Self-replicating cracks: a collaborative fracture mode in thin films

Straight cracks are observed in thin coatings under residual tensile stress, resulting into the classical network pattern observed in china crockery, old paintings or dry mud. Here, we present a novel fracture mechanism where delamination and propagation occur simultaneously, leading to the spontaneous self-replication of an initial template. Surprisingly, this mechanism is active below the standard critical tensile load for channel cracks and selects a robust interaction length scale on the order of 30 times the film thickness. Depending on triggering mechanisms, crescent alleys, spirals or long bands are generated over a wide range of experimental parameters. We describe with a simple physical model the selection of the fracture path and provide a configuration diagram displaying the different failure modes

Wrapping an adhesive sphere with a sheet

We study the adhesion of an elastic sheet on a rigid spherical substrate. Gauss'Theorema Egregium shows that this operation necessarily generates metric distortions (i.e. stretching) as well as bending. As a result, a large variety of contact patterns ranging from simple disks to complex branched shapes are observed as a function of both geometrical and material properties. We describe these different morphologies as a function of two non-dimensional parameters comparing respectively bending and stretching energies to adhesion. A complete configuration diagram is finally proposed

Optimização de Rotas: Aplicação à Recolha de Lixo do Concelho de Viseu

A sessão apresentada no âmbito das comemorações do Ana Mundial da Matemática, abordou o problema de organização do sistema de recolha de resíduos sólidos municipais do concelho de Viseu. A recolha de resíduos sólidos nos arredores de Viseu e na zona rural do concelho é executada pelos Serviços Municipalizados da Câmara Municipal de Viseu e efectuava-se em moldes que não serviam, nem a população abrangida, nem os funcionários da Câmara. Foi então desenvolvido um sistema de planeamento das rotas semanais ou diárias e definição do calendário das visitas a cada local, de modo a melhorar significativamente a situação então em vigor

Implications of ideas on super-hydrophobicity for water repellent soil

Water repellence is an important factor in soil erosion due to its role in inhibiting the re-establishment of vegetation after fire and due to its enhancement of run-off. Water repellence is studied across a range of diverse disciplines, such as chemistry, materials, textiles and soil and reclamation science. In recent years many basic studies of water repellence of materials have focused on the role of the sub-mm surface topography of a material in modifying the intrinsic hydrophobicity imparted by the surface chemistry to create super-hydrophobicity. In this report, we first illustrate the types of hydrophobic effects created by a suitable coupling of small scale surface topography with surface chemistry using three examples of materials: an etched metal, a foam and a micro-fabricated pillar structure. These examples demonstrate the general applicability of the ideas and suggest that they could apply to a granular material, such as a fine sandy soil, particularly when the grains have become coated with a hydrophobic layer. This applicability is confirmed by contact angle measurements of droplets of water on hydrophobic sand. A theoretical model describing the application of these ideas to a loose-packed, but regular, array of uniform spherical grains is then presented and discussed. When the grains are in a dry initial state the effect of the surface is to increase the apparent water repellence as observed through the contact angle. However, when the spaces between the grains are initially filled with water, the effect is to provide greater wetting. To qualitatively confirm the enhancement of contact angle caused by the granular structure, model surfaces using 600 µm and 250 µm hydrophobic glass beads were created. On these surfaces, the contact angle of droplets of water was increased from 108° to 126° and 140°, respectively

Vamos Jogar no Totoloto?

Tendo como objectivo despertar o interesse dos alunos pelo cálculo de probabilidades, as autoras desta sessão de trabalho, pegaram num tema bem conhecido de todos, o jogo do Totoloto, e fizeram dele um tema de trabalho em probabilidades para cerca de uma hora. As autoras começaram por despertar nos alunos a curiosidade por saber quais são as chances de ganhar o 1º, 2º, 3º, 4º e 5º prémio, no jogo do Totoloto, fazendo apenas uma aposta. Para alguns, o cálculo da probabilidade de ganhar o 1º prémio já não era novidade, mas o mesmo já não se passava no que diz respeito aos 2º, 3º, 4º e 5º prémios

Droplet actuation induced by coalescence: experimental evidences and phenomenological modeling

This paper considers the interaction between two droplets placed on a substrate in immediate vicinity. We show here that when the two droplets are of different fluids and especially when one of the droplet is highly volatile, a wealth of fascinating phenomena can be observed. In particular, the interaction may result in the actuation of the droplet system, i.e. its displacement over a finite length. In order to control this displacement, we consider droplets confined on a hydrophilic stripe created by plasma-treating a PDMS substrate. This controlled actuation opens up unexplored opportunities in the field of microfluidics. In order to explain the observed actuation phenomenon, we propose a simple phenomenological model based on Newton's second law and a simple balance between the driving force arising from surface energy gradients and the viscous resistive force. This simple model is able to reproduce qualitatively and quantitatively the observed droplet dynamics

Measuring Attitudes Towards Motorcycle Helmet Use in Laos

This paper examines attitude towards use of motorcycle helmet in Laos. A quantitative approach using the survey questionnaire method was adopted to assess this attitude. A total of 257 university students in Vientiane, Laos was interviewed. Forward translation, backward translation, and cognitive debriefing were carried out. Factor analysis of the principal components was also performed. The four-factor solution was used to explain the 58.867% of total variance. The correlation between items showed values between .01 and .566. The total item correlation values were between .129 and .566. Cronbach alpha coefficient was .764 for overall scale and between .801 and .601 on the four factors. Spearman Brown prediction formula was used to test psychometric properties and reliability of the items. A total of 17 items were considered reliable, such as such as susceptibility, trafficability, safety and usability, in determining overall attitudes of Laotians in using motorcycle helmet. These can be used in future research