[show abstract][hide abstract] ABSTRACT: We present a new numerical Monte Carlo approach to determine the scaling
behavior of lattice field theories far from equilibrium. The presented methods
are generally applicable to systems where classical-statistical fluctuations
dominate the dynamics. As an example, these methods are applied to the
random-force-driven one-dimensional Burgers' equation - a model for
hydrodynamic turbulence. For a self-similar forcing acting on all scales the
system is driven to a nonequilibrium steady state characterized by a Kolmogorov
energy spectrum. We extract correlation functions of single- and multi-point
quantities and determine their scaling spectrum displaying anomalous scaling
for high-order moments. Varying the external forcing we are able to tune the
system continuously from equilibrium, where the fluctuations are short-range
correlated, to the case where the system is strongly driven in the infrared. In
the latter case the nonequilibrium scaling of small-scale fluctuations are
shown to be universal.
[show abstract][hide abstract] ABSTRACT: We report a high-precision finite-size scaling study of the critical behavior
of the three-dimensional Ising Edwards-Anderson model (the Ising spin glass).
We have thermalized lattices up to L=40 using the Janus dedicated computer. Our
analysis takes into account leading-order corrections to scaling. We obtain Tc
= 1.1019(29) for the critical temperature, \nu = 2.562(42) for the thermal
exponent, \eta = -0.3900(36) for the anomalous dimension and \omega = 1.12(10)
for the exponent of the leading corrections to scaling. Standard (hyper)scaling
relations yield \alpha = -5.69(13), \beta = 0.782(10) and \gamma = 6.13(11). We
also compute several universal quantities at Tc.
[show abstract][hide abstract] ABSTRACT: This paper describes the architecture, the development and the implementation
of Janus II, a new generation application-driven number cruncher optimized for
Monte Carlo simulations of spin systems (mainly spin glasses). This domain of
computational physics is a recognized grand challenge of high-performance
computing: the resources necessary to study in detail theoretical models that
can make contact with experimental data are by far beyond those available using
commodity computer systems. On the other hand, several specific features of the
associated algorithms suggest that unconventional computer architectures, which
can be implemented with available electronics technologies, may lead to order
of magnitude increases in performance, reducing to acceptable values on human
scales the time needed to carry out simulation campaigns that would take
centuries on commercially available machines. Janus II is one such machine,
recently developed and commissioned, that builds upon and improves on the
successful JANUS machine, which has been used for physics since 2008 and is
still in operation today. This paper describes in detail the motivations behind
the project, the computational requirements, the architecture and the
implementation of this new machine and compares its expected performances with
those of currently available commercial systems.
[show abstract][hide abstract] ABSTRACT: A track reconstruction system for the trigger of the ATLAS detector at the Large Hadron Col-lider is described. The Fast Tracker is a highly parallel hardware system designed to operate at the Level-1 trigger output rate. It will provide high-quality tracks reconstructed over the entire inner detector by the start of processing in the Level-2 trigger. The system is based on associa-tive memories for pattern recognition and fast FPGA's for track reconstruction. Its design and expected performance under instantaneous luminosities up to 3 × 10 34 /cm 2 /s are discussed.
[show abstract][hide abstract] ABSTRACT: We study the off-equilibrium dynamics of the three-dimensional Ising spin
glass in the presence of an external magnetic field. We have performed
simulations both at fixed temperature and with an annealing protocol. Thanks to
the Janus special-purpose computer, based on FPGAs, we have been able to reach
times equivalent to 0.01 seconds in experiments. We have studied the system
relaxation both for high and for low temperatures, clearly identifying a
dynamical transition point. This dynamical temperature is strictly positive and
depends on the external applied magnetic field. We discuss different
possibilities for the underlying physics, which include a thermodynamical
spin-glass transition or a mode-coupling crossover.
[show abstract][hide abstract] ABSTRACT: a b s t r a c t The Fast Tracker (FTK) processor is an approved ATLAS upgrade that will reconstruct tracks using the full silicon tracker at Level-1 rate (up to 100 KHz). FTK uses a completely parallel approach to read the silicon tracker information, execute the pattern matching and reconstruct the tracks. This approach, according to detailed simulation results, allows full tracking with nearly offline resolution within an execution time of 100 ms. A central component of the system is the associative memories (AM); these special devices reduce the pattern matching combinatoric problem, providing identification of coarse resolution track candidates. The system consists of a pipeline of several components with the goal to organize and filter the data for the AM, then to reconstruct and filter the final tracks. This document presents an overview of the system and reports the status of the different elements of the system. & 2013 CERN. Published by Elsevier B.V. All rights reserved.
