727 research outputs found
Barkhausen Noise and Critical Scaling in the Demagnetization Curve
The demagnetization curve, or initial magnetization curve, is studied by
examining the embedded Barkhausen noise using the non-equilibrium, zero
temperature random-field Ising model. The demagnetization curve is found to
reflect the critical point seen as the system's disorder is changed. Critical
scaling is found for avalanche sizes and the size and number of spanning
avalanches. The critical exponents are derived from those related to the
saturation loop and subloops. Finally, the behavior in the presence of long
range demagnetizing fields is discussed. Results are presented for simulations
of up to one million spins.Comment: 4 pages, 4 figures, submitted to Physical Review Letter
Experimental evidence of accelerated seismic release without critical failure in acoustic emissions of compressed nanoporous materials
The total energy of acoustic emission (AE) events in externally stressed
materials diverges when approaching macroscopic failure. Numerical and
conceptual models explain this accelerated seismic release (ASR) as the
approach to a critical point that coincides with ultimate failure. Here, we
report ASR during soft uniaxial compression of three silica-based (SiO)
nanoporous materials. Instead of a singular critical point, the distribution of
AE energies is stationary and variations in the activity rate are sufficient to
explain the presence of multiple periods of ASR leading to distinct brittle
failure events. We propose that critical failure is suppressed in the AE
statistics by dissipation and transient hardening. Some of the critical
exponents estimated from the experiments are compatible with mean field models,
while others are still open to interpretation in terms of the solution of
frictional and fracture avalanche models.Comment: preprint, Main article: 7 pages, 3 figures. Supplementary material
included in \anc folder: 6 pages, 3 figure
Magnetic hysteresis in Ising-like dipole-dipole model
Using zero temperature Monte Carlo simulations we have studied the magnetic
hysteresis in a three-dimensional Ising model with nearest neighbor exchange
and dipolar interaction. The average magnetization of spins located inside a
sphere on a cubic lattice is determined as a function of magnetic field varied
periodically. The simulations have justified the appearance of hysteresis and
allowed us to have a deeper insight into the series of metastable states
developed during this process.Comment: REVTEX, 10 pages including 4 figure
Spanning avalanches in the three-dimensional Gaussian Random Field Ising Model with metastable dynamics: field dependence and geometrical properties
Spanning avalanches in the 3D Gaussian Random Field Ising Model (3D-GRFIM)
with metastable dynamics at T=0 have been studied. Statistical analysis of the
field values for which avalanches occur has enabled a Finite-Size Scaling (FSS)
study of the avalanche density to be performed. Furthermore, direct measurement
of the geometrical properties of the avalanches has confirmed an earlier
hypothesis that several kinds of spanning avalanches with two different fractal
dimensions coexist at the critical point. We finally compare the phase diagram
of the 3D-GRFIM with metastable dynamics with the same model in equilibrium at
T=0.Comment: 16 pages, 17 figure
Crackling Noise, Power Spectra and Disorder Induced Critical Scaling
Crackling noise is observed in many disordered non-equilibrium systems in
response to slowly changing external conditions. Examples range from Barkhausen
noise in magnets to acoustic emission in martensites to earthquakes. Using the
non-equilibrium random field Ising model, we derive universal scaling
predictions for the dependence of the associated power spectra on the disorder
and field sweep rate, near an underlying disorder-induced non-equilibrium
critical point. Our theory applies to certain systems in which the crackling
noise results from avalanche-like response to a (slowly) increasing external
driving force, and is characterized by a broad power law scaling regime of the
power spectra. We compute the critical exponents and discuss the relevance of
the results to experiments.Comment: 27 Latex Pages, 14 eps figure
Overview of (pro-)Lie group structures on Hopf algebra character groups
Character groups of Hopf algebras appear in a variety of mathematical and
physical contexts. To name just a few, they arise in non-commutative geometry,
renormalisation of quantum field theory, and numerical analysis. In the present
