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Memory and rejuvenation effects in the magnetic response of off-equilibrium spin glasses have been widely regarded as the doorway into the experimental exploration of ultrametricity and temperature chaos (maybe the most exotic features in glassy free-energy landscapes). Unfortunately, despite more than twenty years of theoretical efforts following the experimental discovery of memory and rejuvenation, these effects have thus far been impossible to simulate reliably. Yet, three recent developments convinced us to accept this challenge: first, the custom-built Janus II supercomputer makes it possible to carry out "numerical experiments" in which the very same quantities that can be measured in single crystals of CuMn are computed from the simulation, allowing for parallel analysis of the simulation/experiment data. Second, Janus II simulations have taught us how numerical and experimental length scales should be compared. Third, we have recently understood how temperature chaos materializes in aging dynamics. All three aspects have proved crucial for reliably reproducing rejuvenation and memory effects on the computer. Our analysis shows that (at least) three different length scales play a key role in aging dynamics, while essentially all theoretical analyses of the aging dynamics emphasize the presence and the crucial role of a single glassy correlation length., Comment: Main text:13 pages, 4 figures SM: 7 pages, 8 figures

The synergy between experiment, theory, and simulations enables a microscopic analysis of spin-glass dynamics in a magnetic field in the vicinity of and below the spin-glass transition temperature $T_\mathrm{g}$. The spin-glass correlation length, $\xi(t,t_\mathrm{w};T)$, is analysed both in experiments and in simulations in terms of the waiting time $t_\mathrm{w}$ after the spin glass has been cooled down to a stabilised measuring temperature $T

We find a dynamic effect in the non-equilibrium dynamics of a spin glass that closely parallels equilibrium temperature chaos. This effect, that we name dynamic temperature chaos, is spatially heterogeneous to a large degree. The key controlling quantity is the time-growing spin-glass coherence length. Our detailed characterization of dynamic temperature chaos paves the way for the analysis of recent and forthcoming experiments. This work has been made possible thanks to the most massive simulation to date of non-equilibrium dynamics, carried out on the Janus~II custom-built supercomputer., Comment: Version accepted for publication in Communication Physics 10 pages, 9 figures

We present a new method for the numerical solution of the radiative-transfer equation (RTE) in multidimensional scenarios commonly encountered in computational astrophysics. The method is based on the direct solution of the Boltzmann equation via an extension of the Lattice Boltzmann (LB) equation and allows to model the evolution of the radiation field as it interacts with a background fluid, via absorption, emission, and scattering. As a first application of this method, we restrict our attention to a frequency independent ("grey") formulation within a special-relativistic framework, which can be employed also for classical computational astrophysics. For a number of standard tests that consider the performance of the method in optically thin, optically thick and intermediate regimes with a static fluid, we show the ability of the LB method to produce accurate and convergent results matching the analytic solutions. We also contrast the LB method with commonly employed moment-based schemes for the solution of the RTE, such as the M1 scheme. In this way, we are able to highlight that the LB method provides the correct solution for both non-trivial free-streaming scenarios and the intermediate optical-depth regime, for which the M1 method either fails or provides inaccurate solutions. When coupling to a dynamical fluid, on the other hand, we present the first self-consistent solution of the RTE with LB methods within a relativistic-hydrodynamic scenario. Finally, we show that besides providing more accurate results in all regimes, the LB method features smaller or comparable computational costs compared to the M1 scheme., Comment: 22 pages, 16 figures, matches version accepted in MNRAS

The correlation length $\xi$, a key quantity in glassy dynamics, can now be precisely measured for spin glasses both in experiments and in simulations. However, known analysis methods lead to discrepancies either for large external fields or close to the glass temperature. We solve this problem by introducing a scaling law that takes into account both the magnetic field and the time-dependent spin-glass correlation length. The scaling law is successfully tested against experimental measurements in a CuMn single crystal and against large-scale simulations on the Janus II dedicated computer., Comment: Revised version, including supplemental material

