Spinning rough disc moving in a rarefied medium

We study the Magnus effect: deflection of the trajectory of a spinning body moving in a gas. It is well known that in rarefied gases, the inverse Magnus effect takes place, which means that the transversal component of the force acting on the body has opposite signs in sparse and relatively dense gases. The existing works derive the inverse effect from nonelastic interaction of gas particles with the body. We propose another (complementary) mechanism of creating the transversal force owing to multiple collisions of particles in cavities of the body surface. We limit ourselves to the two-dimensional case of a rough disc moving through a zero-temperature medium on the plane, where reflections of the particles from the body are elastic and mutual interaction of the particles is neglected. We represent the force acting on the disc and the moment of this force as functionals depending on ‘shape of the roughness’, and determine the set of all admissible forces. The disc trajectory is determined for several simple cases. The study is made by means of billiard theory, Monge–Kantorovich optimal mass transport and by numerical methodsFundação para a Ciência e a Tecnologia (FCT

Uma forma bidimensional que maximiza a resistência aerodinâmica newtoniana

In a previous work [18, 19] it is investigated, by means of computational simulations, shapes of nonconvex bodies that maximize resistance to its motion on a rare ed medium, considering that bodies are moving forward and at the same time slowly rotating. Here the previous results are improved: we obtain a two-dimensional geometric shape that confers to the body a resistance very close to the supremum value (R = 1:4965 < 1:5). Um corpo bidimensional, apresentando um ligeiro movimento rotacional, desloca-se num meio rarefeito de partículas que colidem com ele de uma forma perfeitamente elástica. Em investigações que os dois primeiros autores realizaram anteriormente [18, 19], procuraram-se formas de corpos que maximizassem a força de travagem do meio ao seu movimento. Dando continuidade a esse estudo, encetam-se agora novas investigações que culminam num resultado que representa um grande avanço qualitativo relativamente aos então alcançados. Esse resultado, que agora se apresenta, consiste numa forma bidimensional que confere ao corpo uma resistência muito próxima do seu limite teórico. Mas o seu interesse não se fica pela maximização da resistência newtoniana; atendendo às suas características, apontam-se ainda outros domínios de aplicação onde se pensa poder vir a revelar-se de grande utilidade. Tendo a forma óptima encontrada resultado de estudos numéricos, é objecto de um estudo adicional de natureza analítica, onde se demonstram algumas propriedades importantes que explicam em grande parte o seu virtuosismo

Uma forma bidimensional que maximiza a resistência aerodinâmica newtoniana

In a previous work [18, 19] it is investigated, by means of computational simulations, shapes of nonconvex bodies that maximize resistance to its motion on a rare ed medium, considering that bodies are moving forward and at the same time slowly rotating. Here the previous results are improved: we obtain a two-dimensional geometric shape that confers to the body a resistance very close to the supremum value (R = 1:4965 < 1:5). Um corpo bidimensional, apresentando um ligeiro movimento rotacional, desloca-se num meio rarefeito de partículas que colidem com ele de uma forma perfeitamente elástica. Em investigações que os dois primeiros autores realizaram anteriormente [18, 19], procuraram-se formas de corpos que maximizassem a força de travagem do meio ao seu movimento. Dando continuidade a esse estudo, encetam-se agora novas investigações que culminam num resultado que representa um grande avanço qualitativo relativamente aos então alcançados. Esse resultado, que agora se apresenta, consiste numa forma bidimensional que confere ao corpo uma resistência muito próxima do seu limite teórico. Mas o seu interesse não se fica pela maximização da resistência newtoniana; atendendo às suas características, apontam-se ainda outros domínios de aplicação onde se pensa poder vir a revelar-se de grande utilidade. Tendo a forma óptima encontrada resultado de estudos numéricos, é objecto de um estudo adicional de natureza analítica, onde se demonstram algumas propriedades importantes que explicam em grande parte o seu virtuosismo

Two-dimensional body of maximum mean resistance

A two-dimensional body, exhibiting a slight rotational movement, moves in a rarefied medium of particles which collide with it in a perfectly elastic way. In previously realized investigations by the first two authors, Plakhov & Gouveia (2007, Nonlinearity, 20), shapes of nonconvex bodies were sought which would maximize the braking force of the medium on their movement. Giving continuity to this study, new investigations have been undertaken which culminate in an outcome which represents a large qualitative advance relative to that which was achieved earlier. This result, now presented, consists of a two-dimensional shape which confers on the body a resistance which is very close to its theoretical supremum value. But its interest does not lie solely in the maximization of Newtonian resistance; on regarding its characteristics, other areas of application are seen to begin to appear which are thought to be capable of having great utility. The optimal shape which has been encountered resulted from numerical studies, thus it is the object of additional study of an analytical nature, where it proves some important properties which explain in great part its effectiveness.Comment: Accepted (April 16, 2009) for publication in the journal "Applied Mathematics and Computation

Parametric phenomena of the particle dynamics in a periodic gravitational wave field

