1,625 research outputs found
Disorder effects on the static scattering function of star branched polymers
We present an analysis of the impact of structural disorder on the static
scattering function of f-armed star branched polymers in d dimensions. To this
end, we consider the model of a star polymer immersed in a good solvent in the
presence of structural defects, correlated at large distances r according to a
power law \sim r^{-a}. In particular, we are interested in the ratio g(f) of
the radii of gyration of star and linear polymers of the same molecular weight,
which is a universal experimentally measurable quantity. We apply a direct
polymer renormalization approach and evaluate the results within the double
\varepsilon=4-d, \delta=4-a-expansion. We find an increase of g(f) with an
increasing \delta. Therefore, an increase of disorder correlations leads to an
increase of the size measure of a star relative to linear polymers of the same
molecular weight.Comment: 17 pages, 7 figure
Shapes of macromolecules in good solvents: field theoretical renormalization group approach
In this paper, we show how the method of field theoretical renormalization
group may be used to analyze universal shape properties of long polymer chains
in porous environment. So far such analytical calculations were primarily
focussed on the scaling exponents that govern conformational properties of
polymer macromolecules. However, there are other observables that along with
the scaling exponents are universal (i.e. independent of the chemical structure
of macromolecules and of the solvent) and may be analyzed within the
renormalization group approach. Here, we address the question of shape which is
acquired by the long flexible polymer macromolecule when it is immersed in a
solvent in the presence of a porous environment. This question is of relevance
for understanding of the behavior of macromolecules in colloidal solutions,
near microporous membranes, and in cellular environment. To this end, we
consider a previously suggested model of polymers in d-dimensions [V.
Blavats'ka, C. von Ferber, Yu. Holovatch, Phys. Rev. E, 2001, 64, 041102] in an
environment with structural obstacles, characterized by a pair correlation
function h(r), that decays with distance r according to a power law: h(r) \sim
r-a. We apply the field-theoretical renormalization group approach and estimate
the size ratio / and the asphericity ratio \hat{A}_d up to the
first order of a double \epsilon=4-d, \delta=4-a expansion.Comment: 20 pages, 5 figure
Scaling in public transport networks
We analyse the statistical properties of public transport networks. These
networks are defined by a set of public transport routes (bus lines) and the
stations serviced by these. For larger networks these appear to possess a
scale-free structure, as it is demonstrated e.g. by the Zipf law distribution
of the number of routes servicing a given station or for the distribution of
the number of stations which can be visited from the chosen one without
changing the means of transport. Moreover, a rather particular feature of the
public transport network is that many routes service common subsets of
stations. We discuss the possibility of new scaling laws that govern intrinsic
features of such subsets.Comment: 9 pages, 4 figure
Entropic equation of state and scaling functions near the critical point in scale-free networks
We analyze the entropic equation of state for a many-particle interacting
system in a scale-free network. The analysis is performed in terms of scaling
functions which are of fundamental interest in the theory of critical phenomena
and have previously been theoretically and experimentally explored in the
context of various magnetic, fluid, and superconducting systems in two and
three dimensions. Here, we obtain general scaling functions for the entropy,
the constant-field heat capacity, and the isothermal magnetocaloric coefficient
near the critical point in scale-free networks, where the node-degree
distribution exponent appears to be a global variable and plays a
crucial role, similar to the dimensionality for systems on lattices. This
extends the principle of universality to systems on scale-free networks and
allows quantification of the impact of fluctuations in the network structure on
critical behavior.Comment: 8 pages, 4 figure
Network Harness: Metropolis Public Transport
We analyze the public transport networks (PTNs) of a number of major cities
of the world. While the primary network topology is defined by a set of routes
each servicing an ordered series of given stations, a number of different
neighborhood relations may be defined both for the routes and the stations. The
networks defined in this way display distinguishing properties, the most
striking being that often several routes proceed in parallel for a sequence of
stations. Other networks with real-world links like cables or neurons embedded
in two or three dimensions often show the same feature - we use the car
engineering term "harness" for such networks. Geographical data for the routes
reveal surprising self-avoiding walk (SAW) properties. We propose and simulate
an evolutionary model of PTNs based on effectively interacting SAWs that
reproduces the key features.Comment: 5 pages, 4 figure
Star polymers in correlated disorder
We analyze the impact of a porous medium (structural disorder) on the scaling
of the partition function of a star polymer immersed in a good solvent. We show
that corresponding scaling exponents change if the disorder is
long-range-correlated and calculate the exponents in the new universality
class. A notable finding is that star and chain polymers react in qualitatively
different manner on the presence of disorder: the corresponding scaling
exponents increase for chains and decrease for stars. We discuss the physical
consequences of this difference.Comment: Submitted to the Proceedings of the International Conference "Path
Integrals - New Trends and Perspectives", September 23-28, 2007, Dresden,
German
Entropy-induced separation of star polymers in porous media
We present a quantitative picture of the separation of star polymers in a
solution where part of the volume is influenced by a porous medium. To this
end, we study the impact of long-range-correlated quenched disorder on the
entropy and scaling properties of -arm star polymers in a good solvent. We
assume that the disorder is correlated on the polymer length scale with a
power-law decay of the pair correlation function . Applying
the field-theoretical renormalization group approach we show in a double
expansion in and that there is a range of
correlation strengths for which the disorder changes the scaling
behavior of star polymers. In a second approach we calculate for fixed space
dimension and different values of the correlation parameter the
corresponding scaling exponents that govern entropic effects. We
find that , the deviation of from its mean field value
is amplified by the disorder once we increase beyond a threshold. The
consequences for a solution of diluted chain and star polymers of equal
molecular weight inside a porous medium are: star polymers exert a higher
osmotic pressure than chain polymers and in general higher branched star
polymers are expelled more strongly from the correlated porous medium.
Surprisingly, polymer chains will prefer a stronger correlated medium to a less
or uncorrelated medium of the same density while the opposite is the case for
star polymers.Comment: 14 pages, 7 figure
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