The minimality of the map x/|x| for weighted energy

In this paper, we investigate the minimality of the map $\frac{x}{\|x\|}$ from the euclidean unit ball $\mathbf{B}^n$ to its boundary $\mathbb{S}^{n-1}$ for weighted energy functionals of the type $E\_{p,f}= \int\_{\mathbf{B}^n}f(r)\|\nabla u\|^p dx$, where $f$ is a non-negative function. We prove that in each of the two following cases: i) $p=1$ and $f$ is non-decreasing, i)) $p$ is an integer, $p \leq n-1$ and $f= r^{\alpha}$ with $\alpha \geq 0$, the map $\frac{x}{\|x\|}$ minimizes $E\_{p,f}$ among the maps in $W^{1,p}(\mathbf{B}^n, \mathbb{S}^{n-1})$ which coincide with $\frac{x}{\|x\|}$ on $\partial \mathbf{B}^n$. We also study the case where $f(r)= r^{\alpha}$ with $-n+2 < \alpha < 0$ and prove that $\frac{x}{\|x\|}$ does not minimize $E\_{p,f}$ for $\alpha$ close to $-n+2$ and when $n \geq 6$, for $\alpha$ close to $4-n$

Analytical ray-tracing in planetary atmospheres

Ground-based astro-geodetic observations and atmospheric occultations, are two examples of observational techniques requiring a scrutiny analysis of atmospheric refraction. In both cases, the measured changes in observables are geometrically related to changes in the photon path and the light time of the received electromagnetic signal. In the context of geometrical optics, the change in the physical properties of the signal are related to the refractive profile of the crossed medium. Therefore, having a clear knowledge of how the refractivity governs the photon path and the light time evolution is of prime importance to clearly understand observational features. Analytical studies usually focused on spherically symmetric atmospheres and only few aimed at exploring the effect of the non-spherical symmetry on the observables. In this paper, we analytically perform the integration of the photon path and the light time of rays traveling across a planetary atmosphere. We do not restrict our attention to spherically symmetric atmospheres and introduce a comprehensive mathematical framework which allows to handle any kind of analytical studies in the context of geometrical optics. To highlight the capabilities of this new formalism, we carry out five realistic applications for which we derive analytical solutions. The accuracy of the method of integration is assessed by comparing our results to a numerical integration of the equations of geometrical optics in the presence of a quadrupolar moment $J_2$. This shows that the analytical solution leads to the determination of the light time and the refractive bending with relative errors at the level of one part in $10^8$ and one part in $10^5$, for typical values of the refractivity and the $J_2$ parameter at levels of $10^{-4}$ and $10^{-2}$, respectively

Preferential concentration of inertial sub-kolmogorov particles. The roles of mass loading of particles, Stokes and Reynolds numbers

Turbulent flows laden with inertial particles present multiple open questions and are a subject of great interest in current research. Due to their higher density compared to the carrier fluid, inertial particles tend to form high concentration regions, i.e. clusters, and low concentration regions, i.e. voids, due to the interaction with the turbulence. In this work, we present an experimental investigation of the clustering phenomenon of heavy sub-Kolmogorov particles in homogeneous isotropic turbulent flows. Three control parameters have been varied over significant ranges: $Re_{\lambda} \in [170 - 450]$, $St\in [0.1 - 5]$ and volume fraction $\phi_v\in [2\times 10^{-6} - 2\times 10^{-5}]$. The scaling of clustering characteristics, such as the distribution of Vorono\"i areas and the dimensions of cluster and void regions, with the three parameters are discussed. In particular, for the polydispersed size distributions considered here, clustering is found to be enhanced strongly (quasi-linearly) by $Re_{\lambda}$ and noticeably (with a square-root dependency) with $\phi_v$, while the cluster and void sizes, scaled with the Kolmogorov lengthscale $\eta$, are driven primarily by $Re_{\lambda}$. Cluster length $\sqrt{\langle A_c \rangle}$ scales up to $\approx 100 {\eta}$, measured at the highest $Re_{\lambda}$, while void length $\sqrt{\langle A_v \rangle}$ scaled also with $\eta$ is typically two times larger ($\approx 200 {\eta}$). The lack of sensitivity of the above characteristics to the Stokes number lends support to the "sweep-stick" particle accumulation scenario. The non-negligible influence of the volume fraction, however, is not considered by that model and can be connected with collective effects

