4,853 research outputs found
Control of multiscale systems with constraints. 1. Basic principles of the concept of evolution of systems with varying constraints
Physical fundamentals of the self-organizing theory for the system with
varying constraints are considered. A variation principle, specifically the
principle of dynamic harmonization as a generalization of the Gauss-Hertz
principle for the systems with varying internal structure is formulated. In
compliance with this principle the system evolves through dynamics of the
processes leading to harmonization of the internal multiscale structure of the
system and its connections with external actions as a result of minimizing the
dynamic harmonization function. Main principles of the shell model of
self-organization under the action of the dominating entropic disturbance are
formulated.Comment: First par
Distribution of averages in a correlated Gaussian medium as a tool for the estimation of the cluster distribution on size
Calculation of the distribution of the average value of a Gaussian random
field in a finite domain is carried out for different cases. The results of the
calculation demonstrate a strong dependence of the width of the distribution on
the spatial correlations of the field. Comparison with the simulation results
for the distribution of the size of the cluster indicates that the distribution
of an average field could serve as a useful tool for the estimation of the
asymptotic behavior of the distribution of the size of the clusters for "deep"
clusters where value of the field on each site is much greater than the rms
disorder.Comment: 15 pages, 6 figures, RevTe
On the classification of discrete Hirota-type equations in 3D
In the series of recent publications we have proposed a novel approach to the
classification of integrable differential/difference equations in 3D based on
the requirement that hydrodynamic reductions of the corresponding
dispersionless limits are `inherited' by the dispersive equations. In this
paper we extend this to the fully discrete case. Our only constraint is that
the initial ansatz possesses a non-degenerate dispersionless limit (this is the
case for all known Hirota-type equations). Based on the method of deformations
of hydrodynamic reductions, we classify discrete 3D integrable Hirota-type
equations within various particularly interesting subclasses. Our method can be
viewed as an alternative to the conventional multi-dimensional consistency
approach.Comment: 29 page
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