Articles

P. Dähmlow and S. C. Müller
Pattern Formation in Microemulsions Affected by Electrical Fields
In: Complexity and Synergetics (Eds. S. C. Müller, P. J. Plath, G. Radons, A. Fuchs)
Springer Series of Complexity, Springer, Berlin Heidelberg, pp. 117-128 (2018)

Abstract:
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.

J. Luengviriya, M. Sutthiopad, M. Phantu, P. Porjai, S. C. Müller and C. Luengviriya
Unpinning of Spiral Waves
In: Complexity and Synergetics (Eds. S. C. Müller, P. J. Plath, G. Radons, A. Fuchs)
Springer Series of Complexity, Springer, Berlin Heidelberg, pp. 129-138 (2018)

Abstract:
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.

S. C. Müller
Observation of Chemical Reactions Induced by Impact of a Droplet
In: The Macro-World Observed by Ultra High-Speed Cameras (Ed. K. Tsuji)
Springer, Berlin Heidelberg, pp. 343-543 (2018)

Abstract:
In order to investigate, how a chemical reaction starts and develops, we select the moment of the impact of a droplet falling into a reactive solution and observe the initial stage of the reaction with a high-speed camera. As examples, we use the pH indicator system with bromothymol blue (BTB) reaction, as well as the Belousov-Zhabotinsky (BZ) reaction forming an excitable medium, in which superthreshold disturbance propagates as an excitation wave and thus gives rise to a reaction-diffusion structure. Focusing on the BTB solution, we observe the color change caused by the droplet containing a pH indicator when impinging on the surface of alkaline solution. Contrary to our expectation, this reaction starts at the equatorial line, and not at the protruding edge of the droplet, where it first gets into touch with its reaction partner. Small vertical fingers emerge from the front line within 1.5 ms. Some arguments make it is likely that heat diffusion is responsible for the finger formation. For the BZ reaction, where due to a redox reaction the color changes from red to blue and vice versa, we do not observe this color change in our experiment. However, the effects on the drop shape (from spherical to ellipsoidal) is the same as observed in the BTB solution. Independently of the chemical systems, a thin needle-like tip developed from the protruding edge within about 300 μs after the drop has touched the solution surface. The emergence of this thin pin cannot be due to chemical processes, but to the physical impact of the droplet.

O. Inomoto, M. J. B. Hauser, R. Kobayashi and S. C. Müller
Acceleration of chemical reaction fronts. II. Gas-phase-diffusion limited frontal dynamics
Eur. Phys. J. Special Topics 227, 509-520 (2018)

Abstract:
The propagation of reaction-diffusion fronts in an open liquid solution layer is critically affected by mass transfer between the liquid solution and the adjacent gas phase. This is the case in the iodate{arsenous acid (IAA) reaction when run under stoichiometric excess of iodate. Here, iodine is the reaction product, which has a low solubility in the liquid phase, hence, excess iodine rapidly evaporates. In the gas phase, it diffuses and overtakes the reaction front propagating in the liquid medium because its diffusion coefficient in the gas phase is considerably larger than that in aqueous solution. Evaporated iodine is re-dissolved into the reaction medium ahead of the reaction front. Since iodine is the autocatalytic species of the IAA reaction, this additional gas-phase transport may lead to an acceleration of the propagating reaction front.

K. Tsuji and S. C. Müller
Cultural History (Spirals and Vortices in Our Universe)
In: K. Tsuji and S. C. Müller
Spirals and Vortices – In Culture, Nature, and Science
The Frontiers Collection, Springer Nature Switzerland, Cham, pp. 3 - 29 (2019)

Abstract:
We introduce various spirals which were made during the time from
11,000 BC (Neolithic Period) to 1500 AD (early Renaissance). Concentric circles
were created much earlier (40,000–20,000 BC). For the period between 5000 and
2000 BC spirals in Megalithic arts, Scythian treasures and Japanese clay figures are
presented as examples. From 2000 to 1 BC spirals are found worldwide: in Europe,
Egypt, Thailand, India, or South America. From 1 to 1500 AD a large number of
spirals in Christian, Moslem and Buddhistic cultures were created. At the end spirals
and vortices in the Nordic, Medieval and Renaissance arts are exhibited.

