05391 Abstracts Collection -- Algebraic and Numerical Algorithms and Computer-assisted Proofs

From 25.09.05 to 30.09.05, the Dagstuhl Seminar 05391 ``Algebraic and Numerical Algorithms and Computer-assisted Proofs\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. Links to extended abstracts or full papers are provided, if available

05391 Executive Summary -- Numerical and Algebraic Algorithms and Computer-assisted Proofs

The common goal of self-validating methods and computer algebra methods is to solve mathematical problems with complete rigor and with the aid of computers. The seminar focused on several aspects of such methods for computer-assisted proofs

A Hopf bifurcation in the planar Navier-Stokes equations

We consider the Navier-Stokes equation for an incompressible viscous fluid on a square, satisfying Navier boundary conditions and being subjected to a time-independent force. As the kinematic viscosity is varied, a branch of stationary solutions is shown to undergo a Hopf bifurcation, where a periodic cycle branches from the stationary solution. Our proof is constructive and uses computer-assisted estimates.Comment: 16 pages, 1 figur

The confined Muskat problem: differences with the deep water regime

We study the evolution of the interface given by two incompressible fluids with different densities in the porous strip \RR\times[-l,l]. This problem is known as the Muskat problem and is analogous to the two phase Hele-Shaw cell. The main goal of this paper is to compare the qualitative properties between the model when the fluids move without boundaries and the model when the fluids are confined. We find that, in a precise sense, the boundaries decrease the diffusion rate and the system becomes more singular.Comment: Revised version. 32 pages, 4 figure

On turning waves for the inhomogeneous Muskat problem: a computer-assisted proof

We exhibit a family of graphs that develop turning singularities (i.e. their Lipschitz seminorm blows up and they cease to be a graph, passing from the stable to the unstable regime) for the inhomogeneous, two-phase Muskat problem where the permeability is given by a nonnegative step function. We study the influence of different choices of the permeability and different boundary conditions (both at infinity and considering finite/infinite depth) in the development or prevention of singularities for short time. In the general case (inhomogeneous, confined) we prove a bifurcation diagram concerning the appearance or not of singularities when the depth of the medium and the permeabilities change. The proofs are carried out using a combination of classical analysis techniques and computer-assisted verification.Comment: 30 pages, 6 figure

Rigorous numerics for analytic solutions of differential equations : the radii polynomial approach

Judicious use of interval arithmetic, combined with careful pen and paper estimates, leads to effective strategies for computer assisted analysis of nonlinear operator equations. The method of radii polynomials is an efficient tool for bounding the smallest and largest neighborhoods on which a Newton-like operator associated with a nonlinear equation is a contraction mapping. The method has been used to study solutions of ordinary, partial, and delay differential equations such as equilibria, periodic orbits, solutions of initial value problems, heteroclinic and homoclinic connecting orbits in the Ck category of functions. In the present work we adapt the method of radii polynomials to the analytic category. For ease of exposition we focus on studying periodic solutions in Cartesian products of infinite sequence spaces. We derive the radii polynomials for some specific application problems and give a number of computer assisted proofs in the analytic framework

Fluid flow modeling inside heat collection pipes with finite element method

Builders and heat pump and pipe manufactures have faced new challenges as the demand on efficiency has become greater in the geoenergy sector. One method that can be used for increasing the heat transfer capacity in the heat collection systems is to use twisted tape or axially placed fins inside heat collection pipes. These inner structure modifications increase turbulent flow behavior which increases the heat transfer effect by force of convection. The aim of this thesis was to model fluid flow behavior inside the heat collection pipes with the finite element method. The most important properties which need to be taken into account in order the heat collection fluid flow to be rather turbulent than laminar, are analyzed. The analysis consists of modeling with COMSOL Multiphysics. COMSOL Multiphysics is a finite element method - based on modeling and simulation software. In this thesis flow behavior inside heat collection pipes with different inner surface structures was modeled. The aim was to find out what kind of flow environment would turn the flow from laminar to turbulent inside the heat collection pipes. Also how the pressure drop and pumping power vary when the inner profile of the heat collection pipe changes is examined. The models that have been built are meant to be mainly indicative. The aim of this thesis was not to design a completely new pipe profile. The aim of this thesis was to demonstrate how turbulent flow behavior in the heat collection pipes of a ground source heat pump system can be achieved. COMSOL models showed that a minor inner surface modification increases turbulence inside the heat collection pipes. The models and results discussed in this thesis are well known and very common in heat recovery engineering solutions, but they have not been discussed before in the field of ground source heat pump systems and heat collection pipes.fi=Opinnäytetyö kokotekstinä PDF-muodossa.|en=Thesis fulltext in PDF format.|sv=Lärdomsprov tillgängligt som fulltext i PDF-format

SciTech News Volume 70, No. 4 (2016)

Columns and Reports From the Editor 3 Division News Science-Technology Division 4 SLA Annual Meeting 2016 Report (S. Kirk Cabeen Travel Stipend Award recipient) 6 Reflections on SLA Annual Meeting (Diane K. Foster International Student Travel Award recipient) 8 SLA Annual Meeting Report (Bonnie Hilditch International Librarian Award recipient)10 Chemistry Division 12 Engineering Division 15 Reflections from the 2016 SLA Conference (SPIE Digital Library Student Travel Stipend recipient)15 Fundamentals of Knowledge Management and Knowledge Services (IEEE Continuing Education Stipend recipient) 17 Makerspaces in Libraries: The Big Table, the Art Studio or Something Else? (by Jeremy Cusker) 19 Aerospace Section of the Engineering Division 21 Reviews Sci-Tech Book News Reviews 22 Advertisements IEEE 17 WeBuyBooks.net 2