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At least 1,315 records · Page 73
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Scaling neural simulations in STACS

Abstract As modern neuroscience tools acquire more details about the brain, the need to move towards biological-scale neural simulations continues to grow. However, effective simulations at scale remain a challenge. Beyond just the tooling required to enable parallel execution, there is also the unique structure of the synaptic interconnectivity, which is globally sparse but has relatively high connection density and non-local interactions per neuron. There are also various practicalities to consider in high performance computing applications, such as the need for serializing neural networks to support potentially long-running simulations that require checkpoint-restart. Although acceleration on neuromorphic hardware is also a possibility, development in this space can be difficult as hardware support tends to vary between platforms and software support for larger scale models also tends to be limited. In this paper, we focus our attention on Simulation Tool for Asynchronous Cortical Streams (STACS), a spiking neural network simulator that leverages the Charm++ parallel programming framework, with the goal of supporting biological-scale simulations as well as interoperability between platforms. Central to these goals is the implementation of scalable data structures suitable for efficiently distributing a network across parallel partitions. Here, we discuss a straightforward extension of a parallel data format with a history of use in graph partitioners, which also serves as a portable intermediate representation for different neuromorphic backends. We perform scaling studies on the Summit supercomputer, examining the capabilities of STACS in terms of network build and storage, partitioning, and execution. We highlight how a suitably partitioned, spatially dependent synaptic structure introduces a communication workload well-suited to the multicast communication supported by Charm++. We evaluate the strong and weak scaling behavior for networks on the order of millions of neurons and billions of synapses, and show that STACS achieves competitive levels of parallel efficiency.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

On behaviour and scaling of small repeating earthquakes in rate and state fault models

With abundant seismic data for small repeating earthquakes, it is important to construct a dynamic model that can explain various aspects of related observations. We report on small repeating earthquakes on a fault governed by rate- and state-dependent friction laws. The earthquakes occur on a velocity-weakening patch surrounded by a much larger velocity-strengthening region. The whole fault is subject to long-term tectonic loading. The model with a circular patch and the aging form of rate- and state-dependent friction laws has been shown to reproduce the scaling of recurrence time versus seismic moment for small repeating earthquakes in a previous study. In this work we investigate the behaviour of small repeating earthquakes in related models under different scenarios, including several forms of the state evolution equations in rate- and state-dependent friction laws, rectangular velocity-weakening patch geometries, quasi-dynamic versus fully dynamic representation of inertial effects and 2-D versus 3-D simulations. We discover that the simulated scalings between the recurrence time and seismic moment for these different scenarios is similar while differences do exist. We propose a theoretical consideration for the scaling between the recurrence time and seismic moment of small repeating earthquakes. For patch radii smaller than or comparable to the full nucleation size, the scaling is explained by the increase of seismic to aseismic slip ratio with magnitude. For patch radii larger than the full nucleation size, the scaling is explained by the model in which the recurrence time is determined by the earthquake nucleation time, which is in turn determined by the time for aseismic slip to penetrate the distance of the full nucleation size into the patch. The obtained theoretical insight is used to find the combinations of fault properties that allow the model to fit the observed scaling and range of the seismic moment and recurrence time.

58 GEOSCIENCES↗
DOE OSTI2016

Weighing the giants– V. Galaxy cluster scaling relations

Here, we present constraints on the scaling relations of galaxy cluster X-ray luminosity, temperature and gas mass (and derived quantities) with mass and redshift, employing masses from robust weak gravitational lensing measurements. These are the first such results obtained from an analysis that simultaneously accounts for selection effects and the underlying mass function, and directly incorporates lensing data to constrain total masses. Our constraints on the scaling relations and their intrinsic scatters are in good agreement with previous studies, and reinforce a picture in which departures from self-similar scaling laws are primarily limited to cluster cores. However, the data are beginning to reveal new features that have implications for cluster astrophysics and provide new tests for hydrodynamical simulations. We find a positive correlation in the intrinsic scatters of luminosity and temperature at fixed mass, which is related to the dynamical state of the clusters. While the evolution of the nominal scaling relations over the redshift range 0.0 < z < 0.5 is consistent with self-similarity, we find tentative evidence that the luminosity and temperature scatters, respectively, decrease and increase with redshift. Physically, this likely related to the development of cool cores and the rate of major mergers. We also examine the scaling relations of redMaPPer richness and Compton Y from Planck . While the richness–mass relation is in excellent agreement with recent work, the measured Y–mass relation departs strongly from that assumed in the Planck cluster cosmology analysis. Furthermore, the latter result is consistent with earlier comparisons of lensing and Planck scaling relation-derived masses.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Erratum: Weighing the giants – V. Galaxy cluster scaling relations

