Solutions of some nonlinear parabolic equations with initial blow-up

We study the existence and uniqueness of solutions of $\partial_tu-\Delta u+u^q=0$ ($q>1$) in $\Omega\times (0,\infty)$ where $\Omega\subset\mathbb R^N$ is a domain with a compact boundary, subject to the conditions $u=f\geq 0$ on $\partial\Omega\times (0,\infty)$ and the initial condition $\lim_{t\to 0}u(x,t)=\infty$. By means of Brezis' theory of maximal monotone operators in Hilbert spaces, we construct a minimal solution when $f=0$, whatever is the regularity of the boundary of the domain. When $\partial\Omega$ satisfies the parabolic Wiener criterion and $f$ is continuous, we construct a maximal solution and prove that it is the unique solution which blows-up at $t=0$

Initial trace of solutions of semilinear heat equation with absorption

We study the initial trace problem for positive solutions of semilinear heat equations with strong absorption. We show that in general this initial trace is an outer regular Borel measure. We emphasize in particular the case where $u$ satisfies (E) $\partial_t u-\Delta u+t^\alpha |u|^{q-1}u=0$, with $q>1$ and $\alpha>-1$ and prove that in the subcritical case $

On uniqueness of large solutions of nonlinear parabolic equations in nonsmooth domains

We study the existence and uniqueness of the positive solutions of the problem (P): $\partial_tu-\Delta u+u^q=0$ ($q>1$) in $\Omega\times (0,\infty)$, $u=\infty$ on $\partial\Omega\times (0,\infty)$ and $u(.,0)\in L^1(\Omega)$, when $\Omega$ is a bounded domain in $\mathbb R^N$. We construct a maximal solution, prove that this maximal solution is a large solution whenever $q<N/(N-2)$ and it is unique if $\partial\Omega=\partial\bar\Omega^c$. If $\partial\Omega$ has the local graph property, we prove that there exists at most one solution to problem (P)Comment: 16 page

Crude oil and refinery streams desulphurization using slurry dispersed catalysts and ionic liquids

Petroleum refining is among the most important industries in the world. The oil refinery products contribute in many essential issues in the human life including transportation fuels, heating fuels, petrochemical industries, etc. Although oil refining is an old process started in the mid of the 19th century, new developments and technologies are introduced frequently due to the large amount of studies conducted around the world research centres. Some of the petroleum refining processes gain more attention in terms of research and development in the last couple of decades. For example, the importance of developing the hydrocracking process is increasing due to the increasing amount of heavy unconventional oil reserves. Another hot topic is the development of the hydrodesulphurization process due to the environmental concern about the sulphur oxides emissions produced by using oil refinery streams that contain several organic sulphur compounds. In this work, commercially available slurry catalyst precursors are tested to study the impact of the catalyst preparation conditions on its characteristic and activity. Those types of catalysts are used for hydrocracking and upgrading processes of heavy crude and residue including sulphur and other metal removal. The main subject was to approach the desulphurization activity and selectivity of the catalyst in removing dibenzothiophene (DBT) from model feed. DBT is one of the refractory sulphur compounds in the heavy oil fractions. It was found that changing the preparation conditions in terms of temperature, pressure and sulphiding agent influenced the activity and selectivity of the produced catalyst between the direct desulphurization reaction pathway and hydrogenation reaction pathway in removing DBT. The highest conversion was achieved by using cobalt-molybdenum-sulphide catalyst (Co-Mo-S) where up to 94.0 wt% of the DBT was converted. Adding the same catalyst precursor directly to Arab heavy crude oil, high desulphurization level was achieved where 70 wt% of the sulphur content of the feed has been removed. In addition, there is a high potential to increase this desulphurization level in treating heavy crude by applying the optimum operation conditions used in presulphiding the catalyst precursor. Ionic liquids (ILs) were also employed for sulphur removal from refinery streams by liquid-liquid extraction process. The ILs are organic salts with low melting points, mostly at room temperatures. Although the sulphur extraction level was very low comparing with the conventional hydrotreating process, this process has the advantage of minimizing the operation costs by reducing the reaction severity in terms of temperature and hydrogen consumption. Around 80 wt% of DBT was removed from model compound using one of the tested ILs. The nitrogen removal was also very high where almost 99 wt% of pyridine was removed from the model oil. However, the sulphur extraction level decreased in treating diesel fuel due to several factors such as the aromatic contents of the feed and the existence of several sulphur and metal compounds. To overcome this problem, the extraction process was repeated several times using fresh batches of ILs. This point has driven the importance of developing an efficient regeneration method for the used IL which was also approached in this work

