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  • 1
    Electronic Resource
    Electronic Resource
    Gyrotaxis: A plume model for self-focusing micro-organisms (1994)
    Springer
    Bulletin of mathematical biology 56 (1994), S. 187-206 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We consider the phenomenon of self-focusing pattern formation of motile micro-organisms (“streamer”). The focusing mechanism is based on gyrotaxis, a physical phenomenon, and it results from the balance between viscous and gravitational moments on the organisms. Under particular circumstances such streamers are stabilized and sink, resulting in vertical transport of micro-organisms as well as horizontal heterogeneity in cell concentration. We develop a plume model for the streamer, which consists of the equations of continuity, momentum, and cell concentration. These equations are further simplified to three basic equations representing volume, momentum and concentration fluxes of the steady-state plume. Asymptotic analytical solutions for the plume are obtained. From numerical solutions we find the shape of the plume which takes the form of a vertical string with lengths ranging from 1 to 10 cm. The streamer formation can be related to algal blooms occurring in the sea and to algal cultures grown in the laboratory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460639
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  • 2
    Electronic Resource
    Electronic Resource
    Diffusion-driven instability in a predator-prey system with time-varying diffusivities (1992)
    Springer
    Journal of mathematical biology 30 (1992), S. 307-320 
    Details
    ISSN: 1432-1416
    Keywords: Reaction-diffusion equation ; Variable diffusivity ; Criteria for diffusive instability ; Hill's equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We consider an ecological model by Levin and Segel (1976) for predator-prey planktonic species, which consists of two reaction-diffusion equations, and extend it to plankton populations with time-varying diffusivities. The local stability of uniform equilibria is examined both analytically and numerically. It is found that diffusive instability is less likely to occur in systems with time-varying diffusivity than those with constant diffusivity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00176153
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  • 3
    Electronic Resource
    Electronic Resource
    Winkelverteilung und Wirkungsquerschnitt der Reaktion Li7 (p, α) α unterhalb 600 keV (1958)
    Springer
    Naturwissenschaften 45 (1958), S. 204-205 
    Details
    ISSN: 1432-1904
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology , Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00639602
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  • 4
    Electronic Resource
    Electronic Resource
    Winkelverteilung und Wirkungsquerschnitt der Reaktion Li7 (p, α)α unterhalb 600 keV (1957)
    Springer
    Naturwissenschaften 44 (1957), S. 279-279 
    Details
    ISSN: 1432-1904
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology , Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00597327
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  • 5
    Electronic Resource
    Electronic Resource
    Gyrotaxis: Interaction between algae and flagellates (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 631-650 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We describe the behaviour of motile microorganisms (e.g. flagellates) attracted by “gyrotaxis” to a sinking, non-motile particle (e.g. an algal cell). The model is based on the application of Stokes' solution for the flow field around the settling cell. The volume within which the flagellate is attracted to the sinking particle is determined from the trajectories of the flagellate. The model of gyrotaxis has several applications; these include the colonization of sinking marine snow particles with motile microoganisms and suspension feeding by protozoa.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461844
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  • 6
    Electronic Resource
    Electronic Resource
    Photolyse von Cycloalkeno-1,2,3-thiadiazolen (1979)
    Weinheim : Wiley-Blackwell
    Berichte der deutschen chemischen Gesellschaft 112 (1979), S. 3728-3736 
    Details
    ISSN: 0009-2940
    Keywords: Chemistry ; Inorganic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Photolysis of Cycloalkeno-1,2,3-thiadiazolesPhotolysis of the title compounds leads to several types of heterocycles: 1,4-dithiins 5, 1,3-dithioles 9, thiophenes 11, and 1,2,4,5-tetrathianes 12. The yields of the reaction routes 1 - VI depend on the ring size of the cycloalkeno-l,2,3-thiadiazoles (table 1).
    Notes: Bei der Photolyse der Titelverbindungen 1a-d werden Heterocyclen der Typen 1,4-Dithiin 5, 1,3-Dithiol 9, Thiophen 11 und 1,2,4,5-Tetrathian 12 isoliert. Die Ausbeute auf den Reaktionswegen I-VI in Abhängigkeit von der Cycloalkeno-l,2,3-thiadiazol-Ringgröße ist von Interesse (Tab. 1).
