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  • 1
    Electronic Resource
    Electronic Resource
    Nonlinear resonance for quasilinear hyperbolic equation (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 2593-2602 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The purpose of this paper is to study the wave behavior of hyperbolic conservation laws with a moving source. Resonance occurs when the speed of the source is too close to one of the characteristic speeds of the system. For the nonlinear system characteristic speeds depend on the basic dependence variables and resonance gives rise to nonlinear interactions which lead to rich wave phenomena. Motivated by physical examples a scalar model is proposed and analyzed to describe the qualitative behavior of waves for a general system in resonance with the source. Analytical understanding is used to design a numerical scheme based on the random choice method. An important physical example is transonic gas flow through a nozzle. This analysis provides a transparent and revealing qualitative understanding of wave behavior of gas flow, including such phenomena as nonlinear stability, instability, and changing types of waves.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527751
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  • 2
    Electronic Resource
    Electronic Resource
    Kinetics of triaminoguanidine nitrate synthesis (1989)
    s.l. : American Chemical Society
    Industrial & engineering chemistry research 28 (1989), S. 431-437 
    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/ie00088a010
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  • 3
    Electronic Resource
    Electronic Resource
    A scalar combustion model (1991)
    Springer
    Archive for rational mechanics and analysis 114 (1991), S. 297-312 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00376136
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  • 4
    Electronic Resource
    Electronic Resource
    Transonic gas flow in a duct of varying area (1982)
    Springer
    Archive for rational mechanics and analysis 80 (1982), S. 1-18 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00251521
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  • 5
    Electronic Resource
    Electronic Resource
    L1 Stability Estimates for n×n Conservation Laws (1999)
    Springer
    Archive for rational mechanics and analysis 149 (1999), S. 1-22 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract . Let $u_t+f(u)_x=0$ be a strictly hyperbolic $n\times n$ system of conservation laws, each characteristic field being linearly degenerate or genuinely nonlinear. In this paper we explicitly define a functional $\Phi=\Phi(u,v)$ , equivalent to the $\L^1$ distance, which is “almost decreasing” i.e., $$ \Phi\big( u(t),~v(t)\big)-\Phi\big( u(s),~v(s)\big)\leq \O(\ve)\cdot (t-s)\quad\hbox{for all}~~t〉s\geq 0,$$ for every pair of ε-approximate solutions u, v with small total variation, generated by a wave front tracking algorithm. The small parameter ε here controls the errors in the wave speeds, the maximum size of rarefaction fronts and the total strength of all non-physical waves in u and in v. From the above estimate, it follows that front-tracking approximations converge to a unique limit solution, depending Lipschitz continuously on the initial data, in the ${\vec L}^1$ norm. This provides a new proof of the existence of the standard Riemann semigroup generated by a n×n system of conservation laws.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002050050165
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  • 6
    Electronic Resource
    Electronic Resource
    Propagation of a Stationary Shock Layer in the Presence of a Boundary (1997)
    Springer
    Archive for rational mechanics and analysis 139 (1997), S. 57-82 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We are interested in the large-time behavior of a stationary shock layer in the presence of a boundary effect. It is shown that the stationary shock propagates away from the boundary with speed inversely proportional to the time $t$ . Consequently, the location of the wave front is of order $\log \thinspace (1+t)$ . We show therefore that the zero-viscosity and time-asymptotic limits do not commute. Our analysis involves detailed point-wise estimates, which allow us to trace the shock.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002050050047
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  • 7
    Electronic Resource
    Electronic Resource
    Initial-boundary value problems for gas dynamics (1977)
    Springer
    Archive for rational mechanics and analysis 64 (1977), S. 137-168 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00280095
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  • 8
    Electronic Resource
    Electronic Resource
    A new computational technique for the stability analysis of slender rods (1992)
    Springer
    Archive of applied mechanics 62 (1992), S. 347-360 
    Details
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Übersicht Es wird ein neues Berechnungsverfahren für die Stabilitätsanalyse schlanker Stäbe mit veränderlichem Querschnitt unter allgemeinen Belastungen vorgestellt. Dabei werden die abhängigen Variablen und die variablen Koeffizienten der Bestimmungsgleichung in eine endliche Reihe von Tschebyscheff-Polynomen entwickelt. Die wesentliche Eigenschaft dieses Verfahrens ist die Reduzierung des ursprünglichen Randwertproblems einer Differentialgleichung auf ein algebraisches Eigenwertproblem. Angewandt wird die vorgeschlagene Methode auf die Euler-Knickung und das Flatterverhalten eines Kragträgers unter tangentialer Folgelast als konstanter Streckenlast. Die numerischen Ergebnisse nach diesem Verfahren erweisen sich als sehr genau im Vergleich zu Ergebnissen anderer Methoden, die in der Literatur zu finden sind. Es wird gezeigt, daß bei dieser Methode auch symbolische Lösungsverfahren angewandt werden können. Der Vorzug dieser neuen Methode gegenüber den Standard-Lösungsverfahren wie Finite-Differenzen- und Galerkin-Verfahren wird diskutiert.
