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  • 1
    Electronic Resource
    Electronic Resource
    A generalized reaction field method for molecular dynamics simulations (1995)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 102 (1995), S. 5451-5459 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Molecular dynamics simulations of ionic systems require the inclusion of long-range electrostatic forces. We propose an expression for the long-range electrostatic forces based on an analytical solution of the Poisson–Boltzmann equation outside a spherical cutoff, which can easily be implemented in molecular simulation programs. An analytical solution of the linearized Poisson–Boltzmann (PB) equation valid in a spherical region is obtained. From this general solution special expressions are derived for evaluating the electrostatic potential and its derivative at the origin of the sphere. These expressions have been implemented for molecular dynamics (MD) simulations, such that the surface of the cutoff sphere around a charged particle is identified with the spherical boundary of the Poisson–Boltzmann problem. The analytical solution of the Poisson–Boltzmann equation is valid for the cutoff sphere and can be used for calculating the reaction field forces on the central charge, assuming a uniform continuum of given ionic strength beyond the cutoff. MD simulations are performed for a periodic system consisting of 2127 SPC water molecules with 40 NaCl ions (1 molar). We compare the structural and dynamical results obtained from MD simulations in which the long range electrostatic interactions are treated differently; using a cutoff radius, using a cutoff radius and a Poisson–Boltzmann generalized reaction field force, and using the Ewald summation. Application of the Poisson–Boltzmann generalized reaction field gives a dramatic improvement of the structure of the solution compared to a simple cutoff treatment, at no extra computational cost. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.469273
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  • 2
    Electronic Resource
    Electronic Resource
    On a mathematical model describing the aggregation of amoebae (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 555-571 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper an extension of a mathematical model of Keller and Segel (1970) describing the aggregation of amoebae is presented. In their paper (Keller and Segel, 1970) they showed that the onset of the aggregation could be viewed as a spatial instability. Their instability condition involved diffusion constants of the cyclic AMP and of the amoebae as well as a constant describing the chemotactic behavior of the amoebae. In our case we consider a temporal instability that depends only on the kinetics of cyclic AMP production, degradation and transport through the cell wall. Our model then explains the oscillatory behavior of the cyclic AMP in well-stirred suspensions of amoebae. In addition we discuss existence and non-existence of nonuniform steady states of the nonlinear parabolic system involved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458330
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  • 3
    Electronic Resource
    Electronic Resource
    Applications of Rellich's perturbation theory to a classical boundary and eigenvalue problem (1973)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 24 (1973), S. 709-720 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Zusammenfassung Mit Hilfe der Rellichschen Störungstheorie wird die analytische Abhängigkeit der Lösungen eines Randwert- und eines Eigenwertproblems gezeigt, sowie des tiefsten Eigenwertes λ1(α) von einem Parameter α, der in den Randbedingungen auftritt. Als Anwendung ergeben sich Schranken für das Energieintegral und λ1(α). Ferner wird die Definition der RobinfunktionR(P, Q; α) erweitert auf negative Werte von α, insbesondere singuläre Werte −p j .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01597075
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  • 4
    Electronic Resource
    Electronic Resource
    Nonlinear diffusion-reaction problems with time-dependent diffusion coefficient (1979)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 30 (1979), S. 663-675 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung In dieser Arbeit wird das Problemu ,t =D(t)Δu+f(u) untersucht. Ein parabolisches Maximumprinzip wird hergeleitet, mit dessen Hilfe verschiedene Grössen, die im obigen Problem von Interesse sind, abgeschätzt werden können.
    Notes: Abstract In this paper the problemu ,t =D(t)Δu+f(u) is studied. A parabolic maximum principle is derived which allows us to get some estimates for different quantities of interest in this problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01590844
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  • 5
    Electronic Resource
    Electronic Resource
    Buchbesprechung (1980)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 31 (1980), S. 542-548 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01590868
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  • 6
    Electronic Resource
    Electronic Resource
    Isoperimetric inequalities in a boundary value problem on a Riemannian manifold (1980)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 31 (1980), S. 740-753 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Diese Arbeit behandelt das Problem Δu+1=0 in Ω,u=0 auf ∂Ω, wobei Ω ein Gebiet auf einer zweidimensionalen Riemann'schen Mannigfaltigkeit ist, und Δ der zugehörige Laplace-Beltrami Operator. Es werden isoperimetrische Schranken für das Maximum vonu und |Δu| aus gewissen Maximumsprinzipien hergeleitet, sowie einige verwandte Resultate.
