Ill-Posedness, Regularization and Number of Degrees of Freedom

info:eu-repo/semantics/published

Superresolution and number of degrees of freedom in inverse diffraction with subwavelength sources

info:eu-repo/semantics/published

Number of degrees of freedom in inverse diffraction

The problem of inverse diffraction from plane to plane is considered in the case where a finite aperture exists in the boundary plane. Singular values and singular functions for the problem are introduced, and the number of degrees of freedom is defined in terms of the distribution of the singular values. Numerical computations are presented for the one-dimensional problem, and it is shown that the effect of evanescent waves disappears at a distance of approximately one wavelength from the boundary plane, even when the dimension of the slit is comparable with the wavelength of the diffracted field. © 1983 Taylor & Francis Group, LLC.

High number of antigen binding cells in unimmunized mice and possible occurrence of multispecific lymphocytes

A high frequency of Tobacco Mosaic virus (TMV) binding cells was found in spleen cells from unimmunized mice (about 3 to 4%). TMV binding is strongly inhibited by previous incubation with anti immunoglobulin antisera. After stripping of membrane receptors, a full recovery for antigen binding capacity can be observed after 24 hr culture. Experiments are presented to exclude artefactual fluorescent cells: interaction of TMV with some non immunoglobulin membrane components; interaction of fluorescent anti TMV antibody with the Fc receptor of B cells; the binding of TMV to cytophilic immunoglobulins. The occurrence of lymphocytes able to bind several non crossreactive antigens is suggested by three lines of evidence: the high number of antigen binding cells in unimmunized mice, presence of surface immunoglobulins on some TMV binding cells after complete capping of TMV receptors and the direct demonstration of lymphocytes binding TMV and hemocyanin at different membrane sites.

Difficulties and errors in number reasoning development

The detailed study of difficulties and errors in young learner comprehension is a relevant and productive research field in Mathematics Education. Studies in the field are numerous although somewhat too varied. The present paper is suggesting methodological perspectives and principles applying to the field of research; we also show an example with school work. The use of figurate numbers as a representation system gives richer conceptual values, boosts visual reasoning and facilitates learner understanding.

Monotone scheme and boundary conditions for finite volume simulation of magnetohydrodynamic internal flows at high Hartmann number

A monotone scheme for finite volume simulation of magnetohydrodynamic internal flows at high Hartmann number is presented. The numerical stability is analysed with respect to the electromagnetic force. Standard central finite differences applied to finite volumes can only be numerically stable if the vector products involved in this force are computed with a scheme using a fully staggered grid. The electromagnetic quantities (electric currents and electric potential) must be shifted by half the grid size from the mechanical ones (velocity and pressure). An integral treatment of the boundary layers is used in conjunction with boundary conditions for electrically conducting walls. The simulations are performed with inhomogeneous electrical conductivities of the walls and reach high Hartmann numbers in three-dimensional simulations, even though a non-adaptive grid is used.

Low Reynolds number turbulence models for accurate thermal simulations of electronic components

The electronics industry and the problems associated with the cooling of microelectronic equipment are developing rapidly. Thermal engineers now find it necessary to consider the complex area of equipment cooling at some level. This continually growing industry also faces heightened pressure from consumers to provide electronic product miniaturization, which in itself increases the demand for accurate thermal management predictions to assure product reliability. Computational fluid dynamics (CFD) is considered a powerful and almost essential tool for the design, development and optimization of engineering applications. CFD is now widely used within the electronics packaging design community to thermally characterize the performance of both the electronic component and system environment. This paper discusses CFD results for a large variety of investigated turbulence models. Comparison against experimental data illustrates the predictive accuracy of currently used models and highlights the growing demand for greater mathematical modelling accuracy with regards to thermal characterization. Also a newly formulated low Reynolds number (i.e. transitional) turbulence model is proposed with emphasis on hybrid techniques.

Remote sensing of assimilation number for marine phytoplankton

Estimating primary production at large spatial scales is key to our understanding of the global carbon cycle. Algorithms to estimate primary production are well established and have been used in many studies with success. One of the key parameters in these algorithms is the chlorophyll-normalised production rate under light saturation (referred to as the light saturation parameter or the assimilation number). It is known to depend on temperature, light history and nutrient conditions, but assigning a magnitude to it at particular space-time points is difficult. In this paper, we explore two models to estimate the assimilation number at the global scale from remotely-sensed data that combine methods to estimate the carbon-to-chlorophyll ratio and the maximum growth rate of phytoplankton. The inputs to the algorithms are the surface concentration of chlorophyll, seasurface temperature, photosynthetically-active radiation af the surface of the sea, sea surface nutrient concentration and mixed-layer depth. A large database of in situ estimates of the assimilation number is used to develop the models and provide elements of validation. The comparisons with in situ observations are promising and global maps of assimilation number are produced.