The Fundamental Solution of the Linearized Navier–Stokes Equations for Spinning Bodies in Three Spatial Dimensions – Time Dependent Case

Explicit formulae for the fundamental solution of the linearized time dependent Navier–Stokes equations in three spatial dimensions are obtained. The linear equations considered in this paper include those used to model rigid bodies that are translating and rotating at a constant velocity. Estimates extending those obtained by Solonnikov in [23] for the fundamental solution of the time dependent Stokes equations, corresponding to zero translational and angular velocity, are established. Existence and uniqueness of solutions of these linearized problems is obtained for a class of functions that includes the classical Lebesgue spaces L^p(R³), 1 < p < ∞. Finally, the asymptotic behavior and semigroup properties of the fundamental solution are established.     

What role for public health in genetics and vice versa?

Some epidemiologists and geneticists claim that integrating genetics into public health policies and programs is necessary and unavoidable. OBJECTIVE: To examine the extent to which further integration of public health and genetics is warranted. METHODS: Synthesis of the literature in four areas: research, genetic services, regulation, and education. The analysis is limited to human genetics. RESULTS: Public support for basic genetic research has and will continue to lead to new applications and to further understanding of human origins and dispersions. Some applied research, particularly for genetic risk factors for common complex diseases, has low yield and is better supported by private funds. The only genetic service for which a public health role is paramount is newborn screening. With the patenting of genes, and the proliferation of commercial interests in genetic tests and directly advertising them to the public, regulation by public health agencies is increasingly important. As most genetic testing and other services will be provided in the personal health care system, education about genetics is best left to the educational and medical systems. Public health practitioners should be aware of the limitations of genetic tests. CONCLUSIONS: There is little need for further integration of genetic services and education into public health especially in countries in which public and private health services are dichotomized. Newborn screening and follow-up, however, are most safely and effectively provided under public health auspices. The most important area for strengthening the public health role is in the regulation of genetic tests and other genetic services provided primarily by the private sector. Continued support for basic genetic research is needed.     

Tomographic reconstruction of shock layer flows

The tomographic reconstruction of supersonic flows faces two challenges. Firstly, techniques used in the past, such as the direct Fourier method (DFM) (Gottlieb and Gustafsson in On the direct Fourier method for computer tomography, 1998; Morton in Tomographic imaging of supersonic flows, 1995) or various backprojection (Kak and Slaney in Principles of computerized tomographic imaging, vol. 33 in Classics in Applied Mathematics, 2001) techniques, have only been able to reconstruct areas of the flow which are upstream of any opaque objects, such as a model. Secondly, shock waves create sharp discontinuities in flow properties, which can be difficult to reconstruct both in position and in magnitude with limited data. This paper will present a reconstruction method, matrix inversion using ray-tracing and least squares conjugate gradient (MI-RLS), which uses geometric ray-tracing and a sparse matrix iterative solver (Paige and Saunders in ACM Trans. Math. Softw. 8(1):43–71, 1982) to overcome both of these challenges. It will be shown, through testing with a phantom object described in tomographic literature, that the results compare favourably to those produced by the DFM technique. Finally, the method will be used to reconstruct three-dimensional density fields from interferometric shock layer images, with good resolution (Faletič in Tomographic reconstruction of shock layer flows, 2005). This paper was based on work that was presented at the 3rd International Symposium on Interdisciplinary Shock Wave Research, Canberra, Australia, March 1–3, 2006.     

A Set of Bounded Solutions of a Linear Weakly Perturbed System

For weakly perturbed systems of linear differential equations, we establish conditions for the point = 0 to bifurcate into a set of solutions bounded on the entire axis R in the case where the corresponding unperturbed homogeneous linear differential system is exponentially dichotomous on the semiaxes R ₊ and R _–. We determine the number of linearly independent solutions bounded on R and give an algorithm for finding these solutions.     

Numerical simulation of large amplitude oscillatory shear of a high-density polyethylene melt using the MSF model

We study the flow response in large amplitude oscillatory shear of the molecular stress function (MSF) model that has recently been proposed by Wagner et al. [M.H. Wagner, P. Rubio, H. Bastian, The molecular stress function model for polydisperse polymer melts with dissipative convective constraint release, J. Rheol. 45 (2001) 1387–1412]. The MSF model is derived from molecular theory and has only two parameters to describe the non-linear material response. The model predictions are analysed in both the frequency and time domain. It shows good agreement with experimental data for a linear high-density polyethylene melt. At low and medium strains, MSF model predictions are in excellent agreement with experimental data and predictions of a six-mode Giesekus model which has six parameters to describe the non-linear material response. At medium strains, the basic Doi–Edwards model, which has no non-linear parameters, already underpredicts the data. At high strains, the MSF model predictions agree slightly better with the experimental data than the Giesekus model. Surprisingly, however, it is the Doi–Edwards model that shows excellent agreement with experimental data at high strains. For the linear melt we consider, it outperforms the models that have non-linear parameters, both in the time and frequency domain.     

