Related papers: Dynamical fractalization of ring systems
We describe a $q$-deformed dynamical system corresponding to the quantum free particle moving along the circle. The algebra of observables is constructed and discussed. We construct and classify irreducible representations of the system.
We consider the energy stored in a one-dimensional ballistic ring with a barrier subject to a linearly time-dependent magnetic flux. An exact analytic solution for the quantum dynamics of electrons in the ring is found for the case when the…
The processes of radiation defects formation and evolution have been simulated in cubic dielectric crystals by the computational method of cellular automata. If suppose that the defects concentration as a parameter, which characterizes a…
The level statistics of pseudointegrable fractal drums is studied numerically using periodic orbit theory. We find that the spectral rigidity $\Delta_3(L)$, which is a measure for the correlations between the eigenvalues, decreases to quite…
In the interstellar medium, as well as in the Universe, large density fluctuations are observed, that obey power-law density distributions and correlation functions. These structures are hierarchical, chaotic, turbulent, but are also…
We present and validate a novel semi-analytical approach to study the effect of dynamical friction on the orbits of massive perturbers in rotating stellar discs. We find that dynamical friction efficiently circularises the orbit of…
We construct meta-intransitive systems of independent random variables of any finite order from basic tuple of random variables which generalize intransitive dice. Under this construction, the equality of some linear functional is…
We study domain formation in the two-dimensional O(3) model near criticality. The fractal dimension of these domains is determined with good statistical accuracy.
This paper provides a new model to compute the fractal dimension of a subset on a generalized-fractal space. Recall that fractal structures are a perfect place where a new definition of fractal dimension can be given, so we perform a…
We use the fractional integrals in order to describe dynamical processes in the fractal media. We consider the "fractional" continuous medium model for the fractal media and derive the fractional generalization of the equations of balance…
Relativistic thick ring models are constructed using previously found analytical Newtonian potential-density pairs for flat rings and toroidal structures obtained from Kuzmin-Toomre family of discs. In particular, we present systems with…
The paper deals with a dynamical system analysis related to phantom cosmological model . Here gravity is coupled to phantom scalar field having scalar coupling function and a potential. The field equations are reduced to an autonomous…
We provide a minimal continuum model for mesoscale plasticity, explaining the cellular dislocation structures observed in deformed crystals. Our dislocation density tensor evolves from random, smooth initial conditions to form self-similar…
The problem of constructing flexible stochastic models to describe the variability in shape of solid particles is challenging. Natural objects often exhibit mono- or multi-fractal features, i.e. irregular shapes and self-similar patterns.…
We study the center-of-mass motion in systems of trapped interacting particles with space- and velocity-dependent friction and anharmonic traps. Our approach, based on a dynamical ansatz assuming a fixed density profile, allows us to obtain…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
We consider a statistical mechanics and thermodynamics of a rotating ideal gas of classical relativistic particles with nonzero mass and spin. Applying the Gibbs theory of canonical ensembles for a system rotating with constant angular…
We investigate the geometry of the critical fluctuations for a general system undergoing a thermal second order phase transition. Adopting a generalized effective action for the local description of the fluctuations of the order parameter…
The dynamics and the transition to the centrifugal regime are studied analytically and numerically for particles in rotating drum. The importance of the particle-wall friction coefficient is demonstrated by studying first the motion of one…
We consider the influence of the Fermi statistics of nucleons on the binding energy of a new type of nuclear structures such as fractal nuclear clusters (fractal isomers of nuclei). It is shown that the fractal nuclear isomers possess a…