Autowave

Chemical waves are a phenomenon of non-equilibrium thermodynamics (or the Chemistry and Biology ), and a special case of dissipative structures. Thereby occur in a medium (such as a reaction mixture or a colony of cells) in space and time migratory concentration changes, which are generated and maintained by a self-energizing or positive feedback response in the medium. The energy for the maintenance does not like classical waves ( eg sound or electromagnetic waves ) from the outside but from the medium itself ( self - excited oscillations). Well-known examples are concentration waves in oscillating chemical reactions such as the Belousov -Zhabotinsky reaction, and the spread of excitation in the heart muscle.

In sub-areas of physical chemistry and theoretical biology the short name auto wave is used and applied to other examples of structure formation in active media. The German translation test car wave is unusual. It was therefore chosen auto wave in analogy to the English auto- oscillations, self - excited oscillations.

Physical Description

Chemical waves occur in systems, which are typically characterized by a non-linear, (positive) feedback reaction system with spatial coupling by a transfer process. In many cases, the transport process is normal diffusion. Mathematically, this can be described approximately by a reaction diffusion equation of such a system. Without the non-linearity and the feedback system would approach a state of equilibrium with no patterning. Without the spatial coupling without spatial phenomena, such as would be possible and the wave propagation time to a maximum of oscillations can be observed ( for example, when the reaction mixture is continuously stirred for an oscillatory response ). Is still necessary for the occurrence of chemical waves that the systems are far away from thermodynamic equilibrium. This means in particular that it contains energy that can be spent on the structure formation. This can be understood by a Entropiebetrachtung: Ordered structures, such as waves, lead to a local decrease of entropy. After the second law of thermodynamics such a Entropieerniedrigung is only possible if this energy is expended. In the case described here, this energy comes from the non- reversible approximation of the system to the stationary equilibrium state (eg by non- reversible chemical reactions take place ), is released in the energy. Typically chemical waves are in a closed system is therefore not stable and can only be observed for a certain period. The process ends when the system approaches a state of equilibrium or when all reaction educts are consumed. In an open system, starting from a steady state, however, are stable chemical waves as energy is supplied from the outside for its maintenance (e.g. in the form of a "fresh " reaction starting ). Therefore, the waves can be energized again, and the system remains far from the equilibrium. In both cases, the energy for the pattern formation so derived from the medium itself

Due to their self - reinforcing character satisfy even small local disturbances, such as microscopic concentration or temperature differences, for example, the heating of the reaction mixture with a hot needle to trigger chemical waves. Therefore, it is often spoken of the " spontaneous appearance " of such structures. These disturbances act as agent centers, one of which spread reaction fronts. In these, the reaction proceeds in a different phase than in the preceding surrounding medium. For example, running from the beginning of the front, a first reaction step, which leads to a color change. The products of this step further react later and partially re-formed in the sense of autocatalysis, which can lead to a renewed color change. So Various partial reactions run at different points from the front at different rates.

The visibility of chemical waves is often due to local differences in concentration of a colored component of the reaction mixture. Alternatively, indicators may be added to respond to the local concentration with a color change.

This chemical waves of other phenomena can be distinguished: It can, for example, purely temporal oscillations occur that are not wave due to the lack of spatial spread. Even purely spatial, temporal stationary pattern, so-called Turing patterns are different from it. All these phenomena are often grouped under the term dissipative structures for the investigation of Ilya Prigogine was awarded the 1977 Nobel Prize in Chemistry. Gerhard Ertl received the 2007 Nobel Prize in Chemistry among others for the study of chemical waves in the oxidation of carbon monoxide on platinum surfaces.

Properties

As a solution of a nonlinear differential equation of chemical waves have certain characteristics that distinguish them from the usual " linear waves " (eg, water waves, light and other electromagnetic waves). In other properties they are similar:

• Analogous to conventional waves wavelength, frequency and velocity of propagation can be defined in these propagating patterns mostly.
• If two opposing chemical wavefronts each other, so they cancel each other often, while overlap undisturbed conventional shafts. Thus, the superposition principle does not apply, such as the nonlinear character of the descriptive differential equation shows.
• For certain chemical wave reflection and refraction phenomena were observed, which differ in some respects from analogous properties of linear waves.
• As a special waveform occur spiral waves, or (for three-dimensional waves) also called vortex waves scroll waves.

Examples

Chemical waves can be observed in many systems:

• Non- homogenized ( non- agitated ) approaches oscillating reactions such as the Belousov- Zhabotinsky reaction, or as the oxidation of arsenious acid with iodate
• In the oxidation of carbon monoxide on the platinum surface soliton waves are observed
• Biochemical transmission of impulses in the nervous system
• Spread of the slime mold Dictostelium discoideum
• Excitation waves in cardiac muscle
• Models for pattern formation (eg color patterns on clam ) in biological organisms
• A simple and often discussed theoretical example of an autocatalytic reaction system shows the wave propagation with a diffusion term, the so-called Brusselator (see animation right).

There are some non- chemical processes, which show a similar phenomenology and can be described by similar equations:

• The " stadium wave" La ola ( the fans are at the same time exciting and Transmitter )
• Congestion in road traffic
• Many cellular automata exhibit wave phenomena that correspond to chemical waves, such as Conway's Game of Life or Wator