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  • 1
    Call number: PIK M 311-92-1080
    Type of Medium: Monograph available for loan
    Pages: 34 p.
    Series Statement: Working paper ;
    Branch Library: PIK Library
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  • 2
    ISSN: 1432-2234
    Keywords: Lotka-Volterra model ; Explodator ; Linearized part ; Uniqueness ; Design of periodic reactions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The Lotka-Volterra model is shown to be the simplest unique model among those models having the same linearized form. We also show that the two-dimensional explodator model is not unique in its own class: there are four models possessing the same linearized form. Finally, we propose a method for the construction of formal chemical models having prescribed properties (i.e. having prescribed a type of one or more equilibrium points).
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    s.l. ; Stafa-Zurich, Switzerland
    Materials science forum Vol. 589 (June 2008), p. 55-60 
    ISSN: 1662-9752
    Source: Scientific.Net: Materials Science & Technology / Trans Tech Publications Archiv 1984-2008
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The heating of basic material is considered the first step of the plastic hot forming. Mostof the „prescriptions” concerning this process are based on practical data and basically they can belimited to the checking of the surface temperature of the billet. The model described in this papermakes it possible to determine the temperature distribution developing inside the billet while thesystem of the conditions of warm-up can be planned and optimized as a function of the physicalparameters of the heated material
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1573-0530
    Keywords: 80A30 ; Master equation ; rate constants ; Fokker-Planck equation ; Percolidis model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We show, using a specific example of a chemical reaction, that the rate constants predicted from the discrete master equation and its continuum Fokker-Planck approximations differ in exponential order with respect to the size of the system.
    Type of Medium: Electronic Resource
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  • 5
    ISSN: 1573-1634
    Keywords: displacement ; injection ; production ; fractional flow ; laboratory core floods ; break-through ; average saturation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Abstract. An accurate analytical interpretation method to determine the Leverett function (fw)and its derivative (fw′) from immiscible displacement data in core plugs is presented. Linear equations are developed to describe the displacement processes occurring before and after breakthrough. A quadratic function is introduced to represent the saturation distribution along the cores. The relationships derived in this study can be used for analysis of core tests involving constant injection rates and constant pressure differences. The applicability, practicality, and accuracy of the new analytical method are verified by means of the experimental data obtained in the present study and by those reported in the literature.
    Type of Medium: Electronic Resource
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  • 6
    ISSN: 1573-0530
    Keywords: Master equation ; Fokker-Planck equation ; rate constants ; entropy.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A usual approximation of the master equation is provided by the Fokker–Planck equation. For chemical systems with one species, we prove generally that the prediction of the rate constant of the metastable state given by the Master equation and the Fokker–Planck approximation differ exponentially with respect to the size of the system. We show that this is related to the fact that the entropy of the metastable state is not described correctly by the Fokker–Planck equation. We prove that the rate given by the Fokker–Planck equation overestimates that rate given by the Master equation.
    Type of Medium: Electronic Resource
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  • 7
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A general analysis of approximate nonlinear lumping for a chemical kinetic system described by an n-dimensional first order ordinary differential equation system dy/dt=f(y) is presented. There is a one-to-one relation between the differential equation system and the linear partial differential operator A=∑ni=1fi(y)(∂/∂yi). The algebraic method in nonlinear perturbation theory is utilized to approximately transform A into some canonical forms in which the new dependent variables are partly separated. These canonical forms of A will give the generalized eigenfunctions or other higher dimensional unconstrained nonlinear lumping schemes of the original system approximately. Unconstrained nonlinear lumping gives a reduced differential equation system describing new variables which are nonlinear functions of the original ones. This approach may supply some purely fast variables. The solutions of original dependent variables can be obtained by the inverse transformation from the lumped variables and the approximate analytical solutions of the purely fast variables. The theoretical basis of this approach is presented. A simple example is used for illustration.
    Type of Medium: Electronic Resource
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  • 8
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A general analysis of approximate constrained nonlinear lumping is presented for a chemical kinetic system described by an n-dimensional set of first order ordinary differential equations dy/dt=f(y). There is a one-to-one relation between the differential equation system and the linear partial differential operator A=∑ni=1fi(y)(∂/∂yi). The algebraic method in nonlinear perturbation theory for lumping is extended to include constrained nonlinear lumping, in which the operator A is only transformed to a partially canonical form and some variables are left unlumped. A singular perturbation method is used to provide approximate analytical expressions for the solutions of the lumped variables. The resulting expressions can then be substituted into the equations describing the unlumped species, leading to a low dimensional system. The method is illustrated by application to a simple model describing the nonisothermal oxidation of hydrogen in a closed vessel. The results show that the method of constrained lumping leads to an accurate representation of the ignition features and maximum temperature rise given by the full model. The singular perturbation technique is proved to be only a special case of a general constrained lumping approach based on the algebraic method in nonlinear perturbation theory when the equations are linear in the deleted variables. Consequently the quasisteady-state approximation (QSSA) is the zeroth order approximation within the slow invariant manifold of the constrained approach. In cases where QSSA is not a good approximation, the first order correction generally provides significant improvement of the results.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 99 (1993), S. 3562-3574 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A singular perturbation method is employed for the determination of an approximate nonlinear lumped model for a chemical kinetic system described by a set of first order ordinary differential equations with a group of small positive parameters corresponding to different time scales. New variables, called purely fast variables, are introduced and determined. Substituting their explicit expressions into the original kinetic equation system yields a lumped differential equation system containing the independent variable t. The lumped system can reach any desired accuracy for any initial composition. A further approximation to this lumped system, obtained by omitting transient exponential functions of t, is shown to define the dynamics of the system on a slow invariant manifold. Two simple examples are used to illustrate this approach.
    Type of Medium: Electronic Resource
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  • 10
    facet.materialart.
    Unknown
    Budapest: Hungarian Academy of Sciences, Institute of Economics
    Publication Date: 2015-03-25
    Description: We study a model of tax evasion, where a flat-rate tax only finances the provision of public goods. Deciding on reported income, each individual takes into account that the less he reports, the higher is his private consumption but the lower is his moral satisfaction. The latter depends on his own current report and average previous reports of his neighbors. Under quite general assumptions, the steady state reported income is symmetric and the process converges to the steady state.
    Keywords: C62 ; H26 ; ddc:330 ; tax evasion ; steady state ; asymptotic stability ; symmetrization ; networks ; monotone maps ; Steuervermeidung ; Modellierung
    Repository Name: EconStor: OA server of the German National Library of Economics - Leibniz Information Centre for Economics
    Language: English
    Type: doc-type:workingPaper
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