8,237 research outputs found
Chain length dependence of the polymer-solvent critical point parameters
We report grand canonical Monte Carlo simulations of the critical point
properties of homopolymers within the Bond Fluctuation model. By employing
Configurational Bias Monte Carlo methods, chain lengths of up to N=60 monomers
could be studied. For each chain length investigated, the critical point
parameters were determined by matching the ordering operator distribution
function to its universal fixed-point Ising form. Histogram reweighting methods
were employed to increase the efficiency of this procedure. The results
indicate that the scaling of the critical temperature with chain length is
relatively well described by Flory theory, i.e. \Theta-T_c\sim N^{-0.5}. The
critical volume fraction, on the other hand, was found to scale like \phi_c\sim
N^{-0.37}, in clear disagreement with the Flory theory prediction \phi_c\sim
N^{-0.5}, but in good agreement with experiment. Measurements of the chain
length dependence of the end-to-end distance indicate that the chains are not
collapsed at the critical point.Comment: 13 Pages Revtex, 9 epsf embedded figs. gzipped tar file. To appear in
J. Chem. Phy
Scaling and singularity characteristics of solar wind and magnetospheric fluctuations
Preliminary results are presented which suggest that scaling and singularity
characteristics of solar wind and ground based magnetic fluctuations appear to
be a significant component in the solar wind - magnetosphere interaction
processes. Of key importance is the intermittence of the "magnetic turbulence"
as seen in ground based and solar wind magnetic data. The methods used in this
paper (estimation of flatness and multifractal spectra) are commonly used in
the studies of fluid or MHD turbulence. The results show that single
observatory characteristics of magnetic fluctuations are different from those
of the multi-observatory AE-index. In both data sets, however, the influence of
the solar wind fluctuations is recognizable. The correlation between the
scaling/singularity features of solar wind magnetic fluctuations and the
corresponding geomagnetic response is demonstrated in a number of cases. The
results are also discussed in terms of patchy reconnection processes in
magnetopause and forced or/and self-organized criticality (F/SOC) of internal
magnetosphere dynamics.Comment: 28 pages, 12 figure
Luttinger liquid, singular interaction and quantum criticality in cuprate materials
With particular reference to the role of the renormalization group approach
and Ward identities, we start by recalling some old features of the
one-dimensional Luttinger liquid as the prototype of non-Fermi-liquid behavior.
Its dimensional crossover to the Landau normal Fermi liquid implies that a
non-Fermi liquid, as, e.g., the normal phase of the cuprate high temperature
superconductors, can be maintained in d>1, only in the presence of a
sufficiently singular effective interaction among the charge carriers. This is
the case when, nearby an instability, the interaction is mediated by
fluctuations. We are then led to introduce the specific case of
superconductivity in cuprates as an example of avoided quantum criticality. We
will disentangle the fluctuations which act as mediators of singular
electron-electron interaction, enlightening the possible order competing with
superconductivity and a mechanism for the non-Fermi-liquid behavior of the
metallic phase. This paper is not meant to be a comprehensive review. Many
important contributions will not be considered. We will also avoid using
extensive technicalities and making full calculations for which we refer to the
original papers and to the many good available reviews. We will here only
follow one line of reasoning which guided our research activity in this field.Comment: 23 pages, 10 figure
Understanding scaling through history-dependent processes with collapsing sample space
History-dependent processes are ubiquitous in natural and social systems.
Many such stochastic processes, especially those that are associated with
complex systems, become more constrained as they unfold, meaning that their
sample-space, or their set of possible outcomes, reduces as they age. We
demonstrate that these sample-space reducing (SSR) processes necessarily lead
to Zipf's law in the rank distributions of their outcomes. We show that by
adding noise to SSR processes the corresponding rank distributions remain exact
power-laws, , where the exponent directly corresponds to
the mixing ratio of the SSR process and noise. This allows us to give a precise
meaning to the scaling exponent in terms of the degree to how much a given
process reduces its sample-space as it unfolds. Noisy SSR processes further
allow us to explain a wide range of scaling exponents in frequency
distributions ranging from to . We discuss several
applications showing how SSR processes can be used to understand Zipf's law in
word frequencies, and how they are related to diffusion processes in directed
networks, or ageing processes such as in fragmentation processes. SSR processes
provide a new alternative to understand the origin of scaling in complex
systems without the recourse to multiplicative, preferential, or self-organised
critical processes.Comment: 7 pages, 5 figures in Proceedings of the National Academy of Sciences
USA (published ahead of print April 13, 2015
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