Author
Bateman Manuscript
Bio: Bateman Manuscript is an academic researcher. The author has contributed to research in topics: Daniell integral & Transcendental equation. The author has an hindex of 2, co-authored 2 publications receiving 12606 citations.
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TL;DR: Fractional kinetic equations of the diffusion, diffusion-advection, and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion and non-exponential relaxation patterns.
7,412 citations
TL;DR: In this paper, a simple theory is developed that accounts for many of the observed physical properties of micelles, both globular and rod-like, and of bilayer vesicles composed of ionic or zwitterionic amphiphiles.
Abstract: A simple theory is developed that accounts for many of the observed physical properties of micelles, both globular and rod-like, and of bilayer vesicles composed of ionic or zwitterionic amphiphiles. The main point of departure from previous theories lies in the recognition and elucidation of the role of geometric constraints in self-assembly. The linking together of thermodynamics, interaction free energies and geometry results in a general framework which permits extension to more complicated self-assembly problems.
4,563 citations
TL;DR: A review of dielectric data for a wide range of solids proves the existence of a remarkable "universality" of frequency and time responses which is essentially incompatible with the multiplicity of currently accepted detailed interpretations as discussed by the authors.
Abstract: A review of dielectric data for a wide range of solids proves the existence of a remarkable ‘universality’ of frequency and time responses which is essentially incompatible with the multiplicity of currently accepted detailed interpretations. Certain unique features of the universal behaviour strongly suggest the dominant role of many-body interactions.
4,234 citations
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01 Jan 1979TL;DR: In this article, a brief description is given of the various manifestations of the universal fractional power law relaxation processes, which are contrasted with the classical or Debye law, and a novel very general approach based on the so-called energy criterion is introduced.
Abstract: A brief description is given of the various manifestations of the universal fractional power law relaxation processes, which are contrasted with the classical or Debye law. It is shown that the universal law is indeed found in a remarkable variety of physical and chemical situations, and this is deemed to merit a special attempt at finding a suitably general theoretical model. Several such models are briefly described, and a novel very general approach based on the so-called energy criterion is introduced. It is concluded that it is not yet possible to establish with certainty the validity of any of the models. >
4,012 citations
TL;DR: In this article, a fractional-order PI/sup/spl lambda/D/sup /spl mu/controller with fractionalorder integrator and fractional order differentiator is proposed.
Abstract: Dynamic systems of an arbitrary real order (fractional-order systems) are considered. The concept of a fractional-order PI/sup /spl lambda//D/sup /spl mu//-controller, involving fractional-order integrator and fractional-order differentiator, is proposed. The Laplace transform formula for a new function of the Mittag-Leffler-type made it possible to obtain explicit analytical expressions for the unit-step and unit-impulse response of a linear fractional-order system with fractional-order controller for both open- and closed-loops. An example demonstrating the use of the obtained formulas and the advantages of the proposed PI/sup /spl lambda//D/sup /spl mu//-controllers is given.
2,479 citations