Images in Christmas Balls

We describe light-reflection properties of spherically curved mirrors, like balls in the Christmas tree. In particular, we study the position of the image which is formed somewhere beyond the surface of a spherical mirror, when an eye observes the image of a pointlike light source. The considered problem, originally posed by Abu Ali Hasan Ibn al-Haitham -- alias Alhazen -- more than a millennium ago, turned out to have the now well known analytic solution of a biquadratic equation, being still of great relevance, e.g. for the aberration-free construction of telescopes. We do not attempt to perform an exhaustive survey of the rich historical and engineering literature on the subject, but develop a simple pedagogical approach to the issue, which we believe to be of continuing interest in view of its maltreating in many high-school textbooks.Comment: 13 pages, 7 figures plain LaTeX; Also see http://cft.fis.uc.pt/eef/mirrors.htm, revised version has simplified formulas, more transparent for a wider audience, one reference adde

Characterizing and modeling the apparent anomalous behavior of resistivity in Cr–Si–O thin films

The Cr-Si-O material system is of interest for use as a thin film resistor. The films are sputter deposited onto conducting substrates from metal oxide compacts using a reactive gas mixture. the cermet films composition range from 50 to 100 vol.% SiO{sub 2} as determined from elemental measurements of the Cr, Si and O content. In a wide range of resistivities from 10{sup 1} to 10 {sup 14} {omega}-cm measured through the film thickness, an apparent anomalous behavior is found with the Cr, Si and O composition. The anomaly can be deducted to a discontinuous variation of resistivity with film composition near 80 vol.% SiO{sub 2}. The film microstructure is characterized as a distribution of conducting metal-silicide particles within an insulating matrix. The effective medium theory is used to predict the variation of conductivity and successfully models the anomalous resistivity behavior

Working with simple machines

A set of examples is provided that illustrate the use of work as applied to simple machines. The ramp, pulley, lever and hydraulic press are common experiences in the life of a student and their theoretical analysis therefore makes the abstract concept of work more real. The mechanical advantage of each of these systems is also discussed so that students can evaluate their usefulness as machines.Comment: 9 pages, 4 figure

Simultaneous free-volume modeling of the self-diffusion coefficient and dynamic viscosity at high pressure

International audienceA free-volume model of the dynamic viscosity and the self-diffusion coefficients was discussed. The temperature-pressure variations of the dynamic viscosity and the self-diffusion coefficients of small molecules were predicted. The compounds, carbon tetrachloride, cyclohexane, benzene, chlorotrifluoromethane, tetramethylsilane and methylcyclohexane were used for the investigation. The relation between microstructure, free volume and different complex thermophysical properties were emphasized by the model

An inverse for the Jaumann derivative and some applications to the rheology of viscoelastic fluids

By using a generalization of the matrizant of matrix calculus, it is shown how one can construct formally an inverse, or integral, for the well-known Jaumann derivative of continuum mechanics. Some applications to fluid rheology are then considered. First, it is shown that this integral provides, via the Boltzmann super-position principle, a generalization of Oldroyd's quasi-linear fluid model, which is related to the molecular model of Bueche . Explicit expressions for the stresses arising in a general laminar shear flow are then derived for this model. Secondly, it is indicated how the operation can be used with rheological equations which are nonlinear in the deformation-rate, but quasi-linear in stress, to solve explicitly for the stress in terms of kinematic quantities. As an example, a rheological equation for suspensions of viscoelastic spheres in a Newton ian fluid is treated.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47218/1/397_2005_Article_BF01982423.pd

Children reading to dogs: a systematic review of the literature

Background Despite growing interest in the value of human-animal interactions (HAI) to human mental and physical health the quality of the evidence on which postulated benefits from animals to human psychological health are based is often unclear. To date there exist no systematic reviews on the effects of HAI in educational settings specifically focussing on the perceived benefits to children of reading to dogs. With rising popularity and implementation of these programmes in schools, it is essential that the evidence base exploring the pedagogic value of these initiatives is well documented. Methods Using PRISMA guidelines we systematically investigated the literature reporting the pedagogic effects of reading to dogs. Because research in this area is in the early stages of scientific enquiry we adopted broad inclusion criteria, accepting all reports which discussed measurable effects related to the topic that were written in English. Multiple online databases were searched during January-March 2015; grey literature searches were also conducted. The search results which met the inclusion criteria were evaluated, and discussed, in relation to the Oxford Centre for Evidence Based Medicine levels of evidence; 27 papers were classified as Level 5, 13 as Level 4, 7 as Level 2c and 1 as Level 2b. Conclusion The evidence suggests that reading to a dog may have a beneficial effect on a number of behavioural processes which contribute to a positive effect on the environment in which reading is practiced, leading to improved reading performance. However, the evidence base on which these inferences are made is of low quality. There is a clear need for the use of higher quality research methodologies and the inclusion of appropriate controls in order to draw causal inferences on whether or how reading to dogs may benefit children’s reading practices. The mechanisms for any effect remain a matter of conjectur

Sucrose in the concentrated solution or the supercooled “state” : a review of caramelisation reactions and physical behaviour

Sucrose is probably one of the most studied molecules by food scientists, since it plays an important role as an ingredient or preserving agent in many formulations and technological processes. When sucrose is present in a product with a concentration near or greater than the saturation point—i.e. in the supercooled state—it possesses high potentialities for the food industry in areas as different as pastry industry, dairy and frozen desserts or films and coatings production. This paper presents a review on critical issues and research on highly concentrated sucrose solutions—mainly, on sucrose thermal degradation and relaxation behaviour in such solutions. The reviewed works allow identifying several issues with great potential for contributing to significant advances in Food Science and Technology.Authors are grateful for the valuable discussions with Teresa S. Brandao and Rosiane Lopes da Cunha during this research. Author M. A. C. Quintas acknowledges the financial support of her research by FCT grant SFRH/BPD/41715/2007

Principles of physics

xvii, 741 p.; 26 cm