This paper presents numerical cross-comparisons and benchmark results for two different kinetic numerical methods, capable of describing relativistic dissipative fluid dynamics in a wide range of kinematic regimes, typical of relevant physics applications, such as transport phenomena in quark-gluon plasmas. We refer to relativistic lattice Boltzmann versus Montecarlo Test-Particle methods. Lacking any realistic option for accurate validation vis-a-vis experimental data, we check the consistency of our results against established simulation packages available in the literature. We successfully cross-compare the results of the two aforementioned numerical approaches for momentum integrated quantities like the hydrostatic and dynamical pressure profiles, the collective flow and the heat flux. These results corroborate the confidence on the robustness and correctness of these computational methods and on the accurate calibration of their numerical parameters with respect to the physical transport coefficients. Our numerical results are made available as supplemental material, with the aim of establishing a reference benchmark for other numerical approaches.

We derive an analytical connection between kinetic relaxation rate and bulk viscosity of a relativistic fluid in d spatial dimensions, all the way from the ultra-relativistic down to the near non-relativistic regime. Our derivation is based on both Chapman-Enskog asymptotic expansion and Grad's method of moments. We validate our theoretical results against a benchmark flow, providing further evidence of the correctness of the Chapman-Enskog approach; we define the range of validity of this approach and provide evidence of mounting departures at increasing Knudsen number. Finally, we present numerical simulations of transport processes in quark gluon plasmas, with special focus on the effects of bulk viscosity which might prove amenable to future experimental verification.

We present a systematic account of recent developments of the relativistic Lattice Boltzmann method (RLBM) for dissipative hydrodynamics. We describe in full detail a unified, compact and dimension-independent procedure to design relativistic LB schemes capable of bridging the gap between the ultra-relativistic regime, $k_{\rm B} T \gg mc^2$, and the non-relativistic one, $k_{\rm B} T \ll mc^2$. We further develop a systematic derivation of the transport coefficients as a function of the kinetic relaxation time in $d=1,2,3$ spatial dimensions. The latter step allows to establish a quantitative bridge between the parameters of the kinetic model and the macroscopic transport coefficients. This leads to accurate calibrations of simulation parameters and is also relevant at the theoretical level, as it provides neat numerical evidence of the correctness of the Chapman-Enskog procedure. We present an extended set of validation tests, in which simulation results based on the RLBMs are compared with existing analytic or semi-analytic results in the mildly-relativistic ($k_{\rm B} T \sim mc^2$) regime for the case of shock propagations in quark-gluon plasmas and laminar electronic flows in ultra-clean graphene samples. It is hoped and expected that the material collected in this paper may allow the interested readers to reproduce the present results and generate new applications of the RLBM scheme.

We present an analytical derivation of the transport coefficients of a relativistic gas in (2+1) dimensions for both Chapman-Enskog (CE) asymptotics and Grad's expansion methods. Moreover, we develop a systematic calibration method, connecting the relaxation time of relativistic kinetic theory to the transport parameters of the associated dissipative hydrodynamic equations. Comparison between the analytical results and numerical simulations, shows that the CE method correctly captures dissipative effects, while Grad's method does not. The resulting calibration procedure based on the CE method opens the way to the quantitative kinetic description of dissipative relativistic fluid dynamics under fairly general conditions, namely flows with strongly non-linearities, in non-ideal geometries, across both ultra-relativistic and near-non-relativistic regimes.

We introduce a variant of the Hybrid Monte Carlo (HMC) algorithm to address large-deviation statistics in stochastic hydrodynamics. Based on the path-integral approach to stochastic (partial) differential equations, our HMC algorithm samples space-time histories of the dynamical degrees of freedom under the influence of random noise. First, we validate and benchmark the HMC algorithm by reproducing multiscale properties of the one-dimensional Burgers equation driven by Gaussian and white-in-time noise. Second, we show how to implement an importance sampling protocol to significantly enhance, by orders of magnitudes, the probability to sample extreme and rare events, making it possible to estimate moments of field variables of extremely high order (up to 30 and more). By employing reweighting techniques, we map the biased configurations back to the original probability measure in order to probe their statistical importance. Finally, we show that by biasing the system towards very intense negative gradients, the HMC algorithm is able to explore the statistical fluctuations around instanton configurations. Our results will also be interesting and relevant in lattice gauge theory since they provide insight into reweighting techniques., Comment: 23 pages, 16 figures; revised manuscript and updated figures based on published version

Based on extensive numerical simulations, accounting for electrostatic interactions and dissipative electron-phonon scattering, we propose experimentally realizable geometries capable of sustaining electronic pre-turbulence in graphene samples. In particular, pre-turbulence is predicted to occur at experimentally attainable values of the Reynolds number between 10 and 50, over a broad spectrum of frequencies between 10 and 100 GHz.