Blowing coefficient with arbitrary variation of the mass flow rate of the blown gas past a body around which flows a stream with an exponential change in the velocity

Formulas are derived permitting calculation of the linear corrections to the friction and heat-transfer coefficients with the blowing into the boundary layer of different gases, in small amounts but with a mass flow rate varying arbitrarily along the body. The case of a Mach number equal to zero and a temperature factor equal to unity was studied. Here it is postulated that bringing the relative heat-transfer coefficient down to a dependence on the dimensionless blowing renders possible, as with blowing which permits a self-similar solution, the use of the results obtained for arbitrary values of these parameters [1]. The proposed method of solution is based on the application, in the linear approximation, of a Duhamel integral for an arbitrary law of change in the mass flow rate along the body, if a solution is known with a discontinuous change in the mass flow rate. For a discontinuous change in the mass flow rate, the solution is sought using a Laplace transform; in this sense, the proposed method is similar to the method of [5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 55–63, July–August, 1970.     

The approximate determination of the hunting movement of a railway vehicle by aid of the method of Krylov and Bogoljubov

Summary The author deals with the problem of the lateral oscillations of a railway vehicle moving on a straight track. Because of the possibility that the flange of each of the wheels temporarily contacts the rail belonging to it, the problem lies in the field of the self-sustained vibrations of non-linear mechanical systems with more than one degree of freedom. In the case under consideration, in which the vehicle and the track had been strongly simplified, the limit-cycle for the motion as well as its stability were determined approximately by the method of Krylov and Bogoljubov. This method is described in §§ 2 and 3. § 3 is more specially devoted to the so-called method of the equivalent linear equations. The latter equations are considered valid not only in the case in which the motion is purely periodic (in which a limit-cycle has been reached), but also in the neighbouring case, in which the motion slightly damps out or increases. This enables us to determine not only the limit-cycle but also its stability. In § 4 the method is applied to the problem of the hunting movement of the railway vehicle. The number of degrees of freedom is equal to 2, and we chose for the two generalised coordinates the lateral displacements of the leading wheel set and the trailing wheel set respectively. The linear creep law is assumed to be valid for the relation between the so-called slip coefficients and the tangential forces which the rails exert on the tyres and conversely. The limit-cycle obtained by applying Krylov and Bogoljubov's method corresponds to the limit-cycle previously found by means of Ritz' method. As to the stability it appears that the limit-cycle is always stable.Paper delivered at the Xth International Congress of Applied Mechanics at Stresa Aug. 31st to Sept. 7th, 1960.     

Complexification phenomenon in an example of sensitive singular perturbationPhénomène de complexification dans un exemple de perturbation singulière sensitive

We consider singular perturbation problems depending on a parameter ε?0 such that for ε>0 the solution u^ε belongs to a Sobolev space on a domain $\text{Ω}$, but the limit u⁰ is not a distribution on $\text{Ω}$. A very simple model problem, solvable by Fourier transform allows us to study the complexification process of u^ε as $\text{ε↘0}$. The limit holds in the topology of a space of analytical functionals. To cite this article: C.A. De Souza, É. Sanchez-Palencia, C. R. Mecanique 332 (2004).     

The computation of three-dimensional systems with various turbulence model variations

The standardk-? equations and other turbulence corrections are evaluated and reported with respect to their applicability in three-dimensional flows. The turbulence models are formulated on the assumption that an isotropic eddy viscosity and the modified Boussinesq hypothesis adequately describe the stress distributions, and that the source of predictive error is a consequence of the modelled terms in thek-? equations. Turbulence model corrections are incorporated to investigate their impact on these errors. Predictions from various turbulence models are compared with experimental data from an isothermal 3-D configuration. The data comparisons delineate the relative advantages and disadvantages of various modifications. Thek-? model performs competitively with other model corrections and in some instances is judged to be superior than the modified treatments. However, given the additional computational time and the marginal superiority of the investigated models, it is recommended that present 3-D computational code calculations retain the standardk-? model.     

Transient compressible boundary layer on a wedge impulsively set into motion

Summary The development of a compressible boundary layer over a wedge impulsively set into motion is studied in this paper. The initial motion is independent of the leading edge effect and the solutions are those of a Rayleigh-type problem. The motion tends to an ultimate steady state of Falkner-Skan type. The equations governing the transient boundary layer from the initial steady state to the terminal steady-state change their character after certain time due to the leading edge effect and thereafter solution depends on both the end conditions. Numerical solutions are obtained through the second-order accuracy upwind scheme. The effects of the Falkner-Skan parameter and the surface temperature on the transient flow and heat transfer are also studied. It has been found that the flow separation does not occur form–0.0707 when _w = 1.5 (hot wall), andm–0.118 when _0.5 (cold wall).