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  • 1
    Monograph available for loan
    Monograph available for loan
    Budapest : Selbstverlag
    Call number: PIK M 311-92-1080
    Type of Medium: Monograph available for loan
    Pages: 34 p.
    Series Statement: Working paper ;
    Location: A 18 - must be ordered
    Branch Library: PIK Library
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  • 2
    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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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 101 (1994), S. 1172-1187 
    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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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 101 (1994), S. 1188-1201 
    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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  • 5
    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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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 70 (1986), S. 143-150 
    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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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Letters in mathematical physics 40 (1997), S. 101-115 
    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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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Letters in mathematical physics 37 (1996), S. 285-292 
    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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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Transport in porous media 31 (1998), S. 347-363 
    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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  • 10
    Publication Date: 2020-07-08
    Description: The world population will reach 9.8 billion by 2050, with increased urbanization. Cycling is one of the fastest developing sustainable transport solutions. With the spread of public bike sharing (PBS) systems, it is very important to understand the differences between systems. This article focuses on the clustering of different bike sharing systems around the world. The lack of a comprehensive database about PBS systems in the world does not allow comparing or evaluating them. Therefore, the first step was to gather data about existing systems. The existing systems could be categorized by grouping criterions, and then typical models can be defined. Our assumption was that 90% of the systems could be classified into four clusters. We used clustering techniques and statistical analysis to create these clusters. However, our estimation proved to be too optimistic, therefore, we only used four distinct clusters (public, private, mixed, other) and the results were acceptable. The analysis of the different clusters and the identification of their common features is the next step of this line of research; however, some general characteristics of the proposed clusters are described. The result is a general method that could identify the type of a PBS system.
    Electronic ISSN: 2071-1050
    Topics: Energy, Environment Protection, Nuclear Power Engineering
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