№ 120(6), June, 2016
Public date: 30.06.2016
Archive of journal: Articles count 112, 299 kb
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01.00.00 Physical-mathematical sciences
LOGARITHMIC LAW AND EMERGENCE PARAMETER OF CLASSICAL AND QUANTUM SYSTEMS
01.00.00 Physical-mathematical sciences
DescriptionThe work discusses various examples of physical systems which state is determined by the logarithmic law - quantum and classical statistical systems and relativistic motion in multidimensional spaces. It was established that the Fermi-Dirac statistics and BoseEinstein-Maxwell-Boltzmann distribution could be described by a single equation, which follows from Einstein's equations for systems with central symmetry. We have built the rate of emergence of classical and quantum systems. The interrelation between statistical and dynamic parameters in supergravity theory in spaces of arbitrary dimension was established. It is shown that the description of the motion of a large number of particles can be reduced to the problem of motion on a hypersphere. Radial motion in this model is reduced to the known distributions of quantum and classical statistics. The model of angular movement is reduced to a system of nonlinear equations describing the interaction of a test particle with sources logarithmic type. The HamiltonJacobi equation was integrated under the most general assumptions in the case of centrally-symmetric metric. The dependence of actions on the system parameters and metrics was found out. It is shown that in the case of fermions the action reaches extremum in fourdimensional space. In the case of bosons there is a local extremum of action in spaces of any dimension
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01.00.00 Physical-mathematical sciences
DescriptionIn the article we present a spatial structure of largescale transport systems. The model of a transport network can be presented in the form of a graph, with a set of the nodes corresponding to elements of a network and a set of edges – to sections of roads the connecting these nodes. As the model of a card of roads, it is offered to use prefractal graphs which naturally reflect structure of communications when reviewing a transport network in different scales (the states, regions, areas). Prefractal graphs allow describing structural dynamics of the studied system in the discrete time. One of the most widespread scenarios of structural dynamics is the growth of structure. The statement of tasks of the organization of transport routes contains requirements criteria to finding of optimal solutions. Often these requirements and criteria are contradicting each other. It leads to appearance of a multicriteria problem definition. The multicriteria problem definition on a class of prefractal graphs is considered. The optimum algorithm of separation of the greatest maximum paths by the given criterion is constructed and estimates by remaining criteria are given. In operation computing complexity of the constructed algorithm of separation of the greatest maximum paths on a prefractal graph is calculated and advantage of operation of algorithm on last before algorithm of separation of the greatest maximum paths on normal graphs is justified. The constructed algorithm on prefractal graphs has polynomial complexity