S. C. Müller and K. Tsuji
Appearance in Nature (Spirals and Vortices in Our Universe)
In: K. Tsuji and S. C. Müller
Spirals and Vortices – In Culture, Nature, and Science
The Frontiers Collection, Springer Nature Switzerland, Cham, pp. 31 - 66 (2019)

Abstract:
Many spirals and vortices appear in nature both in the inanimate and the
living world. As examples of the non-living nature some spirals and vortices of
various sizes are selected: spiral galaxies, hurricanes and tornadoes, aerodynamic
turbulence, crystal growth on surfaces and carbon nanotubes. In the realm of living
structures, we consider rigid spiral forms (for example, seashells and snails), as
well as flexible ones like the tail of a chameleon or a sea horse. Beyond fauna we
find in flora many flowers and leaves that are arranged in spiral form. A general
spiral tendency in vegetation is discussed, following ideas proposed by J.W. Goethe.
The Fibonacci numbers, which are closely related to the positioning of leaves, are
introduced. Other interesting topics are Leonardo’s flying spiral, insect eyes and fish
vortices.

K. Tsuji and S. C. Müller
The Arts and Beyond (Spirals and Vortices in Our Universe)
In: K. Tsuji and S. C. Müller
Spirals and Vortices – In Culture, Nature, and Science
The Frontiers Collection, Springer Nature Switzerland, Cham, pp. 67 - 87 (2019)

Abstract:
Spirals play a very favorite role as motives for modern European paintings.
Here we assemble some examples for quiescent spirals (Klimt), spirals starting to
move (Itten and Klee) and storming spirals (da Vinci, van Gogh, and Turner). There
are also circles or curved lines which look like spirals, but are not. In parallel to
the European culture, a lot of spiral patterns appear in Japan, as well: for example
the famous Ukiyo-e of the Naruto whirlpools, patterns for Kimonos and toys. In
our daily life spiral forms are used for practical and/or ornamental reasons: musical
instruments, staircases, data storage devices like CD and DVD, and others.

S. C. Müller
Generation of Spirals in Excitable Media
In: K. Tsuji and S. C. Müller
Spirals and Vortices – In Culture, Nature, and Science
The Frontiers Collection, Springer Nature Switzerland, Cham, pp. 141 - 155 (2019)

Abstract:
The generation of dynamic spirals under conditions of excitability is presented.
After a short description of some basic principles of nonlinear dynamics
illustrated in the phase plane, we explain what excitable systems are, how excitation
waves propagate, and why external forces influence rotating or moving spirals. Some
images of such dynamic spirals are exhibited.

T. Mair, M. A. Dahlem and S. C. Müller
Yet More Spirals
In: K. Tsuji and S. C. Müller
Spirals and Vortices – In Culture, Nature, and Science
The Frontiers Collection, Springer Nature Switzerland, Cham, pp. 225 - 235 (2019)

Abstract:
Having presented several systems in which biologically and medically
relevant processes induce rotating spiral waves, we add several more examples of
comparable nature: glycolytic waves in yeast, calcium waves in egg cells, wave-like
patterns during spreading depression, and spiral waves in the epileptic neocortex.

B. Ponboonjaroenchai, J. Luengviriya, M. Sutthiopad, P. Wungmool, N. Kumchaiseemak, S. C. Müller and C. Luengviriya
Self-organization of multi-armed spiral waves in excitable media
Phys. Rev. E 100, 042203 (2019)

Abstract:
We present an investigation of self-organized multiarmed spiral waves pinned to unexcitable circular obstacles in a thin layer of the excitable Belousov-Zhabotinsky reaction and in simulations using the Oregonator model. The multiarmed waves are initiated by a series of wave stimuli. In the proximity of the obstacle boundary, the wave rotation around the obstacle causes damped oscillations of the wave periods of all spiral arms. The dynamics of wave periods cause the wave velocities as well as the angular displacements between the adjacent arms to oscillate with decaying amplitudes. Eventually, all displacements approach approximately the same stable value so that all arms are distributed evenly around the obstacle. A further theoretical analysis reveals that the temporal dynamics of the angular displacements can be interpreted as underdamped harmonic oscillations. Far from the obstacles, the wave dynamics are less pronounced. The wave period becomes stable very soon after the initiation. When the number of spiral arms increases, the rotation of individual arms slows down but the wave period of the multiarmed spiral waves decreases. Due to their short period, multiarmed spiral waves emerging in the heart potentially result in severe pathological conditions.