Relaxation through homogenization for optimal design problems with gradient constraints

The problem of the relaxation of optimal design problems for multiphase composite structures in the presence of constraints on the gradient of the state variable is addressed. A relaxed formulation for the problem is given in the presence of either a finite or infinite number of constraints. The relaxed formulation is used to identify minimizing sequences of configurations of phases

Tevatron Detector Upgrades

The D0 and CDF experiments are in the process of upgrading their detectors to cope with the high luminosities projected for the remainder of Tevatron Run II. They discuss the expected Tevatron environment through 2009, the detector challenges due to increasing luminosity in this period, and the solutions undertaken by the two experiments to mitigate detector problems and maximize physics results

Inverse homogenization and design of microstructure for pointwise stress control

New higher-order homogenization results are employed in an inverse homogenization procedure to identify graded microstructures that provide desirable structural response while ensuring stress control near joints or junctions between structural elements. The methodology is illustrated for long cylindrical shafts reinforced with stiff cylindrical elastic fibres with generators parallel to the shaft. The local fibre geometry can change across the shaft cross-section. The methodology is implemented numerically for cross-sectional shapes that possesses reentrant corners typically seen in lap joints and junctions of struts. Graded locally layered microgeometries are identified that provide the required structural rigidity with respect to torsion loading while at the same time mitigating the influence of stress concentrations at the reentrant corners. © The Author 2005. Published by Oxford University Press; all rights reserved

Tunable Double Negative Band Structure from Non-Magnetic Coated Rods

A system of periodic poly-disperse coated nano-rods is considered. Both the coated nano-rods and host material are non-magnetic. The exterior nano-coating has a frequency dependent dielectric constant and the rod has a high dielectric constant. A negative effective magnetic permeability is generated near the Mie resonances of the rods while the coating generates a negative permittivity through a field resonance controlled by the plasma frequency of the coating and the geometry of the crystal. The explicit band structure for the system is calculated in the sub-wavelength limit. Tunable pass bands exhibiting negative group velocity are generated and correspond to simultaneously negative effective dielectric permittivity and magnetic permeability. These can be explicitly controlled by adjusting the distance between rods, the coating thickness, and rod diameters

Finite element approximation of nonlocal dynamic fracture models

In this work we estimate the convergence rate for time stepping schemes applied to nonlocal dynamic fracture modeling. Here we use the nonlocal formulation given by the bond based peridynamic equation of motion. We begin by establishing the existence of H2 peridynamic solutions over any finite time interval. For this model the gradients can become large and steep slopes appear and localize when the non-locality of the model tends to zero. In this treatment spatial approximation by finite elements are used. We consider the central-difference scheme for time discretization and linear finite elements for discretization in the spatial variable. The fully discrete scheme is shown to converge to the actual H2 solution in the mean square norm at the rate CtΔt + Csh2=/2. Here h is the mesh size, Δ is the length scale of nonlocal interaction and Δt is the time step. The constants Ct and Cs are independent of Δt, and h. In the absence of nonlinearity a CFL like condition for the energy stability of the central difference time discretization scheme is developed. As an example we consider Plexiglass and compute constants in the a-priori error bound

Heuristic algorithms for the min-max edge 2-coloring problem

In multi-channel Wireless Mesh Networks (WMN), each node is able to use multiple non-overlapping frequency channels. Raniwala et al. (MC2R 2004, INFOCOM 2005) propose and study several such architectures in which a computer can have multiple network interface cards. These architectures are modeled as a graph problem named \emph{maximum edge $q$-coloring} and studied in several papers by Feng et. al (TAMC 2007), Adamaszek and Popa (ISAAC 2010, JDA 2016). Later on Larjomaa and Popa (IWOCA 2014, JGAA 2015) define and study an alternative variant, named the \emph{min-max edge $q$-coloring}. The above mentioned graph problems, namely the maximum edge $q$-coloring and the min-max edge $q$-coloring are studied mainly from the theoretical perspective. In this paper, we study the min-max edge 2-coloring problem from a practical perspective. More precisely, we introduce, implement and test four heuristic approximation algorithms for the min-max edge $2$-coloring problem. These algorithms are based on a \emph{Breadth First Search} (BFS)-based heuristic and on \emph{local search} methods like basic \emph{hill climbing}, \emph{simulated annealing} and \emph{tabu search} techniques, respectively. Although several algorithms for particular graph classes were proposed by Larjomaa and Popa (e.g., trees, planar graphs, cliques, bi-cliques, hypergraphs), we design the first algorithms for general graphs. We study and compare the running data for all algorithms on Unit Disk Graphs, as well as some graphs from the DIMACS vertex coloring benchmark dataset.Comment: This is a post-peer-review, pre-copyedit version of an article published in International Computing and Combinatorics Conference (COCOON'18). The final authenticated version is available online at: http://www.doi.org/10.1007/978-3-319-94776-1_5