[show abstract][hide abstract] ABSTRACT: We describe Janus, a massively parallel FPGA-based computer optimized for the
simulation of spin glasses, theoretical models for the behavior of glassy
materials. FPGAs (as compared to GPUs or many-core processors) provide a
complementary approach to massively parallel computing. In particular, our
model problem is formulated in terms of binary variables, and floating-point
operations can be (almost) completely avoided. The FPGA architecture allows us
to run many independent threads with almost no latencies in memory access, thus
updating up to 1024 spins per cycle. We describe Janus in detail and we
summarize the physics results obtained in four years of operation of this
machine; we discuss two types of physics applications: long simulations on very
large systems (which try to mimic and provide understanding about the
experimental non-equilibrium dynamics), and low-temperature equilibrium
simulations using an artificial parallel tempering dynamics. The time scale of
our non-equilibrium simulations spans eleven orders of magnitude (from
picoseconds to a tenth of a second). On the other hand, our equilibrium
simulations are unprecedented both because of the low temperatures reached and
for the large systems that we have brought to equilibrium. A finite-time
scaling ansatz emerges from the detailed comparison of the two sets of
simulations. Janus has made it possible to perform spin-glass simulations that
would take several decades on more conventional architectures. The paper ends
with an assessment of the potential of possible future versions of the Janus
architecture, based on state-of-the-art technology.
The European Physical Journal Special Topics 04/2012; 210(1). · 1.80 Impact Factor
[show abstract][hide abstract] ABSTRACT: Spin glasses are a longstanding model for the sluggish dynamics that appears
at the glass transition. However, spin glasses differ from structural glasses
for a crucial feature: they enjoy a time reversal symmetry. This symmetry can
be broken by applying an external magnetic field, but embarrassingly little is
known about the critical behaviour of a spin glass in a field. In this context,
the space dimension is crucial. Simulations are easier to interpret in a large
number of dimensions, but one must work below the upper critical dimension
(i.e., in d<6) in order for results to have relevance for experiments. Here we
show conclusive evidence for the presence of a phase transition in a
four-dimensional spin glass in a field. Two ingredients were crucial for this
achievement: massive numerical simulations were carried out on the Janus
special-purpose computer, and a new and powerful finite-size scaling method.
Proceedings of the National Academy of Sciences 02/2012; 109(17). · 9.74 Impact Factor
[show abstract][hide abstract] ABSTRACT: The OPERA Collaboration reported evidence for muonic neutrinos traveling slightly faster than light in vacuum. While waiting further checks from the experimental community, here we aim at exploring some theoretical consequences of the hypothesis that muonic neutrinos are superluminal, considering in particular the tachyonic and the Coleman-Glashow cases. We show that a tachyonic interpretation is not only hardly reconciled with OPERA data on energy dependence, but that it clashes with neutrino production from pion and with neutrino oscillations. A Coleman-Glashow superluminal neutrino beam would also have problems with pion decay kinematics for the OPERA setup; it could be easily reconciled with SN1987a data, but then it would be very problematic to account for neutrino oscillations.
[show abstract][hide abstract] ABSTRACT: We propose a simple algorithm able to identify a set of temperatures for a Parallel Tempering Monte Carlo simulation, that maximizes the probability that the configurations drift across all temperature values, from the coldest to the hottest ones, and vice versa. The proposed algorithm starts from data gathered from relatively short Monte Carlo simulations and is straightforward to implement. We assess its effectiveness on a test case simulation of an Edwards–Anderson spin glass on a lattice of 123 sites.
Journal of Computational Physics 01/2012; 231:1524-1532. · 2.14 Impact Factor
[show abstract][hide abstract] ABSTRACT: A special feature of Rayleigh-Taylor systems with chemical reactions is the competition between turbulent mixing and the "burning processes", which leads to a highly non-trivial dynamics. We studied the problem performing high resolution numerical simulations of a 2d system, using a thermal lattice Boltzmann (LB) model. We spanned the various regimes emerging at changing the relative chemical/turbulent time scales, from slow to fast reaction; in the former case we found numerical evidence of an enhancement of the front propagation speed (with respect to the laminar case), providing a phenomenological argument to explain the observed behaviour. When the reaction is very fast, instead, the formation of sharp fronts separating patches of pure phases, leads to an increase of intermittency in the small scale statistics of the temperature field.