We establish exactly solvable models for the motion of neutral particles, electrically charged point and spin particles (U(1) symmetry), isospin particles (SU(2) symmetry), and particles with color charges (SU(3) symmetry) in a gravitational wave background. Special attention is devoted to parametric effects induced by the gravitational field. In particular, we discuss parametric instabilities of the particle motion and parametric oscillations of the vectors of spin, isospin, and color charge.Comment: 26 pages, to be published in J. Math. Phy

Geospatial analysis and living urban geometry

This essay outlines how to incorporate morphological rules within the exigencies of our technological age. We propose using the current evolution of GIS (Geographical Information Systems) technologies beyond their original representational domain, towards predictive and dynamic spatial models that help in constructing the new discipline of "urban seeding". We condemn the high-rise tower block as an unsuitable typology for a living city, and propose to re-establish human-scale urban fabric that resembles the traditional city. Pedestrian presence, density, and movement all reveal that open space between modernist buildings is not urban at all, but neither is the open space found in today's sprawling suburbs. True urban space contains and encourages pedestrian interactions, and has to be designed and built according to specific rules. The opposition between traditional self-organized versus modernist planned cities challenges the very core of the urban planning discipline. Planning has to be re-framed from being a tool creating a fixed future to become a visionary adaptive tool of dynamic states in evolution

Long memory conditional volatility and asset allocation

Pre-print version dated May 2011 issued as Discussion paper by University of Exeter. A definitive version was subsequently published in International Journal of Forecasting Volume 29, Issue 2, April–June 2013, Pages 258–273. Available online at http://www.sciencedirect.com/In this paper, we evaluate the economic benefits that arise from allowing for long memory when forecasting the covariance matrix of returns over both short and long horizons, using the asset allocation framework of Engle and Colacito (2006) In particular, we compare the statistical and economic performances of four multivariate long memory volatility models (the long memory EWMA, long memory EWMA–DCC, FIGARCH-DCC and component GARCH-DCC models) with those of two short memory models (the short memory EWMA and GARCH-DCC models). We report two main findings. First, for longer horizon forecasts, long memory models generally produce forecasts of the covariance matrix that are statistically more accurate and informative, and economically more useful than those produced by short memory models. Second, the two parsimonious long memory EWMA models outperform the other models–both short and long memory–across most forecast horizons. These results apply to both low and high dimensional covariance matrices and both low and high correlation assets, and are robust to the choice of the estimation window

Complete solutions to the metric of spherically collapsing dust in an expanding spacetime with a cosmological constant

We present semi-analytical solutions to the background equations describing the Lema\^itre-Tolman-Bondi (LTB) metric as well as the homogeneous Friedmann equations, in the presence of dust, curvature and a cosmological constant Lambda. For none of the presented solutions any numerical integration has to be performed. All presented solutions are given for expanding and collapsing phases, preserving continuity in time and radius. Hence, these solutions describe the complete space time of a collapsing spherical object in an expanding universe. In the appendix we present for completeness a solution of the Friedmann equations in the additional presence of radiation, only valid for the Robertson-Walker metric.Comment: 23 pages, one figure. Numerical module for evaluation of the solutions released at http://web.physik.rwth-aachen.de/download/valkenburg/ColLambda/ Matches published version, published under Open Access. Note change of titl

Non-monotonic variation with salt concentration of the second virial coefficient in protein solutions

The osmotic virial coefficient $B_2$ of globular protein solutions is calculated as a function of added salt concentration at fixed pH by computer simulations of the ``primitive model''. The salt and counter-ions as well as a discrete charge pattern on the protein surface are explicitly incorporated. For parameters roughly corresponding to lysozyme, we find that $B_2$ first decreases with added salt concentration up to a threshold concentration, then increases to a maximum, and then decreases again upon further raising the ionic strength. Our studies demonstrate that the existence of a discrete charge pattern on the protein surface profoundly influences the effective interactions and that non-linear Poisson Boltzmann and Derjaguin-Landau-Verwey-Overbeek (DLVO) theory fail for large ionic strength. The observed non-monotonicity of $B_2$ is compared to experiments. Implications for protein crystallization are discussed.Comment: 43 pages, including 17 figure

Selection against variants in the genome associated with educational attainment

Epidemiological and genetic association studies show that genetics play an important role in the attainment of education. Here, we investigate the effect of this genetic component on the reproductive history of 109,120 Icelanders and the consequent impact on the gene pool over time. We show that an educational attainment polygenic score, POLYEDU, constructed from results of a recent study is associated with delayed reproduction (P < 10-100) and fewer children overall. The effect is stronger for women and remains highly significant after adjusting for educational attainment. Based on 129,808 Icelanders born between 1910 and 1990, we find that the average POLYEDU has been declining at a rate of ∼0.010 standard units per decade, which is substantial on an evolutionary timescale. Most importantly, because POLYEDU only captures a fraction of the overall underlying genetic component the latter could be declining at a rate that is two to three times faster