Scattering and bound states of spin-0 particles in a nonminimal vector double-step potential

The problem of spin-0 particles subject to a nonminimal vector double-step potential is explored in the context of the Duffin-Kemmer-Petiau theory. Surprisingly, one can never have an incident wave totally reflected and the transmission amplitude has complex poles corresponding to bound states. The interesting special case of bosons embedded in a sign potential with its unique bound-state solution is analyzed as a limiting case.Comment: 1 figur

Pseudo-Differential Operators in a Wave Diffraction Problem with Impedance Conditions

Mathematics Subject Classification: 35J05, 35J25, 35C15, 47H50, 47G30We consider an impedance boundary-value problem for the Helmholtz equation which models a wave diffraction problem with imperfect conductivity on a strip. Pseudo-differential operators are used to deal with this wave diffraction problem. Therefore, single and double layer potentials allow a reformulation of the problem into a system of integral equations. By using operator theoretical methods, the well-posedness of the problem is obtained for a set of impedance parameters, and in a framework of Bessel potential spaces.∗ This work is partially supported by the Portuguese Science Foundation (FCT–Fundação para a Ciência ea Tecnologia) through Unidade de Investigação Matemática e Aplicações of the University of Aveiro, Portugal. * The second author is supported by the Portuguese Science Foundation through grant number SFRH/BPD/20524/2004

Diffraction by a half-plane with different face impedances on an obstacle perpendicular to the boundary

The paper is devoted to study classes of plane wave diffraction problems by a region which involves a crack with impedance boundary conditions. Conditions on the wave number and impedance parameters are found to ensure the well-posedness of the problems in a scale of Bessel potential spaces. Under such conditions, representations of the solutions are also obtained upon the consideration of some associated operators which, in a sense, combine operators of Wiener-Hopf and Hankel type

A Bessel differential heat initial value problem in a reproducing kernel Hilbert space framework

For modified Bessel heat equations subjected to an initial condition, we investigate integral transforms with kernels related to the solutions of those equations by using the theory of reproducing kernels. In particular, a new framework within reproducing kernel Hilbert spaces is proposed where we construct the unique solutions of the corresponding initial value problems

Initial value problems in linear integral operator equations

For some general linear integral operator equations, we investigate consequent initial value problems by using the theory of reproducing kernels. A new method is proposed which -- in particular -- generates a new field among initial value problems, linear integral operators, eigenfunctions and values, integral transforms and reproducing kernels. In particular, examples are worked out for the integral equations of Lalesco-Picard, Dixon and Tricomi types

How to catch smoothing properties and analyticity of functions by computers?

We would like to propose a new method in view to catch smoothing properties and analyticity of functions by computers. Of course, in the strict sense, such goal is impossible. However, we would like to propose some practical method that may be applied for many concrete cases for some good functions (but not for bad functions, in a sense). Therefore, this may be viewed as a procedure proposal which includes numerical experiments for the just mentioned challenge and within a new method

Methodology for Abrasive Wear Evaluation in Elevator Stage Centrifugal Pump Impellers

The abrasion resistance of the impellers depends on the characteristics of the materials used in their manufacture. In this work, a methodology is proposed for the evaluation of the abrasive wear of the plates of the centrifugal pump impellers, used in the gross water infrastructure station (GWIS) of sedimentary rivers, due to the sediment load variation and the river fluviometric dimension. In order to determine the wear mode and the relationship of the material-specific wear coefficient (K), due to the sediment concentration, a rotating ball abrasometer test was performed on SAE 8620, gray cast iron (GCI), and nodular cast iron (NCI), used in the manufacture of impellers. As an abrasive suspension, the concentrations of 1, 2, 3, 5, and 10 g L−1 of sediment were used in distilled water. The wear volume as a function of the relative velocity of the mixture in relation to the impeller blades was estimated mathematically. The results show that: i) The abrasive capacity of the sediments in different concentrations; ii) SAE 8620 steel was more resistant to abrasive wear; and iii) the rotational control of the pump as a function of sediment concentration and river level showed the possibility of reducing wear by 30%

Wave diffraction by wedges having arbitrary aperture angle

The problem of plane wave diffraction by a wedge sector having arbitrary aperture angle has a very long and interesting research background. In fact, we may recognize significant research on this topic for more than one century. Despite this fact, up to now no clear unified approach was implemented to treat such a problem from a rigourous mathematical way and in a consequent appropriate Sobolev space setting. In the present paper, we are considering the corresponding boundary value problems for the Helmholtz equation, with complex wave number, admitting combinations of Dirichlet and Neumann boundary conditions. The main ideas are based on a convenient combination of potential representation formulas associated with (weighted) Mellin pseudo-differential operators in appropriate Sobolev spaces, and a detailed Fredholm analysis. Thus, we prove that the problems have unique solutions (with continuous dependence on the data), which are represented by the single and double layer potentials, where the densities are solutions of derived pseudo-differential equations on the half-line

Artificial and natural radioactivity in edible mushrooms from Sao Paulo, Brazil

Environmental biomonitoring has demonstrated that organisms such as crustaceans, fish and mushrooms are useful to evaluate and monitor both ecosystem contamination and quality. Particularly, some mushroom species have a high capacity to retain radionuclides and some toxic elements from the soil and the air. The potential of mushrooms to accumulate radionuclides in their fruit-bodies has been well documented. However, there are no studies that determine natural and artificial radionuclide composition in edible mushrooms, in Brazil. Artificial (137Cs) and natural radioactivity (40K, 226Ra, 228Ra) were\ud determined in 17 mushroom samples from 3 commercialized edible mushroom species. The edible mushrooms collected were Agaricus sp., Pleurotus sp. and Lentinula sp. species. The activity measurements were carried out by gamma spectrometry. The levels of 137Cs varied from 1.45 0.04 to 10.6 0.3 Bq kg 1, 40K levels varied from 461 2 to 1535 10 Bq kg 1, 226Ra levels varied from 14 3 to 66 12 Bq kg 1 and 228Ra levels varied from 6.2 0.2 to 54.2 1.7 Bq kg 1. 137Cs levels in Brazilian mushrooms are in accordance with the radioactive fallout in the Southern Hemisphere. The artificial and natural activities determined in this study were found to be below the maximum permissible levels as\ud established by national legislation. Thus, these mushroom species can be normally consumed by the population without any apparent risks to human health

Numerical analysis of the crosswind in small solar chimney

The solar chimney (or solar updraft tower) consists of a circular solar collector, a tower in the center of the collector, and turbines installed in the collector output or the tower entrance. The solar radiation passes through the translucent collector, reaches the ground surface and heats it. The air within the device is heated by the radiation emitted by the ground and by convection currents formed under the collector. The thermal energy is stored in the absorber layer of the ground when there is incidence of solar radiation and it is released from the ground when solar radiation is low. The density difference between the hot air inside the device and the ambient air creates convection currents that drive the air in the collector from the base to the top of the tower. Finally, the airflow in the tower drives the turbines which are coupled to electrical generators. The environmental winds influence the performance of the solar updraft towers in three main ways: heat losses by convection from the outer surface of the collector to the environment, heated air drag out of the cover and drag on the top of the chimney generating a suction effect and enhancing the upward flow in the tower. This work studied the influence of crosswinds on the system flow conditions through a numerical analysis using CFD. Results indicate that an increase on the environmental crosswinds speed from 0 to 25 m/s decreased the outlet temperature of the device in 0.3% and increased the outlet velocity in 50.26%, increasing the energetic efficiency of the device in 56.31%.Papers presented to the 12th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Costa de Sol, Spain on 11-13 July 2016