The Mpemba effect occurs when a hot system cools faster than an initially colder one, when both are refrigerated in the same thermal reservoir. Using the custom built supercomputer Janus II, we study the Mpemba effect in spin glasses and show that it is a non-equilibrium process, governed by the coherence length \xi of the system. The effect occurs when the bath temperature lies in the glassy phase, but it is not necessary for the thermal protocol to cross the critical temperature. In fact, the Mpemba effect follows from a strong relationship between the internal energy and \xi that turns out to be a sure-tell sign of being in the glassy phase. Thus, the Mpemba effect presents itself as an intriguing new avenue for the experimental study of the coherence length in supercooled liquids and other glass formers., Comment: Version accepted for publication in PNAS. 6 pages, 7 figures

We present an extension of recent relativistic Lattice Boltzmann methods based on Gaussian quadratures for the study of fluids in (2+1) dimensions. The new method is applied to the analysis of electron flow in graphene samples subject to electrostatic drive; we show that the flow displays hydro-electronic whirlpools in accordance with recent analytical calculations as well as experimental results.

Energy consumption is increasingly becoming a limiting factor to the design of faster large-scale parallel systems, and development of energy-efficient and energy-aware applications is today a relevant issue for HPC code-developer communities. In this work we focus on energy performance of the Knights Landing (KNL) Xeon Phi, the latest many-core architecture processor introduced by Intel into the HPC market. We take into account the 64-core Xeon Phi 7230, and analyze its energy performance using both the on-chip MCDRAM and the regular DDR4 system memory as main storage for the application data-domain. As a benchmark application we use a Lattice Boltzmann code heavily optimized for this architecture and implemented using different memory data layouts to store its lattice. We assessthen the energy consumption using different memory data-layouts, kind of memory (DDR4 or MCDRAM) and number of threads per core.

Experiments on spin glasses can now make precise measurements of the exponent $z(T)$ governing the growth of glassy domains, while our computational capabilities allow us to make quantitative predictions for experimental scales. However, experimental and numerical values for $z(T)$ have differed. We use new simulations on the Janus II computer to resolve this discrepancy, finding a time-dependent $z(T, t_w)$, which leads to the experimental value through mild extrapolations. Furthermore, theoretical insight is gained by studying a crossover between the $T = T_c$ and $T = 0$ fixed points., Comment: Version accepted for publication in PRL. 12 pages, 9 figures

We first reproduce on the Janus and Janus II computers a milestone experiment that measures the spin-glass coherence length through the lowering of free-energy barriers induced by the Zeeman effect. Secondly we determine the scaling behavior that allows a quantitative analysis of a new experiment reported in the companion Letter [S. Guchhait and R. Orbach, Phys. Rev. Lett. 118, 157203 (2017)]. The value of the coherence length estimated through the analysis of microscopic correlation functions turns out to be quantitatively consistent with its measurement through macroscopic response functions. Further, non-linear susceptibilities, recently measured in glass-forming liquids, scale as powers of the same microscopic length., Comment: 6 pages, 4 figures

Despite a long record of intense efforts, the basic mechanisms by which dissipation emerges from the microscopic dynamics of a relativistic fluid still elude a complete understanding. In particular, no unique pathway from kinetic theory to hydrodynamics has been identified as yet, with different approaches leading to different values of the transport coefficients. In this Letter, we approach the problem by matching data from lattice kinetic simulations with analytical predictions. Our numerical results provide neat evidence in favour of the Chapman-Enskog procedure, as suggested by recently theoretical analyses, along with qualitative hints at the basic reasons why the Chapman-Enskog expansion might be better suited than Grad's method to capture the emergence of dissipative effects in relativistic fluids.

