316 research outputs found
Convolution of multifractals and the local magnetization in a random field Ising chain
The local magnetization in the one-dimensional random-field Ising model is
essentially the sum of two effective fields with multifractal probability
measure. The probability measure of the local magnetization is thus the
convolution of two multifractals. In this paper we prove relations between the
multifractal properties of two measures and the multifractal properties of
their convolution. The pointwise dimension at the boundary of the support of
the convolution is the sum of the pointwise dimensions at the boundary of the
support of the convoluted measures and the generalized box dimensions of the
convolution are bounded from above by the sum of the generalized box dimensions
of the convoluted measures. The generalized box dimensions of the convolution
of Cantor sets with weights can be calculated analytically for certain
parameter ranges and illustrate effects we also encounter in the case of the
measure of the local magnetization. Returning to the study of this measure we
apply the general inequalities and present numerical approximations of the
D_q-spectrum. For the first time we are able to obtain results on multifractal
properties of a physical quantity in the one-dimensional random-field Ising
model which in principle could be measured experimentally. The numerically
generated probability densities for the local magnetization show impressively
the gradual transition from a monomodal to a bimodal distribution for growing
random field strength h.Comment: An error in figure 1 was corrected, small additions were made to the
introduction and the conclusions, some typos were corrected, 24 pages,
LaTeX2e, 9 figure
Orbits and phase transitions in the multifractal spectrum
We consider the one dimensional classical Ising model in a symmetric
dichotomous random field. The problem is reduced to a random iterated function
system for an effective field. The D_q-spectrum of the invariant measure of
this effective field exhibits a sharp drop of all D_q with q < 0 at some
critical strength of the random field. We introduce the concept of orbits which
naturally group the points of the support of the invariant measure. We then
show that the pointwise dimension at all points of an orbit has the same value
and calculate it for a class of periodic orbits and their so-called offshoots
as well as for generic orbits in the non-overlapping case. The sharp drop in
the D_q-spectrum is analytically explained by a drastic change of the scaling
properties of the measure near the points of a certain periodic orbit at a
critical strength of the random field which is explicitly given. A similar
drastic change near the points of a special family of periodic orbits explains
a second, hitherto unnoticed transition in the D_q-spectrum. As it turns out, a
decisive role in this mechanism is played by a specific offshoot. We
furthermore give rigorous upper and/or lower bounds on all D_q in a wide
parameter range. In most cases the numerically obtained D_q coincide with
either the upper or the lower bound. The results in this paper are relevant for
the understanding of random iterated function systems in the case of moderate
overlap in which periodic orbits with weak singularity can play a decisive
role.Comment: The article has been completely rewritten; the title has changed; a
section about the typical pointwise dimension as well as several references
and remarks about more general systems have been added; to appear in J. Phys.
A; 25 pages, 11 figures, LaTeX2
The randomly driven Ising ferromagnet, Part I: General formalism and mean field theory
We consider the behavior of an Ising ferromagnet obeying the Glauber dynamics
under the influence of a fast switching, random external field. After
introducing a general formalism for describing such systems, we consider here
the mean-field theory. A novel type of first order phase transition related to
spontaneous symmetry breaking and dynamic freezing is found. The
non-equilibrium stationary state has a complex structure, which changes as a
function of parameters from a singular-continuous distribution with Euclidean
or fractal support to an absolutely continuous one.Comment: 12 pages REVTeX/LaTeX format, 12 eps/ps figures. Submitted to Journal
of Physics
Phase diagram of the random field Ising model on the Bethe lattice
The phase diagram of the random field Ising model on the Bethe lattice with a
symmetric dichotomous random field is closely investigated with respect to the
transition between the ferromagnetic and paramagnetic regime. Refining
arguments of Bleher, Ruiz and Zagrebnov [J. Stat. Phys. 93, 33 (1998)] an exact
upper bound for the existence of a unique paramagnetic phase is found which
considerably improves the earlier results. Several numerical estimates of
transition lines between a ferromagnetic and a paramagnetic regime are
presented. The obtained results do not coincide with a lower bound for the
onset of ferromagnetism proposed by Bruinsma [Phys. Rev. B 30, 289 (1984)]. If
the latter one proves correct this would hint to a region of coexistence of
stable ferromagnetic phases and a stable paramagnetic phase.Comment: Article has been condensed and reorganized; Figs 3,5,6 merged; Fig 4
omitted; Some discussion added at end of Sec. III; 9 pages, 5 figs, RevTeX4,
AMSTe
Randomly Evolving Idiotypic Networks: Structural Properties and Architecture
We consider a minimalistic dynamic model of the idiotypic network of
B-lymphocytes. A network node represents a population of B-lymphocytes of the
same specificity (idiotype), which is encoded by a bitstring. The links of the
network connect nodes with complementary and nearly complementary bitstrings,
allowing for a few mismatches. A node is occupied if a lymphocyte clone of the
corresponding idiotype exists, otherwise it is empty. There is a continuous
influx of new B-lymphocytes of random idiotype from the bone marrow.
