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  • 1
    Monograph available for loan
    Monograph available for loan
    Fraktale, Formen, Punktfelder : Methoden der Geometrie-Statistik (1992)
    Berlin : Akad.-Verl.
    Details Availability
    Call number: M 95.0353 ; PIK M 490-92-0684
    Type of Medium: Monograph available for loan
    Pages: 394 S.
    ISBN: 3055014286
    Classification:
    Petrophysics
    Language: German
    Location: Upper compact magazine
    Location: A 18 - must be ordered
    Branch Library: GFZ Library
    Branch Library: PIK Library
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  • 2
    Monograph available for loan
    Monograph available for loan
    Stochastische Geometrie : eine Einführung ; mit 4 Tabellen (1983)
    Berlin : Akademie-Verl.
    Associated volumes
    Details Availability
    Call number: 20/MR 90.0980/275
    In: Wissenschaftliche Taschenbücher
    Type of Medium: Monograph available for loan
    Pages: 132 S.
    Series Statement: Wissenschaftliche Taschenbücher 275 : Mathematik Physik
    Language: German
    Location: Reading room
    Branch Library: GFZ Library
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  • 3
    Monograph available for loan
    Monograph available for loan
    Stochastic geometry and its applications (1987)
    Berlin : Akad.-Verl.
    Associated volumes
    Details Availability
    Call number: O 6429
    In: Mathematische Lehrbücher und Monographien
    Type of Medium: Monograph available for loan
    Pages: 345 S. : graph. Darst.
    ISBN: 3055000323
    Series Statement: Mathematische Lehrbücher und Monographien : Abt. 2, Mathematische Monographien 69
    Location: Upper compact magazine
    Branch Library: GFZ Library
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  • 4
    Electronic Resource
    Electronic Resource
    Random Sequential Adsorption: Relationship to Dead Leaves and Characterization of Variability (2000)
    Springer
    Journal of statistical physics 100 (2000), S. 969-979 
    Details
    ISSN: 1572-9613
    Keywords: coverage ; dead leaves model ; Matérn's hardcore process ; random disk packing ; random sequential adsorption ; two-point distribution ; variability of spatial disk distribution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A new construction for the planar unbounded random sequential adsorption (RSA) model is presented, which allows for a direct comparison with Matheron's “dead leaves” model. Furthermore, for the case of disks with random radii the problem of statistical determination of the proposal radius distribution is discussed. Finally, second order characteristics related to the pair correlation function are suggested for describing the variability of the RSA disk systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018769422266
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Set-Valued Means of Random Particles (1997)
    Springer
    Journal of mathematical imaging and vision 7 (1997), S. 111-121 
    Details
    ISSN: 1573-7683
    Keywords: estimation ; expectation ; figure ; orbit space ; particle ; random set ; shape ; support function ; variance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Planar images of powder particles or sand grains can be interpreted as “figures”, i.e., equivalence classes of directlycongruent compact sets. The paper introduces a concept of set-valuedmeans and real-valued variances for samples of such figures. Inobtaining these results, the images are registered to have similarlocations and orientations. The method is applied to find a mean figure of a sample of polygonal particles.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008289104136
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  • 6
    Electronic Resource
    Electronic Resource
    On the validity of the Weibull failure model for brittle particles (2000)
    Springer
    Granular matter 2 (2000), S. 165-170 
    Details
    ISSN: 1434-7636
    Keywords: Key words Weibull distribution, fracture probabilities, brittle particles, experimental data, Weibull modulus
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The Weibull theory of material strength and fracture assumes that the Weibull modulus m is a material parameter, which does not depend on shape and size of the loaded object. Based on large data sets from single-particle fracture experiments with brittle materials (glass, clinker cement, limestone), the authors show that the Weibull modulus of nearly spherical particles seems to decrease with increasing particle diameter. A possible explanation is that the inner structure of the particles depends on their size so that small particles are much stronger than large ones.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s100350000052
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  • 7
    Electronic Resource
    Electronic Resource
    The use of marked point processes in ecological and environmental forest studies (1995)
    Springer
    Environmental and ecological statistics 2 (1995), S. 331-344 
    Details
    ISSN: 1573-3009
    Keywords: Damage ; forest ; mark connection function ; pair correlation function ; spatial interaction ; variogram