High-performance computing systems are more and more often based on accelerators. Computing applications targeting those systems often follow a host-driven approach in which hosts offload almost all compute-intensive sections of the code onto accelerators; this approach only marginally exploits the computational resources available on the host CPUs, limiting performance and energy efficiency. The obvious step forward is to run compute-intensive kernels in a concurrent and balanced way on both hosts and accelerators. In this paper we consider exactly this problem for a class of applications based on Lattice Boltzmann Methods, widely used in computational fluid-dynamics. Our goal is to develop just one program, portable and able to run efficiently on several different combinations of hosts and accelerators. To reach this goal, we define common data layouts enabling the code to exploit efficiently the different parallel and vector options of the various accelerators, and matching the possibly different requirements of the compute-bound and memory-bound kernels of the application. We also define models and metrics that predict the best partitioning of workloads among host and accelerator, and the optimally achievable overall performance level. We test the performance of our codes and their scaling properties using as testbeds HPC clusters incorporating different accelerators: Intel Xeon-Phi many-core processors, NVIDIA GPUs and AMD GPUs.

We present a systematic derivation of relativistic lattice kinetic equations for finite-mass particles, reaching close to the zero-mass ultra-relativistic regime treated in the previous literature. Starting from an expansion of the Maxwell-Juettner distribution on orthogonal polynomials, we perform a Gauss-type quadrature procedure and discretize the relativistic Boltzmann equation on space-filling Cartesian lattices. The model is validated through numerical comparison with standard benchmark tests and solvers in relativistic fluid dynamics such as Boltzmann approach multiparton scattering (BAMPS) and previous relativistic lattice Boltzmann models. This work provides a significant step towards the formulation of a unified relativistic lattice kinetic scheme, covering both massive and near-massless particles regimes.

This paper describes a massively parallel code for a state-of-the art thermal lattice- Boltzmann method. Our code has been carefully optimized for performance on one GPU and to have a good scaling behavior extending to a large number of GPUs. Versions of this code have been already used for large-scale studies of convective turbulence. GPUs are becoming increasingly popular in HPC applications, as they are able to deliver higher performance than traditional processors. Writing efficient programs for large clusters is not an easy task as codes must adapt to increasingly parallel architectures, and the overheads of node-to-node communications must be properly handled. We describe the structure of our code, discussing several key design choices that were guided by theoretical models of performance and experimental benchmarks. We present an extensive set of performance measurements and identify the corresponding main bot- tlenecks; finally we compare the results of our GPU code with those measured on other currently available high performance processors. Our results are a production-grade code able to deliver a sustained performance of several tens of Tflops as well as a design and op- timization methodology that can be used for the development of other high performance applications for computational physics.

An increasingly large number of HPC systems rely on heterogeneous architectures combining traditional multi-core CPUs with power efficient accelerators. Designing efficient applications for these systems has been troublesome in the past as accelerators could usually be programmed using specific programming languages threatening maintainability, portability and correctness. Several new programming environments try to tackle this problem. Among them, OpenACC offers a high-level approach based on compiler directive clauses to mark regions of existing C, C++ or Fortran codes to run on accelerators. This approach directly addresses code portability, leaving to compilers the support of each different accelerator, but one has to carefully assess the relative costs of portable approaches versus computing efficiency. In this paper we address precisely this issue, using as a test-bench a massively parallel Lattice Boltzmann algorithm. We first describe our multi-node implementation and optimization of the algorithm, using OpenACC and MPI. We then benchmark the code on a variety of processors, including traditional CPUs and GPUs, and make accurate performance comparisons with other GPU implementations of the same algorithm using CUDA and OpenCL. We also asses the performance impact associated to portable programming, and the actual portability and performance-portability of OpenACC-based applications across several state-of-the- art architectures.

