The typical cell in anisotropic tessellations

The typical cell is a key concept for stochastic-geometry based modeling in communication networks, as it provides a rigorous framework for describing properties of a serving zone associated with a component selected at random in a large network. We consider a setting where network components are located on a large street network. While earlier investigations were restricted to street systems without preferred directions, in this paper we derive the distribution of the typical cell in Manhattan-type systems characterized by a pattern of horizontal and vertical streets. We explain how the mathematical description can be turned into a simulation algorithm and provide numerical results uncovering novel effects when compared to classical isotropic networks.Comment: 7 pages, 7 figure

Magnetoviscous Effects of Magnetized Particle Threads in Magnetized Ferrofluid

The magnetoviscous effect of applied fields on ferrofluids has been utilized in many applications in which the ferrofluid must remain in a fixed position while this effect on ferrofluids in motion has yet to be rigorously explored. In light of potential biomedical applications such as drug targeting, experiments were conducted to probe the rheology of ferrofluids on the micrometer scale. A non-conducting glass sphere of diameter 550 μm is dropped into a cylindrical container of magnetized ferrofluid of inner diameter 5.2 mm. This was repeated for two applied field strengths (980 gauss and 480 gauss) and over multiple angles with both a 4: 1 diluted ferrofluid and a 4: 1 diluted ferrofluid that had the larger particles removed (purified). Data from dilute ferrofluid show an angle-dependent in magnetized ferrofluid where maximal drag is attained when the applied field and the direction of the falling sphere are perpendicular to each other. This angle-dependence was not present in the purified ferrofluid which displayed a near-constant drag across all angles. These two results indicate that the main component of the drag experienced in the magnetized ferrofluid is due to the formation of magnetized particle threads within the ferrofluid and that large-diameter particles are responsible for this thread formation. A mathematical model was developed that formulates the drag as a fluid interaction between the array of threads within the ferrofluid and the Stokes flow due to the falling sphere. The model captures the angle-dependence seen in the experiments. The model results for falling spheres of multiple radii in a cylinder are qualitatively similar to those of uniform flow in a cylinder, implying that relative drag increases are mainly dependent upon sphere radius and negligibly affected by flow profile and wall effects

Concert recording 2016-12-08

[Track 1]. Traditional Taiwanese melodies for two flutes / Gary Schocker -- [Track 2]. The lotus pond (Bohayrat al-lotus) / Gamal Abdel-Rahim -- [Track 3]. Pièce pour flûte seule / Jacques Ibert -- [Track 4]. Maya / Ian Clarke -- [Track 5]. Flute sonata in A minor / Carl Phillip Emanuel Bach -- [Track 6]. Lament for Michelle / Theodore Antoniou -- [Track 7]. Whippoorwill cokpelvpelv / Grace Wiley Smith -- [Track 8]. Fantasie / Gabriel Fauré

The typical cell in anisotropic tessellations

The typical cell is a key concept for stochastic-geometry based modeling in communication networks, as it provides a rigorous framework for describing properties of a serving zone associated with a component selected at random in a large network. We consider a setting where network components are located on a large street network. While earlier investigations were restricted to street systems without preferred directions, in this paper we derive the distribution of the typical cell in Manhattan-type systems characterized by a pattern of horizontal and vertical streets. We explain how the mathematical description can be turned into a simulation algorithm and provide numerical results uncovering novel effects when compared to classical isotropic networks

Chase-escape in dynamic device-to-device networks

The present paper features results on global survival and extinction of an infection in a multi-layer network of mobile agents. Expanding on a model first presented in CHJW22, we consider an urban environment, represented by line-segments in the plane, in which agents move according to a random waypoint model based on a Poisson point process. Whenever two agents are at sufficiently close proximity for a sufficiently long time the infection can be transmitted and then propagates into the system according to the same rule starting from a typical device. Inspired by wireless network architectures, the network is additionally equipped with a second class of agents that is able to transmit a patch to neighboring infected agents that in turn can further distribute the patch, leading to a chase-escape dynamics. We give conditions for parameter configurations that guarantee existence and absence of global survival as well as an in-and-out of the survival regime, depending on the speed of the devices. We also provide complementary results for the setting in which the chase-escape dynamics is defined as an independent process on the connectivity graph. The proofs mainly rest on percolation arguments via discretization and multiscale analysis

