The Neumann problem in thin domains with very highly oscillatory boundaries

In this paper we analyze the behavior of solutions of the Neumann problem posed in a thin domain of the type $R^\epsilon = \{(x_1,x_2) \in \R^2 \; | \; x_1 \in (0,1), \, - \, \epsilon \, b(x_1) < x_2 < \epsilon \, G(x_1, x_1/\epsilon^\alpha) \}$ with $\alpha>1$ and $\epsilon > 0$, defined by smooth functions $b(x)$ and $G(x,y)$, where the function $G$ is supposed to be $l(x)$-periodic in the second variable $y$. The condition $\alpha > 1$ implies that the upper boundary of this thin domain presents a very high oscillatory behavior. Indeed, we have that the order of its oscillations is larger than the order of the amplitude and height of $R^\epsilon$ given by the small parameter $\epsilon$. We also consider more general and complicated geometries for thin domains which are not given as the graph of certain smooth functions, but rather more comb-like domains.Comment: 20 pages, 4 figure

Semilinear elliptic equations in thin regions with terms concentrating on oscillatory boundaries

In this work we study the behavior of a family of solutions of a semilinear elliptic equation, with homogeneous Neumann boundary condition, posed in a two-dimensional oscillating thin region with reaction terms concentrated in a neighborhood of the oscillatory boundary. Our main result is concerned with the upper and lower semicontinuity of the set of solutions. We show that the solutions of our perturbed equation can be approximated with ones of a one-dimensional equation, which also captures the effects of all relevant physical processes that take place in the original problem

REVITALIZING RESEARCH IN THE JUNIOR HIGH SCHOOL PROGRAM: INPUTS FOR CURRICULUM DEVELOPMENT AND FACULTY DEVELOPMENT PROGRAM

The study aims to find out the experiences and observations of teachers in teaching Research to Junior High School students. In particular, it wants to identify what needs to be enhanced in the research curriculum and faculty development program, particularly in terms of the knowledge and skills of research teachers and the other teachers in the junior high school department. It found out that students consider research a difficult subject that makes them less interested. Research theories and concepts appropriate for junior high school must be identified for curriculum revision. Teachers believed that they need to enhance their knowledge and skills and gain more experience in writing to become creative and confident research teachers. For teachers to be actively engaged in research, they have to be provided with training and workshops related to research and be strongly encouraged to do at least action research. The faculty development program may also include creating research mentors and the provision of opportunities for publicatio

Supersolutions for a class of semilinear heat equations

A semilinear heat equation $u_{t}=\Delta u+f(u)$ with nonnegative initial data in a subset of $L^{1}(\Omega)$ is considered under the assumption that $f$ is nonnegative and nondecreasing and $\Omega\subseteq \R^{n}$. A simple technique for proving existence and regularity based on the existence of supersolutions is presented, then a method of construction of local and global supersolutions is proposed. This approach is applied to the model case $f(s)=s^{p}$, $\phi\in L^{q}(\Omega)$: new sufficient conditions for the existence of local and global classical solutions are derived in the critical and subcritical range of parameters. Some possible generalisations of the method to a broader class of equations are discussed.Comment: Expanded version of the previous submission arXiv:1111.0258v1. 14 page

Efecto Talbot no paraxial en una red unidimensional de periodo comparable a la longitud de onda

The Talbot effect is a diffractive phenomenon which was found since its inception in the Gaussian optics, but when the period of the object is comparable with the wavelength is considered entering its non-paraxial regime. There, it has attracted interest for its applications related to the design of objects and their restorative effects posing in damaged gratings on this scale. In this contribution a study of this phenomenon at level non-paraxial (metaxial) is presented by using scalar diffraction theory in plane waves representation for periodic transversal fields. To this end, a one-dimensional amplitude grating of period p is used which is illuminated by a monochromatic plane wave of wavelength λ where p ranges between 1,5 λ and 4,2 λ.El efecto Talbot es un fenómeno difractivo ubicado desde su origen en la óptica Gaussiana, pero cuando la longitud de onda es comparable con el periodo del objeto se considera que este efecto entra en su régimen no paraxial, el cual nuevamente ha despertado el interés por su volumen de aplicación relacionado con el diseño de objetos y sus efectos curativo que presenta en redes averiadas a esta escala En esta contribución presentamos un estudio de este fenómeno a nivel no paraxial (metaxial),usando la teoría escalar de difracción en representación de ondas planas para campos periódicos transversal. Para ello se utiliza como objeto periódico una red de amplitud unidimensional de periodo p, iluminada con una onda plana monocromática de amplitud unitaria y longitud de onda λ, donde p se encuentra entre 1,5 λ y 4,2 λ.Centro de Investigaciones Óptica

Efecto Talbot no paraxial en una red unidimensional de periodo comparable a la longitud de onda

The Talbot effect is a diffractive phenomenon which was found since its inception in the Gaussian optics, but when the period of the object is comparable with the wavelength is considered entering its non-paraxial regime. There, it has attracted interest for its applications related to the design of objects and their restorative effects posing in damaged gratings on this scale. In this contribution a study of this phenomenon at level non-paraxial (metaxial) is presented by using scalar diffraction theory in plane waves representation for periodic transversal fields. To this end, a one-dimensional amplitude grating of period p is used which is illuminated by a monochromatic plane wave of wavelength λ where p ranges between 1,5 λ and 4,2 λ.El efecto Talbot es un fenómeno difractivo ubicado desde su origen en la óptica Gaussiana, pero cuando la longitud de onda es comparable con el periodo del objeto se considera que este efecto entra en su régimen no paraxial, el cual nuevamente ha despertado el interés por su volumen de aplicación relacionado con el diseño de objetos y sus efectos curativo que presenta en redes averiadas a esta escala En esta contribución presentamos un estudio de este fenómeno a nivel no paraxial (metaxial),usando la teoría escalar de difracción en representación de ondas planas para campos periódicos transversal. Para ello se utiliza como objeto periódico una red de amplitud unidimensional de periodo p, iluminada con una onda plana monocromática de amplitud unitaria y longitud de onda λ, donde p se encuentra entre 1,5 λ y 4,2 λ.Centro de Investigaciones Óptica

Source apportionment and Elemental Composition of Atmospheric total Suspended Particulates (TSP) Over the Red Sea Coast of Saudi Arabia

This work presents a comprehensive study on concentrations and elemental composition of total suspended atmospheric particulates for a semi-urban site on the Red Sea coast, and on-board a research vessel, which collected off-shore samples along the Red Sea. We conducted one of the most extended measurement campaigns of atmospheric particulates ever for the region, with continuous measurements over 27 months. The overall mean concentrations (± st. dev.) of TSP were 125 ± 197 µg m−3 for the permanent semi-urban site, and 108 ± 193 µg m−3 for the off-shore mobile site. The region is frequently severely impacted by both localised and widespread dust storms, which on occasion, can increase atmospheric particulate concentrations to levels above mg m−3 (> 1000 µg m−3). Median concentrations were not as variable between seasons, indicating a stable, permanent presence of atmospheric particulates independent of the time of year. The primary chemical elements contributing to particulate mass were Na, Ca, S, Al and Fe. We employed Positive Matrix Factorisation (EPA PMF v5.0.14) to identify different major sources of particulates, which were crustal, marine, fuel oil combustion/secondary sulphate and mixed anthropogenic. The crustal source was characterised by tracers Al, Fe, K, Mg and Sn, and was present to some extent in the other identified sources due to the permanent presence of dust particles in the atmosphere. The fuel oil combustion/secondary sulphate source was identifiable by the almost exclusive presence of S, and to a lesser extent V, emitted from oil combustion as primary emissions and also secondary sulphate formation following the release of S to the atmosphere. A mixed anthropogenic source was characterised by Zn, Ni, Cr, Cu and Pb, emitted from traffic, industry, power generation and water desalination. This study highlights that the natural sources of particulates in this desert region give rise to frequent episodes of extremely poor air quality, and this problem is compounded by significant emissions of anthropogenic pollution, which has an impact across the entire Red Sea basin. Further stringent measures should be adopted to improve air quality across the region and prevent long-term damage to the health of the local population and ecosystems.En prens

Bioenergy transition as a strategic mechanism to diversify energy sources in rural areas in Colombia

Received: February 1st, 2023 ; Accepted: May 27th, 2023 ; Published: October 14th, 2023 ; Correspondence: [email protected], [email protected] growth in population has resulted in an increase in the consumption of goods and services, which has led to a surge in waste generation and the use of fossil fuels. To mitigate the envi-ronmental issues associated with improper waste management and reduce greenhouse gas emissions from fossil fuels, residual organic matter can be used to produce bioenergy in the form of biogas and biomethane through anaerobic digestion (AD). These biofuels can act as substitutes for liquefied petroleum gas (LPG) and natural gas (NG) and can be utilized for power and heat generation. In Colombia, the current production of biogas is 4 MW, and the government aims to increase its utilization by promoting the inclusion of biogas and biomethane in the energy matrix through a supportive regulatory framework. Studies suggest that the theoretical energy potential of livestock waste in Colombia is estimated to be 2,673 MW, but the current technological conditions allow for the utilization of only 198 MW, with the pork sector contributing 34%. This study examines the legal context and the present state of biogas in the Colombian energy matrix, while exploring the potential of the Colombian pig farming sector for biogas production. The social, economic, and environmental barriers and opportunities faced by this sector in becoming an energy producer during the transition period are also identified. The findings suggest that biogas presents a sustainable energy solution for rural areas of Colombia where pig farming is a prominent economic activity. Biogas can replace traditional fuels like LPG and firewood for cooking purposes or serve as a complementary source for electricity and thermal energy production in non-interconnected zones. This could mitigate environmental issues and reduce the prevalence of respiratory diseases associated with the use of firewood