4,931 research outputs found

    Guidance properties of a cylindrical defocusing waveguide

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    summary:We discuss the propagation of electromagnetic waves of a special form through an inhomogeneous isotropic medium which has a cylindrical symmetry and a nonlinear dielectric response. For the case where this response is of self-focusing type the problem is treated in [1]. Here we continue this study by dealing with a defocusing dielectric response. This tends to inhibit the guidance properties of the medium and so guidance can only be expected provided that the cylindrical stratification is such that guidance would occur for the linear response that is obtained in the limit of zero field strength. The guided modes that we seek correspond to solutions of the boundary value problem −u′′+34ur2−q(r)u+p(r,u)u=λu-u'' + \frac 34 \frac u{r^2} - q(r) u + p( r, u ) u = \lambda u for r>0r > 0 with u∈H01(0,∞) u \in H^1_0 ( 0, \infty ) and its linearisation is −u′′+34ur2−q(r)u=λu-u'' + \frac 34 \frac u{r^2} - q( r ) u = \lambda u with u∈H01(0,∞) u \in H_0^1 ( 0, \infty ). This linear problem has the interval [0,∞)[0, \infty ) as its essential spectrum and the requirement that guidance should occur in the limit of zero field strength leads us to suppose that it has at least one negative eigenvalue. Solutions of the nonlinear problem are then obtained by bifurcation from such an eigenvalue. The main interest concerns the global behaviour of a branch of solutions since this determines the principal features of the waveguide. If the branch is bounded in L2(0,∞) L^2 ( 0, \infty ) there is an upper limit to the intensity of the guided beams (high-power cut-off), whereas if the branch is unbounded in L2(0,∞) L^2 ( 0, \infty ) then guidance is possible at arbitrarily high intensities. Our results show how these behaviours depend upon the properties of dielectric response

    FREDHOLM AND PROPERNESS PROPERTIES OF QUASILINEAR ELLIPTIC SYSTEMS OF SECOND ORDER

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    For a large class of subsets Ω⊂RN\varOmega\subset\mathbb{R}^{N} (including unbounded domains), we discuss the Fredholm and properness properties of second-order quasilinear elliptic operators viewed as mappings from W2,p(Ω;Rm)W^{2,p}(\varOmega;\mathbb{R}^{m}) to Lp(Ω;Rm)L^{p}(\varOmega;\mathbb{R}^{m}) with N\ltp\lt\infty and m≥1m\geq1. These operators arise in the study of elliptic systems of mm equations on Ω\varOmega. A study in the case of a single equation (m=1m=1) on RN\mathbb{R}^{N} was carried out by Rabier and Stuart. AMS 2000 Mathematics subject classification: Primary 35J45; 35J60. Secondary 47A53; 47F0

    Exponential decay and Fredholm properties in second-order quasilinear elliptic systems

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    AbstractWe consider second-order quasilinear elliptic systems on unbounded domains in the setting of Sobolev spaces. We complete our earlier work on the Fredholm and properness properties of the associated differential operators by giving verifiable conditions for the linearization to be Fredholm of index zero. This opens the way to using the degree for C1-Fredholm maps of index zero as a tool in the study of such quasilinear systems. Our work also enables us to check the Fredholm assumption which plays an important role in Rabier's approach to proving exponential decay to zero at infinity of solutions

    Global branches of positive weak solutions of semilinear elliptic problems over nonsmooth domains

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    We consider the nonlinear eigenvalue problem posed by a parameter-dependent semilinear second-order elliptic equation on a bounded domain with the Dirichlet boundary condition. The coefficients of the elliptic operator are bounded measurable functions and the boundary of the domain is only required to be regular in the sense of Wiener. The main results establish the existence of an unbounded branch of positive weak solution

    Innate sensing of chitin and chitosan

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    Chitin is the second most common polysaccharide found in nature. It is present in crustacean shells, insect exoskeletons, parasitic nematode eggs and gut linings, and in the cell wall of fungi. The deacetylated derivative of chitin, chitosan, is less common but is particularly evident in certain species of fungi, such as Cryptococcus, and the cyst wall of Entamoeba. How mammals sense and respond to these polymers is not well understood, and conflicting reports on their immunological activity have led to some controversy. Despite this, promising translational applications that exploit the unique properties of chitin and chitosan are being developed

