In this paper, a hybrid Lagrangian–Eulerian topology optimization (LETO) method is proposed to solve the elastic force equilibrium with Material Point Method (MPM). LETO transfers density information from freely movable Lagrangian carrier particles fixed set of Eulerian quadrature points. This transfer based on smooth radial kernel involved in compliance objective avoid artificial checkerboard ...

Tiling pervades the art and architecture of various ancient civilizations. Toddlers grapple with tiling problems when they pack away their wooden blocks and home renovators encounter similar problems in the bathroom. However, rather than being a frivolous pastime, mathematicians have found the art of tiling to be brimming with beautiful mathematics, problems of fiendish difficulty, as well as i...

1. Abstract Traditionally, standard Lagrangian-type finite elements, such as linear quads and triangles, have been the elements of choice in the field of topology optimization. In general, finite element meshes with these elements exhibit the well-known checkerboard pathology in the iterative solution of topology optimization problems. Voronoi and Wachspress-type finite elements are less suscep...

The persistence of a spatially structured population is determined by the rate of dispersal among habitat patches. If the local dynamic at the subpopulation level is extinction-prone, the system viability is maximal at intermediate connectivity where recolonization is allowed, but full synchronization that enables correlated extinction is forbidden. Here we developed and used an algorithm for a...

It is known that the area of all Catalan paths of length n is equal to 4− ` 2n+1

This note derives the characteristic polynomial of a graph that represents nonjump moves in a generalized game of checkers. The number of spanning trees is also determined.

Context. We present the results of the first laboratory experiment of checkerboard shaped pupil binary mask coronagraphs using visible light, in the context of the R&D activities for future mid-infrared space missions such as the 3.5 m SPICA telescope. Aims. The primary aim of this work is to demonstrate the coronagraphic performance of checkerboard masks down to a 10 −6 peak-to-peak contrast, ...

Sophoraflavanone B (SPF-B), a known prenylated flavonoid, was isolated from the roots of Desmodium caudatum. The aim of this study was to determine the antimicrobial synergism of SPF-B combined with antibiotics against methicillin-resistant Staphylococcus aureus (MRSA). MRSA, a multidrug-resistant pathogen, causes both hospital- and community-acquired infections worldwide. The antimicrobial act...

BACKGROUND There are several synergistic methods available. However, there is a vast discrepancy in the interpretation of the synergistic results. Also, these synergistic methods do not assess the influence the tested components (drugs, plant and natural extracts), have upon one another, when more than two components are combined. METHODS A modified checkerboard method was used to evaluate th...

Thermodynamic quantities and correlation functions (CFs) of the classical antiferromagnet on the checkerboard lattice are studied for the exactly solvable infinite-component spin-vector model, D → ∞. In contrast to conventional two-dimensional magnets with continuous symmetry showing extended short-range order at distances smaller than the correlation length, r ∼ ξc ∝ exp(T /T ), correlations i...