The unifying feature of glass formers (such as polymers, supercooled liquids, colloids, granulars, spin glasses, superconductors, ...) is a sluggish dynamics at low temperatures. Indeed, their dynamics is so slow that thermal equilibrium is never reached in macroscopic samples: in analogy with living beings, glasses are said to age. Here, we show how to relate experimentally relevant quantities with the experimentally unreachable low-temperature equilibrium phase. We have performed a very accurate computation of the non-equilibrium fluctuation-dissipation ratio for the three-dimensional Edwards-Anderson Ising spin glass, by means of large-scale simulations on the special-purpose computers Janus and Janus II. This ratio (computed for finite times on very large, effectively infinite, systems) is compared with the equilibrium probability distribution of the spin overlap for finite sizes. The resulting quantitative statics-dynamics dictionary, based on observables that can be measured with current experimental methods, could allow the experimental exploration of important features of the spin-glass phase without uncontrollable extrapolations to infinite times or system sizes., Comment: Version accepted for publication in PNAS. Reuploaded to fix a typo in the list of authors

We study the turbulent evolution originated from a system subjected to a Rayleigh-Taylor instability with a double density at high resolution in a 2 dimensional geometry using a highly optimized thermal Lattice Boltzmann code for GPUs. The novelty of our investigation stems from the initial condition, given by the superposition of three layers with three different densities, leading to the development of two Rayleigh-Taylor fronts that expand upward and downward and collide in the middle of the cell. By using high resolution numerical data we highlight the effects induced by the collision of the two turbulent fronts in the long time asymptotic regime. We also provide details on the optimized Lattice-Boltzmann code that we have run on a cluster of GPUs

We perform equilibrium parallel-tempering simulations of the 3D Ising Edwards-Anderson spin glass in a field. A traditional analysis shows no signs of a phase transition. Yet, we encounter dramatic fluctuations in the behaviour of the model: Averages over all the data only describe the behaviour of a small fraction of it. Therefore we develop a new approach to study the equilibrium behaviour of the system, by classifying the measurements as a function of a conditioning variate. We propose a finite-size scaling analysis based on the probability distribution function of the conditioning variate, which may accelerate the convergence to the thermodynamic limit. In this way, we find a non-trivial spectrum of behaviours, where a part of the measurements behaves as the average, while the majority of them shows signs of scale invariance. As a result, we can estimate the temperature interval where the phase transition in a field ought to lie, if it exists. Although this would-be critical regime is unreachable with present resources, the numerical challenge is finally well posed., Comment: 42 pages, 19 figures. Minor changes and added figure (results unchanged)

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., Comment: 9 pages, 5 figures

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., Comment: 28 pages, 6 figures

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, a mode-coupling crossover or an interpretation reminiscent of the random first-order picture of structural glasses., Comment: Version accepted in PRE. 23 pages, 23 figures

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., Comment: 19 pages, 3 figures

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., Comment: 10 pages, 6 figures

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, Comment: 11 pages, 8 figures; version accepted for publication on PRB and updated Refs

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., Comment: 6 pages, 6 figures

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., Comment: 10 pages, 5 figures

We present results of a high resolution numerical study of two dimensional (2d) Rayleigh-Taylor turbulence using a recently proposed thermal lattice Boltzmann method (LBT). The goal of our study is both methodological and physical. We assess merits and limitations concerning small- and large-scale resolution/accuracy of the adopted integration scheme. We discuss quantitatively the requirements needed to keep the method stable and precise enough to simulate stratified and unstratified flows driven by thermal active fluctuations at high Rayleigh and high Reynolds numbers. We present data with spatial resolution up to 4096 x 10000 grid points and Rayleigh number up to Ra ~ 10^11 . The statistical quality of the data allows us to investigate velocity and temperature fluctuations, scale-by-scale, over roughly four decades. We present a detailed quantitative analysis of scaling laws in the viscous, inertial and integral range, supporting the existence of a Bolgiano-like inertial scaling, as expected in 2d systems. We also discuss the presence of small/large intermittent deviation to the scaling of velocity/temperature fluctuations and the Rayleigh dependency of gradients flatness., Comment: 31 pages, 21 figures

We numerically study the aging properties of the dynamical heterogeneities in the Ising spin glass. We find that a phase transition takes place during the aging process. Statics-dynamics correspondence implies that systems of finite size in equilibrium have static heterogeneities that obey Finite-Size Scaling, thus signaling an analogous phase transition in the thermodynamical limit. We compute the critical exponents and the transition point in the equilibrium setting, and use them to show that aging in dynamic heterogeneities can be described by a Finite-Time Scaling Ansatz, with potential implications for experimental work., Comment: Version accepted for publication in Phys. Rev. Lett. 4 pages, 3 postscript figures