Cities as emergent models: the morphological logic of Manhattan and Barcelona

This paper is set to unveil several particulars about the logic embedded in the diachronic model of city growth and the rules which govern the emergence of urban spaces. The paper outlines an attempt to detect and define the generative rules of a growing urban structure by means of evaluation techniques. The initial approach in this regards will be to study the evolution of existing urban regions or cities which in our case are Manhattan and Barcelona and investigate the rules and causes of their emergence and growth. The paper will concentrate on the spatial aspect of the generative rules and investigate their behaviour and dimensionality. Several Space Syntax evaluation methods will be implemented to capture the change of spatial configurations within the growing urban structures. In addition, certain spatial elements will be isolated and tested aiming to illustrate their influence on the main spatial structures. Both urban regions were found to be emergent products of a bottom up organic growth mostly distinguished in the vicinities of the first settlements. Despite the imposition of a uniform grid on both cities in later stages of their development these cities managed to deform the regularity in the preplanned grid in an emergent manner to end up with an efficient model embodied in their current spatial arrangement. The paper reveals several consistencies in the spatial morphology of both urban regions and provides explanation of these regularities in an approach to extract the underlying rules which contributed to the growth optimization process

Thermal Reshaping of Gold Nanorods in Micellar Solution of Water/Glycerol Mixtures

Gold nanorods (Nds) with aspect ratios of 4, 3.5, and 2.8 were prepared by the electrochemical method. The nanorods were thermally studied in binary solvents of aqueous glycerol at different ratios (25%–75%). The results illustrated that the longitudinal surface plasmon resonance (SPL) is strongly dependent on the dielectric constant. The maximum absorption is red shifted with increasing the glycerol/water ratio. This was attributed to the decreasing value of the dielectric constant of the binary solvents. Moreover, by increasing the temperatures, the results showed relative instability of the gold nanorods. This attributed to the relative instability of the micelle capping the nanorods

THE MUSLIM AND THE JEW: A STUDY OF JOHN UPDIKE’S TERRORIST

The perception of Muslims and Islam has changed after the attacks on the World Trade Center on September 11th 2001. Muslims have been projected as essential and natural-born terrorists. Thus, authors have taken this projection and reflected it into their works. John Updike, in his novel Terrorist, has done the same. He has portrayed two characters, a Muslim and a Jew. The contrast between the two characters reinforces the Islamophobic concerns of Western audience, in general, and ,American audience, in particular. Through lexical choices, narration technique, motifs and symbolism, Updike manages to further cast away the Muslim character from his society. Therefore, this research paper examines the Islamophobic, Orientalist aspects represented in Updike's Terrorist, through the comparison made between the .Egyptian-American, Muslim Ahmad, and the American, Jewish Levy

Towards an extended network-based description for BIM and Smart Cities

The pervasive deployment of “smart city” and “smart building” projects in cities world-wide is driving innovation on many fronts including; technology, telematics, engineering and entrepreneurship. Traditionally, descriptive models of built form were adapted to predict performance by using few data sets. This trend has recently diverted towards making short-term predictions and visualizing real-time information enabled by Big Data and the Internet of Things. Building and urban morphology need yet to adapt new frameworks to embrace these new technologies in the design and evolution of sustainable infrastructure. Through representing relationships between different infrastructure components and linking the resultant network to smart systems, it is perhaps possible to provide better predictions of the operational performance of buildings and cities. This workshop was dedicated to provide a platform for discussing these challenges between academics, construction and engineering experts, and policy makers. Together with a team of academics and researchers from UCL, the BIM Task Group at the Government Department of Business Innovation and Skills has scored success at releasing the Digital Built Britain construction strategy. The strategy will execute the UK government plans for BIM Level’3, making a shift from file-based collaboration to the more scalable and flexible semantic web. This is thought to provide opportunities for acquiring information about how performance data could support the design and operation phases of buildings and how BIM could constitute a bottom up approach to smart cities. The “Towards an extended network-based description for BIM and Smart Cities” workshop, which took place at Space Syntax Limited, was dedicated to tackle these challenges and plan for a start on the BIM level’3 project by attending to the morphological and performance aspects of the built environment and the wealth of research that was done in this field at UCL over the last decades. The workshop was intended to discuss a wide-range of theoretical frameworks and representational schemes for establishing network-based models as to structure data in building and urban information models and respond to social and environmental performance requirements of the built environment. The workshop has also discussed some applications and challenges presented by IoT, and by the data available on energy performance of buildings. The core discussion was centred on whether network-based models are fundamental to comprehend and represent the complexity of cities and inform urban design and public policy practices, during the design, construction, and operation phases of infrastructure projects