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cber.19791121121
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  • 7
    Electronic Resource
    Electronic Resource
    Die Bildung von Phenylthiiren (1980)
    Weinheim : Wiley-Blackwell
    Berichte der deutschen chemischen Gesellschaft 113 (1980), S. 2519-2529 
    Details
    ISSN: 0009-2940
    Keywords: Chemistry ; Inorganic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: The Formation of PhenylthiirenePhotolysis and thermolysis of 4- and 5-phenyl-[13C]-1,2,3-thiadiazole (4a and 4a′) furnish the phenylthioacetic acid O-esters 19 and 21, respectively, and the 1,3-dithioles 22. A product analysis by 13C NMR spectroscopy shows on the basis of a kinetic scheme that starting with 4a′ the intermediate 2-phenyl-[213C]thiirene (1a) is formed photochemically to a considerable extent and thermally nearly up to 100%. In contrast no thiirene intermediate can be found in the decomposition of 4a.
    Notes: Die Photolyse und Thermolyse von 4- und 5-Phenyl-[13C]-1,2,3-thiadiazol (4a und 4a′) liefern die Phenylthioessigsäure-O-ester 19 bzw. 21 und die 1,3-Dithiole 22. Die 13C-NMR-Analyse der Produkte zeigt an Hand eines kinetischen Schemas, daß ausgehend von 4a′ die 2-Phenyl-[2-13C]thiiren-Zwischenstufe 1a photochemisch deutlich, thermisch zu fast 100% durchlaufen wird, nicht jedoch bei der Zersetzung von 4a.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cber.19801130718
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  • 8
    Electronic Resource
    Electronic Resource
    Über die Bildung von Oxirenen aus cyclischen α-Diazoketonen (1978)
    Weinheim : Wiley-Blackwell
    Berichte der deutschen chemischen Gesellschaft 111 (1978), S. 1549-1557 
    Details
    ISSN: 0009-2940
    Keywords: Chemistry ; Inorganic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: On the Formation of Oxirenes from Cyclic α-DiazoketonesThe reactions following the nitrogen elimination from 2-diazo-12-methyl-1-cyclododecanone (15) are studied. In the intermediate 12-membered α-oxocarbene 17 the first example of a photochemically and thermally induced 1,2-shift of oxygen in a cyclic α-oxocarbene is described. The rearrangement involves the condensed oxirene system 18. The occurrence of the two isomeric α-oxocarbenes 17 and 17′ is demonstrated by the subsequent 1,2-hydrogen rearrangement to isomeric α,β-unsaturated ketones (19, 20 and 19′, 20′). In contrast no oxirene participation is found in the silver oxide-catalysed reaction.
    Notes: Die Folgereaktionen nach der Stickstoff-Abspaltung aus 2-Diazo-12-methyl-1-cyclododecanon (15) werden untersucht. Am intermediären 12-Ring-α-oxocarben 17 wird das erste Beispiel einer photochemisch und thermisch ausgelösten 1,2-Sauerstoffverschiebung in cyclischen α-Oxocarbenen beschrieben. Die Umlagerung verläuft über das kondensierte Oxiren-System 18. Das Auftreten der beiden isomeren α-Oxocarbene 17 und 17′ wird durch die nachfolgende 1,2-Wasserstoff-verschiebung zu isomeren α,β-ungesättigten Ketonen (19, 20 und 19′, 20′) belegt. Im Gegensatz dazu wird bei der silberoxid-katalysierten Reaktion keine Oxiren-Beteiligung gefunden.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cber.19781110436
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  • 9
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    Self- and mutual shading effect on competing algal distribution (1991)
    Elsevier
    Details
    Publication Date: 1991-01-01
    Print ISSN: 0362-546X
    Electronic ISSN: 1873-5215
    Topics: Mathematics
    Published by Elsevier
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  • 10
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    Self- and mutual shading and competition effect on competing algal distributions: Biological implications of the model (1991)
    Elsevier
    Details
    Publication Date: 1991-12-01
    Print ISSN: 0304-3800
    Electronic ISSN: 1872-7026
    Topics: Biology
    Published by Elsevier
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