Existence of Global Solutions to Supercritical Semilinear Wave Equations

∗The author was partially supported by Alexander von Humboldt Foundation and the Contract MM-516 with the Bulgarian Ministry of Education, Science and Thechnology.

Linear Fractional PDE, Uniqueness of Global Solutions

Mathematics Subject Classification: 26A33, 47A60, 30C15.

SOLITON SOLUTIONS TO SYSTEMS OF COUPLED SCHRODINGER EQUATIONS OF HAMILTONIAN TYPE

We study the existence of positive solutions of Hamiltonian-type systems of second-order elliptic PDE in the whole space. The systems depend on a small parameter and involve a potential having a global well structure. We use dual variational methods, a mountain-pass type approach and Fourier analysis to prove positive solutions exist for sufficiently small values of the parameter.

GLOBAL WELL-POSEDNESS AND NON-LINEAR STABILITY OF PERIODIC TRAVELING WAVES FOR A SCHRODINGER-BENJAMIN-ONO SYSTEM

The objective of this paper is two-fold: firstly, we develop a local and global (in time) well-posedness theory for a system describing the motion of two fluids with different densities under capillary-gravity waves in a deep water flow (namely, a Schrodinger-Benjamin-Ono system) for low-regularity initial data in both periodic and continuous cases; secondly, a family of new periodic traveling waves for the Schrodinger-Benjamin-Ono system is given: by fixing a minimal period we obtain, via the implicit function theorem, a smooth branch of periodic solutions bifurcating a Jacobian elliptic function called dnoidal, and, moreover, we prove that all these periodic traveling waves are nonlinearly stable by perturbations with the same wavelength.

POSITIVITY PROPERTIES OF THE FOURIER TRANSFORM AND THE STABILITY OF PERIODIC TRAVELLING-WAVE SOLUTIONS

In this paper we establish a method to obtain the stability of periodic travelling-wave solutions for equations of Korteweg-de Vries-type u(t) + u(p)u(x) - Mu(x) = 0, with M being a general pseudodifferential operator and where p >= 1 is an integer. Our approach uses the theory of totally positive operators, the Poisson summation theorem, and the theory of Jacobi elliptic functions. In particular we obtain the stability of a family of periodic travelling waves solutions for the Benjamin Ono equation. The present technique gives a new way to obtain the existence and stability of cnoidal and dnoidal waves solutions associated with the Korteweg-de Vries and modified Korteweg-de Vries equations, respectively. The theory has prospects for the study of periodic travelling-wave solutions of other partial differential equations.

Non-linear modal analysis for beams subjected to axial loads: Analytical and finite-element solutions

A rigorous derivation of non-linear equations governing the dynamics of an axially loaded beam is given with a clear focus to develop robust low-dimensional models. Two important loading scenarios were considered, where a structure is subjected to a uniformly distributed axial and a thrust force. These loads are to mimic the main forces acting on an offshore riser, for which an analytical methodology has been developed and applied. In particular, non-linear normal modes (NNMs) and non-linear multi-modes (NMMs) have been constructed by using the method of multiple scales. This is to effectively analyse the transversal vibration responses by monitoring the modal responses and mode interactions. The developed analytical models have been crosschecked against the results from FEM simulation. The FEM model having 26 elements and 77 degrees-of-freedom gave similar results as the low-dimensional (one degree-of-freedom) non-linear oscillator, which was developed by constructing a so-called invariant manifold. The comparisons of the dynamical responses were made in terms of time histories, phase portraits and mode shapes. (C) 2008 Elsevier Ltd. All rights reserved.

The influence of oscillations on global existence for a class of semi-linear wave equations

The goal of this paper is to study the global existence of small data solutions to the Cauchy problem for the nonlinear wave equation u(tt) - a(t)(2) Delta u = u(t)(2) - a(t)(2)vertical bar del u vertical bar(2). In particular we are interested in statements for the 1D case. We will explain how the interplay between the increasing and oscillating behavior of the coefficient will influence global existence of small data solutions. Copyright c 2011 John Wiley & Sons, Ltd.