We present constraints on the scaling relations of galaxy cluster X-ray luminosity, temperature and gas mass (and derived quantities) with mass and redshift, employing masses from robust weak gravitational lensing measurements. These are the first such results obtained from an analysis that simultaneously accounts for selection effects and the underlying mass function, and directly incorporates lensing data to constrain total masses. Our constraints on the scaling relations and their intrinsic scatters are in good agreement with previous studies, and reinforce a picture in which departures from self-similar scaling laws are primarily limited to cluster cores. However, the data are beginning to reveal new features that have implications for cluster astrophysics and provide new tests for hydrodynamical simulations. We find a positive correlation in the intrinsic scatters of luminosity and temperature at fixed mass, which is related to the dynamical state of the clusters. While the evolution of the nominal scaling relations over the redshift range 0.0 < z < 0.5 is consistent with self similarity, we find tentative evidence that the luminosity and temperature scatters respectively decrease and increase with redshift. Physically, this likely related to the development of cool cores and the rate of major mergers. We also examine the scaling relations of redMaPPer richness and Compton Y from Planck . While the richness{mass relation is in excellent agreement with recent work, the measured Y {mass relation departs strongly from that assumed in the Planck cluster cosmology analysis. Furthermore, the latter result is consistent with earlier comparisons of lensing and Planck scaling-relation-derived masses.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Scale-up of the production of highly reactive biogenic magnetite nanoparticles using Geobacter sulfurreducens

Although there are numerous examples of large-scale commercial microbial synthesis routes for organic bioproducts, few studies have addressed the obvious potential for microbial systems to produce inorganic functional biomaterials at scale. Here we address this by focusing on the production of nanoscale biomagnetite particles by the Fe(III)-reducing bacterium Geobacter sulfurreducens , which was scaled up successfully from laboratory- to pilot plant-scale production, while maintaining the surface reactivity and magnetic properties which make this material well suited to commercial exploitation. At the largest scale tested, the bacterium was grown in a 50 l bioreactor, harvested and then inoculated into a buffer solution containing Fe(III)-oxyhydroxide and an electron donor and mediator, which promoted the formation of magnetite in under 24 h. This procedure was capable of producing up to 120 g of biomagnetite. The particle size distribution was maintained between 10 and 15 nm during scale-up of this second step from 10 ml to 10 l, with conserved magnetic properties and surface reactivity; the latter demonstrated by the reduction of Cr(VI). The process presented provides an environmentally benign route to magnetite production and serves as an alternative to harsher synthetic techniques, with the clear potential to be used to produce kilogram to tonne quantities.

Science & Technology - Other Topics↗
DOE OSTI2026

Constraints on Large-Scale White Noise in the Cosmic Density Field

We present observational constraints on large-scale white noise (LSWN) in the cosmic density field, a phenomenon predicted to arise from non-linear mode coupling during cosmological evolution. Building on the theoretical framework of Paper I, where we demonstrated that non-linearities inevitably redistribute power from small to large scales through mode mixing, we confront these predictions with current cosmological data. We modify the CLASS Boltzmann code to incorporate a white noise component $k_\mathrm{BH}/k$ in the primordial power spectrum and perform parameter estimation using current cosmological data. The non-detection of excess power on the largest observable scales places stringent upper bounds: $k_\mathrm{BH} \leq 1.80 \times 10^{-13}~\mathrm{Mpc}^{-1}$ at 99% confidence. These constraints imply the primordial power spectrum must deviate from perfect scale invariance on small scales, either through a cutoff at $k_{\mathrm{cut}} \lesssim 3~\mathrm{pc}^{-1}$ or through running of the spectral index with $α_s \lesssim -0.015$. Our results demonstrate that LSWN provides a powerful probe of the primordial spectrum at scales orders of magnitude smaller than directly observable, offering unique constraints on early-universe physics.

