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  • 1
    Electronic Resource
    Electronic Resource
    Bifurcations of an interated mapping with retardations (1996)
    Springer
    Journal of statistical physics 83 (1996), S. 1183-1197 
    Details
    ISSN: 1572-9613
    Keywords: Iterated mappings ; dynamics with retardation ; bifurcations ; nonuniversal power law decay ; dynamical scaling laws
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An elementary example for an iterated mapping with retardation is defined, which exhibits a Whitney fold bifurcation of the long-time limit. The long-time dynamics is quite different from the bifurcation scenario known for conventional iterated mappings. There appear two nontrivial power-law exponents, one describing the decay toward a plateau value and the other describing the one below this plateau, which vary continuously with a model parameter. The slowing down of the dynamics near the critical point is ruled by two divergent time scales, characterized by two different nonuniversal exponents. This leads to a stretching of the relaxation over large time intervals. A scaling law description of the bifurcation dynamics is derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02179557
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  • 2
    Electronic Resource
    Electronic Resource
    A schematic model discussion of the conductor to insulator transition for particle motion in a random potential (1990)
    Springer
    The European physical journal 78 (1990), S. 21-25 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A schematic model for the dynamics of a particle moving in a random environment is discussed where the latter is assumed to cause normal scattering and also scattering with time inversion symmetry breaking. The second mechanism changes the exponent unity to one half for the vanishing of the conductivity near the percolation threshold. It alters also the exponent of the critical conductivity spectrum from 1/2 to 1/3. The dynamics near the transition including all cross over phenomena to the usual effective medium theory results are described by a two parameter scaling law.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01317352
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  • 3
    Electronic Resource
    Electronic Resource
    The glass transition singularity (1987)
    Springer
    The European physical journal 65 (1987), S. 415-427 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The mode coupling equations which were derived before within a kinetic theory approach for a dynamical description of simple classical liquids, are truncated such that leading and next to leading order contributions to the relaxation kernels caused by density fluctuations are kept. As a result closed non linear equations for density and current fluctuations are obtained which extend the equations used by Bengtzelius et al. for the discussion of the liquid glass transition. Considering the correlations as functions of vertex parameters and frequencies, singularities for zero frequency and certain subsets in parameter space are identified. For a schematic model the correlation functions near the singularities can be discussed in terms of various scaling laws. If a temperature variation drives the system close to the singularity the latter cause strong anomalies of the low frequency dynamics. The anomalies are discussed and shown to correlate qualitatively with the experimentally known ones for glass transitions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01303763
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  • 4
    Electronic Resource
    Electronic Resource
    β relaxation theory for simple systems: some addenda (1992)
    Springer
    The European physical journal 87 (1992), S. 43-49 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The evolution of the tagged particle probability density for a hard sphere system is evaluated within the β-relaxation window. Relaxation curves obtained by molecular dynamics studies by Barrat, Hansen and Roux for a binary mixture are analyzed quantitatively with β-relaxation scaling formulae. The dynamical light scattering data obtained by Pusey and van Megen for colloidal suspensions are described by the combined α- and β-relaxation scaling results. The range of validity of asymptotic expressions near a glass transition singularity is discussed for the Debye-Waller factor as a function of packing fraction. The applied theoretical formulae are those of the mode coupling theory for the liquid to glass transition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01308255
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  • 5
    Electronic Resource
    Electronic Resource
    Elastic constants of nonionic anharmonic crystals (1968)
    Springer
    The European physical journal 217 (1968), S. 170-187 
    Details
    ISSN: 1434-601X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Taking into account the entire anharmonicity of the crystal an exact relation between the long-wavelength limit of the static self-energy and the isothermal elastic constants is established. The result can be reformulated as a sum rule for the displacement correlation function. The diagram technique is also employed to discuss the equation for the elastic constants in the pseudoharmonic approximation as well as to derive the integral equations for the quasiparticle parameters.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390505
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  • 6
    Electronic Resource
    Electronic Resource
    On the static susceptibility in the kondo problem (1970)
    Springer
    The European physical journal 235 (1970), S. 52-58 
    Details
    ISSN: 1434-601X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The dynamical susceptibility of thes-d-model is calculated in second order. It turns out, that only the impurity-impurity part of the static susceptibility contains logarithmically divergent terms. In order to obtain convergent results belowT=T k a partial summation is carried out for this part. The final result is expressed in terms of Suhl's spin flip scattering amplitude. We find an interpolation formula for the temperature dependence of the susceptibility with complete screening of the impurity spin forS=1/2 atT=0.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01399755
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  • 7
    Electronic Resource
    Electronic Resource
    Rheologische Messungen an thixotropen Anstrichmitteln (1962)
    Springer
    Rheologica acta 2 (1962), S. 254-260 
    Details
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Zusammenfassung Bei der Reaktion bestimmter Polyamide mit fetten Ölen bzw. Alkydharzen entstehen Produkte, deren Lösungen in apolaren Lösungsmitteln thixotrope Eigenschaften aufweisen. Die Thixotropie ist vom Umsetzungsgrad abhängig und durchläuft ein Maximum, während parallel dazu die Lösungen verschiedene Trübungszustände annehmen. Der Einfluß der Reaktionsbedingungen auf die Thixotropie und eine zu ihrer Messung geeigneten Methode werden beschrieben.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01983960
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  • 8
    Electronic Resource
    Electronic Resource
    Further phase transition scenarios described by the self consistent current relaxation theory (1988)
    Springer
    The European physical journal 72 (1988), S. 403-412 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Two scenarios for dynamical phase transitions from ergodic to non ergodic dynamics as described by the self consistent current relaxation theory are examined and exemplified by numerical results. The first deals with endpoints of type B transition lines and its signature is logarithmic decay in time or (1/f)-noise for the spectra. The second deals with crossings of phase transition lines and it is characterized by the known relaxation pattern of one transition accompanied by strong precursors following the pattern of another transition. The possible relevance of the results for a description of liquid glass transitions and spin glass transitions is indicated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01312829
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  • 9
    Electronic Resource
    Electronic Resource
    Some aspects of phase transitions described by the self consistent current relaxation theory (1984)
    Springer
    The European physical journal 56 (1984), S. 139-154 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A mathematical model for a nonlinear equation of motion for correlation functions is considered which describes the essential features of the self consistent current relaxation theory for a system experiencing some interaction with a static random field in addition to some quadratic self interaction. It is shown that the plane spanned by the two coupling parameters is separated into a region of ergodic motion and another region where the motion is nonergodic. At the separation line of the two phases all correlation functions can be discussed in terms of scaling laws. The critical exponents vary along the separation line continuously and they can be evaluated explicitely. The separation line consists of two pieces. Transitions across the first piece are characterized by a polarization catastrophy, by a vanishing of the transport coefficient and by a diverging low frequency spectrum ruled by one critical frequency scale. Transitions across the second piece do not exhibit a polarization divergence but show also a power law decrease to zero of the transport coefficient. The low frequency spectrum is the sum of two diverging parts. Each part is described by a scaling law, but the scaling frequencies and the scaling functions are quite different.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01469695
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  • 10
    Electronic Resource
    Electronic Resource
    Properties of the glass instability treated within a mode coupling theory (1985)
    Springer
    The European physical journal 60 (1985), S. 195-203 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The anomalies at the liquid glass transition discussed recently by Bengtzelius et al. within a mode coupling theory are demonstrated to be due to an isolated eigenvalue of a certain stability matrix to approach unity at the critical point. Within this scenario it is shown how to derive the asymptotic results for the correlations functions analytically up to the determination of two eigenvectors and the evaluation of some wave vector integrals. As a result it is found that the Debye-Waller factor, the Lamb-Mössbauer factor, the localization length for a tagged particle, and the elastic moduli approach their asymptotic limit at the glass instability point with critical exponent one half. The critical dynamics for the coherent and incoherent scattering functions and for the transversal currents is given by a single wave vector independend scaling function. A formula for the critical exponent parameter is obtained and the scaling equation is shown to agree with the one discussed earlier for a schematic model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01304439
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