signal-to-noise ratios, and are often prone to various biases. Furthermore, the high dimensionality of the data itself leads directly to potential errors in programming of analysis algorithms and overinterpretation of statistically significant but biologically insignificant findings. Given this situation, we advocate for the complementary use of the classical biological approach: the use of simplified preparations which may be limited in scope, but which highlight fundamental principles. We illustrate this approach with three experimental examples which use experimental and observational approaches to coarse-grain dynamic spatiotemporal activity patterns, to make coarse-graining observations of clinically relevant oscillations, and to coarse-grain complex behavior in mammalian discrimination learning.
Kentaroh Takagaki, Frank W. Ohl

Coordination Dynamics and Synergetics: From Finger Movements to Brain Patterns and Ballet Dancing

Starting with a brief review of the original Haken-Kelso-Bunz model and its generalizations from the 1980s, we discuss three examples from more than three decades of our research on coordination dynamics. From the 1990s, we show how movement coordination can be used to probe the brain of individual subjects and how coordination patterns in behavior are also manifested in brain signals. From the 2000s, we present an experiment on social coordination in brain and behavior and introduce an analysis technique for EEG signals recorded in such settings. Most recently, we recorded the performance of a professional ballet dancer, where we found the coordination patterns of in-phase and anti-phase as elementary building blocks in complex movements.
Armin Fuchs, J. A. Scott Kelso

The Human Dynamic Clamp: A Probe for Coordination Across Neural, Behavioral, and Social Scales

Humans (with their brains, bodies and behaviors) are complex dynamical systems embedded in an environment that includes a multitude of other conspecifics. Moving beyond previous brain- centered views of the human mind requires to develop a parsimonious yet integrative account that relates neural, behavioral, and social scales. Social neuroscience has recently started to acknowledge the importance of relational dynamics when it extended its purview from social stimuli to human-human interactions. Human-machine interaction s also constitute promising tools to probe multiple scales in a controlled manner. Inspired by the electrophysiological method of the dynamic clamp, Virtual Partner Interaction (VPI) allows real time interaction between human subjects and their simulations as dynamical system. This provides a new test bed for operationalizing theoretical models in experimental settings. We discuss how VPI can be generalized into a Human Dynamic Clamp (HDC) , a paradigm that allows the exploration of the parameter spaces of interactional dynamics in various contexts: from rhythmic and discrete coordination to adaptive and intentional behaviors, including learning. HDC brings humans and machines together to question our understanding of the natural and our theory behind the artificial.
Guillaume Dumas, Aline Lefebvre, Mengsen Zhang, Emmanuelle Tognoli, J. A. Scott Kelso

Design Principle for a Population-Based Model of Epileptic Dynamics

Epilepsy is defined as the brain’s susceptibility to recurrent, hypersynchronous discharges that disrupt normal neuronal function. Over the last decades, progress has been made in using dynamical systems theory and computational analyses to characterise the nature of seizure-like activity. Using simplified models of population dynamics, macroscale features of epileptic seizures can be described as expressions of model interactions. There is a trade-off between complexity of these models and their explanatory power: Models that represent biophysical components of the brain often contain many degrees of freedom and nonlinearities, which can make them challenging to interpret and often means that different model parameterisations can produce similar results. Simple models, on the other hand, do not usually have a direct correlate in brain anatomy or physiology, but rather capture more abstract quantities in the brain. However, the effects of individual parameters are easier to interpret. Here we suggest a design principle to generate the complex rhythmic evolution of tonic-clonic epileptic seizures in a neural population approach. Starting from a simple neuronal oscillator with a single nonlinearity , we show in a step-by-step analysis how complex neuronal dynamics derived from patient observations can be reconstructed.
Gerold Baier, Richard Rosch, Peter Neal Taylor, Yujiang Wang