We present a massive equilibrium simulation of the three-dimensional Ising spin glass at low temperatures. The Janus special-purpose computer has allowed us to equilibrate, using parallel tempering, L=32 lattices down to T=0.64 Tc. We demonstrate the relevance of equilibrium finite-size simulations to understand experimental non-equilibrium spin glasses in the thermodynamical limit by establishing a time-length dictionary. We conclude that non-equilibrium experiments performed on a time scale of one hour can be matched with equilibrium results on L=110 lattices. A detailed investigation of the probability distribution functions of the spin and link overlap, as well as of their correlation functions, shows that Replica Symmetry Breaking is the appropriate theoretical framework for the physically relevant length scales. Besides, we improve over existing methodologies to ensure equilibration in parallel tempering simulations., Comment: 48 pages, 19 postscript figures, 9 tables. Version accepted for publication in the Journal of Statistical Mechanics

We study the 3D Disordered Potts Model with p=5 and p=6. Our numerical simulations (that severely slow down for increasing p) detect a very clear spin glass phase transition. We evaluate the critical exponents and the critical value of the temperature, and we use known results at lower $p$ values to discuss how they evolve for increasing p. We do not find any sign of the presence of a transition to a ferromagnetic regime., Comment: 9 pages and 9 Postscript figures. Final version published in J. Stat. Mech

We describe the architecture evolution of the highly-parallel dedicated processor FTK, which is driven by the simulation of LHC events at high luminosity (1034 cm-2 s-1). FTK is able to provide precise on-line track reconstruction for future hadronic collider experiments. The processor, organized in a two-tiered pipelined architecture, execute very fast algorithms based on the use of a large bank of pre-stored patterns of trajectory points (first tier) in combination with full resolution track fitting to refine pattern recognition and to determine off-line quality track parameters. We describe here how the high luminosity simulation results have produced a new organization of the hardware inside the FTK processor core., Comment: 11th ICATPP conference

QPACE is a novel parallel computer which has been developed to be primarily used for lattice QCD simulations. The compute power is provided by the IBM PowerXCell 8i processor, an enhanced version of the Cell processor that is used in the Playstation 3. The QPACE nodes are interconnected by a custom, application optimized 3-dimensional torus network implemented on an FPGA. To achieve the very high packaging density of 26 TFlops per rack a new water cooling concept has been developed and successfully realized. In this paper we give an overview of the architecture and highlight some important technical details of the system. Furthermore, we provide initial performance results and report on the installation of 8 QPACE racks providing an aggregate peak performance of 200 TFlops., Comment: 21 pages. Poster by T. Maurer and plenary talk by D. Pleiter presented at the "XXVII International Symposium on Lattice Field Theory", July 26-31 2009, Peking University, Beijing, China. Information on recent Green500 ranking added and list of authors extended

We perform numerical simulations, including parallel tempering, on the Potts glass model with binary random quenched couplings using the JANUS application-oriented computer. We find and characterize a glassy transition, estimating the location of the transition and the value of the critical exponents. We show that there is no ferromagnetic transition in a large temperature range around the glassy critical temperature. We also compare our results with those obtained recently on the "random permutation" Potts glass., Comment: 7 pages and 3 figures. Corrected minor typos

Using the dedicated computer Janus, we follow the nonequilibrium dynamics of the Ising spin glass in three dimensions for eleven orders of magnitude. The use of integral estimators for the coherence and correlation lengths allows us to study dynamic heterogeneities and the presence of a replicon mode and to obtain safe bounds on the Edwards-Anderson order parameter below the critical temperature. We obtain good agreement with experimental determinations of the temperature-dependent decay exponents for the thermoremanent magnetization. This magnitude is observed to scale with the much harder to measure coherence length, a potentially useful result for experimentalists. The exponents for energy relaxation display a linear dependence on temperature and reasonable extrapolations to the critical point. We conclude examining the time growth of the coherence length, with a comparison of critical and activated dynamics., Comment: 38 pages, 26 figures

