3,766 research outputs found
Weighted and unweighted network of amino acids within protein
The information regarding the structure of a single protein is encoded in the
network of interacting amino acids. Considering each protein as a weighted and
unweighted network of amino acids we have analyzed a total of forty nine
protein structures that covers the three branches of life on earth. Our results
show that the probability degree distribution of network connectivity follows
Poisson's distribution; whereas the probability strength distribution does not
follow any known distribution. However, the average strength of amino acid node
depends on its degree (k). For some of the proteins, the strength of a node
increases linearly with k. On the other hand, for a set of other proteins,
although the strength increases linaerly with k for smaller values of k, we
have not obtained any clear functional relationship of strength with degree at
higher values of k. The results also show that the weight of the amino acid
nodes belonging to the highly connected nodes tend to have a higher value. The
result that the average clustering coefficient of weighted network is less than
that of unweighted network implies that the topological clustering is generated
by edges with low weights. The ratio of average clustering coefficients of
protein network to that of the corresponding classical random network varies
linearly with the number (N) of amino acids of a protein; whereas the ratio of
characteristic path lengths varies logarithmically with N. The power law
behaviour of clustering coefficients of weighted and unweighted network as a
function of degree k indicates that the network has a signature of hierarchical
network. It has also been observed that the network is of assortative type
Mean-field theory for scale-free random networks
Random networks with complex topology are common in Nature, describing
systems as diverse as the world wide web or social and business networks.
Recently, it has been demonstrated that most large networks for which
topological information is available display scale-free features. Here we study
the scaling properties of the recently introduced scale-free model, that can
account for the observed power-law distribution of the connectivities. We
develop a mean-field method to predict the growth dynamics of the individual
vertices, and use this to calculate analytically the connectivity distribution
and the scaling exponents. The mean-field method can be used to address the
properties of two variants of the scale-free model, that do not display
power-law scaling.Comment: 19 pages, 6 figure
Quantum Dot and Hole Formation in Sputter Erosion
Recently it was experimentally demonstrated that sputtering under normal
incidence leads to the formation of spatially ordered uniform nanoscale islands
or holes. Here we show that these nanostructures have inherently nonlinear
origin, first appearing when the nonlinear terms start to dominate the surface
dynamics. Depending on the sign of the nonlinear terms, determined by the shape
of the collision cascade, the surface can develop regular islands or holes with
identical dynamical features, and while the size of these nanostructures is
independent of flux and temperature, it can be modified by tuning the ion
energy
Quantum Dot and Hole Formation in Sputter Erosion
Recently it was experimentally demonstrated that sputtering under normal
incidence leads to the formation of spatially ordered uniform nanoscale islands
or holes. Here we show that these nanostructures have inherently nonlinear
origin, first appearing when the nonlinear terms start to dominate the surface
dynamics. Depending on the sign of the nonlinear terms, determined by the shape
of the collision cascade, the surface can develop regular islands or holes with
identical dynamical features, and while the size of these nanostructures is
independent of flux and temperature, it can be modified by tuning the ion
energy
Nanowire formation on sputter eroded surfaces
Rotated ripple structures (RRS) on sputter eroded surfaces are potential
candidates for nanoscale wire fabrication. We show that the necessary condition
for RRS formation is that the width of the collision cascade in the
longitudinal direction has to be larger than that in the transverse direction,
which can be achieved by using high energy ion beams. By calculating the
structure factor for the RRS we find that they are more regular and their
amplitude is more enhanced compared to the much studied ripple structure
forming in the linear regime of sputter erosion.Comment: 3 pages, 5 figures, 2 column revtex format, submitted to Appl. Phys.
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