https://www.tau.ac.il/%7Eklafter1/258.pdf

The random walk's guide to anomalous diffusion: a fractional dynamics approach

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.

Theory of self-assembly of hydrocarbon amphiphiles into micelles and bilayers

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.

The ‘universal’ dielectric response

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. >

The universal dielectric response

This paper is concerned with the evaluation and tabulation of certain integrals of the type (* 00 I(p, v; A) = J J fa t) ) e~cttxdt. In part I of this paper, a formula is derived for the integrals in terms of an integral of a hypergeometric function. This new integral is evaluated in the particular cases which are of most frequent use in mathematical physics. By means of these results, approximate expansions are obtained for cases in which the ratio b/a is small or in which b~a and is small. In part II, recurrence relations are developed between integrals with integral values of the parameters pt, v and A. Tables are given by means of which 7(0, 0; 1), 7(0, 1; 1), 7(1, 0; 1), 7(1,1; 1), 7(0, 0 ;0), 7(1, 0;90), 7(0, 1; 0), 7(1, 1; 0), 7(0,1; - 1 ), 7(1,0; - 1 ) and 7(1,1; - 1 ) may be evaluated for 0

On Certain Integrals of Lipschitz-Hankel Type Involving Products of Bessel Functions

Higher Transcendental Functions

Tables of integral transforms

Higher transcendental functions

Preface Introduction 1. The Classical Equations 2. Applications of the integral theorems of green and stokes 3. Two-dimensional problems 4. Conformal Representation 5. Equations in three variables 6. Polar Co-ordinates 7. Cylindrical Co-ordinates 8. Ellipsoidal Co-ordinates 9. Paraboloidal Co-ordinates 10. Toroidal Co-ordinates 11. Diffraction problems 12. Non-linear equations

Harry Bateman

Papers

Higher Transcendental Functions

Tables of integral transforms

Higher transcendental functions

Partial differential equations of mathematical physics

Some recent researches on the motion of fluids