Existence and Uniqueness of Singular Solutions for a Conservation Law Arising in Magnetohydrodynamics

The Brio system is a two-by-two system of conservation laws arising as a simplified model in ideal magnetohydrodynamics (MHD). The system has the form \begin{align*} \partial_t u+\partial_x \Big({\textstyle \frac{u^2+v^2}{2}}\Big)=0,\\ \partial_t v+\partial_x \big(v(u-1)\big)=0. \end{align*} It was found in previous works that the standard theory of hyperbolic conservation laws does not apply to this system since the characteristic fields are not genuinely nonlinear on the set $v=0$. As a consequence, certain Riemann problems have no weak solutions in the traditional class of functions of bounded variation. It was argued in Nonlinearity 9, 1547--1563 (1996) that in order to solve the system, singular solutions containing Dirac masses along the shock waves might have to be used. Solutions of this type were exhibited in Proc. Edinb. Math. Soc. 55, 711--729 (2012) and Russ. J. Math. Phys. 22, 518--527 (2015), but uniqueness was not obtained. In the current work, we introduce a nonlinear change of variables which makes it possible to solve the Riemann problem in the framework of the standard theory of conservation laws. In addition, we develop a criterion which leads to an admissibility condition for singular solutions of the original system, and it can be shown that admissible solutions are unique in the framework developed here.Comment: 20 pages, 7 figure

Deljeni delta talasi i primene na sisteme zakona održanja

There are many real models in which unbounded solution to conservation law system occur. Most often we have some kind of delta function in the solution as a result of the accumulation of mass or some other variable. There is no general method of approaching such problems with nonlinearities. This dissertation provides solutions to conservation law systems that contain division by a dependent variable, which is a problematic part when working with measures. For example, a basic model of chromatography and similar chemical processes has a division with a variable that is unbounded in some cases. The denition of the split delta shock and the general method of using it in such systems is given. Finally, the solution for the singular chromatography model is given.  Postoji mnogo realnih modela u kojima se javljaju neoranicena resenja zakona odrzanja. Najcesce imamo neku vrstu delta funkcije u resenju kao posledicu nagomilavanja mase ili neke druge velicine. Ne postoji opsti metod prilaza takvim problemima sa nelinearnostima. U ovoj disertaciji su data resenja problema zakona odrzanja koja sadrze delenje zavisnom promenljivom, sto je problematican deo kod rada sa merama. Na primer, osnovni model hromatograje i slicnih hemijskih procesa ima delenje promenljivom koja je neogranicena u nekim slucajevima. Data je denicija inverza delenjog delta udarnog talasa i opsti metod primene u takvim sistemima. Na kraju je dato resenje kod modela singularne hromatograje.

Deljeni delta talasi i primene na sisteme zakona održanja

There are many real models in which unbounded solution to conservation law system occur. Most often we have some kind of delta function in the solution as a result of the accumulation of mass or some other variable. There is no general method of approaching such problems with nonlinearities. This dissertation provides solutions to conservation law systems that contain division by a dependent variable, which is a problematic part when working with measures. For example, a basic model of chromatography and similar chemical processes has a division with a variable that is unbounded in some cases. The denition of the split delta shock and the general method of using it in such systems is given. Finally, the solution for the singular chromatography model is given.  Postoji mnogo realnih modela u kojima se javljaju neoranicena resenja zakona odrzanja. Najcesce imamo neku vrstu delta funkcije u resenju kao posledicu nagomilavanja mase ili neke druge velicine. Ne postoji opsti metod prilaza takvim problemima sa nelinearnostima. U ovoj disertaciji su data resenja problema zakona odrzanja koja sadrze delenje zavisnom promenljivom, sto je problematican deo kod rada sa merama. Na primer, osnovni model hromatograje i slicnih hemijskih procesa ima delenje promenljivom koja je neogranicena u nekim slucajevima. Data je denicija inverza delenjog delta udarnog talasa i opsti metod primene u takvim sistemima. Na kraju je dato resenje kod modela singularne hromatograje.

Aeronautical engineering: A continuing bibliography with indexes (supplement 269)

This bibliography lists 539 reports, articles, and other documents introduced into the NASA scientific and technical information system in August, 1991. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics

Gulf Estuarine Research Society 2014 Meeting

Table of Contents: Thank You to Our Sponsors! (p. 3) -- About the Gulf Estuarine Research Society (p. 4) -- Student Travel Award winners (p. 5) -- Abbreviated Schedule (p. 7) -- 2014 Plenary Speaker – Dr. Michael Osland (p. 8) -- 2014 Plenary Speaker – Dr. Maggie Walser (p. 9) -- Full Schedule (p. 10) -- Poster Session Directory (p. 17) -- Oral Presentation Abstracts (p. 21) -- Poster Presentation Abstracts (p. 38) -- Things to Do in Port Aransas (p. 52) -- Greening the Meeting (p. 53) -- Map of University of Texas Marine Science Institute (p. 54)Coastal and Estuarine Research Foundation, Port Aransas, Gulf of Mexico Foundation, Coastal Bend Bays & Estuaries Program, Lotek Wireless Fish & Wildlife Monitoring, Sea Grant Mississippi-Alabama, Sea Grant Louisiana, Sea Grant Texas, The University of Austin Marine Science Institute, Mission-Aransas National Estuarine Research ReserveMarine Scienc

