342 research outputs found
Focal cerebellar pathology in early relapsing-remitting multiple sclerosis patients: a MP2RAGE study at 3T and 7T MRI
Fractal dimension and degree of order in sequential deposition of mixture
We present a number models describing the sequential deposition of a mixture
of particles whose size distribution is determined by the power-law , . We explicitly obtain the scaling function in
the case of random sequential adsorption (RSA) and show that the pattern
created in the long time limit becomes scale invariant. This pattern can be
described by an unique exponent, the fractal dimension. In addition, we
introduce an external tuning parameter beta to describe the correlated
sequential deposition of a mixture of particles where the degree of correlation
is determined by beta, while beta=0 corresponds to random sequential deposition
of mixture. We show that the fractal dimension of the resulting pattern
increases as beta increases and reaches a constant non-zero value in the limit
when the pattern becomes perfectly ordered or non-random
fractals.Comment: 16 pages Latex, Submitted to Phys. Rev.
Universality of low-energy scattering in (2+1) dimensions
We prove that, in (2+1) dimensions, the S-wave phase shift, , k
being the c.m. momentum, vanishes as either as . The constant is universal and .
This result is established first in the framework of the Schr\"odinger equation
for a large class of potentials, second for a massive field theory from proved
analyticity and unitarity, and, finally, we look at perturbation theory in
and study its relation to our non-perturbative result. The
remarkable fact here is that in n-th order the perturbative amplitude diverges
like as , while the full amplitude vanishes as . We show how these two facts can be reconciled.Comment: 23 pages, Late
Z_3 Quantum Criticality in a spin-1/2 chain model
The stability of the magnetization plateau phase of the XXZ spin-1/2
Heisenberg chain with competing interactions is investigated upon switching on
a staggered transverse magnetic field. Within a bosonization approach, it is
shown that the low-energy properties of the model are described by an effective
two-dimensional XY model in a three-fold symmetry-breaking field. A phase
transition in the three-state Potts universality class is expected separating
the plateau phase to a phase where the spins are polarized along the
staggered magnetic field. The Z critical properties of the transition are
determined within the bosonization approach.Comment: 5 pages, revised versio
Polydisperse Adsorption: Pattern Formation Kinetics, Fractal Properties, and Transition to Order
We investigate the process of random sequential adsorption of polydisperse
particles whose size distribution exhibits a power-law dependence in the small
size limit, . We reveal a relation between pattern
formation kinetics and structural properties of arising patterns. We propose a
mean-field theory which provides a fair description for sufficiently small
. When , highly ordered structures locally identical
to the Apollonian packing are formed. We introduce a quantitative criterion of
the regularity of the pattern formation process. When , a sharp
transition from irregular to regular pattern formation regime is found to occur
near the jamming coverage of standard random sequential adsorption with
monodisperse size distribution.Comment: 8 pages, LaTeX, 5 figures, to appear in Phys.Rev.
A strong-coupling analysis of two-dimensional O(N) sigma models with on square, triangular and honeycomb lattices
Recently-generated long strong-coupling series for the two-point Green's
functions of asymptotically free lattice models are
analyzed, focusing on the evaluation of dimensionless renormalization-group
invariant ratios of physical quantities and applying resummation techniques to
series in the inverse temperature and in the energy . Square,
triangular, and honeycomb lattices are considered, as a test of universality
and in order to estimate systematic errors. Large- solutions are carefully
studied in order to establish benchmarks for series coefficients and
resummations. Scaling and universality are verified. All invariant ratios
related to the large-distance properties of the two-point functions vary
monotonically with , departing from their large- values only by a few per
mille even down to .Comment: 53 pages (incl. 5 figures), tar/gzip/uuencode, REVTEX + psfi
Critical properties of Ising model on Sierpinski fractals. A finite size scaling analysis approach
The present paper focuses on the order-disorder transition of an Ising model
on a self-similar lattice. We present a detailed numerical study, based on the
Monte Carlo method in conjunction with the finite size scaling method, of the
critical properties of the Ising model on some two dimensional deterministic
fractal lattices with different Hausdorff dimensions. Those with finite
ramification order do not display ordered phases at any finite temperature,
whereas the lattices with infinite connectivity show genuine critical behavior.
In particular we considered two Sierpinski carpets constructed using different
generators and characterized by Hausdorff dimensions d_H=log 8/log 3 = 1.8927..
and d_H=log 12/log 4 = 1.7924.., respectively.
The data show in a clear way the existence of an order-disorder transition at
finite temperature in both Sierpinski carpets.
By performing several Monte Carlo simulations at different temperatures and
on lattices of increasing size in conjunction with a finite size scaling
analysis, we were able to determine numerically the critical exponents in each
case and to provide an estimate of their errors.
Finally we considered the hyperscaling relation and found indications that it
holds, if one assumes that the relevant dimension in this case is the Hausdorff
dimension of the lattice.Comment: 21 pages, 7 figures; a new section has been added with results for a
second fractal; there are other minor change
Long-term trends of land use and demography in Greece: a comparative study
This paper offers a comparative study of land use and demographic development in northern and southern Greece from the Neolithic to the Byzantine period. Results from summed probability densities (SPD) of archaeological radiocarbon dates and settlement numbers derived from archaeological site surveys are combined with results from cluster-based analysis of published pollen core assemblages to offer an integrated view of human pressure on the Greek landscape through time. We demonstrate that SPDs offer a useful approach to outline differences between regions and a useful complement to archaeological site surveys, evaluated here especially for the onset of the Neolithic and for the Final Neolithic (FN)/Early Bronze Age (EBA) transition. Pollen analysis highlight differences in vegetation between the two sub-regions, but also several parallel changes. The comparison of land cover dynamics between two sub-regions of Greece further demonstrates the significance of the bioclimatic conditions of core locations and that apparent oppositions between regions may in fact be two sides of the same coin in terms of socio-ecological trajectories. We also assess the balance between anthropogenic and climate-related impacts on vegetation and suggest that climatic variability was as an important factor for vegetation regrowth. Finally, our evidence suggests that the impact of humans on land cover is amplified from the Late Bronze Age (LBA) onwards as more extensive herding and agricultural practices are introduced.Domesticated Landscapes of the Peloponnese (DoLP
Critical behavior of the two-dimensional N-component Landau-Ginzburg Hamiltonian with cubic anisotropy
We study the two-dimensional N-component Landau-Ginzburg Hamiltonian with
cubic anisotropy. We compute and analyze the fixed-dimension perturbative
expansion of the renormalization-group functions to four loops. The relations
of these models with N-color Ashkin-Teller models, discrete cubic models,
planar model with fourth order anisotropy, and structural phase transition in
adsorbed monolayers are discussed. Our results for N=2 (XY model with cubic
anisotropy) are compatible with the existence of a line of fixed points joining
the Ising and the O(2) fixed points. Along this line the exponent has
the constant value 1/4, while the exponent runs in a continuous and
monotonic way from 1 to (from Ising to O(2)). For N\geq 3 we find a
cubic fixed point in the region , which is marginally stable or
unstable according to the sign of the perturbation. For the physical relevant
case of N=3 we find the exponents and at the cubic
transition.Comment: 14 pages, 9 figure
Survival of women with breast cancer in Ottawa, Canada: variation with age, stage, histology, grade and treatment
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