article we review recent results on the structure of character groups of Hopf
algebras as infinite-dimensional (pro-)Lie groups. It turns out that under mild
assumptions on the Hopf algebra or the target algebra the character groups
possess strong structural properties. Moreover, these properties are of
interest in applications of these groups outside of Lie theory. We emphasise
this point in the context of two main examples: The Butcher group from
numerical analysis and character groups which arise from the Connes--Kreimer
theory of renormalisation of quantum field theories.Comment: 31 pages, precursor and companion to arXiv:1704.01099, Workshop on
"New Developments in Discrete Mechanics, Geometric Integration and
Lie-Butcher Series", May 25-28, 2015, ICMAT, Madrid, Spai
On the robustness of scale invariance in SOC models
A random neighbor extremal stick-slip model is introduced. In the
thermodynamic limit, the distribution of states has a simple analytical form
and the mean avalanche size, as a function of the coupling parameter, is
exactly calculable. The system is critical only at a special point Jc in the
coupling parameter space. However, the critical region around this point, where
approximate scale invariance holds, is very large, suggesting a mechanism for
explaining the ubiquity of scale invariance in Nature.Comment: 6 pages, 4 figures; submitted to Physical Review E;
http://link.aps.org/doi/10.1103/PhysRevE.59.496
Bar-driven Transport of Molecular Gas to Galactic Centers and Its Consequences
We study the characteristics of molecular gas in the central regions of
spiral galaxies on the basis of our CO(J=1-0) imaging survey of 20 nearby
spiral galaxies using the NRO and OVRO millimeter arrays. Condensations of
molecular gas at galactic centers with sizescales < 1 kpc and CO-derived masses
M_gas(R<500pc) = 10^8 - 10^9 M_sun are found to be prevalent in the gas-rich
L^* galaxies. Moreover, the degree of gas concentration to the central kpc is
found to be higher in barred systems than in unbarred galaxies. This is the
first statistical evidence for the higher central concentration of molecular
gas in barred galaxies, and it strongly supports the theory of bar-driven gas
transport. It is most likely that more than half of molecular gas within the
central kpc of a barred galaxy was transported there from outside by the bar.
The supply of gas has exceeded the consumption of gas by star formation in the
central kpc, resulting in the excess gas in the centers of barred systems. The
mean rate of gas inflow is statistically estimated to be larger than 0.1 - 1
M_sun/yr.
The correlation between gas properties in the central kpc and the type of
nuclear spectrum (HII, LINER, or Seyfert) is investigated. A correlation is
found in which galaxies with larger gas-to-dynamical mass ratios tend to have
HII nuclear spectra, while galaxies with smaller ratios show spectra indicating
AGN.
Also, the theoretical prediction of bar-dissolution by condensation of gas to
galactic centers is observationally tested. It is suggested that the timescale
for bar dissolution is larger than 10^8 - 10^10 yr, or a bar in a L^* galaxy is
not destroyed by a condensation of 10^8 - 10^9 M_sun gas in the central kpc.Comment: AASTeX, 20 pages, 8 eps figs, ApJ in press (10 Nov. 1999 issue
Renormalizing the Schwinger-Dyson equations in the auxiliary field formulation of field theory
In this paper we study the renormalization of the Schwinger-Dyson equations
that arise in the auxiliary field formulation of the O(N) field
theory. The auxiliary field formulation allows a simple interpretation of the
large-N expansion as a loop expansion of the generating functional in the
auxiliary field , once the effective action is obtained by integrating
over the fields. Our all orders result is then used to obtain finite
renormalized Schwinger-Dyson equations based on truncation expansions which
utilize the two-particle irreducible (2-PI) generating function formalism. We
first do an all orders renormalization of the two- and three-point function
equations in the vacuum sector. This result is then used to obtain explicitly
finite and renormalization constant independent self-consistent S-D equations
valid to order~1/N, in both 2+1 and 3+1 dimensions. We compare the results for
the real and imaginary parts of the renormalized Green's functions with the
related \emph{sunset} approximation to the 2-PI equations discussed by Van Hees
and Knoll, and comment on the importance of the Landau pole effect.Comment: 20 pages, 10 figure
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