553 research outputs found
Fractal Measures of Sea, Lake, Strait, and Dam-Reserve Shores: Calculation, Differentiation, and Interpretation
The fractal dimensions d_f of the shore lines of the Mediterranean, the
Aegean, the Black Sea, the Bosphorus Straits (on both the Asian and European
sides), the Van Lake, and the lake formed by the Ataturk Dam have been
calculated. Important distinctions have been found and explained.Comment: 3 pages, 2 figures, 1 tabl
An Analytic Equation of State for Ising-like Models
Using an Environmentally Friendly Renormalization we derive, from an
underlying field theory representation, a formal expression for the equation of
state, , that exhibits all desired asymptotic and analyticity
properties in the three limits , and . The only
necessary inputs are the Wilson functions , and
, associated with a renormalization of the transverse vertex
functions. These Wilson functions exhibit a crossover between the Wilson-Fisher
fixed point and the fixed point that controls the coexistence curve.
Restricting to the case N=1, we derive a one-loop equation of state for naturally parameterized by a ratio of non-linear scaling fields. For
we show that a non-parameterized analytic form can be deduced. Various
asymptotic amplitudes are calculated directly from the equation of state in all
three asymptotic limits of interest and comparison made with known results. By
positing a scaling form for the equation of state inspired by the one-loop
result, but adjusted to fit the known values of the critical exponents, we
obtain better agreement with known asymptotic amplitudes.Comment: 10 pages, 2 figure
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The landscape of psoriasis provision in the UK.
Psoriasis remains one of the commonest conditions seen in dermatological practice, and its treatment is one of the greatest cost burdens for the UK National Health Service. Treatment of psoriasis is complex, with numerous overlapping lines and therapies used in combination. This complexity reflects the underlying pathophysiology of the disease as well as the heterogeneous population that it affects. National Institute for Health and Care Excellence (NICE) guidance for the treatment of psoriasis has been available since 2013, and has been the subject of three national audits conducted by the British Association of Dermatologists. This report synthesizes the results of the most recent of those exercises and places it in the context of the NICE guidance and previous audits. It clearly shows the significant burden of disease, issues with provision of services and long waiting times and the marked shift in therapies towards targeted biologic therapies
Excitation Spectrum Gap and Spin-Wave Stiffness of XXZ Heisenberg Chains: Global Renormalization-Group Calculation
The anisotropic XXZ spin-1/2 Heisenberg chain is studied using
renormalization-group theory. The specific heats and nearest-neighbor spin-spin
correlations are calculated thoughout the entire temperature and anisotropy
ranges in both ferromagnetic and antiferromagnetic regions, obtaining a global
description and quantitative results. We obtain, for all anisotropies, the
antiferromagnetic spin-liquid spin-wave velocity and the Isinglike
ferromagnetic excitation spectrum gap, exhibiting the spin-wave to spinon
crossover. A number of characteristics of purely quantum nature are found: The
in-plane interaction s_i^x s_j^x + s_i^y s_j^y induces an antiferromagnetic
correlation in the out-of-plane s_i^z component, at higher temperatures in the
antiferromagnetic XXZ chain, dominantly at low temperatures in the
ferromagnetic XXZ chain, and, in-between, at all temperatures in the XY chain.