We give an overview of the QPACE project, which is pursuing the development of a massively parallel, scalable supercomputer for LQCD. The machine is a three-dimensional torus of identical processing nodes, based on the PowerXCell 8i processor. The nodes are connected by an FPGA-based, application-optimized network processor attached to the PowerXCell 8i processor. We present a performance analysis of lattice QCD codes on QPACE and corresponding hardware benchmarks., Comment: 7 pages, poster presented at the XXVI International Symposium on Lattice Field Theory, July 14-19, 2008, Williamsburg, Virginia, USA

We study numerically the nonequilibrium dynamics of the Ising Spin Glass, for a time that spans eleven orders of magnitude, thus approaching the experimentally relevant scale (i.e. {\em seconds}). We introduce novel analysis techniques that allow to compute the coherence length in a model-independent way. Besides, we present strong evidence for a replicon correlator and for overlap equivalence. The emerging picture is compatible with non-coarsening behavior., Comment: 4 pages, 4 eps color figures. Version accepted for publication in Phys. Rev. Lett

This paper describes JANUS, a modular massively parallel and reconfigurable FPGA-based computing system. Each JANUS module has a computational core and a host. The computational core is a 4x4 array of FPGA-based processing elements with nearest-neighbor data links. Processors are also directly connected to an I/O node attached to the JANUS host, a conventional PC. JANUS is tailored for, but not limited to, the requirements of a class of hard scientific applications characterized by regular code structure, unconventional data manipulation instructions and not too large data-base size. We discuss the architecture of this configurable machine, and focus on its use on Monte Carlo simulations of statistical mechanics. On this class of application JANUS achieves impressive performances: in some cases one JANUS processing element outperfoms high-end PCs by a factor ~ 1000. We also discuss the role of JANUS on other classes of scientific applications., Comment: 11 pages, 6 figures. Improved version, largely rewritten, submitted to Computing in Science & Engineering

We evaluate IBM's Enhanced Cell Broadband Engine (BE) as a possible building block of a new generation of lattice QCD machines. The Enhanced Cell BE will provide full support of double-precision floating-point arithmetics, including IEEE-compliant rounding. We have developed a performance model and applied it to relevant lattice QCD kernels. The performance estimates are supported by micro- and application-benchmarks that have been obtained on currently available Cell BE-based computers, such as IBM QS20 blades and PlayStation 3. The results are encouraging and show that this processor is an interesting option for lattice QCD applications. For a massively parallel machine on the basis of the Cell BE, an application-optimized network needs to be developed., Comment: 7 pages, 3 figures, contribution to Lattice 2007 (Regensburg, Germany)

We describe the hardwired implementation of algorithms for Monte Carlo simulations of a large class of spin models. We have implemented these algorithms as VHDL codes and we have mapped them onto a dedicated processor based on a large FPGA device. The measured performance on one such processor is comparable to O(100) carefully programmed high-end PCs: it turns out to be even better for some selected spin models. We describe here codes that we are currently executing on the IANUS massively parallel FPGA-based system., Comment: 19 pages, 8 figures; submitted to Computer Physics Communications

Dedicated machines designed for specific computational algorithms can outperform conventional computers by several orders of magnitude. In this note we describe {\it Ianus}, a new generation FPGA based machine and its basic features: hardware integration and wide reprogrammability. Our goal is to build a machine that can fully exploit the performance potential of new generation FPGA devices. We also plan a software platform which simplifies its programming, in order to extend its intended range of application to a wide class of interesting and computationally demanding problems. The decision to develop a dedicated processor is a complex one, involving careful assessment of its performance lead, during its expected lifetime, over traditional computers, taking into account their performance increase, as predicted by Moore's law. We discuss this point in detail.

We present the APE (Array Processor Experiment) project for the development of dedicated parallel computers for numerical simulations in lattice gauge theories. While APEmille is a production machine in today's physics simulations at various sites in Europe, a new machine, apeNEXT, is currently being developed to provide multi-Tflops computing performance. Like previous APE machines, the new supercomputer is largely custom designed and specifically optimized for simulations of Lattice QCD., Comment: Poster at the XXIII Physics in Collisions Conference (PIC03), Zeuthen, Germany, June 2003, 3 pages, Latex. PSN FRAP15. Replaced for adding forgotten author