    Notes: Summary A new computational technique for the stability analysis of slender rods with variable cross-sections under general loading conditions is presented. In this approach, the dependent variable and the variable coefficients appearing in the governing equations are expanded in a finite series of Chebyshev polynomials. The main feature of this technique is that the original boundary value problem associated with the differential equation is reduced to an algebraic eigenvalue problem. The proposed technique is applied to study the static buckling of Euler column and the flutter behavior of a cantilever column subjected to uniformly distributed tangential loading. The numerical results from the suggested technique are found to be extremely accurate when compared to other techniques available in literature. It is shown that this approach can also be employed in a symbolic form. The merits of the present method in comparison to the standard solution procedures like finite difference and Galerkin methods are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00788642
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  • 9
    Electronic Resource
    Electronic Resource
    On nonlinear stability of general undercompressive viscous shock waves (1995)
    Springer
    Communications in mathematical physics 174 (1995), S. 319-345 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We study the nonlinear stability of general undercompressive viscous shock waves. Previously, the authors showed stability in a special case when the shock phase shift can be determined a priori from the total mass of the perturbation, using new pointwise methods. By examining time invariants associated with the linearized equations, we can now overcome a new difficulty in the general case, namely, nonlinear movement of the shock. We introduce a coordinate transformation suitable to treat this new aspect, and demonstrate our method by analyzing a model system of generic type. We obtain sharp pointwise bounds andL p behavior of the solution for allp, 1≦p≦∞.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02099605
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  • 10
    Electronic Resource
    Electronic Resource
    Permeance of novikoff hepatoma gap junctions: Quantitative video analysis of dye transfer (1987)
    Springer
    The journal of membrane biology 96 (1987), S. 225-233 
    Details
    ISSN: 1432-1424
    Keywords: gap junctions ; dye permeability ; cultured cells ; video analysis ; Lucifer Yellow
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology
    Notes: Summary Fluorescent dyes are commonly used to study permeable (gap) junctions, but only rarely have quantitative values for junctional dye permeability been determined. In the present study, junctional permeance (PA, i.e., the product of the junctional permeability coefficient,P, times the junctional area,A) to Lucifer Yellow CH (LY) has been obtained for pairs of Novikoff hepatoma cells. Dye was microinjected into one cell and the subsequent transfer monitored by a SIT camera and recorded on video tape. The intensities of fluorescence in the injected and “recipient” cell were measured using a Digisector (Microworks) digitizing board and an Apple II Plus computer to analyze the video records. These changes in intensity, along with an estimate of volume of the spherical cells, were used to calculate the junctional permeance (PA) of cell pairs according to Fick's diffusion equation. Junctional permeances show considerable variation ranging from 0.08×10−11 to 27.0×10−11 cm3/sec. Using the meanPA and a previous estimate of the mean number of junctional channels per interface in the Novikoff cultures, a value for diffusion coefficient of LY through gap junctions is calculated to be about 1.4×10−6 cm2/sec. There is a general proportionality between meanPA and cell volume for hepatoma cell pairs of a certain size range. Such a relationship between cell volume and junctional capacity suggests one source of variation ofPA. Other possible sources, e.g., related to position in the cell cycle, are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01869304
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