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract The paper presents new applications of marked point processes in forestry. The tools are pair correlation functions and mark connection functions. Studies of the structures of even-aged pine forests in Siberia show a tendency of development from clustering in young stands towards random distribution in elder stands for the trunk positions. The tree tops as the movable parts of trees are still more regular in old forests. Furthermore, in Siberian fir forests interesting tendencies of attraction between members of several tree classes are detected. Finally, studies of the distribution of damaged trees in some central European forests show that there the damaged trees appear as singletons; dominating trees are preferentially damaged.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00569362
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  • 8
    Electronic Resource
    Electronic Resource
    Models of stochastic geometry — A survey (1993)
    Springer
    Mathematical methods of operations research 38 (1993), S. 235-260 
    Details
    ISSN: 1432-5217
    Keywords: Boolean model ; damaged forests ; mark correlation function ; marked point process ; M/G/∞ ; random compact set ; simulation ; spatial correlation ; spatial statistics ; stochastic model ; tumor
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This paper discusses some models of stochastic geometry which are of potential interest for operations research. These are the Boolean model, a certain model for random compact sets and marked point processes. The Boolean model is a generalization of the well-known queueing systemM/G/∞. The random compact set model may be useful for modelling spatial spreading processes such as fires, cancers or holes in the Earth's surface. Marked point processes are used here as models of forests and used for a statistical study of the spatial distribution of damaged trees.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01416606
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  • 9
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    Reconstructing spatial tree point patterns from nearest neighbour summary statistics measured in small subwindows (2008)
    Canadian Science Publishing
    Details
    Publication Date: 2008-05-01
    Description: Spatial tree data are required for the development of spatially explicit models and for the estimation of summary statistics such as Ripley’s K function. Such data are rare and expensive to gather. This paper presents an efficient method of synthesizing spatial tree point patterns from nearest neighbour summary statistics (NNSS) sampled in small circular subwindows, which uses a stochastic optimization technique based on simulated annealing and conditional simulation. This nonparametric method was tested by comparing tree point patterns, reconstructed from sample data, with the original woodland patterns of three structurally different tree populations. Analysis and validation show that complex spatial woodland structures, including long-range tree interactions, can be successfully reconstructed from NNSS despite the limited range of the subwindows and statistics. The influence of the NNSS varies depending on the woodland under study. In some cases, the sampling results can be improved by reconstruction. Furthermore, it is clearly shown that it is possible to estimate second-order characteristics such as Ripley’s K function from small circular subwindows through the reconstruction technique. The results offer new opportunities for adding value to woodland surveys by making raw data available for further work such as growth projections, visualization, and modelling.
    Print ISSN: 0045-5067
    Electronic ISSN: 1208-6037
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Published by Canadian Science Publishing
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  • 10
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    Edge-correction needs in estimating indices of spatial forest structure (2006)
    Canadian Science Publishing
    Details
    Publication Date: 2006-07-01
    Description: Indices quantifying spatial forest structure are frequently used to monitor spatial aspects of tree attributes including biodiversity in research plots of limited size. The treatment of edge trees, which are close to the plot boundaries, can affect the estimation of such indices that include neighbour effects, since some of their neighbours are likely to fall outside the plot. This paper investigates whether and under what circumstances edge-correction methods are necessary and evaluates the performance of six different approaches: no edge correction, translation, reflection, buffer zone, and two new nearest-neighbour methods. The performance of edge-correction methods depends strongly on the algorithmic structure of the indices and the spatial pattern of tree positions involved. Some edge-correction methods introduce more error than ignoring edge bias altogether. For indices accounting for the diversity of tree positions and especially for those computing angles, translation or buffer zone methods reduce the estimation error regardless of the sample size. The use of the reflection method is associated with large bias values. One of the new nearest-neighbour edge-correction methods proves to be capable of reducing the bias considerably. The results confirm the need for sufficiently large monitoring plots to avoid bias from edge effects. Where this is impossible, neighbours beyond the plot boundary need to be included in the survey, thus providing unbiased estimates but at the cost of extra measurements. Sensitivity analysis is required for newly introduced indices prior to their first application.
    Print ISSN: 0045-5067
    Electronic ISSN: 1208-6037
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Published by Canadian Science Publishing
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