2,056 research outputs found
Two-dimensional Copolymers and Multifractality: Comparing Perturbative Expansions, MC Simulations, and Exact Results
We analyze the scaling laws for a set of two different species of long
flexible polymer chains joined together at one of their extremities (copolymer
stars) in space dimension D=2. We use a formerly constructed field-theoretic
description and compare our perturbative results for the scaling exponents with
recent conjectures for exact conformal scaling dimensions derived by a
conformal invariance technique in the context of D=2 quantum gravity. A simple
MC simulation brings about reasonable agreement with both approaches. We
analyse the remarkable multifractal properties of the spectrum of scaling
exponents.Comment: 5 page
Statistical analysis of 22 public transport networks in Poland
Public transport systems in 22 Polish cities have been analyzed. Sizes of
these networks range from N=152 to N=2881. Depending on the assumed definition
of network topology the degree distribution can follow a power law or can be
described by an exponential function. Distributions of paths in all considered
networks are given by asymmetric, unimodal functions. Clustering, assortativity
and betweenness are studied. All considered networks exhibit small world
behavior and are hierarchically organized. A transition between dissortative
small networks N=500 is observed.Comment: 11 pages, 17 figures, 2 tables, REVTEX4 forma
Longitudinal spin-relaxation in nitrogen-vacancy centers in electron irradiated diamond
We present systematic measurements of longitudinal relaxation rates ()
of spin polarization in the ground state of the nitrogen-vacancy (NV) color
center in synthetic diamond as a function of NV concentration and magnetic
field . NV centers were created by irradiating a Type 1b single-crystal
diamond along the [100] axis with 200 keV electrons from a transmission
electron microscope with varying doses to achieve spots of different NV
center concentrations. Values of () were measured for each spot as a
function of .Comment: 4 pages, 8 figure
Dynamical Scaling Behavior of Percolation Clusters in Scale-free Networks
In this work we investigate the spectra of Laplacian matrices that determine
many dynamic properties of scale-free networks below and at the percolation
threshold. We use a replica formalism to develop analytically, based on an
integral equation, a systematic way to determine the ensemble averaged
eigenvalue spectrum for a general type of tree-like networks. Close to the
percolation threshold we find characteristic scaling functions for the density
of states rho(lambda) of scale-free networks. rho(lambda) shows characteristic
power laws rho(lambda) ~ lambda^alpha_1 or rho(lambda) ~ lambda^alpha_2 for
small lambda, where alpha_1 holds below and alpha_2 at the percolation
threshold. In the range where the spectra are accessible from a numerical
diagonalization procedure the two methods lead to very similar results.Comment: 9 pages, 6 figure
Star copolymers in porous environments: scaling and its manifestations
We consider star polymers, consisting of two different polymer species, in a
solvent subject to quenched correlated structural obstacles. We assume that the
disorder is correlated with a power-law decay of the pair correlation function
g(x)\sim x^{-a}. Applying the field-theoretical renormalization group approach
in d dimensions, we analyze different scenarios of scaling behavior working to
first order of a double \epsilon=4-d, \delta=4-a expansion. We discuss the
influence of the correlated disorder on the resulting scaling laws and possible
manifestations such as diffusion controlled reactions in the vicinity of
absorbing traps placed on polymers as well as the effective short-distance
interaction between star copolymers.Comment: 13 pages, 3 figure
Detailed studies of non-linear magneto-optical resonances at D1 excitation of Rb-85 and Rb-87 for partially resolved hyperfine F-levels
Experimental signals of non-linear magneto-optical resonances at D1
excitation of natural rubidium in a vapor cell have been obtained and described
with experimental accuracy by a detailed theoretical model based on the optical
Bloch equations. The D1 transition of rubidium is a challenging system to
analyze theoretically because it contains transitions that are only partially
resolved under Doppler broadening. The theoretical model took into account all
nearby transitions, the coherence properties of the exciting laser radiation,
and the mixing of magnetic sublevels in an external magnetic field and also
included averaging over the Doppler profile. Great care was taken to obtain
accurate experimental signals and avoid systematic errors. The experimental
signals were reproduced very well at each hyperfine transition and over a wide
range of laser power densities, beam diameters, and laser detunings from the
exact transition frequency. The bright resonance expected at the F_g=1 -->
F_e=2 transition of Rb-87 has been observed. A bright resonance was observed at
the F_g=2 --> F_e=3 transition of Rb-85, but displaced from the exact position
of the transition due to the influence of the nearby F_g=2 --> F_e=2
transition, which is a dark resonance whose contrast is almost two orders of
magnitude larger than the contrast of the bright resonance at the F_g=2 -->
F_e=3 transition. Even in this very delicate situation, the theoretical model
described in detail the experimental signals at different laser detunings.Comment: 11 pages, 9 figure
Two-Dimensional Copolymers and Exact Conformal Multifractality
We consider in two dimensions the most general star-shaped copolymer, mixing
random (RW) or self-avoiding walks (SAW) with specific interactions thereof.
Its exact bulk or boundary conformal scaling dimensions in the plane are all
derived from an algebraic structure existing on a random lattice (2D quantum
gravity). The multifractal dimensions of the harmonic measure of a 2D RW or SAW
are conformal dimensions of certain star copolymers, here calculated exactly as
non rational algebraic numbers. The associated multifractal function f(alpha)
are found to be identical for a random walk or a SAW in 2D. These are the first
examples of exact conformal multifractality in two dimensions.Comment: 4 pages, 2 figures, revtex, to appear in Phys. Rev. Lett., January
199
Multifractality of Brownian motion near absorbing polymers
We characterize the multifractal behavior of Brownian motion in the vicinity
of an absorbing star polymer. We map the problem to an O(M)-symmetric
phi^4-field theory relating higher moments of the Laplacian field of Brownian
motion to corresponding composite operators. The resulting spectra of scaling
dimensions of these operators display the convexity properties which are
necessarily found for multifractal scaling but unusual for power of field
operators in field theory. Using a field-theoretic renormalization group
approach we obtain the multifractal spectrum for absorbtion at the core of a
polymer star as an asymptotic series. We evaluate these series using
resummation techniques.Comment: 18 pages, revtex, 6 ps-figure
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