Barenboim, Gabriela [Valencia U., IFIC; Valencia U↗
DOE OSTI2015

Three energy scales in the superconducting state of hole-doped cuprates detected by electronic Raman scattering

We explore by electronic Raman scattering the superconducting state of the Bi 2 Sr 2 CaCu 2 O 8+δ (Bi-2212) crystal by performing a fine-tuned doping study. We find three distinct energy scales in A 1g , B 1g , and B 2g symmetries which show three distinct doping dependencies. Above p=0.22, the three energies merge; below p=0.12, the A 1g scale is no longer detectable, while the B 1g and B 2g scales become constant in energy. In between, the A 1g and B 1g scales increase monotonically with underdoping, while the B 2g one exhibits a maximum at p=0.16. The three superconducting energy scales appear to be a universal feature of hole-doped cuprates. Furthermore, we propose that the nontrivial doping dependencies of the three scales originate from the Fermi-surface changes and reveal competing orders inside the superconducting dome.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Scaling within the spectral function approach

Scaling features of the nuclear electromagnetic response functions unveil aspects of nuclear dynamics that are crucial for interpreting neutrino-and electron-scattering data. In the large momentum-transfer regime, the nucleon-density response function defines a universal scaling function, which is independent of the nature of the probe. In this work, we analyze the nucleon-density response function of 12 C, neglecting collective excitations. We employ particle and hole spectral functions obtained within two distinct many-body methods, both widely used to describe electroweak reactions in nuclei. We show that the two approaches provide compatible nucleon-density scaling functions that for large momentum transfers satisfy first-kind scaling. Both methods yield scaling functions characterized by an asymmetric shape, although less pronounced than that of experimental scaling functions. Finally, this asymmetry, only mildly affected by final state interactions, is mostly due to nucleon-nucleon correlations, encoded in the continuum component of the hole spectral function.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

Scaling from gauge and scalar radiation in Abelian-Higgs string networks

In this work, we investigate cosmic string networks in the Abelian Higgs model using data from a campaign of large-scale numerical simulations on lattices of up to 409 6 3 grid points. We observe scaling or self-similarity of the networks over a wide range of scales and estimate the asymptotic values of the mean string separation in horizon length units ξ ˙ and of the mean square string velocity v ¯ 2 in the continuum and large time limits. The scaling occurs because the strings lose energy into classical radiation of the scalar and gauge fields of the Abelian Higgs model. We quantify the energy loss with a dimensionless radiative efficiency parameter and show that it does not vary significantly with lattice spacing or string separation. This implies that the radiative energy loss underlying the scaling behavior is not a lattice artifact, and justifies the extrapolation of measured network properties to large times for computations of cosmological perturbations. We also show that the core growth method, which increases the defect core width with time to extend the dynamic range of simulations, does not introduce significant systematic error. We compare ξ ˙ and v ¯ 2 to values measured in simulations using the Nambu-Goto approximation, finding that the latter underestimate the mean string separation by about 25%, and overestimate v ¯ 2 by about 10%. The scaling of the string separation implies that string loops decay by the emission of massive radiation within a Hubble time in field theory simulations, in contrast to the Nambu-Goto scenario which neglects this energy loss mechanism. String loops surviving for only one Hubble time emit much less gravitational radiation than in the Nambu-Goto scenario and are consequently subject to much weaker gravitational wave constraints on their tension.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Observation of Scale Invariance in Two-Dimensional Matter-Wave Townes Solitons

We report near-deterministic generation of two-dimensional (2D) matter-wave Townes solitons, and a precision test on scale invariance in attractive 2D Boses gases. We induce a shape-controlled modulational instability in an elongated 2D matter-wave to create an array of isolated solitary waves of various sizes and peak densities. We confirm scale invariance by observing the collapse of solitary-wave density profiles onto a single curve in a dimensionless coordinate rescaled according to their peak densities, and observe that the scale-invariant profiles measured at different coupling constants can further collapse onto the universal profile of Townes solitons. The reported scaling behavior is tested with a nearly 60-fold difference in soliton interaction energies, and allows us to discuss the impact of a non-negligible magnetic dipole-dipole interaction (MDDI) on 2D scale invariance. Here, we confirm that the effect of MDDI in our alkali cesium quasi-2D samples effectively conforms to the same scaling law governed by a contact interaction to well within our experiment uncertainty.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Generalized scaling relationships on transition metals: Influence of adsorbate-coadsorbate interactions

