A stochastic epidemiological model and a deterministic limit for BitTorrent-like peer-to-peer file-sharing networks

In this paper, we propose a stochastic model for a file-sharing peer-to-peer network which resembles the popular BitTorrent system: large files are split into chunks and a peer can download or swap from another peer only one chunk at a time. We prove that the fluid limits of a scaled Markov model of this system are of the coagulation form, special cases of which are well-known epidemiological (SIR) models. In addition, Lyapunov stability and settling-time results are explored. We derive conditions under which the BitTorrent incentives under consideration result in shorter mean file-acquisition times for peers compared to client-server (single chunk) systems. Finally, a diffusion approximation is given and some open questions are discussed.Comment: 25 pages, 6 figure

High temperature fatigue behaviour in an advanced nickel based superalloy: The effects of oxidation and stress relaxation at notches

The low cycle fatigue performance of the nickel based superalloy RR1000 was investigated under a variety of load waveforms at high temperature, employing a double edge notch geometry under load control. Experiments on a plain cylindrical specimen design under strain control were later performed to simulate the constrained conditions at the root of the notch in order to characterise the interaction between surface constituents and the environment. A significant fatigue debit was demonstrated under both load/strain scenarios when superimposing a dwell period at the minimum point of the cycle. This debit was attributed to a reduction in fatigue crack initiation life resulting from oxidation damage which subsequently cracks under cyclic tension together with a modification to the mean stress through cyclic stabilisation. The same dwell period superimposed at the peak of the cycle was essentially benign for excursions under strain control loading

First normal stress difference and crystallization in a dense sheared granular fluid

The first normal stress difference (${\mathcal N}_1$) and the microstructure in a dense sheared granular fluid of smooth inelastic hard-disks are probed using event-driven simulations. While the anisotropy in the second moment of fluctuation velocity, which is a Burnett-order effect, is known to be the progenitor of normal stress differences in {\it dilute} granular fluids, we show here that the collisional anisotropies are responsible for the normal stress behaviour in the {\it dense} limit. As in the elastic hard-sphere fluids, ${\mathcal N}_1$ remains {\it positive} (if the stress is defined in the {\it compressive} sense) for dilute and moderately dense flows, but becomes {\it negative} above a critical density, depending on the restitution coefficient. This sign-reversal of ${\mathcal N}_1$ occurs due to the {\it microstructural} reorganization of the particles, which can be correlated with a preferred value of the {\it average} collision angle $\theta_{av}=\pi/4 \pm \pi/2$ in the direction opposing the shear. We also report on the shear-induced {\it crystal}-formation, signalling the onset of fluid-solid coexistence in dense granular fluids. Different approaches to take into account the normal stress differences are discussed in the framework of the relaxation-type rheological models.Comment: 21 pages, 13 figure

Pre-notched and corroded low cycle fatigue behaviour of a nickel based alloy for disc rotor applications

Currently there is doubt surrounding the suitability of chemically-induced stress independent pre-conditioning of specimens to simulate turbine corrosion prior to fatigue testing. the thick oxide scales developed using such techniques can lead to net section loss and typically a lack of grain boundary sulphide attack seen in components that experience stress. An alternative approach to a corrosion-fatigue test scenario is suggested by micro-notching fatigue specimens prior to low salt flux corrosion to form grain boundary sulphide particles within channel-like features akin to stress assisted morphologies. On fatigue testing, a trend was identified where a change of mechanism was observed. The grain boundary oxide likely formed in the wake of freshly precipitated sulphide particles fractures around segments of grains leading to a metal loss that contributes to a significant reduction in fatigue properties

Controlled mobility in stochastic and dynamic wireless networks

We consider the use of controlled mobility in wireless networks where messages arriving randomly in time and space are collected by mobile receivers (collectors). The collectors are responsible for receiving these messages via wireless transmission by dynamically adjusting their position in the network. Our goal is to utilize a combination of wireless transmission and controlled mobility to improve the throughput and delay performance in such networks. First, we consider a system with a single collector. We show that the necessary and sufficient stability condition for such a system is given by ρ<1 where ρ is the expected system load. We derive lower bounds for the expected message waiting time in the system and develop policies that are stable for all loads ρ<1 and have asymptotically optimal delay scaling. We show that the combination of mobility and wireless transmission results in a delay scaling of Θ([1 over 1−ρ]) with the system load ρ, in contrast to the Θ([1 over (1−ρ)[superscript 2]]) delay scaling in the corresponding system without wireless transmission, where the collector visits each message location. Next, we consider the system with multiple collectors. In the case where simultaneous transmissions to different collectors do not interfere with each other, we show that both the stability condition and the delay scaling extend from the single collector case. In the case where simultaneous transmissions to different collectors interfere with each other, we characterize the stability region of the system and show that a frame-based version of the well-known Max-Weight policy stabilizes the system asymptotically in the frame length.National Science Foundation (U.S.) (Grant CNS-0915988)United States. Army Research Office. Multidisciplinary University Research Initiative (Grant W911NF-08-1-0238

An Excursion-Theoretic Approach to Stability of Discrete-Time Stochastic Hybrid Systems

We address stability of a class of Markovian discrete-time stochastic hybrid systems. This class of systems is characterized by the state-space of the system being partitioned into a safe or target set and its exterior, and the dynamics of the system being different in each domain. We give conditions for $L_1$-boundedness of Lyapunov functions based on certain negative drift conditions outside the target set, together with some more minor assumptions. We then apply our results to a wide class of randomly switched systems (or iterated function systems), for which we give conditions for global asymptotic stability almost surely and in $L_1$. The systems need not be time-homogeneous, and our results apply to certain systems for which functional-analytic or martingale-based estimates are difficult or impossible to get.Comment: Revised. 17 pages. To appear in Applied Mathematics & Optimizatio

Feeling the past: The absence of experimental evidence for anomalous retroactive influences on text processing

Item does not contain fulltextIn two self-paced reading experiments, we investigated the hypothesis that information moves backward in time to influence prior behaviors (Bem Journal of Personality and Social Psychology 100:407-425, 2011a). In two of Bem's experiments, words were presented after target pictures in a pleasantness judgment task. In a condition in which the words were consistent with the emotional valence of the picture, reaction times to the pictures were significantly shorter , as compared with a condition in which the words were inconsistent with the emotional valence of the picture. Bem Journal of Personality and Social Psychology 100:407-425, (2011a) interpreted these results as showing a "retroactive priming" effect resulting from precognition. To test the precognition hypothesis, we adapted a standard repetition priming paradigm from psycholinguistics. In the experiments, participants read a set of texts. In one condition, the participants read the same text twice. In other conditions, participants read two different texts. The precognition hypothesis predicts that readers who encounter the same text twice will experience reductions in processing load during their first encounter with the text. Hence, these readers' average reading times should be shorter than those of readers who encounter the target text only once. Our results indicated that readers processed the target text faster the second time they read it. Also, their reading times decreased as their experience with the self-paced reading procedure increased. However, participants read the target text equally quickly during their initial encounter with the text, whether or not the text was subsequently repeated. Thus, the experiments demonstrated normal repetition priming and practice effects but offered no evidence for retroactive influences on text processing