Existence of weak solutions for a general porous medium equation with nonlocal pressure

We study the general nonlinear diffusion equation $u_t=\nabla\cdot (u^{m-1}\nabla (-\Delta)^{-s}u)$ that describes a flow through a porous medium which is driven by a nonlocal pressure. We consider constant parameters $m>1$ and $01$ by developing a new approximating method that allows to treat the range $m\ge 3$ that could not be covered by previous works. We also consider as initial data any non-negative measure $\mu$ with finite mass. In passing from bounded initial data to measure data we make strong use of an $L^1$-$L^\infty$ smoothing effect and other functional inequalities. Finite speed of propagation is established for all $m\ge 2$, which implies the existence of free boundaries. The authors had already proved that finite propagation does not hold for $m<2$

Rate of Convergence to Barenblatt Profiles for the Fast Diffusion Equation

We study the asymptotic behaviour of positive solutions of the Cauchy problem for the fast diffusion equation near the extinction time. We find a continuum of rates of convergence to a self-similar profile. These rates depend explicitly on the spatial decay rates of initial data

Refined asymptotics for the infinite heat equation with homogeneous Dirichlet boundary conditions

The nonnegative viscosity solutions to the infinite heat equation with homogeneous Dirichlet boundary conditions are shown to converge as time increases to infinity to a uniquely determined limit after a suitable time rescaling. The proof relies on the half-relaxed limits technique as well as interior positivity estimates and boundary estimates. The expansion of the support is also studied

The Medianet Project: Integration of Multimedia Services for the next Generations Business oriented Internet

This work is at: 10th IEEE International Symposium on Parallel and Distributed Processing with Applications, took place July 10-13, 2012 in Madrid, Spain.This article gathers the foundational premises of the MEDIANET project as well as intermediate results obtained along its firsts two years. MEDIANET is a Spanish project founded by the Comunidad de Madrid government, which strives for a significant scientific advance in the future media Internet where important advances are necessary to allow end-users to perceive a good quality of experience. The network technologies objectives consist of the definition and validation of new proposals for the efficient transport of high bandwidth, real-time data flows in a decentralized way where the network provides mechanisms to seamlessly request and configure devices to increase the quality of experience perceived by end-users. Furthermore, new experiences with layer 2 networks and a cross-layer design will be tested with high bandwidth demanding media services. An important objective is to develop, evaluate in depth and implement on diverse platforms , a new low latency transparent bridge protocol based in on-demand path set up, suitable for campus and data center networks. The global result will be an integrated and independent advancement in future media Internet protocols, algorithms, switching architectures and standards.The funds for the MEDIANET project are provided by the Comunidad de Madrid government under reference number S2009/TIC-1468.Publicad

Large N limit of Extremal Non-supersymmetric Black Holes

The large N limit of extremal non-supersymmetric Type-I five-dimensional string black holes is studied from the point of view of D-branes. We find that the agreement between the D-brane and the black-hole picture is due to an asymptotic restoration of supersymmetry in the large $N$ limit in which both pictures are compared. In that limit Type-I string perturbation theory is effectively embedded into a Type-IIB perturbation theory with unbroken supersymmetric charges whose presence guarantees the non-renormalization of mass and entropy as the effective couplings are increased. In this vein, we also study the near-horizon geometry of the Type-I black hole using D5-brane probes to find that the low energy effective action for the probe is identical to the corresponding one in the auxiliary Type-IIB theory in the large N limit.Comment: 25 pages, harvmac, typos corrected and references adde