Linear scaling relations of adsorbate energies across a range of catalytic surfaces have emerged as a central interpretive paradigm in heterogeneous catalysis. They are, however, typically developed for low adsorbate coverages which are not always representative of realistic heterogeneous catalytic environments. Herein, we present generalized linear scaling relations on transition metals that explicitly consider adsorbate-coadsorbate interactions at variable coverages. The slopes of these scaling relations do not follow the simple bond counting principles that govern scaling on transition metals at lower coverages. In this work, the deviations from bond counting are explained using a pairwise interaction model wherein the interaction parameter determines the slope of the scaling relationship on a given metal at variable coadsorbate coverages, and the slope across different metals at fixed coadsorbate coverage is approximated by adding a coverage-dependent correction to the standard bond counting contribution. The analysis provides a compact explanation for coverage-dependent deviations from bond counting in scaling relationships and suggests a useful strategy for incorporation of coverage effects into catalytic trends studies.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Scaling Out a Combinatorial Algorithm for Discovering Carcinogenic Gene Combinations to Thousands of GPUs

Cancer is a leading cause of death in the US, second only to heart disease. It is primarily a result of a combination of an estimated two-nine genetic mutations (multi-hit combinations). Although a body of research has identified hundreds of cancer-causing genetic mutations, we don’t know the specific combination of mutations responsible for specific instances of cancer for most cancer types. An approximate algorithm for solving the weighted set cover problem was previously adapted to identify combinations of genes with mutations that may be responsible for individual instances of cancer. However, the algorithm’s computational requirement scales exponentially with the number of genes, making it impractical for identifying more than three-hit combinations, even after the algorithm was parallelized and scaled up to a V100 GPU. Since most cancers have been estimated to require more than three hits, we scaled out the algorithm to identify combinations of four or more hits using 1000 nodes (6000 V100 GPUs with ≈48×106 processing cores) on the Summit supercomputer at Oak Ridge National Laboratory. Efficiently scaling out the algorithm required a series of algorithmic innovations and optimizations for balancing an exponentially divergent workload across processors and for minimizing memory latency and inter-node communication. We achieved an average strong scaling efficiency of 90.14% (80.96%–97.96% for 200 to 1000 nodes), compared to a 100 node run, with 84.18% scaling efficiency for 1000 nodes. With experimental validation, the multi-hit combinations identified here could provide further insight into the etiology of different cancer subtypes and provide a rational basis for targeted combination therapy.

Dash, Sajal↗
DOE OSTI2024

DICER: Data Intensive Computing Environment and Runtime for Evaluating Unprecedented Scale of Geospatial-Temporal Human Mobility Data

With the significant increase in sources and volume of human mobility data through commercial data vendors as well as microsimulation of cities, the scale of geospatial-temporal data to analyze and assess for mobility characterization has grown to the level of Big Data. There are mobility related commercial organizations deploying scalable computing, but often the system architecture, workflow, and intermediate processing components are not fully disclosed in relevant scope. Current research literature has a notable lack of studies demonstrating architectures and workflows for human mobility analytics that are implemented on a TeraByte scale of geospatial-temporal data. In this context, this paper presents a hyperscale-level system solution named DICER (Data Intensive Computing Environment and Runtime) for processing and analytics of geospatial-temporal data at big data scale. Although the cluster computing architecture of DICER with Apache Spark job running on Kubernetes cluster is not new, there are innovations in the workflow, hierarchical processing logic, and a wide range of intermediate preprocessing and mobility metrics calculation. We have performed case studies to validate the effectiveness of DICER system solution by performing detailed analytics and assessment of human mobility microsimulation output at three different scopes and scale, including a usecase with 16.97 TeraByte and 259.2 Billion rows of data. In addition, we have presented another case study of utilizing DICER to perform the same mobility processing and comparative analytics on large-scale commercially available geospatial-temporal data. All these case studies validate the efficiency and usefulness of DICER in computing population mobility characteristics from geospatial-temporal trajectory data at an unprecedented scale (not only just data volume, but also combination of: number of user entities, temporal frequency, spatial resolution, data duration).

