Dense Packings of Congruent Circles in Rectangles with a Variable Aspect Ratio

We use computational experiments to find the rectangles of minimum area into which a given number n of non-overlapping congruent circles can be packed. No assumption is made on the shape of the rectangles. Most of the packings found have the usual regular square or hexagonal pattern. However, for 1495 values of n in the tested range n =< 5000, specifically, for n = 49, 61, 79, 97, 107,... 4999, we prove that the optimum cannot possibly be achieved by such regular arrangements. The evidence suggests that the limiting height-to-width ratio of rectangles containing an optimal hexagonal packing of circles tends to 2-sqrt(3) as n tends to infinity, if the limit exists.Comment: 21 pages, 13 figure

Waste Cellulose from Tetra Pak Packages as Reinforcement of Cement Concrete

The development of the packaging industry has promoted indiscriminately the use of disposable packing as Tetra Pak, which after a very short useful life turns into garbage, helping to spoil the environment. One of the known processes that can be used for achievement of the compatibility between waste materials and the environment is the gamma radiation, which had proved to be a good tool for modi cation of physicochemical properties of materials. The aim of this work is to study the e ects of waste cellulose fromTetra Pak packing and gammaradiation on themechanical properties of cement concrete.Concrete specimens were elaborated with waste cellulose at concentrations of 3, 5, and 7 wt% and irradiated at 200 , 250 , and 300 kGy of gamma dose. The results show highest improvement on the mechanical properties for concrete with 3 wt% of waste cellulose and irradiated at 300 kGy; such improvements were related with the surface morphology of fracture zones of cement concrete observed by SEM microscopy

Natural Stone Waste Powders Applied to SCC Mix Design

In order to comply with current trends concerning sustainability, saving of primary materials and energy\ud savings, this paper addresses Eco-concrete. The major focus thereby is on the increased efficiency of cement\ud use. Applying a new mix design method for concrete, cement contents can be decreased and partially be substituted\ud by other fine powders, preferentially by waste powders which have no mass application so far. This\ud paper is giving examples of successfully introduced waste powders and characterizes the concretes produced\ud with these powders. These innovative, low cement concrete types obtain medium strength and exhibit furthermore\ud self-compacting abilities. This paper additionally highlights possibilities for the direct use of natural\ud stone sludges or filter cakes. A new grading based design method, developed in the authors’ research\ud group, enables the efficient use of all materials available. The method is applicable to self-compacting concretes,\ud earth-moist concretes and conventionally vibrated concretes