Discrete Modeling for a Minimal Circuit in the Hippocampus

We present a simple discrete model for a minimal circuit in the hippocampal area CA3, which consists of various types of connected cells that differ in morphology and functional properties (pyramidal, basket and O-LM cells). This model allows for reproducing not only basic characteristics of the cells oscillations for all these types (period, amplitude and phase shift) but also to demonstrably explain the key property of switching between different rhythms using only one control parameter. The model results are confirmed via comparison with in vitro experimental results and discussed.
Anastasia I. Lavrova, Eugene B. Postnikov

Additional Topics


I See What You Do Not See

The World Observed with High-Speed Cameras
High-speed cameras are very useful and important tools for studying fast phenomena that we cannot follow with our own eyes. Recent developments of photosensitive semiconductors with memory (sensors with on-chip memory) enable us to take images of up to 10 million frames/s without losing spatial resolution. We explain the principles of these sensors (a CCD (charge coupled device) sensor and a CMOS (complementary metal oxide semiconductor) sensor, both with on-chip memory), and their trigger systems for high-speed cameras . As typical applications the following four experiments are shown: 1. material testing : destruction processes of a piece of CFRP (carbon fiber reinforced plastic) by tensile strain observed with two cameras synchronously, 2. cavitation: behavior of a microbubble in various geometries of their environment, 3. shock waves: their propagation observed with a Mach-Zehnder interferometer , and 4. crack formation: the process of glass cracking. Applications to chemical, biological and medical fields are on-going promising projects.
Kinko Tsuji

Performative Science—Transgressions from Scientific to Artistic Practices and Reverse

Performative Science is a research practice that is inherently processual and takes up a first person stance on epistemic things. It bears resemblance to phenomenological, that is to say, artistic practices and is most notably characterised by its reflective power. The current era of harsh reification of the meaning of Being in the course of an ongoing cybernetisation demands for such a reflection. Performative Science is a veritable attempt to turn technology into a hermeneutic practice, and if possible, even as part of an hermeneutics of facticity, that is to say, the inherently temporal understanding of (human) Being. A few concrete applications are introduced that partially have self-deconstructive features in order to emphasise the radical openness of Performative Science, that is far from being a scientific method. Rather, a method becomes emergent by tuning oneself into the epistemic thing.
Hans H. Diebner

Dynamics and Synchronisation in Wind Farms

Renewable energy sources such as wind power and photovoltaics shall account for about 20% of the total energy consumption by 2020 and 60% by 2050 in the European Union. These renewable resources which are spatiotemporally stochastic in nature, can influence the stability of the power grids. Therefore, a detailed modelling and understanding of their statistical behaviour is necessary to achieve an optimal design and operation of future power grids . Here, we present results on the complex statistics of wind power in general and the local phase synchronisation of turbines in a wind farm.
Mehrnaz Anvari, M. Reza Rahimi Tabar, Joachim Peinke, Matthias Wächter

Special Lecture


A Primer for Deterministic Thermodynamics and Cryodynamics

Dedicated to the Founder of Synergetics Hermann Haken
The basic laws of deterministic many-body systems are summarized in the footsteps of the deterministic approach pioneered by Yakov Sinai . Two fundamental cases, repulsive and attractive, are distinguished. To facilitate comparison, long-range potentials are assumed both in the repulsive case and in the new attractive case. In Part I, thermodynamics —including the thermodynamics of irreversible processes along with chemical and biological evolution—is presented without paying special attention to the ad hoc constraint of long-range repulsion. In Part II, the recently established new fundamental discipline of cryodynamics, based on long-range attraction, is described in a parallel format. In Part III finally, the combination (“dilute hot-plasma dynamics”) is described as a composite third sister discipline with its still largely unknown properties. The latter include the prediction of a paradoxical “double-temperature equilibrium” or at least quasi-equilibrium existing, which has a promising technological application in the proposed interactive local control of hot-plasma fusion reactors. The discussion section puts everything into a larger perspective which even touches on cosmology.
Otto E. Rossler, Frank Kuske, Dieter Fröhlich, Hans H. Diebner, Thimo Böhl, Demetris T. Christopoulos, Christophe Letellier


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