Decreased AIRE Expression and Global Thymic Hypofunction in Down Syndrome

The Down syndrome (DS) immune phenotype is characterized by thymus hypotrophy, higher propensity to organ-specific autoimmune disorders, and higher susceptibility to infections, among other features. Considering that AIRE (autoimmune regulator) is located on 21q22.3, we analyzed protein and gene expression in surgically removed thymuses from 14 DS patients with congenital heart defects, who were compared with 42 age-matched controls with heart anomaly as an isolated malformation. Immunohistochemistry revealed 70.48 +/- 49.59 AIRE-positive cells/mm(2) in DS versus 154.70 +/- 61.16 AIRE-positive cells/mm(2) in controls (p < 0.0001), and quantitative PCR as well as DNA microarray data confirmed those results. The number of FOXP3-positive cells/mm(2) was equivalent in both groups. Thymus transcriptome analysis showed 407 genes significantly hypoexpressed in DS, most of which were related, according to network transcriptional analysis (FunNet), to cell division and to immunity. Immune response-related genes included those involved in 1) Ag processing and presentation (HLA-DQB1, HLA-DRB3, CD1A, CD1B, CD1C, ERAP) and 2) thymic T cell differentiation (IL2RG, RAG2, CD3D, CD3E, PRDX2, CDK6) and selection (SH2D1A, CD74). It is noteworthy that relevant AIRE-partner genes, such as TOP2A, LAMNB1, and NUP93, were found hypoexpressed in DNA microarrays and quantitative real-time PCR analyses. These findings on global thymic hypofunction in DS revealed molecular mechanisms underlying DS immune phenotype and strongly suggest that DS immune abnormalities are present since early development, rather than being a consequence of precocious aging, as widely hypothesized. Thus, DS should be considered as a non-monogenic primary immunodeficiency. The Journal of Immunology, 2011, 187: 3422-3430.

Fluid Replacement With Hypertonic or Isotonic Solutions Guided by Mixed Venous Oxygen Saturation in Experimental Hypodynamic Sepsis

Background: Splanchnic perfusion is prone to early injury and persists despite normalization of global hemodynamic variables in sepsis. Volume replacement guided by oxygen derived variables has been recommended in the management of septic patients. Our hypothesis was that a hypertonic isoneotic solution Would improve the benefits of crystalloids replacement guided by mixed venous oxygen saturation. Methods: Seventeen anesthetized and mechanically ventilated mongrel dogs received an intravenous infusion of live E. coli in 30 minutes. They were then randomized into three groups: control group (n = 3) bacterial infusion without treatment; normal saline (n = 7), initial fluid replacement with 32 mL/kg of normal saline during 20 minutes; hypertonic solution (n = 7), initial fluid replacement with 4 mL/kg of hypertonic solution during 5 minutes. After 30 and 60 Minutes, additional boluses of normal saline were administered when mixed venous oxygen saturation remained below 70%. Mean arterial pressure, cardiac output; regional blood flows, systemic and regional oxygen-derived variables, and lactate levels were assessed. Animals were observed for 90 minutes and then killed. Hystopathological analysis including apoptosis detection using terminal deoxynucleotidil transferase mediated dUTP-biotin nick end labeling was performed. Results: A hypodynamic septic shock was observed after bacterial infusion. Both the fluid-treated groups presented similar transient benefits in systemic and regional variables. A greater degree of gut epithelial cells apoptosis was observed in normal saline-treated animals. Conclusions: Although normalization of mixed venous oxygen saturation was not associated with restoration of markers of splanchnic or other systemic perfusion variables, the initial fluid savings with hypertonic saline and its latter effect on gut apoptosis may be of interest in sepsis management.

The strain-driven pyrochlore to "defect fluorite" phase transition in rare earth sesquioxide stabilized cubic zirconias

The relationship between the ordering characteristic of the pyrochlore structure type and that characteristic of the defect fluorite structure type (immediately on either side of two phase regions separating the two structure types) in a range of rare eath sesquioxide stabilized cubic zirconias is investigated via electron diffraction and imaging. Systematic structural change as a function of composition and relative size of the constituent metal ions is highlighted and a multi-q to single-q = 1/2 [111]* model proposed for the observed pyrochlore to defect fluorite phase transition. Strain introduced into the close-packed {111} metal ion planes of the defect fluorite average structure by the local cation and oxygen vacancy distribution is pointed to as the likely origin of the observed behavior. (C) 2001 Academic Press

Fighting climate change in the air: lessons from the EU directive on global aviation

The European Union's (EU) decision to include aviation into the Emissions Trade Scheme was heatedly contested. Countries around the world, but mainly the Brazil, Russia, India, China and South Africa group (BRICS) and the US, denounced the EU's initiate as illegal and unilateral. Following a decade of frustrated negotiations at the International Civil Aviation Organization (ICAO), this paper interrogates why such measure, in principle climate-friendly, inspired so much global resentment. I argue that concerns with competitiveness and risks of legal inconsistency are important, but insufficient elements to explain the core of the conflict. The paper suggests that the EU was strongly criticized because third countries perceived this action as an imposed solution, which fostered an environment of distrust. Therefore, I claim that the problem has more to do with a normative divide than with a substantive divergence on what should be done regarding aviation emissions. My analysis is informed by the present literature on the links between trade and climate change, but gives particular weight to first-hand information through interviews with key stakeholders. The paper is divided in three parts. First, it presents the scope of the EU directive in historical perspective. Second, it explores the EU's measure through three different angles: legal, economical and political. The final part explores some possible solutions to overcome these divergences.