Journal of Physics Conference Series 12/2011; 318(9):092024.
[show abstract][hide abstract] ABSTRACT: We study the sample-to-sample fluctuations of the overlap probability
densities from large-scale equilibrium simulations of the three-dimensional
Edwards-Anderson spin glass below the critical temperature. Ultrametricity,
Stochastic Stability and Overlap Equivalence impose constraints on the moments
of the overlap probability densities that can be tested against numerical data.
We found small deviations from the Ghirlanda-Guerra predictions, which get
smaller as system size increases. We also focus on the shape of the overlap
distribution, comparing the numerical data to a mean-field-like prediction in
which finite-size effects are taken into account by substituting delta
functions with broad peaks
[show abstract][hide abstract] ABSTRACT: The parametrization of small-scale turbulent fluctuations in convective systems and in the presence of strong stratification is a key issue for many applied problems in oceanography, atmospheric science, and planetology. In the presence of stratification, one needs to cope with bulk turbulent fluctuations and with inversion regions, where temperature, density, or both develop highly nonlinear mean profiles due to the interactions between the turbulent boundary layer and the unmixed-stable-flow above or below it. We present a second-order closure able to cope simultaneously with both bulk and boundary layer regions, and we test it against high-resolution state-of-the-art two-dimensional numerical simulations in a convective and stratified belt for values of the Rayleigh number up to Ra∼10(10). Data are taken from a Rayleigh-Taylor system confined by the existence of an adiabatic gradient.
[show abstract][hide abstract] ABSTRACT: We present state-of-the-art numerical simulations of a two-dimensional Rayleigh-Taylor instability for a compressible stratified fluid. We describe the computational algorithm and its implementation on the QPACE supercomputer. High resolution enables the statistical properties of the evolving interface that we characterize in terms of its fractal dimension to be studied.
Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences 06/2011; 369(1945):2448-55. · 2.89 Impact Factor
[show abstract][hide abstract] ABSTRACT: Reactive Rayleigh-Taylor systems are characterized by the competition between
the growth of the instability and the rate of reaction between cold (heavy) and
hot (light) phases. We present results from state-of-the-art numerical
simulations performed at high resolution in 2d by means of a self-consistent
lattice Boltzmann method which evolves the coupled momentum and thermal
equations and includes a reactive term. We tune the parameters affecting flame
properties, in order to address the competition between turbulent mixing and
reaction, ranging from slow to fast-reaction rates. We also study the mutual
feedback between turbulence evolution driven by the Rayleigh-Taylor instability
and front propagation against gravitational acceleration. We quantify both the
enhancement of flame propagation due to turbulent mixing for the case of slow
reaction-rate as well as the slowing down of turbulence growth for the fast
reaction case, when the flame quickly burns the gravitationally unstable phase.
An increase of intermittency at small scales for temperature characterizes the
case of fast reaction, associated to the formation of sharp wrinkled fronts
separating pure hot/cold fluids regions.
[show abstract][hide abstract] ABSTRACT: The parameterization of small-scale turbulent fluctuations in convective
systems and in the presence of strong stratification is a key issue for many
applied problems in oceanography, atmospheric science and planetology. In the
presence of stratification, one needs to cope with bulk turbulent fluctuations
and with inversion regions, where temperature, density -or both- develop highly
non-linear mean profiles due to the interactions between the turbulent boundary
layer and the unmixed -stable- flow above/below it. We present a second order
closure able to cope simultaneously with both bulk and boundary layer regions,
and we test it against high-resolution state-of-the-art 2D numerical
simulations in a convective and stratified belt for values of the Rayleigh
number, up to Ra = 10^9. Data are taken from a Rayleigh-Taylor system confined
by the existence of an adiabatic gradient.
Journal of Physics Conference Series 01/2011; 318(4).
[show abstract][hide abstract] ABSTRACT: We develop a Lattice Boltzmann code for computational fluid-dynamics and optimize it for massively parallel systems based on multi-core processors. Our code describes 2D multi-phase compressible flows. We analyze the performance bottlenecks that we find as we gradually expose a larger fraction of the available parallelism, and derive appropriate solutions. We obtain a sustained performance for this ready-for-physics code that is a large fraction of peak. Our results can be easily applied to most present (or planned) HPC architectures, based on latest generation multi-core Intel processor architectures.