Malware propagation in urban D2D networks

We introduce and analyze models for the propagation of malware in pure D2D networks given via stationary Cox--Gilbert graphs. Here, the devices form a Poisson point process with random intensity measure λ, Λ where Λ is stationary and given, for example, by the edge-length measure of a realization of a Poisson--Voronoi tessellation that represents an urban street system. We assume that, at initial time, a typical device at the center of the network carries a malware and starts to infect neighboring devices after random waiting times. Here we focus on Markovian models, where the waiting times are exponential random variables, and non-Markovian models, where the waiting times feature strictly positive minimal and finite maximal waiting times. We present numerical results for the speed of propagation depending on the system parameters. In a second step, we introduce and analyze a counter measure for the malware propagation given by special devices called white knights, which have the ability, once attacked, to eliminate the malware from infected devices and turn them into white knights. Based on simulations, we isolate parameter regimes in which the malware survives or is eliminated, both in the Markovian and non-Markovian setting

Phase transitions for chase-escape models on Poisson–Gilbert graphs

We present results on phase transitions of local and global survival in a two-species model on Poisson–Gilbert graphs. Initially, there is an infection at the origin that propagates on the graph according to a continuous-time nearest-neighbor interacting particle system. The graph consists of susceptible nodes and nodes of a second type, which we call white knights. The infection can spread on susceptible nodes without restriction. If the infection reaches a white knight, this white knight starts to spread on the set of infected nodes according to the same mechanism, with a potentially different rate, giving rise to a competition of chase and escape. We show well-definedness of the model, isolate regimes of global survival and extinction of the infection and present estimates on local survival. The proofs rest on comparisons to the process on trees, percolation arguments and finite-degree approximations of the underlying random graphs

Connectivity in mobile device-to-device networks in urban environments

In this article we setup a dynamic device-to-device communication system where devices, given as a Poisson point process, move in an environment, given by a street system of random planar-tessellation type, via a random-waypoint model. Every device independently picks a target location on the street system using a general waypoint kernel, and travels to the target along the shortest path on the streets with an individual velocity. Then, any pair of devices becomes connected whenever they are on the same street in sufficiently close proximity, for a sufficiently long time. After presenting some general properties of the multi-parameter system, we focus on an analysis of the clustering behavior of the random connectivity graph. In our main results we isolate regimes for the almost-sure absence of percolation if, for example, the device intensity is too small, or the connectivity time is too large. On the other hand, we exhibit parameter regimes of sufficiently large intensities of devices, under favorable choices of the other parameters, such that percolation is possible with positive probability. Most interestingly, we also show an in-and-out of percolation as the velocity increases. The rigorous analysis of the system mainly rests on comparison arguments with simplified models via spatial coarse graining and thinning approaches. Here we also make contact to geostatistical percolation models with infinite-range dependencies

Phase transitions for chase-escape models on Gilbert graphs

We present results on phase transitions of local and global survival in a two-species model on Gilbert graphs. At initial time there is an infection at the origin that propagates on the Gilbert graph according to a continuous-time nearest-neighbor interacting particle system. The Gilbert graph consists of susceptible nodes and nodes of a second type, which we call white knights. The infection can spread on susceptible nodes without restriction. If the infection reaches a white knight, this white knight starts to spread on the set of infected nodes according to the same mechanism, with a potentially different rate, giving rise to a competition of chase and escape. We show well-definedness of the model, isolate regimes of global survival and extinction of the infection and present estimates on local survival. The proofs rest on comparisons to the process on trees, percolation arguments and finite-degree approximations of the underlying random graphs.Comment: 13 pages, 3 figure

Concert recording 2016-05-04

[Track 01]. Duo for flute and piano. Flowing ; [Track 02]. Poetic, somewhat mournful ; Lively, with bounce / Aaron Copland -- [Track 03]. Serenade no. 10, op. 79. Larghetto ; [Track 04]. Allegro comodo ; [Track 05]. Andante grazioso ; [Track 06]. Andante cantabile ; [Track 07]. Allegretto ; [Track 08]. Scherzando ; [Track 09]. Adagietto ; [Track 10]. Vivo / Vincent Persichetti -- [Track 11]. Toward the sea. The night ; [Track 12]. Moby Dick ; [Track 13]. Cape Cod / Toru Takemitsu -- [Track 14]. Oshokun (Lady Wang Zhao Jun) / unknown -- [Track 15]. Horai, traditional honkyoku original pieces of the Kokutai-ji school / unknown -- [Track 16]. Flute sonata in D, op. 94. Moderato ; [Track 17]. Scherzo : presto ; [Track 18]. Andante ; [Track 19]. Allegro con brio / Sergei Prokofiev