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  • 1
    Electronic Resource
    Electronic Resource
    The dynamics of a model of a plankton-nutrient interaction
    Amsterdam : Elsevier
    Bulletin of Mathematical Biology 52 (1990), S. 677-696 
    Details
    ISSN: 0092-8240
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1016/S0092-8240(05)80373-8
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    The dynamics of a model of a plankton-nutrient interaction
    Amsterdam : Elsevier
    Bulletin of Mathematical Biology 52 (1990), S. 677-696 
    Details
    ISSN: 0092-8240
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1016/S0092-8240(05)80373-8
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    On the disappearance of criticality in the theory of thermal ignition (1982)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 33 (1982), S. 406-407 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Eine vor kurzem erschienene Arbeit in dieser Zeitschrift von K. K. Tam stellte Ergebnisse für die Werte der Aktivierungsenergie fest, für die ein nichtlineares Eigenwert-Problem, das in der stationären Theorie der thermischen Zündung entsteht, vielfache Lösungen hat. Dieser Bericht weist auf einen darin enthaltenen Fehler hin und gibt die korrigierten Werte der Aktivierungsenergie, für die es vielfache Lösungen gibt.
    Notes: Abstract A recent article by K. K. Tam in this journal stated results on the values of the activation energy for which a nonlinear eigenvalue problem, which arises in the steady-state theory of thermal ignition, has multiple solutions. This report points to an error contained therein and gives the corrected values of the activation energy for which multiplicity occurs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00944448
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Steady size distributions for cells in one-dimensional plant tissues (1991)
    Springer
    Journal of mathematical biology 30 (1991), S. 101-123 
    Details
    ISSN: 1432-1416
    Keywords: Cell population growth ; Exponential growth ; Size/birth-size distributions ; Fission into unequal parts ; Fredholm integral equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We consider a population of cells growing and dividing steadily without mortality, so that the total cell population is increasing, but the proportion of cells in any size class remains constant. The cell division process is non-deterministic in the sense that both the size at which a cell divides, and the proportions into which it divides, are described by probability density functions. We derive expressions for the steady size/birth-size distribution (and the corresponding size/age distribution) in terms of the cell birth-size distribution, in the particular case of one-dimensional growth in plant organs, where the relative growth rate is the same for all cells but may vary with time. This birth-size distribution is shown to be the principal eigenfunction of a Fredholm integral operator. Some special cases of the cell birth-size distribution are then solved using analytical techniques, and in more realistic examples, the eigen-function is found using a simple, generally applicable numerical iteration.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00160330
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    The disappearance of criticality in the theory of thermal ignition (1978)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 29 (1978), S. 971-976 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Wird beim Studium thermischer Explosionen der Reaktionsverbrauch vernachlässigt, so spricht man üblicherweise von einem ‘kritischen Punkt’, wenn dort bei einer kleinen Änderung der äußeren Parameter ein großer Sprung der stationären Maximaltemperatur auftritt. Bei den exakten Gleichungen (ohne die Frank-Kamenetskii'sche Approximation ε≡RT a E≈0) gibt es für große ε keinen kritischen Punkt mehr. In dieser Arbeit wird ein Modell eingeführt, bei dem der Wert von ε, für welchen der kritische Punkt verschwindet, im Fall der unendlichen Platte und des unendlichen Zylinders genau bestimmt werden kann.
    Notes: Summary In the study of thermal ignition, when reactant consumption is neglected, criticality is usually taken as the point at which there is a large jump in the maximum steady temperature for a small change in the external parameters. If the equations are taken in their exact form, without the Frank-Kamenetskii approximation ε≡RT a E≈0, criticality vanishes for ε large. In this paper a model is introduced for which the value of ε at which criticality vanishes can be determined precisely for geometries of an infinite slab and infinite circular cylinder.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01590818
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Criticality in a model for thermal ignition in three or more dimensions (1981)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 32 (1981), S. 594-602 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Mit Hilfe eines explizit lösbaren Modells, das in einer früheren Arbeit eingeführt wurde (siehe [1]), erhält man das exakte Verhalten der zugehörigen Verzweigungskurven. Das Modell approximiert gut das Arrheniussche Gesetz für exotherme Reaktionen in einem sphärischen Topf in drei oder mehr Dimensionen. Für eine Folge von Werten des Parametersε, welches als Reziproke der dimensionslosen Aktivierungsenergie dient, ändert sich die Anzahl der Lösungen zum Eigenwertλ, der durchε gesteuert wird. Weiter gibt es für alleλ mindestens eine Lösung, sofernε ≠ 0 gilt.
    Notes: Abstract An explicitly resolvable model, which was instroduced in a previous paper (see [1]), is used to obtain exact behaviour of its bifurcation curves. The model closely approximates the true Arrhenius law for a spherical vessel of reacting material undergoing an exothermic reaction in three or more dimensions. For a sequence of values of a parameterε, which is the reciprocal of the dimensionless activation energy, the number of the solutions changes for certain values of the eigenparameterλ Further, there exist solutions for allλ thenε is non-zero.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00947024
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    Paper (German National Licenses)
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  • 7
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    An analytical series solution to the steady laminar flow of a Newtonian fluid in a partially filled pipe, including the velocity distribution and the dip phenomenon (2015)
    Oxford University Press
    Details
    Publication Date: 2015-11-20
    Description: In the current work, we advance the integral equation solution of Guo & Meroney (2013, Theoretical solution for laminar flow in partially-filled pipes. J. Hydraul. Res. , 51 , 408–416) for the velocity distribution of a Newtonian fluid flowing under the effect of gravity in a partially filled pipe. Unlike in previous work, our new solution is analytical and is in series form. The solution is able to evaluate the velocity profile in a partially filled pipe for any fill depth. Additionally, the well-known velocity dip phenomenon is observed, and, using our new solution, it is predicted that the dip will begin once the pipe is filled above 86% of the channel depth. Excellent agreement is found between the analytical and a computed numerical solution to the flow problem.
    Print ISSN: 0272-4960
    Electronic ISSN: 1464-3634
    Topics: Mathematics
    Published by Oxford University Press
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  • 8
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    Mathematics, modelling and students in transition (2016)
    Oxford University Press
    Details
    Publication Date: 2016-09-14
    Description: This article is based on data from two major research projects that investigated students involved in mathematically demanding courses during their transition through college and into university. It explores the nature of modelling as a mathematical practice in this important transition phase for students. Theoretical considerations are informed by illustrative accounts of a college mathematical modelling lesson and engineering lecture exemplifying the complex nature of mathematical modelling in these two phases of post-compulsory education. This raises important issues concerning the teaching and learning of mathematical practices in relation to modelling and applications. The discussion presented here is seen through the lens of Cultural Historical Activity Theory that informed the project team’s analysis of the case studies developed of both institutions and individuals. In this article, data and earlier findings are reinterpreted to better understand how we might support students as they move from learning mathematics to learning to use mathematics effectively in pursuit of their other studies. The accounts of classroom and lecture activity illustrate how ‘doing mathematics’ is mediated in different ways ensuring that students experience modelling and applications as mathematical practices very differently in each. This leads me to explain why, but also infer that students are likely to experience difficulties in transition both ‘vertically’ in progression from one activity system to another over time (college to higher education) and ‘horizontally’ between activity systems in which they participate concurrently (maths and engineering classes in university).
    Print ISSN: 0268-3679
    Electronic ISSN: 1471-6976
    Topics: Mathematics
    Published by Oxford University Press
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