Análise e optimização global de uma linha de extrusão

Os objectivos principais deste estudo são a caracterização de uma das linhas de extrusão existentes na Cabelte, nomeadamente a linha de extrusão de referência EP5, composta por duas extrusoras. Pretende-se fazer a determinação de indicadores energéticos e de processo e a optimização do consumo energético, no que diz respeito à energia consumida e às perdas térmicas relativas a esta linha. Para fazer a monitorização da linha de extrusão EP5 foi colocado no quadro geral dessa linha um equipamento central de medida de forma a ser possível a sua monitorização. No entanto, para a extrusora auxiliar as medições foram efectuadas com uma pinça amperimétrica e um fasímetro. Foram também efectuados ensaios onde foi avaliada a quantidade de material transformada, para isso foi utilizado um equipamento de pesagem, doseador gravimétrico aplicado nas extrusoras. As medições de temperatura para os cálculos das perdas térmicas da extrusora principal e para a caracterização dos materiais plásticos, foram efectuadas utilizando um termómetro digital. Foram efectuados ensaios de débito às extrusoras auxiliar e principal e foi estudada a variação do factor de potência em função da rotação do fuso. Na perspectiva do utilizador final a optimização para a utilização racional de energia está na redução de encargos da factura de energia eléctrica. Essa factura não depende só da quantidade mas também do modo temporal como se utiliza essa energia, principalmente a energia eléctrica, bastante dependente do período em que é consumida. Uma metodologia diferente no planeamento da produção, contemplando o fabrico dos cabos com maior custo específico nas horas de menor custo energético, implicaria uma redução dos custos específicos de 18,7% para o horário de verão e de 20,4% para o horário de inverno. Os materiais de revestimento utilizados (PE e PVC), influenciam directamente os custos energéticos, uma vez que o polietileno (PE) apresenta sempre valores de entalpia superiores (0,317 kWh/kg e 0,281 kWh/kg)) e necessita de temperaturas de trabalho mais elevadas do que o policloreto de vinilo (PVC) (0,141 kWh/kg e 0,124 kWh/kg). O consumo específico tendencialmente diminui à medida que aumenta a rotação do fuso, até se atingir o valor de rotação óptimo, a partir do qual esta tendência se inverte. O cosφ para as duas extrusoras em estudo, aumenta sempre com o aumento de rotação do fuso. Este estudo permitiu avaliar as condições óptimas no processo de revestimento dos cabos, de forma a minimizarmos os consumos energéticos. A redução de toda a espécie de desperdícios (sobre consumos, desperdício em purgas) é uma prioridade de gestão que alia também a eficácia à eficiência, e constitui uma ferramenta fundamental para assegurar o futuro da empresa. O valor médio lido para o factor de potência (0,38) da linha EP5, valor extremamente baixo e que vem associado à energia reactiva, além do factor económico que lhe está inerente, condiciona futuras ampliações. A forma de se corrigir o factor de potência é instalando uma bateria de condensadores de 500 kVAr. Considerando o novo sistema tarifário aplicado à energia reactiva, vamos ter um ganho de 36167,4 Euro/ano e o período de retorno de investimento é de 0,37 ano (4,5 meses). Esta medida implica também uma redução anual na quantidade de CO2 emitida de 6,5%. A quantificação das perdas térmicas é importante, pois só desta forma se podem definir modos de actuação de forma a aumentar a eficiência energética. Se não existir conhecimento profundo dos processos e metodologias correctas, não podem existir soluções eficientes, logo é importante medir antes de avançar com qualquer medida de gestão.

Comparative study of amine solutions used in CO2 absorption/desorption cycles

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia Química

Node adaptation for global collocation with radial basis functions using direct multisearch for multiobjective optimization

Meshless methods are used for their capability of producing excellent solutions without requiring a mesh, avoiding mesh related problems encountered in other numerical methods, such as finite elements. However, node placement is still an open question, specially in strong form collocation meshless methods. The number of used nodes can have a big influence on matrix size and therefore produce ill-conditioned matrices. In order to optimize node position and number, a direct multisearch technique for multiobjective optimization is used to optimize node distribution in the global collocation method using radial basis functions. The optimization method is applied to the bending of isotropic simply supported plates. Using as a starting condition a uniformly distributed grid, results show that the method is capable of reducing the number of nodes in the grid without compromising the accuracy of the solution. (C) 2013 Elsevier Ltd. All rights reserved.

Lor’s - Women personal rain protection solutions

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Management from the NOVA – School of Business and Economics