Solid angle subtended by a cylindrical detector at a point source in terms of elliptic integrals

The solid angle subtended by a right circular cylinder at a point source located at an arbitrary position generally consists of a sum of two terms: that defined by the cylindrical surface ($\Omega_{cyl}$) and the other by either of the end circles ($\Omega_{circ}$). We derive an expression for $\Omega_{cyl}$ in terms of elliptic integrals of the first and third kinds and give similar expressions for $\Omega_{circ}$ using integrals of the first and second kinds. These latter can be used alternatively to an expression also in terms of elliptic integrals, due to Philip A. Macklin and included as a footnote in Masket (Rev. Sci. Instr., 28 (3), 191-197, 1957). The solid angle subtended by the whole cylinder when the source is located at an arbitrary location can then be calculated using elliptic integrals.Comment: 10 pages, 3 figures, LaTex. Typos corrected. References added. Accepted in Rad. Phys. Che

The functional integral with unconditional Wiener measure for anharmonic oscillator

In this article we propose the calculation of the unconditional Wiener measure functional integral with a term of the fourth order in the exponent by an alternative method as in the conventional perturbative approach. In contrast to the conventional perturbation theory, we expand into power series the term linear in the integration variable in the exponent. In such a case we can profit from the representation of the integral in question by the parabolic cylinder functions. We show that in such a case the series expansions are uniformly convergent and we find recurrence relations for the Wiener functional integral in the $N$ - dimensional approximation. In continuum limit we find that the generalized Gelfand - Yaglom differential equation with solution yields the desired functional integral (similarly as the standard Gelfand - Yaglom differential equation yields the functional integral for linear harmonic oscillator).Comment: Source file which we sent to journa

Detection of a Moving Rigid Solid in a Perfect Fluid

In this paper, we consider a moving rigid solid immersed in a potential fluid. The fluid-solid system fills the whole two dimensional space and the fluid is assumed to be at rest at infinity. Our aim is to study the inverse problem, initially introduced in [3], that consists in recovering the position and the velocity of the solid assuming that the potential function is known at a given time. We show that this problem is in general ill-posed by providing counterexamples for which the same potential corresponds to different positions and velocities of a same solid. However, it is also possible to find solids having a specific shape, like ellipses for instance, for which the problem of detection admits a unique solution. Using complex analysis, we prove that the well-posedness of the inverse problem is equivalent to the solvability of an infinite set of nonlinear equations. This result allows us to show that when the solid enjoys some symmetry properties, it can be partially detected. Besides, for any solid, the velocity can always be recovered when both the potential function and the position are supposed to be known. Finally, we prove that by performing continuous measurements of the fluid potential over a time interval, we can always track the position of the solid.Comment: 19 pages, 14 figure

Two-dimensional soliton cellular automaton of deautonomized Toda-type

A deautonomized version of the two-dimensional Toda lattice equation is presented. Its ultra-discrete analogue and soliton solutions are also discussed.Comment: 11 pages, LaTeX fil

Local law-of-the-wall in complex topography: a confirmation from wind tunnel experiments

It is well known that in a neutrally-stratified turbulent flow in a deep constant-stress layer above a flat surface, the variation of the mean velocity with respect to the distance from the surface obeys the logarithmic law (the so-called ``law-of-the-wall''). More recently, the same logarithmic law has been found also in the presence of non flat surfaces. It governs the dynamics of the mean velocity (i.e. all the smaller scales are averaged out) and involves renormalized effective parameters. Recent numerical simulations analyzed by the authors of the present Letter show that a more intrinsic logarithmic shape actually takes place also at smaller scales. Such a generalized law-of-the-wall involves effective parameters smoothly depending on the position along the underlying topography. Here, we present wind tunnel experimental evidence confirming and corroborating this new-found property. New results and their physical interpretation are also presented and discussed.Comment: 9 pages, (Latex), 4 figure

