Effect of shape anisotropy on transport in a 2-dimensional computational model: Numerical simulations showing experimental features observed in biomembranes

We propose a 2-d computational model-system comprising a mixture of spheres and the objects of some other shapes, interacting via the Lennard-Jones potential. We propose a reliable and efficient numerical algorithm to obtain void statistics. The void distribution, in turn, determines the selective permeability across the system and bears a remarkable similarity with features reported in certain biological experiments.Comment: 1 tex file, 2 sty files and 5 figures. To appear in Proc. of StatPhys conference held in Calcutta, Physica A 199

Fractional differentiability of nowhere differentiable functions and dimensions

Weierstrass's everywhere continuous but nowhere differentiable function is shown to be locally continuously fractionally differentiable everywhere for all orders below the `critical order' 2-s and not so for orders between 2-s and 1, where s, 1<s<2 is the box dimension of the graph of the function. This observation is consolidated in the general result showing a direct connection between local fractional differentiability and the box dimension/ local Holder exponent. Levy index for one dimensional Levy flights is shown to be the critical order of its characteristic function. Local fractional derivatives of multifractal signals (non-random functions) are shown to provide the local Holder exponent. It is argued that Local fractional derivatives provide a powerful tool to analyze pointwise behavior of irregular signals.Comment: minor changes, 19 pages, Late

Holder exponents of irregular signals and local fractional derivatives

It has been recognized recently that fractional calculus is useful for handling scaling structures and processes. We begin this survey by pointing out the relevance of the subject to physical situations. Then the essential definitions and formulae from fractional calculus are summarized and their immediate use in the study of scaling in physical systems is given. This is followed by a brief summary of classical results. The main theme of the review rests on the notion of local fractional derivatives. There is a direct connection between local fractional differentiability properties and the dimensions/ local Holder exponents of nowhere differentiable functions. It is argued that local fractional derivatives provide a powerful tool to analyse the pointwise behaviour of irregular signals and functions.Comment: 20 pages, Late

Absolute bounds on pion-pion amplitudes in the physical region and threshold behavior

We establish bounds in terms of pion mass alone, on the real part of the &#960;<SUP>0</SUP>&#960;<SUP>0</SUP> amplitude F(s, t<SUB>0</SUB>), t<SUB>0</SUB>&#8805;0, averaged over part of the physical region. E.g. (with &#8722;h=c=m<SUB>&#960;</SUB>=1 and F(4,0)=scattering length); &#8722;7.9&#8804;&#189;&#8747;<SUP>6</SUP><SUB>4</SUB>ds Re F(s, 0)&#8804;9.6; &#8722;55.6&#8804;&#8747;<SUP>6</SUP><SUB>4</SUB> ds (s-4)(6-s) ReF(s, 1)&#8804;72.5

Shape anisotropy of lipid molecules and voids

Biological polymers, viz., proteins, membranes and micelles exhibit structural discontinuities in terms of spaces unfilled by the polymeric phase, termed voids. These voids exhibit dynamics and lead to interesting properties which are experimentally demonstrable. In the specific case of phospholipid membranes, numerical simulations on a two-dimensional model system showed that voids are induced primarily due to the shape anisotropy in binary mixtures of interacting disks. The results offer a minimal description required to explain the unusually large permeation seen in liposomes made up of specific lipid mixtures (Mathai &amp; Sitaramam, 1994). The results are of wider interest, voids being ubiquitous in biopolymers