627 research outputs found
Correlation amplitude and entanglement entropy in random spin chains
Using strong-disorder renormalization group, numerical exact diagonalization,
and quantum Monte Carlo methods, we revisit the random antiferromagnetic XXZ
spin-1/2 chain focusing on the long-length and ground-state behavior of the
average time-independent spin-spin correlation function C(l)=\upsilon
l^{-\eta}. In addition to the well-known universal (disorder-independent)
power-law exponent \eta=2, we find interesting universal features displayed by
the prefactor \upsilon=\upsilon_o/3, if l is odd, and \upsilon=\upsilon_e/3,
otherwise. Although \upsilon_o and \upsilon_e are nonuniversal (disorder
dependent) and distinct in magnitude, the combination \upsilon_o + \upsilon_e =
-1/4 is universal if C is computed along the symmetric (longitudinal) axis. The
origin of the nonuniversalities of the prefactors is discussed in the
renormalization-group framework where a solvable toy model is considered.
Moreover, we relate the average correlation function with the average
entanglement entropy, whose amplitude has been recently shown to be universal.
The nonuniversalities of the prefactors are shown to contribute only to surface
terms of the entropy. Finally, we discuss the experimental relevance of our
results by computing the structure factor whose scaling properties,
interestingly, depend on the correlation prefactors.Comment: v1: 16 pages, 15 figures; v2: 17 pages, improved discussions and
statistics, references added, published versio
Aperiodic quantum XXZ chains: Renormalization-group results
We report a comprehensive investigation of the low-energy properties of
antiferromagnetic quantum XXZ spin chains with aperiodic couplings. We use an
adaptation of the Ma-Dasgupta-Hu renormalization-group method to obtain
analytical and numerical results for the low-temperature thermodynamics and the
ground-state correlations of chains with couplings following several two-letter
aperiodic sequences, including the quasiperiodic Fibonacci and other
precious-mean sequences, as well as sequences inducing strong geometrical
fluctuations. For a given aperiodic sequence, we argue that in the easy-plane
anisotropy regime, intermediate between the XX and Heisenberg limits, the
general scaling form of the thermodynamic properties is essentially given by
the exactly-known XX behavior, providing a classification of the effects of
aperiodicity on XXZ chains. We also discuss the nature of the ground-state
structures, and their comparison with the random-singlet phase, characteristic
of random-bond chains.Comment: Minor corrections; published versio
Mean-field model for a mixture of biaxial nematogens and dipolar nanoparticles
We analyze a mean-field model for mixtures involving biaxial nematogens and
dipolar nanoparticles, taking into account orientational and isotropic pair
interactions between nematogens, but also orientational nematogen-nanoparticle
interactions. We determine bulk equilibrium phase diagrams for a wide range of
interaction strengths, identifying in each case the effect of the nanoparticles
on the stability of nematic phases and on the appearance of multicritical
points. Special attention is given to the limit of low concentration of
nanoparticles, in which their effect on the temperatures of both the
first-order uniaxial-isotropic and the continuous biaxial-uniaxial transitions
is investigated in detail
Analytical approach to directed sandpile models on the Apollonian network
We investigate a set of directed sandpile models on the Apollonian network,
which are inspired on the work by Dhar and Ramaswamy (PRL \textbf{63}, 1659
(1989)) for Euclidian lattices. They are characterized by a single parameter
, that restricts the number of neighbors receiving grains from a toppling
node. Due to the geometry of the network, two and three point correlation
functions are amenable to exact treatment, leading to analytical results for
the avalanche distributions in the limit of an infinite system, for .
The exact recurrence expressions for the correlation functions are numerically
iterated to obtain results for finite size systems, when larger values of
are considered. Finally, a detailed description of the local flux properties is
provided by a multifractal scaling analysis.Comment: 7 pages in two-column format, 10 illustrations, 5 figure
Microstructure identification via detrended fluctuation analysis of ultrasound signals
We describe an algorithm for simulating ultrasound propagation in random
one-dimensional media, mimicking different microstructures by choosing physical
properties such as domain sizes and mass densities from probability
distributions. By combining a detrended fluctuation analysis (DFA) of the
simulated ultrasound signals with tools from the pattern-recognition
literature, we build a Gaussian classifier which is able to associate each
ultrasound signal with its corresponding microstructure with a very high
success rate. Furthermore, we also show that DFA data can be used to train a
multilayer perceptron which estimates numerical values of physical properties
associated with distinct microstructures.Comment: Submitted to Phys. Rev.
Experimental Study of Two Impinging Jets Aligned With a Crossflow
Laser Doppler measurements provide information on the flowfield created by twin impinging jets aligned with a low velocity crossflow. The experiments were carried out for a Reynolds number based on the jet exit conditions of Rej = 4.3 × 104, an impingement height of 20.1 jet diameters and for a velocity ratio between the jet exit and the crossflow VR = Vj/Uo of 22.5, and an inter-jet spacing of S = 6D. The results show a large penetration of the first (upstream) jet that is deflected by the crossflow and impinges on the ground, giving rise to a ground vortex due to the collision of the radial wall and the crossflow that wraps around the impinging point like a scarf. The second jet (located downstream) is not so affected by the crossflow in terms of deflection, but due to the downstream wall jet that flows radially from the impinging point of the first jet it does not reach the ground. The results indicate a new flow pattern not yet reported so far, that is most relevant for a VSTOL aircraft operating in ground vicinity with front wind or small forward movement may result in enhanced under pressures in the aft part of the aircraft causing a suction down force and a change of the pitching moment towards the ground.Fundação para a Ciência e a Tecnologiainfo:eu-repo/semantics/publishedVersio
Fatigue in disordered media
We obtain the Paris law of fatigue crack propagation in a disordered solid
using a fuse network model where the accumulated damage in each resistor
increases with time as a power law of the local current amplitude. When a
resistor reaches its fatigue threshold, it burns irreversibly. Over time, this
drives cracks to grow until the system is fractured in two parts. We study the
relation between the macroscopic exponent of the crack growth rate -- entering
the phenomenological Paris law -- and the microscopic damage-accumulation
exponent, , under the influence of disorder. The way the jumps of the
growing crack, , and the waiting-time between successive breaks,
, depend on the type of material, via , are also
investigated. We find that the averages of these quantities, and
$/$, scale as power laws of the crack length $a$, $
\propto a^{\alpha}$ and $/ \propto a^{-\beta}$, where is
the average rupture time. Strikingly, our results show, for small values of
, a decrease in the exponent of the Paris law in comparison with the
homogeneous case, leading to an increase in the lifetime of breaking materials.
For the particular case of , when fatigue is exclusively ruled by
disorder, an analytical treatment confirms the results obtained by simulation
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