Projecting more sustainable product and service designs

Product and service development based on sustainable criteria is one of the poles of innovation in design activity. Public policies, consumer preferences, and corporate social responsibility lead to the growing importance of applying sustainability principles in the current design process. However, to make this practice widespread, sustainability assessment must be included in the curricula of bachelor’s and master’s degrees in design, so that the graduates have the precise tools to use when they start their professional careers. Furthermore, sustainable design methods have mainly been applied to improve only the environmental behavior of products. In this work, a methodology that simultaneously evaluates environmental, economic, and social aspects was applied to project more sustainable designs of products and services. This approach was implemented in higher education to develop Bachelor’s and Master’s degree final projects by design engineering students. Collaboration with different companies and institutions allowed the study of a number of cases. The production process of a cash management machine, the service provided by a public nursery school, and the development of an itinerary exhibition were addressed. In each case, product and service requirements were analyzed, sustainability indicators were obtained, and more sustainable designs could be proposed. This experience is also part of a global strategy at the University of Zaragoza to support the implementation of the UN’s Sustainable Development Goals, enhancing sustainability education. The intention of this paper is to present a methodology for more sustainable design, and examples of its application that other teachers can easily follow when teaching design of products or services. © 2021 by the authors. Licensee MDPI, Basel, Switzerland

Thermal-aware real-time scheduling using timed continuous Petri Nets

We present a thermal-aware, hard real-time (HRT) global scheduler for a multiprocessor system designed upon three novel techinques. First, we present a modeling methodology based on Timed Continuous Petri nets (TCPN) that yields a complete state variable model, including job arrivals, CPU usage, power, and thermal behavior. The model is accurate and avoids the calibration stage of RC thermal models. Second, based on this model, a linear programming problem (LPP) determines the existence of a feasible HRT thermal-aware schedule. Last, a sliding-mode controller and an online discretization algorithm implement the global HRT scheduler, which is capable of managing thermal constraints, context switching, migrations, and disturbances

Some remarks on the isoperimetric problem for the higher eigenvalues of the Robin and Wentzell Laplacians

We consider the problem of minimising the $k$th eigenvalue, $k \geq 2$, of the ($p$-)Laplacian with Robin boundary conditions with respect to all domains in $\mathbb{R}^N$ of given volume $M$. When $k=2$, we prove that the second eigenvalue of the $p$-Laplacian is minimised by the domain consisting of the disjoint union of two balls of equal volume, and that this is the unique domain with this property. For $p=2$ and $k \geq 3$, we prove that in many cases a minimiser cannot be independent of the value of the constant $\alpha$ in the boundary condition, or equivalently of the volume $M$. We obtain similar results for the Laplacian with generalised Wentzell boundary conditions $\Delta u + \beta \frac{\partial u}{\partial \nu} + \gamma u = 0$.Comment: 16 page

An Analytical Framework to Describe the Interactions Between Individuals and a Continuum

We consider a discrete set of individual agents interacting with a continuum. Examples might be a predator facing a huge group of preys, or a few shepherd dogs driving a herd of sheeps. Analytically, these situations can be described through a system of ordinary differential equations coupled with a scalar conservation law in several space dimensions. This paper provides a complete well posedness theory for the resulting Cauchy problem. A few applications are considered in detail and numerical integrations are provided

iCanCloud: a flexible and scalable cloud infrastructure simulator

Simulation techniques have become a powerful tool for deciding the best starting conditions on pay-as-you-go scenarios. This is the case of public cloud infrastructures, where a given number and type of virtual machines (in short VMs) are instantiated during a specified time, being this reflected in the final budget. With this in mind, this paper introduces and validates iCanCloud, a novel simulator of cloud infrastructures with remarkable features such as flexibility, scalability, performance and usability. Furthermore, the iCanCloud simulator has been built on the following design principles: (1) it's targeted to conduct large experiments, as opposed to others simulators from literature; (2) it provides a flexible and fully customizable global hypervisor for integrating any cloud brokering policy; (3) it reproduces the instance types provided by a given cloud infrastructure; and finally, (4) it contains a user-friendly GUI for configuring and launching simulations, that goes from a single VM to large cloud computing systems composed of thousands of machines.This research was partially supported by the following projects: Spanish MEC project TESIS (TIN2009-14312-C02-01), and Spanish Ministry of Science and Innovation under the grant TIN2010-16497.Publicad