La mobilisation des connaissances en protection de l’enfance

La protection de l’enfance est l’un des secteurs de services qui se développent le plus rapidement au Canada. Cependant, nous en savons étonnamment peu sur l’efficacité des services offerts aux enfants maltraités et négligés. Cet article examine de nouveaux modèles de mobilisation des connaissances conçus pour soutenir l’utilisation plus systématique de la recherche dans les services sociaux. Nous commençons par discuter des limites des modèles traditionnels de diffusion des connaissances. Ensuite, nous considérons certaines des recherches qui ont été faites sur les obstacles et les facteurs facilitant l’utilisation de la recherche en santé, en éducation et dans les services sociaux. Enfin, nous présentons un modèle de mobilisation des connaissances qui est mis à l’essai et évalué dans un organisme de protection de l’enfance au Québec, décrivons les processus locaux utilisés pour affiner les six indicateurs de résultats (récurrence de la maltraitance, retards scolaires, taux de placement, déplacements d’une ressource à une autre, durée des soins et participation d’un tribunal) et concluons en présentant un exemple d’un des indicateurs retenus.Child protection is one of the fastest growing services sectors in Canada, yet we know surprisingly little about the effectiveness of services for abused and neglected children. This article examines emerging knowledge mobilization models designed to support the more systematic use of research in social services. We start by discussing the limits of traditional knowledge dissemination models. We then consider some of the research that has been done on the barriers and facilitators of research utilization in health, education and social services. Finally, we present a knowledge mobilization model that is being pilot tested and evaluated in a child welfare agency in Quebec and describe the local processes used to refine six outcome indicators (recurrence of maltreatment ; school delay ; placement rate ; moves in care ; time in care ; and court involvement) and conclude by presenting an example of one of the selected indicators.La protección de la infancia es uno de los sectores de servicios de más rápido desarrollo en Canadá. Sin embargo, es sorprendente lo poco que sabemos sobre la eficacia de los servicios que se ofrecen a los menores víctimas de maltrato o de negligencia. Este artículo examina nuevos modelos de movilización de conocimientos concebidos para apoyar un uso más sistemático de la investigación en los servicios sociales. Discutimos, primero, los límites de los modelos tradicionales de la difusión de conocimientos. A continuación, consideramos algunas investigaciones sobre los obstáculos y estímulos al uso de la investigación en los ámbitos de la salud, la educación y los servicios sociales. Finalmente, presentamos un modelo de movilización de conocimientos en etapa de práctica piloto y evaluación en una agencia de protección de la infancia en Quebec ; describimos los procesos locales utilizados para afinar seis indicadores de resultados (recurrencia del maltrato, retrasos escolares, tasa de colocación, desplazamiento de un recurso a otro, duración de cuidados y participación de un tribunal) y concluimos presentando un ejemplo de uno de los indicadores seleccionados

Steady Motion of a Rigid Disk of Finite Thickness on a Horizontal Plane

The article discusses the steady motion of a rigid disk of finite thickness rolling on its edge on a horizontal plane under the influence of gravity. The governing equations are presented and two cases allowing for a steady state solution are considered: rolling on consistently rough ground and rolling on perfectly smooth ground. The conditions of steady motion are derived for both kinds of ground and it is shown that the possible steady motion of a disk is either on a straight line in a circle. Also oscillations about steady state are discussed and conditions for stable motion are established.Comment: 28 pages, 7 figure

Bernoulli type polynomials on Umbral Algebra

The aim of this paper is to investigate generating functions for modification of the Milne-Thomson's polynomials, which are related to the Bernoulli polynomials and the Hermite polynomials. By applying the Umbral algebra to these generating functions, we provide to deriving identities for these polynomials

Fluid Mechanical and Electrical Fluctuation Forces in Colloids

Fluctuations in fluid velocity and fluctuations in electric fields may both give rise to forces acting on small particles in colloidal suspensions. Such forces in part determine the thermodynamic stability of the colloid. At the classical statistical thermodynamic level, the fluid velocity and electric field contributions to the forces are comparable in magnitude. When quantum fluctuation effects are taken into account, the electric fluctuation induced van der Waals forces dominate those induced by purely fluid mechanical motions. The physical principles are applied in detail for the case of colloidal particle attraction to the walls of the suspension container and more briefly for the case of forces between colloidal particles.Comment: ReVTeX format, one *.eps figur

Four-vortex motion around a circular cylinder

The motion of two pairs of counter-rotating point vortices placed in a uniform flow past a circular cylinder is studied analytically and numerically. When the dynamics is restricted to the symmetric subspace---a case that can be realized experimentally by placing a splitter plate in the center plane---, it is found that there is a family of linearly stable equilibria for same-signed vortex pairs. The nonlinear dynamics in the symmetric subspace is investigated and several types of orbits are presented. The analysis reported here provides new insights and reveals novel features of this four-vortex system, such as the fact that there is no equilibrium for two pairs of vortices of opposite signs on the opposite sides of the cylinder. (It is argued that such equilibria might exist for vortex flows past a cylinder confined in a channel.) In addition, a new family of opposite-signed equilibria on the normal line is reported. The stability analysis for antisymmetric perturbations is also carried out and it shows that all equilibria are unstable in this case.Comment: 27 pages, 13 figures, to be published in Physics of Fluid