Going through Rough Times: from Non-Equilibrium Surface Growth to Algorithmic Scalability

Efficient and faithful parallel simulation of large asynchronous systems is a challenging computational problem. It requires using the concept of local simulated times and a synchronization scheme. We study the scalability of massively parallel algorithms for discrete-event simulations which employ conservative synchronization to enforce causality. We do this by looking at the simulated time horizon as a complex evolving system, and we identify its universal characteristics. We find that the time horizon for the conservative parallel discrete-event simulation scheme exhibits Kardar-Parisi-Zhang-like kinetic roughening. This implies that the algorithm is asymptotically scalable in the sense that the average progress rate of the simulation approaches a non-zero constant. It also implies, however, that there are diverging memory requirements associated with such schemes.Comment: to appear in the Proceedings of the MRS, Fall 200

Suppressing Roughness of Virtual Times in Parallel Discrete-Event Simulations

In a parallel discrete-event simulation (PDES) scheme, tasks are distributed among processing elements (PEs), whose progress is controlled by a synchronization scheme. For lattice systems with short-range interactions, the progress of the conservative PDES scheme is governed by the Kardar-Parisi-Zhang equation from the theory of non-equilibrium surface growth. Although the simulated (virtual) times of the PEs progress at a nonzero rate, their standard deviation (spread) diverges with the number of PEs, hindering efficient data collection. We show that weak random interactions among the PEs can make this spread nondivergent. The PEs then progress at a nonzero, near-uniform rate without requiring global synchronizations

Conjugate field and fluctuation-dissipation relation for the dynamic phase transition in the two-dimensional kinetic Ising model

The two-dimensional kinetic Ising model, when exposed to an oscillating applied magnetic field, has been shown to exhibit a nonequilibrium, second-order dynamic phase transition (DPT), whose order parameter Q is the period-averaged magnetization. It has been established that this DPT falls in the same universality class as the equilibrium phase transition in the two-dimensional Ising model in zero applied field. Here we study for the first time the scaling of the dynamic order parameter with respect to a nonzero, period-averaged, magnetic `bias' field, H_b, for a DPT produced by a square-wave applied field. We find evidence that the scaling exponent, \delta_d, of H_b at the critical period of the DPT is equal to the exponent for the critical isotherm, \delta_e, in the equilibrium Ising model. This implies that H_b is a significant component of the field conjugate to Q. A finite-size scaling analysis of the dynamic order parameter above the critical period provides further support for this result. We also demonstrate numerically that, for a range of periods and values of H_b in the critical region, a fluctuation-dissipation relation (FDR), with an effective temperature T_{eff}(T, P, H_0) depending on the period, and possibly the temperature and field amplitude, holds for the variables Q and H_b. This FDR justifies the use of the scaled variance of Q as a proxy for the nonequilibrium susceptibility, \partial / \partial H_b, in the critical region.Comment: revised version; 31 pages, 12 figures; accepted by Phys. Rev.

Synchronization Landscapes in Small-World-Connected Computer Networks

Motivated by a synchronization problem in distributed computing we studied a simple growth model on regular and small-world networks, embedded in one and two-dimensions. We find that the synchronization landscape (corresponding to the progress of the individual processors) exhibits Kardar-Parisi-Zhang-like kinetic roughening on regular networks with short-range communication links. Although the processors, on average, progress at a nonzero rate, their spread (the width of the synchronization landscape) diverges with the number of nodes (desynchronized state) hindering efficient data management. When random communication links are added on top of the one and two-dimensional regular networks (resulting in a small-world network), large fluctuations in the synchronization landscape are suppressed and the width approaches a finite value in the large system-size limit (synchronized state). In the resulting synchronization scheme, the processors make close-to-uniform progress with a nonzero rate without global intervention. We obtain our results by ``simulating the simulations", based on the exact algorithmic rules, supported by coarse-grained arguments.Comment: 20 pages, 22 figure

Missing Transverse-Doppler Effect in Time-Dilation Experiments with High-Speed Ions

Recent experiments with high-speed ions have investigated potential deviations from the time-dilation predicted by special relativity (SR). The main contribution of this article is to show that the SR predictions are matched by the experimental results only when the transverse Doppler effect in the observed emissions from the ions are neglected in the analysis. However, the Doppler effect in the emission cannot be neglected because it is similar to the time dilation effect. Thus, the article highlights the need to consider Doppler emission effects when validating SR time dilation using high-speed ion experiments.Comment: 3 pages, 3 figure

The optimal form of the scanning near-field optical microscopy probe

A theoretical approach to determine the optimal form of the near-field optical microscope probe is proposed. An analytical expression of the optimal probe form with subwavelength aperture has been obtained. The advantages of the probe with the optimal form are illustrated using numerical calculations. The conducted calculations show 10 times greater light throughput and the reception possibility of the more compactly localized light at the output probe aperture which could indicate better spatial resolution of the optical images in near-field optical technique using optimal probe.Comment: 12 pages, 6 figure

Monte Carlo Simulation of Magnetization Reversal in Fe Sesquilayers on W(110)

Iron sesquilayers grown at room temperature on W(110) exhibit a pronounced coercivity maximum near a coverage of 1.5 atomic monolayers. On lattices which faithfully reproduce the morphology of the real films, a kinetic Ising model is utilized to simulate the domain-wall motion. Simulations reveal that the dynamics is dominated by the second-layer islands, which act as pinning centers. The simulated dependencies of the coercivity on the film coverage, as well as on the temperature and the frequency of the applied field, are very similar to those measured in experiments. Unlike previous micromagnetic models, the presented approach provides insight into the dynamics of the domain-wall motion and clearly reveals the role of thermal fluctuations.Comment: Final version to appear in Phys. Rev. B. References to related works added. 7 pages, 5 figures, RevTex, mpeg simulations available at http://www.scri.fsu.edu/~rikvol