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  • 1
    Electronic Resource
    Electronic Resource
    Discussion of Paper by Hatch and Rice (1945)
    s.l. : American Chemical Society
    Industrial & engineering chemistry 37 (1945), S. 715-715 
    Details
    ISSN: 1520-5045
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/ie50428a014
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  • 2
    Electronic Resource
    Electronic Resource
    Efficient Treatment of Uncertainty in Numerical Optimization (1997)
    Oxford, UK : Blackwell Publishing Ltd
    Risk analysis 17 (1997), S. 0 
    Details
    ISSN: 1539-6924
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: We have combined the methods of probabilistic risk analysis and optimization to devise a technique suitable for the efficient treatment of uncertainties (or the effects of random fluctuations) in the design and analysis of mathematically describable processes. The key step is the approximation, by a multivariable Taylor series expansion, of the influence of random variables on the objective function. Statistical averaging of this expansion leads to a description of the objective function in terms of the moments of the random variables. Knowledge or estimation of these moments allows the optimization to be carried out using standard calculus based techniques. An example is treated with three variations to illustrate the use of this technique for nonlinear sets of equations and objective functions. The method presented here is applicable to process models in manufacturing, systems analysis, and risk analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1539-6924.1997.tb00847.x
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  • 3
    Electronic Resource
    Electronic Resource
    Carbon Wastes. (1912)
    s.l. : American Chemical Society
    Industrial & engineering chemistry 4 (1912), S. 160-164 
    Details
    ISSN: 1520-5045
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/ie50039a002
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  • 4
    Electronic Resource
    Electronic Resource
    Correction - Prevention of Silica Scale with Sodium Aluminate (1931)
    s.l. : American Chemical Society
    Industrial & engineering chemistry 23 (1931), S. 849-850 
    Details
    ISSN: 1520-5045
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/ie50259a035
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  • 5
    Electronic Resource
    Electronic Resource
    Tokamak m=1 magnetohydrodynamic calculations in toroidal geometry using a full set of nonlinear resistive magnetohydrodynamic equations (1988)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 31 (1988), S. 347-358 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The linear stability and nonlinear evolution of the resistive m=1 mode in tokamaks is studied using a full set of resistive magnetohydrodynamic (MHD) equations in toroidal geometry. The modification of the linear and nonlinear properties of the mode by a combination of strong toroidal effects and low resistivity is the focus of this work. Linearly there is a transition from resistive kink to resistive tearing behavior as the aspect ratio and resistivity are reduced, and there is a corresponding modification of the nonlinear behavior, including a slowing of the island growth and development of a Rutherford regime, as the tearing regime is approached. In order to study the sensitivity of the stability and evolution to assumptions concerning the equation of state, two sets of full nonlinear resistive MHD equations (a pressure convection set and an incompressible set) are used. Both sets give more stable nonlinear behavior as the aspect ratio is reduced. The pressure convection set shows a transition from a Kadomtsev reconnection at large aspect ratio to a saturation at small aspect ratio. The incompressible set yields Kadomtsev reconnection for all aspect ratios, but with a significant lengthening of the reconnection time and development of a Rutherford regime at an aspect ratio approaching the transition from a resistive kink mode to a tearing mode. The pressure convection set gives an incomplete reconnection similar to that sometimes seen experimentally. The pressure convection set is, however, strictly justified only at high beta.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866867
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  • 6
    Electronic Resource
    Electronic Resource
    Stability of ideal and resistive internal kink modes in toroidal geometry (1987)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 30 (1987), S. 1756-1766 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The stability of the ideal and resistive m=1 internal modes is investigated for tokamak equilibria having a variety of different q(r) profiles, including nonmonotonic q(r) with multiple q=1 surfaces. Detailed comparisons between analytic theory and numerical results from a linear toroidal magnetohydrodynamic code are presented. Particular attention is paid to the study of equilibria that are near marginal stability.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866242
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  • 7
    Electronic Resource
    Electronic Resource