B-lymphocytes are stimulated by cross-linking their receptors with
complementary structures. If there are too many complementary structures,
steric hindrance prevents cross-linking. Stimulated cells proliferate and
secrete antibodies of the same idiotype as their receptors, unstimulated
lymphocytes die.
Depending on few parameters, the autonomous system evolves randomly towards
patterns of highly organized architecture, where the nodes can be classified
into groups according to their statistical properties. We observe and describe
analytically the building principles of these patterns, which allow to
calculate number and size of the node groups and the number of links between
them. The architecture of all patterns observed so far in simulations can be
explained this way. A tool for real-time pattern identification is proposed.Comment: 19 pages, 15 figures, 4 table
Randomly Evolving Idiotypic Networks: Modular Mean Field Theory
We develop a modular mean field theory for a minimalistic model of the
idiotypic network. The model comprises the random influx of new idiotypes and a
deterministic selection. It describes the evolution of the idiotypic network
towards complex modular architectures, the building principles of which are
known. The nodes of the network can be classified into groups of nodes, the
modules, which share statistical properties. Each node experiences only the
mean influence of the groups to which it is linked. Given the size of the
groups and linking between them the statistical properties such as mean
occupation, mean life time, and mean number of occupied neighbors are
calculated for a variety of patterns and compared with simulations. For a
pattern which consists of pairs of occupied nodes correlations are taken into
account.Comment: 14 pages, 8 figures, 4 table
Fundamental scaling laws of on-off intermittency in a stochastically driven dissipative pattern forming system
Noise driven electroconvection in sandwich cells of nematic liquid crystals
exhibits on-off intermittent behaviour at the onset of the instability. We
study laser scattering of convection rolls to characterize the wavelengths and
the trajectories of the stochastic amplitudes of the intermittent structures.
The pattern wavelengths and the statistics of these trajectories are in
quantitative agreement with simulations of the linearized electrohydrodynamic
equations. The fundamental distribution law for the durations
of laminar phases as well as the power law of the amplitude distribution
of intermittent bursts are confirmed in the experiments. Power spectral
densities of the experimental and numerically simulated trajectories are
discussed.Comment: 20 pages and 17 figure
Measurement of CP Asymmetries and Branching Fractions in Charmless Two-Body B-Meson Decays to Pions and Kaons
We present improved measurements of CP-violation parameters in the decays
, , and , and of
the branching fractions for and . The
results are obtained with the full data set collected at the
resonance by the BABAR experiment at the PEP-II asymmetric-energy factory
at the SLAC National Accelerator Laboratory, corresponding to
million pairs. We find the CP-violation parameter values and
branching fractions where in each case, the first uncertainties are statistical
and the second are systematic. We observe CP violation with a significance of
6.7 standard deviations for and 6.1 standard deviations for
, including systematic uncertainties. Constraints on the
Unitarity Triangle angle are determined from the isospin relations
among the rates and asymmetries. Considering only the solution
preferred by the Standard Model, we find to be in the range
at the 68% confidence level.Comment: 18 pages, 11 postscript figures, submitted to Phys. Rev.
Time-integrated luminosity recorded by the BABAR detector at the PEP-II e+e- collider
This article is the Preprint version of the final published artcile which can be accessed at the link below.We describe a measurement of the time-integrated luminosity of the data collected by the BABAR experiment at the PEP-II asymmetric-energy e+e- collider at the ϒ(4S), ϒ(3S), and ϒ(2S) resonances and in a continuum region below each resonance. We measure the time-integrated luminosity by counting e+e-→e+e- and (for the ϒ(4S) only) e+e-→μ+μ- candidate events, allowing additional photons in the final state. We use data-corrected simulation to determine the cross-sections and reconstruction efficiencies for these processes, as well as the major backgrounds. Due to the large cross-sections of e+e-→e+e- and e+e-→μ+μ-, the statistical uncertainties of the measurement are substantially smaller than the systematic uncertainties. The dominant systematic uncertainties are due to observed differences between data and simulation, as well as uncertainties on the cross-sections. For data collected on the ϒ(3S) and ϒ(2S) resonances, an additional uncertainty arises due to ϒ→e+e-X background. For data collected off the ϒ resonances, we estimate an additional uncertainty due to time dependent efficiency variations, which can affect the short off-resonance runs. The relative uncertainties on the luminosities of the on-resonance (off-resonance) samples are 0.43% (0.43%) for the ϒ(4S), 0.58% (0.72%) for the ϒ(3S), and 0.68% (0.88%) for the ϒ(2S).This work is supported by the US Department of Energy and National Science Foundation, the Natural Sciences and Engineering Research Council (Canada), the Commissariat à l’Energie Atomique and Institut National de Physique Nucléaire et de Physiquedes Particules (France), the Bundesministerium für Bildung und Forschung and Deutsche Forschungsgemeinschaft (Germany), the Istituto Nazionale di Fisica Nucleare (Italy), the Foundation for Fundamental Research on Matter (The Netherlands), the Research Council of Norway, the Ministry of Education and Science of the Russian Federation, Ministerio de Ciencia e Innovación (Spain), and the Science and Technology Facilities Council (United Kingdom). Individuals have received support from the Marie-Curie IEF program (European Union) and the A.P. Sloan Foundation (USA)
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