From Vlasov fluctuations to the BGL kinetic equation

This paper shows that the spatially homogeneous Balescu-Guernsey-Lenard kinetic equation is associated, at least formally, with a stochastic process that arises naturally as the N →∞ limit of a certain N-particle Hamiltonian system. The process describes the long-time motion of a particle traveling in a Vlasov fluctuation field. The Fokker-Planck equation for the process coincides with the Balescu-Guernsey-Lenard equation whenever the solution is analytic in the velocity variables, but should also be considered as a model in its own right

GASP: Genetic algorithms for service placement in fog computing systems

Fog computing is becoming popular as a solution to support applications based on geographically distributed sensors that produce huge volumes of data to be processed and filtered with response time constraints. In this scenario, typical of a smart city environment, the traditional cloud paradigm with few powerful data centers located far away from the sources of data becomes inadequate. The fog computing paradigm, which provides a distributed infrastructure of nodes placed close to the data sources, represents a better solution to perform filtering, aggregation, and preprocessing of incoming data streams reducing the experienced latency and increasing the overall scalability. However, many issues still exist regarding the efficient management of a fog computing architecture, such as the distribution of data streams coming from sensors over the fog nodes to minimize the experienced latency. The contribution of this paper is two-fold. First, we present an optimization model for the problem of mapping data streams over fog nodes, considering not only the current load of the fog nodes, but also the communication latency between sensors and fog nodes. Second, to address the complexity of the problem, we present a scalable heuristic based on genetic algorithms. We carried out a set of experiments based on a realistic smart city scenario: the results show how the performance of the proposed heuristic is comparable with the one achieved through the solution of the optimization problem. Then, we carried out a comparison among different genetic evolution strategies and operators that identify the uniform crossover as the best option. Finally, we perform a wide sensitivity analysis to show the stability of the heuristic performance with respect to its main parameters

A distributed architecture to support infomobility services

The growing popularity of mobile and location aware devices allows the deployment of infomobility systems that provide access to information and services for the support of user mobility. Current systems for infomobility services assume that most information is already available on the mobile device and the device connectivity is used for receiving critical messages from a central server. However, we argue that the next generation of infomobility services will be characterized by collaboration and interaction among the users, provided through real-time bidirectional communication between the client devices and the infomobility system.In this paper we propose an innovative architecture to support next generation infomobility services providing interaction and collaboration among the mobile users that can travel by several different transportation means, ranging from cars to trains to foot. We discuss the design issues of the architecture, with particular emphasis on scalability, availability and user data privacy, which are critical in a collaborative infomobility scenario. Copyright 2006 ACM

Use of Foundry Sands in the Production of Ceramic and Geopolymers for Sustainable Construction Materials

The aim of this research was to evaluate the possibility of reusing waste foundry sands derived from the production of cast iron as a secondary raw material for the production of building materials obtained both by high-temperature (ceramic tiles and bricks) and room-temperature (binders such as geopolymers) consolidation. This approach can reduce the current demand for quarry sand and/or aluminosilicate precursors from the construction materials industries. Samples for porcelain stoneware and bricks were produced, replacing the standard sand contained in the mixtures with waste foundry sand in percentages of 10%, 50%, and 100% by weight. For geopolymers, the sand was used as a substitution for metakaolin (30, 50, 70 wt%) as an aluminosilicate precursor rather than as an aggregate to obtain geopolymer pastes. Ceramic samples obtained using waste foundry sand were characterized by tests for linear shrinkage, water absorption, and colorimetry. Geopolymers formulations, produced with a Si/Al ratio of 1.8 and Na/Al = 1, were characterized to evaluate their chemical stability through measurements of pH and ionic conductivity, integrity in water, compressive strength, and microstructural analysis. The results show that the addition of foundry sand up to 50% did not significantly affect the chemical-physical properties of the ceramic materials. However, for geopolymers, acceptable levels of chemical stability and mechanical strength were only achieved when using samples made with 30% foundry sand as a replacement for metakaolin

Randomized Load Balancing under Loosely Correlated State Information in Fog Computing

Fog computing infrastructures must support increasingly complex applications where a large number of sensors send data to intermediate fog nodes for processing. As the load in such applications (as in the case of a smart cities scenario) is subject to significant fluctuations both over time and space, load balancing is a fundamental task. In this paper we study a fully distributed algorithm for load balancing based on random probing of the neighbors' status. A qualifying point of our study is considering the impact of delay during the probe phase and analyzing the impact of stale load information. We propose a theoretical model for the loss of correlation between actual load on a node and stale information arriving to the neighbors. Furthermore, we analyze through simulation the performance of the proposed algorithm considering a wide set of parameters and comparing it with an approach from the literature based on random walks. Our analysis points out under which conditions the proposed algorithm can outperform the alternatives

Models of interacting pairs of thin, quasi-geostrophic vortices: steady-state solutions and nonlinear stability

