107 research outputs found
Statistical theory of self-similar time series as a nonextensive thermodynamic system
Within Tsallis' nonextensive statistics, a model is elaborated to address
self-similar time series as a thermodynamic system. Thermodynamic-type
characteristics relevant to temperature, pressure, entropy, internal and free
energies are introduced and tested. Stability conditions of time series
analysis are discussed in details on the basis of Van der Waals model.Comment: 11 pages, LaTe
Complexity of Self-similar Hierarchical Ensembles
Within the framework of generalized combinatorial approach, the complexity is
determined for infinite set of self-similar hierarchical ensembles. This
complexity is shown to increase with strengthening of the hierarchy coupling to
the value, which decreases with growth of both scattering of this coupling and
non-extensivity parameter.Comment: 7 pages, 3 figure
Nonlinear Theory of Stochastic Resonance
Theory of nonlinear resonance, including stochastic one, is developed on the
basis of the statistical field theory and using variables action-angle.
Explicit expressions of action, proper frequency and nonlinearity parameter as
functions of the system energy and the external signal frequency are found for
the cases of nonlinear pendulum and double well potential.Comment: 20 pages (LaTeX), 11 figure
Axiomatic theory of nonequilibrium system
Mutually conjugated synergetic schemes are assumed to address evolution of
nonequilibrium self-organizing system. Within framework of the former, the
system is parameterized by a conserving order parameter being a density, a
conjugate field reducing to gradient of related flux, and control parameter,
whose driven magnitude fixes stationary state. We show that so-introduced
conjugate field and control parameter are relevant to entropy and internal
energy, so that self-organization effect is appeared as a negative temperature.
Along the line of the conjugated scheme, roles of order parameter, conjugate
field and control parameter are played with a flux of conserving value, and
gradients of both chemical potential and temperature. With growth of the
latter, relevant value of the entropy shows to decrease in supercritical regime
related to spontaneous flux-state. We proof that both approach stated on using
density and conjugated flux as order parameters follow from unified field
theory related to the simplest choice of both Lagrangian and dissipative
function.Comment: 10 pages, 2 figures, LaTe
Generalized thermostatistics based on multifractal phase space
We consider the self-similar phase space with reduced fractal dimension
being distributed within domain with spectrum . Related
thermostatistics is shown to be governed by the Tsallis' formalism of the
non-extensive statistics, where role of the non-additivity parameter plays
inverted value of the multifractal function
, being the specific heat, is
multifractal parameter. In this way, the equipartition law is shown to take
place. Optimization of the multifractal spectrum derives the relation
between the statistical weight and the system complexity.Comment: 8 pages, LaTe
Self-consistent theory of the long-range order in solid solutions
On the basis of the assumption that atoms play a role of effective Fermions
at lattice distribution, the study of the long-range ordering is shown to be
reduced to self-consistent consideration of single and collective excitations
being relevant to the space distribution of atoms and Fourier transform of such
distribution, respectively. A diagram method advanced allows to elaborate
complete thermodynamic picture of the long-range ordering of the arbitrary
compositional solid solution. The long-range order parameter is found for
different chemical potentials of the components to obtain a scope of ordering
solid solutions according to relation between degree of the chemical affinity
of the components and mixing energy. The boundary composition of the ordering
phase AB_n is determined as a function of the chemical potentials of the
components and concentrations of impurities and defects.
Temperature-compositional dependencies of the order parameter and the
sublattice difference of the chemical potentials are determined explicitly. The
hydrodynamic behavior of the system is presented by a reactive mode being
result of the interference of condensate and fluctuation components of
collective excitations. The dispersion law of this mode is displayed
experimentally as the Zener peak of the internal friction.Comment: 12 pages, 5 figures, RevTe
Theory of microphase separation of homopolymer-oligomer mixtures
Microphase separated structure consisting of the periodic alternation of the
layers of stretched homopolymer chains surrounded by perpendicularly oriented
oligomeric tails is studied for both, strongly bonded (ionic) systems and
weakly (hydrogen) bonded systems. Our approach is based on the fact that the
structure period is determined by alternating associations between the head
group of the surfactant and the interacting group of the polymer. Oligomer
distribution along the homopolymer chain is described by the effective equation
of motion with the segment number playing the role of time. As a result,
experimentally observed temperature dependence of the structure period, as well
as the dependence of the point of order--disorder transition are determined as
functions of the oligomeric fraction.Comment: 4 pages, 5 figures, RevTe
Supersymmetry Theory of Disordered Heteropolymers
The effective motion equation that describes the different monomer
alternation along the heteropolymer chain is proposed. On its basis the
supersymmetry field scheme that allows to obtain the equations for the
structure factor and Green function is built up. The memory and ergodicity
breaking effects are investigated depending on the temperature and quenched
disorder of the monomer alternation. The phase diagram that determines the
existence of the non-ergodic and freezing states is provided.Comment: 13 pages, 7 figures, LaTe
Synergetic theory for jamming transition in traffic flow
The theory of a jamming transition is proposed for the homogeneous
car-following model within the framework of Lorenz scheme. We represent a
jamming transition as a result of the spontaneous deviations of headway and
velocity that is caused by the acceleration/braking rate to be higher than the
critical value. The stationary values of headway and velocity deviations, and
time of acceleration/braking are derived as functions of control parameter
(time needed for car to take the characteristic velocity).Comment: 10 pages, 2 figures, LaTe
Multifractal spectrum of the phase space related to generalized thermostatistics
We consider the set of monofractals within a multifractal related to the
phase space being the support of a generalized thermostatistics. The
statistical weight exponent is shown to can be modeled by the
hyperbolic tangent deformed in accordance with both Tsallis and Kaniadakis
exponentials whose using allows one to describe explicitly arbitrary
multifractal phase space. The spectrum function , determining the
specific number of monofractals with reduced dimension , is proved to
increases monotonically from minimum value at to maximum at
. The number of monofractals is shown to increase with growth of the phase
space volume at small dimensions and falls down in the limit .Comment: 10 pages, 6 figure
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