    Magnetohydrodynamic stability and nonlinear evolution of the m=1 mode in toroidal geometry for safety factor profiles with an inflection point (1989)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 1 (1989), S. 788-797 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Magnetohydrodynamic (MHD) stability and nonlinear evolution of the m=1 mode are studied in toroidal geometry for safety factor profiles having an inflection point at the q=1 surface. For ideally stable cases, linear growth rates of the resistive m=1 mode are decreased by any combination of the following variations: decreasing the aspect ratio, decreasing shear at the q=1 surface, increasing S, decreasing q0, and/or decreasing beta. Transitions from resistive kink to tearing mode to complete stability are accompanied by increasing localization as the mode is stabilized. The ideal stability of the m=1 mode for low-shear inflection-point profiles is broken at very low, but finite, beta by the appearance of a radially localized ideal interchange mode. As beta is increased, the m=1 mode becomes a global ideal internal kink. These ideal modes are stabilized by decreasing the aspect ratio and, to a lesser extent, by increasing shear at the q=1 surface. Nonlinear evolution of the m=1 mode is found to follow the Kadomtsev complete reconnection process or to be stable, depending on the linear stability of the mode. However, all nonlinear calculations were carried out at Lundquist number S=105 and hence contain substantial resistive kink contributions. Consequently, nonlinear evolution in the m=1 tearing mode regime is not examined. Even for cases in which ideal effects dominate the linear mode, Kadomtsev reconnection is observed. The nonlinear stability of linearly stable modes was also uniformly observed, even for several cases having large initial perturbations. Hence complete linear stabilization resulting from a combination of toroidal effects and low shear at the q=1 surface can suppress sawteeth, as described by the Kadomtsev reconnection process, in tokamaks having safety factor profiles with q0〈1 at the magnetic axis; but, for the S values considered, nonlinear calculations of unstable modes result in complete Kadomtsev reconnection.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.859003
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  • 8
    Electronic Resource
    Electronic Resource
    Nonlinear dynamics of tearing modes in the reversed field pinch (1988)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 31 (1988), S. 1166-1179 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The results of investigations of nonlinear tearing-mode dynamics in reversed field pinch plasmas are described. The linear instabilities have poloidal mode number m=1 and toroidal mode numbers 10(approximately-less-than)n(approximately-less-than)20, and the resonant surfaces are therefore in the plasma core. The nonlinear dynamics result in dual cascade processes. The first process is a rapid m=1 spectral broadening toward high n, with a simultaneous spreading of magnetic turbulence radially outward toward the field-reversal surface. Global m=0 perturbations, which are driven to large amplitudes by the m=1 instabilities, in turn trigger the m=1 spectral broadening by back coupling to the higher n. The second process is a cascade toward large m and is mediated by m=2 modes. The m=2 perturbations have the structure of localized, driven current sheets and nonlinearly stabilize the m=1 modes by transferring m=1 energy to small-scale dissipation. The calculated spectrum has many of the qualitative features observed in experiments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866746
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  • 9
    Electronic Resource
    Electronic Resource
    Nonlinear evolution of the internal kink mode in toroidal geometry for shaped tokamak plasmas (1988)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 31 (1988), S. 1202-1216 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The nonlinear evolution of the internal kink mode is studied in toroidal geometry for noncircular cross-section tokamak plasmas. The study is focused on very low-shear and hollow q profiles, with q(ρ)≥1 for which the internal kink is unstable in the latter case, even at β=0. The nonlinear evolution is dominated by ideal magnetohydrodynamics (MHD), and the instability saturates, giving a quasihelical shift to the magnetic axis. The nonlinear saturation is caused by increased field line bending. Time scales of 103 τHp and axis shifts of 20% are reached when changes in q on the order of 3×10−3 from the marginal profile are produced.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866749
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  • 10
    Electronic Resource
    Electronic Resource
    TEXT tokamak edge turbulence modeling (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 2291-2299 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Experimental results on the Texas Experimental Tokamak (TEXT) [Nucl. Technol./Fusion 1, 479 (1982)] and the Advanced Toroidal Facility (ATF) torsatron [Fusion Technol. 10, 179 (1986)] indicate that electrostatic fluctuations can explain the edge transport of particles and perhaps energy. Certain mechanisms for drive (radiation and ionization, as well as density and temperature gradients) and stabilization (velocity shear) are suggested by these results. The experimental fluctuation levels and turbulence characteristics can be reproduced by considering the nonlinear evolution of fluid-type equations, incorporating thermal and ionization drives.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.859596
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