# H. Engel-Herbert's research while affiliated with Humboldt-Universität zu Berlin and other places

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## Publications (13)

Experimental bifurcation diagrams for the heterogeneous catalytic oxidation of ethanol on a supported palladium catalyst are presented, depending on the oxygen or the ethanol content in the feed as control parameters. The identification of the bifurcations leads to a proposal for the formal construction of a mathematical model following Sheintuch a...

In recent years heterogeneous catalytic reaction systems have been shown to produce a complex dynamic behavior. For example the heterogeneous catalytic oxidation of ethanol on palladium was found to exhibit multistability as well as relaxation oscillations (Jaeger., 1986, Ber. Bunsenges. phys. Chem.90, 1075–1079; 1990, Chem. Engng Sci.45, 947–953)....

The concepts of entropy and lowering of entropy in comparison to the equilibrium state are introduced. It is shown that entropy
lowering is connected with the contraction of the occupied part of the phase space due to the formation of attractors. As
concrete examples the excitation of oscillations in solids and turbulence in liquid flows are discus...

The entropy lowering is calculated in the laminar as well as in the turbulent regime. For the Poiseuille flow it is shown that the entropy lowering increases monotonically if while increasing the Reynolds number the energy of the flow is kept fixed. The transition from laminar to turbulent motion turns out to be a nonequilibrium transition to a mor...

The Brownian motion of nonlinear oscillators imbedded in a heat bath is studied. For the excitation of sustained oscillations, realized by van der Pol oscillators, the entropy is calculated in the limit of weak dissipation and weak noise. At fixed average energy the entropy decreases monotonically if the feedback strength increases.

We investigate the effect of additive colored noise on Hopf-bifurcating systems in the limit of small correlation times. It is shown that it results in an advancement of the oscillating regime. Several examples are studied.

The behaviour of the entropy is studied during a nonequilibrium phase transition. It is shown that for the generation of sustained oscillations the entropy decreases monotonously if the average oscillator energy remains fixed. This result is valid both for hard and soft excitation of oscillations.
Entropieverringerung bei der Anfachung selbsterregt...

The entropy statement formulated by KLIMONTOVICH is discussed by investigating two examples:
Über die Entropie dissipativer und turbulenter Strukturen
Der Entropie-Satz von KLIMONTOVICH wird an Hand von zwei Beispielen untersucht:

Thermodynamics is a rather old discipline of physics, however, it is not oldfashioned. On the contrary,such modern topics as the hot big bang model, the theory of black holes, as well as the theory of biological systems /1,2/, show that thermodynamics goes through a renaissance. Thermodynamics is also intimately related to information theory, a key...

It is well known that under appropriate conditions nonlinear physical, chemical or biological systems show various instabilities such as, for example, transitions leading to multistability, limit cycle oscillations or chaotic motion [1–3]. These instabilities correspond to bifurcations of the underlying dynamic equations. A realistic treatment requ...

The influence of external fluctuations on the bifurcational behavior of two-dimensional dynamical systems exhibiting limit cycles is investigated. Studying both exactly and approximately solvable examples it is shown that the variances of the external fluctuations occur as additional bifurcation parameters. The threshold values for soft as well as...

## Citations

... A system capable of continuously importing free energy from the environment and, at the same time, exporting entropy (the total entropy of the system decreasing over time) was called dissipative structure. These advantageous thermodynamic systems use a part of the energy inflow to produce a new form of energy characterized by lower entropy which self-organizes the systems168169170171. Therefore, the dissipative structure acts as a kind of energy-transforming system that uses a part of the energy inflow to produce a new form of energy which is of higher thermodynamic value (i.e., lower entropy) and the negative variation of entropy corresponds to a positive variation of information172173174 which allows increasing the complexity of the molecular organization, producing higher ordered macro structures and functional dynamic behaviors. ...

... Most programming languages provide root finding methods to solve Eq. (17). However, programmiug lauguages such as R, C and MATLAB are kuowu to feature the error function $ only with a limited precisiou.^^-^^ ...

... The generalization of Gibbs' theorem to open systems was first made by Klimontovich and is called the S-theorem [13][14][15][16][17]. Open systems are those in which the average internal energy is not constant because of the interactions with the environment. ...

... Substitution of the temperature from this equation into Equation (27) yields the expression for the dimensionless rate of entropy production (1/s) due to viscous shear stresses as: ...

Reference: Spectral Entropy in a Boundary-Layer Flow

... These inequalities provide sufficient margin for organization in growing DS by reducing s DS and s E,DS relative to s rel and s E,rel . Combining these inequalities, Equation (8) measures increase in organization relative to immediate surroundings [32], which enables self-organization in a growing DS [33]. ...

... First way [3, 8, 9, 18,202122. We replace Do with/5(7, a, Wo) in the s.p.d.f. ...

Reference: bonitz zfp 88

... Our observation of the reduction in the width of the hysteresis zone in the presence of Gaussian white noise is the first of its kind in experimental results reported in the thermoacoustic literature. However, outside the context of thermoacoustics, a reduction in the width of the hysteresis zone in the presence of noise is observed in various dynamical systems (Sastry & Hijab 1981;Coullet, Elphick & Tirapegui 1985;Geier, Tolstopjatenko & Ebeling 1985;Altares & Nicolis 1988;Lekkas, Schimansky-Geier & EngeI-Herbert 1988;L'Heureux & Kapral 1989;Fedotov, Bashkirtseva & Ryashko 2002;Berthet et al. 2003). ...