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

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

Nonequilibrium electron heating in inter-subband terahertz lasers

Inter-subband laser performance can be critically dependent on the nature of the electron distributions in each subband. In these first Monte Carlo device simulations of optically pumped inter-subband THz lasers, we can see that there are two main causes of electron heating: intersubband decay processes, and inter-subband energy transfer from the "hot" nonequilibrium tails of lower subbands. These processes mean that devices relying on low electron temperatures are disrupted by electron heating, to the extent that slightly populated subbands can have average energies far in excess of the that of either the lattice or other subbands. However, although these heating effects invalidate designs relying on low temperature electron distributions, we see that population inversion is still possible in the high-THz range at 77 K in both stepped and triple-well structures, and that our 11.7 THz triple-well structure even promises inversion at 300 K. © 2002 American Institute of Physics

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

Extreme fluctuations in noisy task-completion landscapes on scale-free networks

We study the statistics and scaling of extreme fluctuations in noisy task-completion landscapes, such as those emerging in synchronized distributed-computing networks, or generic causally-constrained queuing networks, with scale-free topology. In these networks the average size of the fluctuations becomes finite (synchronized state) and the extreme fluctuations typically diverge only logarithmically in the large system-size limit ensuring synchronization in a practical sense. Provided that local fluctuations in the network are short-tailed, the statistics of the extremes are governed by the Gumbel distribution. We present large-scale simulation results using the exact algorithmic rules, supported by mean-field arguments based on a coarse-grained description.Comment: 16 pages, 6 figures, revte

Electronic Green's functions in a T-shaped multi-quantum dot system

We developed a set of equations to calculate the electronic Green's functions in a T-shaped multi-quantum dot system using the equation of motion method. We model the system using a generalized Anderson Hamiltonian which accounts for {\em finite} intradot on-site Coulomb interaction in all component dots as well as for the interdot electron tunneling between adjacent quantum dots. Our results are obtained within and beyond the Hartree-Fock approximation and provide a path to evaluate all the electronic correlations in the multi-quantum dot system in the Coulomb blockade regime. Both approximations provide information on the physical effects related to the finite intradot on-site Coulomb interaction. As a particular example for our generalized results, we considered the simplest T-shaped system consisting of two dots and proved that our approximation introduces important corrections in the detector and side dots Green's functions, and implicitly in the evaluation of the system's transport properties. The multi-quantum dot T-shaped setup may be of interest for the practical realization of qubit states in quantum dots systems.Comment: 13 pages, 2 figure

Multilayer metamaterial absorbers inspired by perfectly matched layers

We derive periodic multilayer absorbers with effective uniaxial properties similar to perfectly matched layers (PML). This approximate representation of PML is based on the effective medium theory and we call it an effective medium PML (EM-PML). We compare the spatial reflection spectrum of the layered absorbers to that of a PML material and demonstrate that after neglecting gain and magnetic properties, the absorber remains functional. This opens a route to create electromagnetic absorbers for real and not only numerical applications and as an example we introduce a layered absorber for the wavelength of $8$~$\mu$m made of SiO$_2$ and NaCl. We also show that similar cylindrical core-shell nanostructures derived from flat multilayers also exhibit very good absorptive and reflective properties despite the different geometry

Elucidation of key odorants and sensory propertiesof five different extra virgin olive oils from Turkey by GC-MS-Olfactometry

The present study investigates the aroma, key odorants and sensory profile of extra virgin olive oils from five well-known Turkish cultivars. The aromatic extract obtained by the purge and trap extraction system, according to a sensory analysis, resembled the odor of olive oil. A total of 22, 21, 18, 22 and 21 aroma-active compounds were detected in the extracts of Ayvalık, Memecik, Gemlik, Sarı Ulak and Beylik olive oils, respectively. The results show that Ayvalık has the highest flavor dilution (FD) value of 1024 with hexanal, (E)-2-hexenal and α-farnesene. Memecik has the highest FD value at 2048 with (E)-2-hexenal. Gemlik has the highest FD value of 1024 with (Z)-3-hexenyl acetate, (E)-2-hexen-1-ol and α-farnesene. Sarı Ulak has the highest FD value at 2048 with (E)-2-hexenal. Beylik has the highest FD value of 2048 with (E)-2-hexenal and hexanal. All cultivars represent the characteristic green, cut-grass, fruity odor notes

Airy Distribution Function: From the Area Under a Brownian Excursion to the Maximal Height of Fluctuating Interfaces

The Airy distribution function describes the probability distribution of the area under a Brownian excursion over a unit interval. Surprisingly, this function has appeared in a number of seemingly unrelated problems, mostly in computer science and graph theory. In this paper, we show that this distribution also appears in a rather well studied physical system, namely the fluctuating interfaces. We present an exact solution for the distribution P(h_m,L) of the maximal height h_m (measured with respect to the average spatial height) in the steady state of a fluctuating interface in a one dimensional system of size L with both periodic and free boundary conditions. For the periodic case, we show that P(h_m,L)=L^{-1/2}f(h_m L^{-1/2}) for all L where the function f(x) is the Airy distribution function. This result is valid for both the Edwards-Wilkinson and the Kardar-Parisi-Zhang interfaces. For the free boundary case, the same scaling holds P(h_m,L)=L^{-1/2}F(h_m L^{-1/2}), but the scaling function F(x) is different from that of the periodic case. We compute this scaling function explicitly for the Edwards-Wilkinson interface and call it the F-Airy distribution function. Numerical simulations are in excellent agreement with our analytical results. Our results provide a rather rare exactly solvable case for the distribution of extremum of a set of strongly correlated random variables. Some of these results were announced in a recent Letter [ S.N. Majumdar and A. Comtet, Phys. Rev. Lett., 92, 225501 (2004)].Comment: 27 pages, 10 .eps figures included. Two figures improved, new discussion and references adde