De, Debraj↗
DOE OSTI2016

Visual Data-Analytics of Large-Scale Parallel Discrete-Event Simulations

Parallel discrete-event simulation (PDES) is an important tool in the codesign of extreme-scale systems because PDES provides a cost-effective way to evaluate designs of highperformance computing systems. Optimistic synchronization algorithms for PDES, such as Time Warp, allow events to be processed without global synchronization among the processing elements. A rollback mechanism is provided when events are processed out of timestamp order. Although optimistic synchronization protocols enable the scalability of large-scale PDES, the performance of the simulations must be tuned to reduce the number of rollbacks and provide an improved simulation runtime. To enable efficient large-scale optimistic simulations, one has to gain insight into the factors that affect the rollback behavior and simulation performance. We developed a tool for ROSS model developers that gives them detailed metrics on the performance of their large-scale optimistic simulations at varying levels of simulation granularity. Model developers can use this information for parameter tuning of optimistic simulations in order to achieve better runtime and fewer rollbacks. In this work, we instrument the ROSS optimistic PDES framework to gather detailed statistics about the simulation engine. We have also developed an interactive visualization interface that uses the data collected by the ROSS instrumentation to understand the underlying behavior of the simulation engine. The interface connects real time to virtual time in the simulation and provides the ability to view simulation data at different granularities. We demonstrate the usefulness of our framework by performing a visual analysis of the dragonfly network topology model provided by the CODES simulation framework built on top of ROSS. The instrumentation needs to minimize overhead in order to accurately collect data about the simulation performance. To ensure that the instrumentation does not introduce unnecessary overhead, we perform a scaling study that compares instrumented ROSS simulations with their noninstrumented counterparts in order to determine the amount of perturbation when running at different simulation scales.

Ross, Caitlin↗
DOE OSTI2020

Community structure – Ecosystem function relationships in the Congo Basin methane cycle depend on the physiological scale of function

Belowground ecosystem processes can be highly variable and difficult to predict using microbial community data. Here, we argue that this stems from at least three issues: (a) complex covariance structure of samples (with environmental conditions or spatial proximity) can make distinguishing biotic drivers a challenge; (b) communities can control ecosystem processes through multiple mechanisms, making the identification of these controls a challenge; and (c) ecosystem function assessments can be broad in physiological scale, encapsulating multiple processes with unique microbially mediated controls. In this work, we test these assertions using methane (CH 4 )-cycling processes in soil samples collected along a wetland-to-upland habitat gradient in the Congo Basin. We perform our measurements of function under controlled laboratory conditions and statistically control for environmental covariates to aid in identifying biotic drivers. We divide measurements of microbial communities into four attributes (abundance, activity, composition, and diversity) that represent different forms of community control. Lastly, our process measurements differ in physiological scale, including broader processes (gross methanogenesis and methanotrophy) that involve more mediating groups, to finer processes (hydrogenotrophic methanogenesis and high-affinity CH 4 oxidation) with fewer mediating groups. We observed that finer scale processes can be more readily predicted from microbial community structure than broader scale processes. In addition, the nature of those relationships differed, with broad processes limited by abundance while fine-scale processes were associated with diversity and composition. These findings demonstrate the importance of carefully defining the physiological scale of ecosystem function and performing community measurements that represent the range of possible controls on ecosystem processes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

Over 150 years of long-term fertilization alters spatial scaling of microbial biodiversity

