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  • dynamical systems note 1
    Note 1 Here it concerns the effect of elements coming from without on the stability of the dynamical system back to main text

    Original URL path: http://www.metafysica.nl/ontology/dynamical_systems_note1.html (2016-02-01)
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  • dynamical systems note 3
    the whole dynamical system we also can where it occurs distinguish between different states in which each individual system element could be in These element states contribute to the overall

    Original URL path: http://www.metafysica.nl/ontology/dynamical_systems_note3.html (2016-02-01)
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  • inorganic categories note 4
    liquid from saturated solutions which then become supersaturated There high order and low specific probability or entropy is achieved only at the expense of lower order and increased entropy of the surroundings The total probability of entropy better The total entropy of the entire system water crystals air vapor etc must increase although the entropy of a part the crystals decreases p 146 7 About 540 calories of heat are released upon condensation of steam to a gram of liquid About 80 calories upon freezing the liquid to ice Does the decrease in entropy accompanying the condensation and freezing violate the Second Law No Upon condensing or freezing the released heat increases the entropy of the surroundings so that the overall entropy is not decreased Where did the heat energy emitted in condensation and freezing come from when the gas changed to water and then to ice They came from the forces that constrain the water molecules and destroy the symmetry The symmetry of water vapor as a homogeneous macroscopic body has maximal symmetry As a liquid the water has lower symmetry but still a considerable high one while as a crystal the symmetry is reduced still further namely to

    Original URL path: http://www.metafysica.nl/ontology/general_ontology_29m5_note4.html (2016-02-01)
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  • inorganic categories note 5
    times its velocity And because in our cases we can assume the mass to be constant we only have to do with the velocity of the particle billiard ball The velocity of a particle is its speed and its direction

    Original URL path: http://www.metafysica.nl/ontology/general_ontology_29m5_note5.html (2016-02-01)
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  • inorganic categories note 6
    are infinitely many more irrational numbers Thus the rationals themselves which are all we are able to handle The irrationals must always be approximated by rational numbers form a highly abnormal selection It is infinitely more probable that the values of the variables of the initial condition will be given by i e actually are irrational numbers And even many rational numbers contain an infinite number of digits such as

    Original URL path: http://www.metafysica.nl/ontology/general_ontology_29m5_note6.html (2016-02-01)
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  • inorganic categories note 7
    a system consisting of to begin with just one moving particle then the dynamic characteristics of this particle at a particular instant in time can be given by its position which needs to be specified by generally three space coordinates and its momentum of which the variable part consists in the velocity of the particle which must be specified by three vectors themselves specifying the particle s speed and direction So six variables in all specify the state of the one particle system And this state can now be represented by a point in a six dimensional space phase space And when the system proceeds i e when one or more values of the particle s variables change continuously then our point traces a trajectory through phase space reflecting the system s time evolution If the system consists of two particles instead of just one then we need 2 x 6 12 variables to characterise the state of the system at a particular instant in time And the value of these 12 variables can now be represented by a point in a 12 dimensional space phase space And again when the system proceeds runs this point traces a trajectory through

    Original URL path: http://www.metafysica.nl/ontology/general_ontology_29m5_note7.html (2016-02-01)
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  • inorganic categories note 8
    to the system s long term evolution If the initial condition is statistically depicted as a blob in phase space then upon evolution of the system the shape of the blob but not its volume changes dramatically With fine branches it speads out over all regions of phase space There are several degrees of instability we have so called mixing flows and we have K flows which latter have a

    Original URL path: http://www.metafysica.nl/ontology/general_ontology_29m5_note8.html (2016-02-01)
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  • 29m5 Figure
    Explanation of an interval expressed in binary Close window to return to main text Close window to return to to main text

    Original URL path: http://www.metafysica.nl/ontology/clockdoubling.html (2016-02-01)
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