    Downward shortwave surface irradiance from 17 sites for the FIRE/SRB Wisconsin experiment

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    A field experiment was conducted in Wisconsin during Oct. to Nov. 1986 for purposes of both intensive cirrus cloud measurments and SRB algorithm validation activities. The cirrus cloud measurements were part of the FIRE. Tables are presented which show data from 17 sites in the First ISCCP (International Satellite Cloud Climatology Project) Regional Experiment/Surface Radiation Budget (FIRE/SRB) Wisconsin experiment region. A discussion of intercomparison results and calibration inconsistencies is also included

    Buckling of a tapered elastica

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    Process Modeling Phase I Summary Report for the Advanced Gas Reactor Fuel Development and Qualification Program

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    This report summarizes the results of preliminary work at Oak Ridge National Laboratory (ORNL) to demonstrate application of computational fluid dynamics modeling to the scale-up of a Fluidized Bed Chemical Vapor Deposition (FBCVD) process for nuclear fuels coating. Specifically, this work, referred to as Modeling Scale-Up Phase I, was conducted between January 1, 2006 and March 31, 2006 in support of the Advanced Gas Reactor (AGR) Program. The objective was to develop, demonstrate and "freeze" a version of ORNL's computational model of the TRI ISOtropic (TRISO) fuel-particle coating process that can be specifically used to assist coater scale-up activities as part of the production of AGR-2 fuel. The results in this report are intended to serve as input for making decisions about initiating additional FBCVD modeling work (referred to as Modeling Scale-Up Phase II) in support of AGR-2. The main computational tool used to implement the model is the general-purpose multiphase fluid-dynamics computer code known as MFIX (Multiphase Flow with Interphase eXchanges), which is documented in detail on the DOE-sponsored website http://www.mfix.org. Additional computational tools are also being developed by ORNL for post-processing MFIX output to efficiently summarize the important information generated by the coater simulations. The summarized information includes quantitative spatial and temporal measures (referred to as discriminating characteristics, or DCs) by which different coater designs and operating conditions can be compared and correlated with trends in product quality. The ORNL FBCVD modeling work is being conducted in conjunction with experimental coater studies at ORNL with natural uranium CO (NUCO) and surrogate fuel kernels. Data are also being obtained from ambient-temperature, spouted-bed characterization experiments at the University of Tennessee and theoretical studies of carbon and silicon carbide chemical vapor deposition kinetics at Iowa State University. Prior to the current scale-up activity, considerable effort has gone in to adapting the MFIX code to incorporate the unique features of fuel coating reactors and also in validating the resulting simulation features with experimental observations. Much of this work is documented in previous AGR reports and publications (Pannala et al., 2004, Pannala et al., 2005, Boyalakuntla et al., 2005a, Boyalakuntla et al., 2005b and Finney et al., 2005). As a result of the previous work described above, the ORNL coater model now has the capability for simulating full spatio-temporal details of the gas-particle hydrodynamics and gas-particle heat and mass transfer in the TRISO coater. This capability provides a great deal of information about many of the processes believed to control quality, but the model is not yet sufficiently developed to fully predict coating quality for any given coater design and/or set of operating conditions because the detailed chemical reaction kinetics needed to make the model fully predictive are not yet available. Nevertheless, the model at its current stage of development already provides the most comprehensive and detailed quantitative information available about gas flows, solid flows, temperatures, and species inside the coater during operation. This level of information ought to be highly useful in expediting the scale-up process (e.g., in correlating observations and minimizing the number of pilot-scale tests required). However, previous work had not yet demonstrated that the typical design and/or operating changes known to affect product quality at the lab scale could be clearly discriminated by the existing model. The Modeling Scale-Up Phase I work was initiated to produce such a demonstration, and two detailed examples are discussed in this report
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