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  • 1
    Electronic Resource
    Electronic Resource
    Fractal scaling mechanisms in biomembranes (1989)
    Springer
    European biophysics journal 16 (1989), S. 375-379 
    Details
    ISSN: 1432-1017
    Keywords: Lipid-protein interactions ; renormalization ; Lévy distributions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Physics
    Notes: Abstract A modified model of the Cohen-Turnbull free volume theory for lateral transport processes in biomembranes is presented. The model which is based on renormalization group theoretical concepts incorporates fractal rather than Markovian diffusion kinetics. It predicts harmonic oscillations in the lateral diffusion coefficient around a dominant power-law trend and clarifies, in addition, recently observed deviations from the Cohen-Turnbull exponential law.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00257887
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  • 2
    Electronic Resource
    Electronic Resource
    Lie transformations, similarity reduction, and solutions for the nonlinear Madelung fluid equations with external potential (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 1250-1260 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The application of Lie-group methods to a system of coupled nonlinear partial differential equations representing what is usually called a Madelung fluid is shown. The generating operators of the transformation group that depends on five arbitrary group constants will be constructed, and all subclasses of systems of ordinary differential equations derived by similarity reduction will be presented in tabular form. Two subclasses of physical interest are investigated in detail and the similarity solutions are compared with solutions found earlier by the application of inverse scattering transform techniques to the cubic nonlinear Schrödinger equation. Similarity solutions for the Madelung equations with linear external potential Γ(x)=−f0x are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527526
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  • 3
    Electronic Resource
    Electronic Resource
    Solutions to the nonlinear Boltzmann equation for particle transport in a host medium (1986)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 29 (1986), S. 2746-2747 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Analytical solutions for nonlinear diffusion of test particles (mass m) into a background system of field particles (mass mˆ) are available only for the mass ratio α=m/mˆ=0. This physical situation for α≠0 and numerical solutions for the moments and the distribution function f (v,τ) are investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865517
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  • 4
    Electronic Resource
    Electronic Resource
    Painlevé test and exact similarity solutions of a class of nonlinear diffusion equations (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2456-2463 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: For (1+1)-dimensional diffusion equations where the diffusion coefficient is an arbitrary power of the dependent variable, a Painlevé test is performed on both the partial differential equation and the similarity reductions. The invariance of the Painlevé property under a large class of similarity reductions is shown. For the reductions with the Painlevé property, the explicit similarity solutions are given. It is demonstrated how results of a Painlevé analysis can be used to obtain further exact similarity solutions, even in cases without the Painlevé property.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529615
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  • 5
    Electronic Resource
    Electronic Resource
    A scaling model for dichotomous branching processes (1987)
    Springer
    Biological cybernetics 56 (1987), S. 155-157 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract We derive an affine scaling law for dichotomous branching processes in biological systems. An application to the human bronchial tree demonstrates good agreement with experimental results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00317990
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  • 6
    Electronic Resource
    Electronic Resource
    Particle transport in a host medium with an external source: Exact solutions for a nonlinear homogeneous Boltzmann equation (1988)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 39 (1988), S. 605-618 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Die Diffusion von Maxwellmolekülen in einem unbegrenzten Hintergrundmedium wird untersucht für den Fall, daß die Teilchenzahldichte aufgrund von „removal“-Effekten und durch den Einfluß einer äußeren Quelle keine Erhaltungsgröße ist. Bisher unbekannte Klassen von Similarity-Lösungen der entsprechenden nichtlinearen, homogenen und isotropen Boltzmanngleichung werden hergeleitet und bereits bekannte spezielle Lösungen werden anhand von Lie-Gruppenkonstanten und removal-Parametern klassifiziert. Die Bedingungen, unter denen diese homogenen Verteilungsfunktionen positiv sind, werden diskutiert, und die Einschränkungen an die Parameter des zugrundeliegenden Stoßmodells werden bestimmt.
    Notes: Abstract The diffusion of Maxwell molecules in an unbounded host medium is considered in the case where the particle density is not conserved in consequence of removal events and through the influence of an external source. Heretofore undiscovered classes of similarity solutions of the corresponding nonlinear isotropic and homogeneous Boltzmann equation are presented and already discovered special solutions are classified in terms of Lie group constants and removal parameters. The conditions under which these homogeneous distribution functions do not violate positivity are discussed, and the restrictions upon the parameters of the underlying collision model are determined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00948725
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  • 7
    Electronic Resource
    Electronic Resource
    Reply to comments on: The origin of fractal scaling mechanisms in ion channel gating kinetics (1990)
    Springer
    Colloid & polymer science 268 (1990), S. 401-401 
    Details
    ISSN: 1435-1536
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01411684
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  • 8
    Electronic Resource
    Electronic Resource
    On the origin of fractal scaling mechanisms in ion channel gating kinetics (1989)
    Springer
    Colloid & polymer science 267 (1989), S. 753-755 
    Details
    ISSN: 1435-1536
    Keywords: Ionchannel ; fractalgatingmodel
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract By applying the Poisson summation formula to the Markovian chain result for protein gating kinetics, we derive a fractal scaling law that indicates something about the origin of the power-law behavior. As a by-product we obtain an amplitude to rate correlation that bridges the gap between Markov and fractal gating models. The predictions of the model will be compared with experimental data sets.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01524380
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  • 9
    Electronic Resource
    Electronic Resource
    Fractional relaxation and the time-temperature superposition principle (1994)
    Springer
    Rheologica acta 33 (1994), S. 337-343 
    Details
    ISSN: 1435-1528
    Keywords: Rheological models ; viscoelasticity ; fractional differentiation ; non-Debye relaxation ; thermo-rheological simplicity ; projection operator
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Relaxation processes in complex systems like polymers or other viscoelastic materials can be described by equations containing fractional differential or integral operators. In order to give a physical motivation for fractional order equations, the fractional relaxation is discussed in the framework of statistical mechanics. We show that fractional relaxation represents a special type of a non-Markovian process. Assuming a separation condition and the validity of the thermo-rheological principle, stating that a change of the temperature only influences the time scale but not the rheological functional form, it is shown that a fractional operator equation for the underlying relaxation process results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00366960
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  • 10
    Electronic Resource
    Electronic Resource
    Number densities and trajectories in 3-D spatially inhomogeneous particle transport theory (1999)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 50 (1999), S. 404-422 
    Details
    ISSN: 0044-2275
    Keywords: Key words. Inhomogenous gas mixtures, nonlinear dynamics, particle trajectories.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract. In this paper the nonlinear integro-partial differential Boltzmann equation, governing the 3-D spatially inhomogeneous time-dependent distribution function $ f (\bar{x}, \bar{v},t)$ of certain test particles, diffusing from a localized source into a bath of certain other field particles, is shown to be convertible - upon a stochastic modeling of the physics of the collisional events - into a nonlinear hyperbolic-functional PDE for the number density $ \rho (\bar{x},t) = \int _{R_3}f(\bar{x},\bar{v},t)d\bar{v}.$ An appropriate decomposition of f and $\rho$ leads to a new strategy for the solution of the relevant Cauchy problem, and for a more comprehensive picture of the diffusion process of the test particles considered. Implications with the classical moment method are made evident.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00001495
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