Vulnerability of the agricultural sector to climate change: The development of a pantropical Climate Risk Vulnerability Assessment to inform sub-national decision making

As climate change continues to exert increasing pressure upon the livelihoods and agricultural sector of many developing and developed nations, a need exists to understand and prioritise at the sub national scale which areas and communities are most vulnerable. The purpose of this study is to develop a robust, rigorous and replicable methodology that is flexible to data limitations and spatially prioritizes the vulnerability of agriculture and rural livelihoods to climate change. We have applied the methodology in Vietnam, Uganda and Nicaragua, three contrasting developing countries that are particularly threatened by climate change. We conceptualize vulnerability to climate change following the widely adopted combination of sensitivity, exposure and adaptive capacity. We used Ecocrop and Maxent ecological models under a high emission climate scenario to assess the sensitivity of the main food security and cash crops to climate change. Using a participatory approach, we identified exposure to natural hazards and the main indicators of adaptive capacity, which were modelled and analysed using geographic information systems. We finally combined the components of vulnerability using equal-weighting to produce a crop specific vulnerability index and a final accumulative score. We have mapped the hotspots of climate change vulnerability and identified the underlying driving indicators. For example, in Vietnam we found the Mekong delta to be one of the vulnerable regions due to a decline in the climatic suitability of rice and maize, combined with high exposure to flooding, sea level rise and drought. However, the region is marked by a relatively high adaptive capacity due to developed infrastructure and comparatively high levels of education. The approach and information derived from the study informs public climate change policies and actions, as vulnerability assessments are the bases of any National Adaptation Plans (NAP), National Determined Contributions (NDC) and for accessing climate finance

The Use of the Internet for Alternative Views on Health

Today, the majority of American adults uses the internet and looks for health information online. Of interest in this dissertation are people who do not subscribe to mainstream views of health, and may use the internet to discover, bolster, or share their alternative views. Although the Centers for Disease Control and Prevention (CDC) have named fluoridated drinking water and vaccination as two of the top ten public health achievements of the 20th century, there is a significant minority of people who has concerns about the safety and effectiveness of these practices. There are two essential purposes for this dissertation. First, it describes the nature of internet use among people who hold nonmainstream views of health issues. Second, it tests the hypotheses that the extent of people\u27s internet use is a reflection of two classes of influence: 1) individual traits, such as demographic characteristics, feelings of estrangement, and need for cognition, and 2) their inability to find support from other sources, specifically mainstream media and their face-to-face social network. These analyses are informed by three sets of data: interviews with people who have varying views on fluoridation, a pair of nationally representative surveys (one on the MMR vaccine, and one on fluoridated water), and a corresponding pair of purposive surveys. The interview results identified important themes and issues surrounding nonmainstream health beliefs, especially their connection to personal experience and perceived credibility of information sources. The representative surveys found that approximately 10% of Americans believe that the MMR vaccine and fluoridated water are unsafe, with the rest of the population about evenly divided between being uncertain and believing that the health measures are safe. Notably, believing that these measures were unsafe was unrelated to any demographic characteristics, but internet use on those topics was strongly related. Internet use on those topics was associated with youth and college education, as well as perceiving the news media as having a different view from their own. The lack of social network support for one\u27s views on these topics, however, was unrelated to internet use. The implications of these findings and future research directions are discussed

Alien Registration- Bourgoin, Marie (Lewiston, Androscoggin County)

https://digitalmaine.com/alien_docs/30637/thumbnail.jp

Alien Registration- Bourgoin, Marie (Lewiston, Androscoggin County)

https://digitalmaine.com/alien_docs/30637/thumbnail.jp