This work was supported by the Office of Naval Research under Grant N00014-11- 1-0087; the National Science Foundation under Grant 1107307; and the UK Engineering and Physical Sciences Research Council under grant EP/H001794/1.We study pairwise interactions of elliptical quasi-geostrophic vortices as the limiting case of vanishingly thin uniform potential vorticity ellipsoids. In this limit, the product of the vertical extent of the ellipsoid and the potential vorticity within it is held fixed to a finite non-zero constant. Such elliptical 'lenses' inherit the property that, in isolation, they steadily rotate without changing shape. Here, we use this property to extend both standard moment models and Hamiltonian ellipsoidal models to approximate the dynamical interaction of such elliptical lenses. By neglecting non-elliptical deformations, the simplified models reduce the dynamics to just four degrees of freedom per vortex. For simplicity, we focus on pairwise interactions between identical elliptical vortices initially separated in both the horizontal and vertical directions. The dynamics of the simplified models are compared with the full quasi-geostrophic (QG) dynamics of the system, and show good agreement as expected for sufficiently distant lenses. The results reveal the existence of families of steadily rotating equilibria in the initial horizontal and vertical separation parameter space. For sufficiently large vertical separations, equilibria with varying shape exist for all horizontal separations. Below a critical vertical separation (stretched by the constant ratio of buoyancy to Coriolis frequencies N/f), comparable to the mean radius of either vortex, a gap opens in horizontal separation where no equilibria are possible. Solutions near the edge of this gap are unstable. In the full QG system, equilibria at the edge of the gap exhibit corners (infinite curvature) along their boundaries. Comparisons of the model results with the full nonlinear QG evolution show that the early stages of the instability are captured by the Hamiltonian elliptical model but not by the moment model that inaccurately estimates shorter-range interactions.Publisher PDFPeer reviewe

A Location-allocation model for fog computing infrastructures

The trend of an ever-increasing number of geographically distributed sensors producing data for a plethora of applications, from environmental monitoring to smart cities and autonomous driving, is shifting the computing paradigm from cloud to fog. The increase in the volume of produced data makes the processing and the aggregation of information at a single remote data center unfeasible or too expensive, while latency-critical applications cannot cope with the high network delays of a remote data center. Fog computing is a preferred solution as latency-sensitive tasks can be moved closer to the sensors. Furthermore, the same fog nodes can perform data aggregation and filtering to reduce the volume of data that is forwarded to the cloud data centers, reducing the risk of network overload. In this paper, we focus on the problem of designing a fog infrastructure considering both the location of how many fog nodes are required, which nodes should be considered (from a list of potential candidates), and how to allocate data flows from sensors to fog nodes and from there to cloud data centers. To this aim, we propose and evaluate a formal model based on a multi-objective optimization problem. We thoroughly test our proposal for a wide range of parameters and exploiting a reference scenario setup taken from a realistic smart city application. We compare the performance of our proposal with other approaches to the problem available in literature, taking into account two objective functions. Our experiments demonstrate that the proposed model is viable for the design of fog infrastructure and can outperform the alternative models, with results that in several cases are close to an ideal solution

On the master equation approach to kinetic theory: linear and nonlinear Fokker--Planck equations

We discuss the relationship between kinetic equations of the Fokker-Planck type (two linear and one non-linear) and the Kolmogorov (a.k.a. master) equations of certain N-body diffusion processes, in the context of Kac's "propagation of chaos" limit. The linear Fokker-Planck equations are well-known, but here they are derived as a limit N->infty of a simple linear diffusion equation on (3N-C)-dimensional N-velocity spheres of radius sqrt(N) (with C=1 or 4 depending on whether the system conserves energy only or energy and momentum). In this case, a spectral gap separating the zero eigenvalue from the positive spectrum of the Laplacian remains as N->infty,so that the exponential approach to equilibrium of the master evolution is passed on to the limiting Fokker-Planck evolution in R^3. The non-linear Fokker-Planck equation is known as Landau's equation in the plasma physics literature. Its N-particle master equation, originally introduced (in the 1950s) by Balescu and Prigogine (BP), is studied here on the (3N-4)-dimensional N-velocity sphere. It is shown that the BP master equation represents a superposition of diffusion processes on certain two-dimensional sub-manifolds of R^{3N} determined by the conservation laws for two-particle collisions. The initial value problem for the BP master equation is proved to be well-posed and its solutions are shown to decay exponentially fast to equilibrium. However, the first non-zero eigenvalue of the BP operator is shown to vanish in the limit N->infty. This indicates that the exponentially fast approach to equilibrium may not be passed from the finite-N master equation on to Landau's nonlinear kinetic equation.Comment: 20 pages; based on talk at the 18th ICTT Conference. Some typos and a few minor technical fixes. Modified title slightl

Phase transition in the collisionless regime for wave-particle interaction

Gibbs statistical mechanics is derived for the Hamiltonian system coupling self-consistently a wave to N particles. This identifies Landau damping with a regime where a second order phase transition occurs. For nonequilibrium initial data with warm particles, a critical initial wave intensity is found: above it, thermodynamics predicts a finite wave amplitude in the limit of infinite N; below it, the equilibrium amplitude vanishes. Simulations support these predictions providing new insight on the long-time nonlinear fate of the wave due to Landau damping in plasmas.Comment: 12 pages (RevTeX), 2 figures (PostScript