Crude Oil Exploration in the World

"Crude Oil Exploration in the World" contains multidisciplinary chapters in the fields of prospection and exploration of crude oils all over the world in addition to environmental impact assessments, oil spills and marketing of crude oils

Proceedings of the Salford Postgraduate Annual Research Conference (SPARC) 2011

These proceedings bring together a selection of papers from the 2011 Salford Postgraduate Annual Research Conference(SPARC). It includes papers from PhD students in the arts and social sciences, business, computing, science and engineering, education, environment, built environment and health sciences. Contributions from Salford researchers are published here alongside papers from students at the Universities of Anglia Ruskin, Birmingham City, Chester,De Montfort, Exeter, Leeds, Liverpool, Liverpool John Moores and Manchester

Development of Novel Oxidation Catalysts for Carbon Isotope Ratio Analysis

The International Rosetta Mission is the name given to the European Space Agency’s bold plan to perform in-situ analysis of a comet. One of the instruments on board, MODULUS, is a Gas Chromatograph - Mass Spectrometer that will use the concepts of chromatography and chemical oxidation to return data on chemical composition, and the carbon isotope ratios of the components of the comet The requirements of the chromatographic columns and oxidation catalysts are severe. The issues of mass, power and stability at launch were concerns for the integration and functionality of the instrument at the comet surface. The unique nature of the analysis system required that a laboratory analogue of the device to be designed and constructed, so that potential components could be tested using an instrument similar to MODULUS. Once developed, the laboratory system allowed performance testing of four chromatographic columns, as well as observing the effect of space qualification (vibration) testing of those columns. Results allowed recommendations of column choice to be passed to the MODULUS science team. Traditionally, oxidation units for isotope ratio analysis consist of oxides of nickel and copper, which operate at high temperatures (800-1000°C) and therefore would draw large amounts of power if used on MODULUS. Compounds that potentially are more efficient were examined, created and tested (using the MODULUS laboratory analogue) for the replacement of such compounds. Oxides of rhodium, palladium and copper-chromium were found to preserve sample isotope integrity, oxidise efficiently, and work at far lower temperatures ( As an application for techniques developed for MODULUS, a new method was created for analysis of 813C in terrestrial atmospheric CH4. The method was tested using headspace samples of air from wetlands in Finland and Scotland. An experiment was devised to observe any 813C shift induced by the addition of sulphate to wetland soil and change in incubation temperature. No significant relationships between 813C of CH4 and incubation conditions were found

Exoteric effects at nanoscopic interfaces - Uncommon negative compressibility of nanoporous materials and unexpected cavitation at liquid/liquid interfaces

This PhD thesis is devoted to the investigation of some peculiar effects happening at nanoscopic interfaces between immiscible liquids or liquids and solids via molecular dynamics simulations. The study of the properties of interfaces at a nanoscopic scale is driven by the promise of many interesting technological applications, including: a novel technology for developing both eco-friendly energy storage devices in the form of mechanical batteries, as well as energy dissipation systems and, in particular, shock absorbers for the automotive market; biomedical applications related to cavitation, such as High-Intensity Focused Ultrasound (HIFU) ablation of cancer tissues and localised drug delivery, and many more. The kinetics of phenomena taking places at these scales is typically determined by large free-energy barriers separating the initial and final states, and even intermediate metastable states, when they are present. Because of such barriers, the phenomena we are interested in are "rare events", i.e. the system attempts the crossing of the barrier(s) many times before finally succeeding when an energy fluctuation makes it possible. At the same time, the magnitude of the barrier is determined by the energetics and dynamics of atoms, which forces us to model the system by taking into account both the femtosecond atomistic timescale and the timescale of the relevant phenomena, typically exceeding the former by several orders of magnitude. These longer timescales are inaccessible to standard molecular dynamics, so, in order to tackle this issue, advanced MD techniques need to be employed. The thesis is divided into two parts, corresponding to the main lines of research investigated, which are (I) the interfaces between water and complex nanoporous solids, and (II) planar solid-liquid and liquid-liquid interfaces. Anticipating some results, atomistic simulations helped uncovering the microscopic mechanism behind the (incredibly rare!) giant negative compressibility exhibited by the ZIF-8 metal organic framework (MOF) upon water intrusion. Molecular dynamics simulations also supported experimental results showing how it is possible to change the intermediate intrusion-extrusion performance of ZIF-8 by changing its grain morphology and arrangement, from a fine powder to compact monolith. Free-energy MD calculations allowed to explain the exceptional stability of surface nanobubbles in water, at undersaturated conditions, on a surprisingly wide variety of substrates, characterized by disparate hydrophobicities and gas affinities; and yet, how they catastrophically destabilize in organic solvents. Finally, through simulations, some light was shed upon the working mechanism behind the novelly discovered phenomenon of how the interface between two immiscible liquids can act as a nucleation site for cavitation

Aeronautical engineering: A continuing bibliography with indexes (supplement 323)

This bibliography lists 518 reports, articles, and other documents introduced into the NASA scientific and technical information system in November 1995. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment, and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics