12 research outputs found
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 π<SUP>0</SUP>π<SUP>0</SUP> amplitude F(s, t<SUB>0</SUB>), t<SUB>0</SUB>≥0, averaged over part of the physical region. E.g. (with −h=c=m<SUB>π</SUB>=1 and F(4,0)=scattering length); −7.9≤½∫<SUP>6</SUP><SUB>4</SUB>ds Re F(s, 0)≤9.6; −55.6≤∫<SUP>6</SUP><SUB>4</SUB> ds (s-4)(6-s) ReF(s, 1)≤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 &
Sitaramam, 1994). The results are of wider interest, voids being ubiquitous in biopolymers