157 research outputs found
Linking Physics and Algorithms in the Random-Field Ising Model
The energy landscape for the random-field Ising model (RFIM) is complex, yet algorithms such as the push-relabel algorithm exist for computing the exact ground state of an RFIM sample in time polynomial in the sample volume. Simulations were carried out to investigate the scaling properties of the push-relabel algorithm. The time evolution of the algorithm was studied along with the statistics of an auxiliary potential field. At very small random fields, the algorithm dynamics are closely related to the dynamics of two-species annihilation, consistent with fractal statistics for the distribution of minima in the potential (``height\u27\u27). For , a correlation length diverging at zero disorder sets a cutoff scale for the magnitude of the height field; our results are most consistent with a power-law correction to the exponential scaling of the correlation length with disorder in . Near the ferromagnetic-paramagnetic transition in , the time to find a solution diverges with a dynamic critical exponent of for a priority queue version and for a first-in first-out queue version of the algorithm. The links between the evolution of auxiliary fields in algorithmic time and the static physical properties of the RFIM ground state provide insight into the physics of the RFIM and a better understanding of how the algorithm functions
Exploring Optimization for the Random-Field Ising Model
The push-relabel algorithm can be used to calculate rapidly the exact ground states for a given sample with a random-field Ising model (RFIM) Hamiltonian. Although the algorithm is guaranteed to terminate after a time polynomial in the number of spins, implementation details are important for practical performance. Empirical results for the timing in dimensions d=1,2, and 3 are used to determine the fastest among several implementations. Direct visualization of the auxiliary fields used by the algorithm provides insight into its operation and suggests how to optimize the algorithm. Recommendations are given for further study of the RFIM
Exploring optimization for the random-field Ising model
The push-relabel algorithm can be used to calculate rapidly the exact ground
states for a given sample with a random-field Ising model (RFIM) Hamiltonian.
Although the algorithm is guaranteed to terminate after a time polynomial in
the number of spins, implementation details are important for practical
performance. Empirical results for the timing in dimensions d=1,2, and 3 are
used to determine the fastest among several implementations. Direct
visualization of the auxiliary fields used by the algorithm provides insight
into its operation and suggests how to optimize the algorithm. Recommendations
are given for further study of the RFIM.Comment: 10 page
Direct Visualization of Dislocation Dynamics in Grain Boundary Scars
Mesoscale objects with unusual structural features may serve as the analogues
of atoms in the design of larger-scale materials with novel optical, electronic
or mechanical behaviour. In this paper we investigate the structural features
and the equilibrium dynamics of micron-scale spherical crystals formed by
polystyrene particles adsorbed on the surface of a spherical water droplet. The
ground state of sufficiently large crystals possesses finite-length grain
boundaries (scars). We determine the elastic response of the crystal by
measuring single-particle diffusion and quantify the fluctuations of individual
dislocations about their equilibrium positions within a scar determining the
dislocation spring constants. We observe rapid dislocation glide with
fluctuations over the barriers separating one local Peierls minimum from the
next and rather weak binding of dislocations to their associated scars. The
long-distance (renormalised) dislocation diffusion glide constant is extracted
directly from the experimental data and is found to be moderately faster than
single particle diffusion. We are also able to determine the parameters of the
Peierls potential induced by the underlying crystalline lattice.Comment: 11 pages, 4 figures, pdf forma
National and subnational short-term forecasting of COVID-19 in Germany and Poland during early 2021
We compare forecasts of weekly case and death numbers for COVID-19 in Germany and Poland based on 15 different modelling approaches. These cover the period from January to April 2021 and address numbers of cases and deaths one and two weeks into the future, along with the respective uncertainties. We find that combining different forecasts into one forecast can enable better predictions. However, case numbers over longer periods were challenging to predict. Additional data sources, such as information about different versions of the SARS-CoV-2 virus present in the population, might improve forecasts in the future
The Mont-Blanc prototype: an alternative approach for high-performance computing systems
High-performance computing (HPC) is recognized as one of the pillars for further advance of science, industry, medicine, and education. Current HPC systems are being developed to overcome emerging challenges in order to reach Exascale level of performance,which is expected by the year 2020. The much larger embedded and mobile market allows for rapid development of IP blocks, and provides more flexibility in designing an application-specific SoC, in turn giving possibility in balancing performance, energy-efficiency and cost. In the Mont-Blanc project, we advocate for HPC systems be built from such commodity IP blocks, currently used in embedded and mobile SoCs.
As a first demonstrator of such approach, we present the Mont-Blanc prototype; the first HPC system built with commodity SoCs, memories, and NICs from the embedded and mobile domain, and off-the-shelf HPC networking, storage, cooling and integration solutions. We present the system’s architecture, and evaluation including both performance and energy efficiency. Further, we compare the system’s abilities against a production level supercomputer. At the end, we discuss parallel scalability, and estimate the maximum scalability point of this approach across a set of HPC applications.Postprint (published version
- …