Localization in an Inhomogeneous Quantum Wire

We study interaction-induced localization of electrons in an inhomogeneous quasi-one-dimensional system--a wire with two regions, one at low density and the other high. Quantum Monte Carlo techniques are used to treat the strong Coulomb interactions in the low density region, where localization of electrons occurs. The nature of the transition from high to low density depends on the density gradient--if it is steep, a barrier develops between the two regions, causing Coulomb blockade effects. Ferromagnetic spin polarization does not appear for any parameters studied. The picture emerging here is in good agreement with measurements of tunneling between two wires.Comment: 4 pages; 2 new figures, substantial revisions and clarification

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

Aflatoxin regulations and global pistachio trade: Insights from social network analysis

Aflatoxins, carcinogenic toxins produced by Aspergillus fungi, contaminate maize, peanuts, and tree nuts in many regions of the world. Pistachios are the main source of human dietary aflatoxins from tree nuts worldwide. Over 120 countries have regulations for maximum allowable aflatoxin levels in food commodities. We developed social network models to analyze the association between nations' aflatoxin regulations and global trade patterns of pistachios from 1996-2010. The main pistachio producing countries are Iran and the United States (US), which together contribute to nearly 75% of the total global pistachio market. Over this time period, during which many nations developed or changed their aflatoxin regulations in pistachios, global pistachio trade patterns changed; with the US increasingly exporting to countries with stricter aflatoxin standards. The US pistachio crop has had consistently lower levels of aflatoxin than the Iranian crop over this same time period. As similar trading patterns have also been documented in maize, public health may be affected if countries without aflatoxin regulations, or with more relaxed regulations, continually import crops with higher aflatoxin contamination. Unlike the previous studies on maize, this analysis includes a dynamic element, examining how trade patterns change over time with introduction or adjustment of aflatoxin regulations. © 2014 Bui-Klimke et al

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

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

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

How Can Reasoner Performance of ABox Intensive Ontologies Be Predicted?

Reasoner performance prediction of ontologies in OWL 2 language has been studied so far from different dimensions. One key aspect of these studies has been the prediction of how much time a particular task for a given ontology will consume. Several approaches have adopted different machine learning techniques to predict time consumption of ontologies already. However, these studies focused on capturing general aspects of the ontologies (i.e., mainly the complexity of their TBoxes), while paying little attention to ABox intensive ontologies. To address this issue, in this paper, we propose to improve the representativeness of ontology metrics by developing new metrics which focus on the ABox features of ontologies. Our experiments show that the proposed metrics contribute to overall prediction accuracy for all ontologies in general without causing side-effects