    Notes: Abstract In this paper the problem Δu+1=0 in Ω,u=0 on ∂Ω is considered. Here Ω is a finite domain on a Riemannian manifold and Δ the associated Laplace-Beltrami operator. By means of maximum principles isoperimetric bounds for the maximum ofu and the maximum of the absolute value of the gradient ofu, as well as some related bounds are derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01594120
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  • 7
    Electronic Resource
    Electronic Resource
    Note on the effectiveness factor of a first order reaction (1984)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 35 (1984), S. 116-121 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Es werden obere und untere Schranken hergeleitet für den Diffusionsfaktor $$\eta : = \int\limits_\Omega {udx/} \int\limits_\Omega {dx} $$ , wobeiu die Lösung ist von Δu=c 2 u inΩ,u=1 auf ∂Ω.
    Notes: Abstract Upper and lower bounds for the effectiveness factor $$\eta : = \int\limits_\Omega {udx/} \int\limits_\Omega {dx} $$ are derived, whereu is the solution of Δu=c 2 u inΩ,u=1 on ∂Ω.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00945181
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  • 8
    Electronic Resource
    Electronic Resource
    Comparison results in a class of reaction-diffusion problems (1981)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 32 (1981), S. 12-21 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung In der vorliegenden Arbeit werden punktweise Schranken für die Lösungenu (x, t) gewisser Reaktions-Diffusions-Probleme hergeleitet. Sie haben die Form $$u(x,t)\mathop \geqq \limits_{( \leqq )} \upsilon (x,t)z(t),$$ wobeiz (t) die Lösung der zugehörigen „kinetischen Gleichung“ undυ (x, t) die Lösung eines reinen Diffusionsproblems ist.
    Notes: Abstract In this paper pointwise bounds for the solutionsu (x, t) of some reaction-diffusion problems are derived. They are of the form $$u(x,t)\mathop \geqq \limits_{( \leqq )} \upsilon (x,t)z(t),$$ wherez (t) is the solution of the associated “kinetic equation” andυ (x, t) is the solution of a pure diffusion problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00953546
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  • 9
    Electronic Resource
    Electronic Resource
    Optimal bounds in semilinear elliptic problems with nonlinear boundary conditions (1993)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 44 (1993), S. 639-653 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A method (developed by L. E. Payne) of constructing optimal sub- or supersolutions in semilinear elliptic problems is extended to the case of nonlinear boundary conditions. One thus obtains bounds for the solution (or related quantities) which are sharp in the limit as the domain degenerates into a infinite slab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00948480
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  • 10
    Electronic Resource
    Electronic Resource
    Untere und obere Schranken für den tiefsten Eigenwert der elastisch gestützten Membran (1972)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 23 (1972), S. 231-244 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Summary This article is concerned with the determination of upper and lower bounds for the lowest eigenvalue λ1(α) of the elastically supported vibrating membrane. The elastic support on the boundary is characterized by α which is regarded as a parameter. The classical Rayleigh-Principle gives upper bounds. The use of a convex functionalJ(α) yields upper and lower bounds for λ1(α). A method of decomposition leads to a lower bound for λ1(α).
    Notes: Zusammenfassung Es werden untere und obere Schranken für den tiefsten Eigenwert λ1(α) der elastisch gestützten schwingenden Membran hergeleitet. Die elastische Bindung der Membran am Rande wird durch α charakterisiert, und α wird als Parameter betrachtet. Die Verwendung des klassischen Rayleigh-Prinzipes liefert obere Schranken, mit Hilfe eines konvexen FunktionalsJ(α) erhält man obere und untere Schranken. Eine Zerlegungsmethode endlich gibt eine untere Schranke für λ1(α).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01593087
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