We find that the converse effect also occurs in the antiferromagnetic XXZ
chain: an antiferromagnetic s_i^z s_j^z interaction induces a correlation in
the s_i^xy component. As another purely quantum effect, (i) in the
antiferromagnet, the value of the specific heat peak is insensitive to
anisotropy and the temperature of the specific heat peak decreases from the
isotropic (Heisenberg) with introduction of either type (Ising or XY)
anisotropy; (ii) in complete contrast, in the ferromagnet, the value and
temperature of the specific heat peak increase with either type of anisotropy.Comment: New results added to text and figures. 12 pages, 18 figures, 3
tables. Published versio
Fractal and Transfractal Recursive Scale-Free Nets
We explore the concepts of self-similarity, dimensionality, and
(multi)scaling in a new family of recursive scale-free nets that yield
themselves to exact analysis through renormalization techniques. All nets in
this family are self-similar and some are fractals - possessing a finite
fractal dimension - while others are small world (their diameter grows
logarithmically with their size) and are infinite-dimensional. We show how a
useful measure of "transfinite" dimension may be defined and applied to the
small world nets. Concerning multiscaling, we show how first-passage time for
diffusion and resistance between hub (the most connected nodes) scale
differently than for other nodes. Despite the different scalings, the Einstein
relation between diffusion and conductivity holds separately for hubs and
nodes. The transfinite exponents of small world nets obey Einstein relations
analogous to those in fractal nets.Comment: Includes small revisions and references added as result of readers'
feedbac
The Critical Properties of Two-dimensional Oscillator Arrays
We present a renormalization group study of two dimensional arrays of
oscillators, with dissipative, short range interactions. We consider the case
of non-identical oscillators, with distributed intrinsic frequencies within the
array and study the steady-state properties of the system. In two dimensions no
macroscopic mutual entrainment is found but, for identical oscillators,
critical behavior of the Berezinskii-Kosterlitz-Thouless type is shown to be
present. We then discuss the stability of (BKT) order in the physical case of
distributed quenched random frequencies. In order to do that, we show how the
steady-state dynamical properties of the two dimensional array of non-identical
oscillators are related to the equilibrium properties of the XY model with
quenched randomness, that has been already studied in the past. We propose a
novel set of recursion relations to study this system within the Migdal
Kadanoff renormalization group scheme, by mean of the discrete clock-state
formulation. We compute the phase diagram in the presence of random dissipative
coupling, at finite values of the clock state parameter. Possible experimental
applications in two dimensional arrays of microelectromechanical oscillators
are briefly suggested.Comment: Contribution to the conference "Viewing the World through Spin
Glasses" in honour of Professor David Sherrington on the occasion of his 65th
birthda
Chaotic Behaviour of Renormalisation Flow in a Complex Magnetic Field
It is demonstrated that decimation of the one dimensional Ising model, with
periodic boundary conditions, results in a non-linear renormalisation
transformation for the couplings which can lead to chaotic behaviour when the
couplings are complex. The recursion relation for the couplings under
decimation is equivalent to the logistic map, or more generally the Mandelbrot
map. In particular an imaginary external magnetic field can give chaotic
trajectories in the space of couplings. The magnitude of the field must be
greater than a minimum value which tends to zero as the critical point T=0 is
approached, leading to a gap equation and associated critical exponent which
are identical to those of the Lee-Yang edge singularity in one dimension.Comment: 8 pages, 2 figures, PlainTeX, corrected some typo
Novel glassy behavior in a ferromagnetic p-spin model
Recent work has suggested the existence of glassy behavior in a ferromagnetic
model with a four-spin interaction. Motivated by these findings, we have
studied the dynamics of this model using Monte Carlo simulations with
particular attention being paid to two-time quantities. We find that the system
shares many features in common with glass forming liquids. In particular, the
model exhibits: (i) a very long-lived metastable state, (ii) autocorrelation
functions that show stretched exponential relaxation, (iii) a non-equilibrium
timescale that appears to diverge at a well defined temperature, and (iv) low
temperature aging behaviour characteristic of glasses.Comment: 6 pages, 5 figure
Real-space renormalization group for the random-field Ising model
We present real--space renormalization group (RG) calculations of the
critical properties of the random--field Ising model on a cubic lattice in
three dimensions. We calculate the RG flows in a two--parameter truncation of
the Hamiltonian space. As predicted, the transition at finite randomness is
controlled by a zero temperature, disordered critical fixed point, and we
exhibit the universal crossover trajectory from the pure Ising critical point.
We extract scaling fields and critical exponents, and study the distribution of
barrier heights between states as a function of length scale.Comment: 12 pages, CU-MSC-757
Critical Fluctuations and Disorder at the Vortex Liquid to Crystal Transition in Type-II Superconductors
We present a functional renormalization group (FRG) analysis of a
Landau-Ginzburg model of type-II superconductors (generalized to complex
fields) in a magnetic field, both for a pure system, and in the presence of
quenched random impurities. Our analysis is based on a previous FRG treatment
of the pure case [E.Br\'ezin et. al., Phys. Rev. B, {\bf 31}, 7124 (1985)]
which is an expansion in . If the coupling functions are
restricted to the space of functions with non-zero support only at reciprocal
lattice vectors corresponding to the Abrikosov lattice, we find a stable FRG
fixed point in the presence of disorder for , identical to that of the
disordered model in dimensions. The pure system has a stable fixed
point only for and so the physical case () is likely to have a
first order transition. We speculate that the recent experimental findings that
disorder removes the apparent first order transition are consistent with these
calculations.Comment: 4 pages, no figures, typeset using revtex (v3.0
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