Spatial scaling is a critical issue in ecology, but how anthropogenic activities like fertilization affect spatial scaling is poorly understood, especially for microbial communities. Here, we determined the effects of long-term fertilization on the spatial scaling of microbial functional diversity and its relationships to plant diversity in the 150-year-old Park Grass Experiment, the oldest continuous grassland experiment in the world. Nested samples were taken from plots with contrasting inorganic fertilization regimes, and community DNAs were analyzed using the GeoChip-based functional gene array. The slopes of microbial gene-area relationships (GARs) and plant species-area relationships (SARs) were estimated in a plot receiving nitrogen (N), phosphorus (P), and potassium (K) and a control plot without fertilization. Our results indicated that long-term inorganic fertilization significantly increased both microbial GARs and plant SARs. Microbial spatial turnover rates (i.e., z values) were less than 0.1 and were significantly higher in the fertilized plot (0.0583) than in the control plot (0.0449) (P < 0.0001). The z values also varied significantly with different functional genes involved in carbon (C), N, P, and sulfur (S) cycling and with various phylogenetic groups (archaea, bacteria, and fungi). Similarly, the plant SARs increased significantly (P < 0.0001), from 0.225 in the control plot to 0.419 in the fertilized plot. Soil fertilization, plant diversity, and spatial distance had roughly equal contributions in shaping the microbial functional community structure, while soil geochemical variables contributed less. Results indicated that long-term agricultural practice could alter the spatial scaling of microbial biodiversity. Determining the spatial scaling of microbial biodiversity and its response to human activities is important but challenging in microbial ecology. Most studies to date are based on different sites that may not be truly comparable or on short-term perturbations, and hence, the results observed could represent transient responses. This study examined the spatial patterns of microbial communities in response to different fertilization regimes at the Rothamsted Research Experimental Station, which has become an invaluable resource for ecologists, environmentalists, and soil scientists. The current study is the first showing that long-term fertilization has dramatic impacts on the spatial scaling of microbial communities. In addition, by identifying the spatial patterns in response to long-term fertilization and their underlying mechanisms, the study makes fundamental contributions to predictive understanding of microbial biogeography.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Subcritical Small-Scale Dynamo in a Helical Random Flow

The possibility of the growth of a small-scale dynamo in a random flow with a weak mirror asymmetry under subcritical generation conditions is investigated. We show that the appearance of an asymmetry in a flow with nonzero helicity leads to the generation of small-scale periodic perturbations. These perturbations, in turn, support active field generation on small scales. We describe the properties of this support, the generation rate, and the characteristic scales dependent on the velocity of the random flow and the degree of its helicity. Transferring the problem to the spectral domain, we demonstrate the formation of a two-component small- and large-scale spectrum that consists of a peak localized on large scales and power laws at large and small k. The possibility of directly checking the spectral properties being described in subcritical laboratory MHD conditions is specially noted.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Is the magnitude of the Peccei–Quinn scale set by the landscape?

Rather general considerations of the string theory landscape imply a mild statistical draw towards large soft SUSY breaking terms tempered by the requirement of proper electroweak symmetry breaking where SUSY contributions to the weak scale are not too far from m weak ~ 100 GeV. Such a picture leads to the prediction that m h ~ 125 GeV while most sparticles are beyond current LHC reach. Here we explore the possibility that the magnitude of the Peccei-Quinn (PQ) scale f a is also set by string landscape considerations within the framework of a compelling SUSY axion model. First, we examine the case where the PQ symmetry arises as an accidental approximate global symmetry from a more fundamental gravity-safe Z$R\atop{24}$$ symmetry and where the SUSY mu parameter arises from a Kim-Nilles operator. The pull towards large soft terms then also pulls the PQ scale as large as possible. Unless this is tempered by rather severe (unknown) cosmological or anthropic bounds on the density of dark matter, then we would expect a far greater abundance of dark matter than is observed. This conclusion cannot be negated by adopting a tiny axion misalignment angle θ i because WIMPs are also overproduced at large f a . Hence, we conclude that setting the PQ scale via anthropics is highly unlikely. Instead, requiring soft SUSY breaking terms of order the gravity-mediation scale m 3/2 ~ 10 -100 TeV places the mixed axion-neutralino dark matter abundance into the intermediate scale sweet zone where f a ~ 10 11 -10 12 GeV. We compare our analysis to the more general case of a generic SUSY DFSZ axion model with uniform selection on theta_i but leading to the measured dark matter abundance: this approach leads to a preference for f a ~ 10 12 GeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