arXiv subjects

A. I. Olemskoi

Publications and source records attributed to A. I. Olemskoi.

At least 19 recordsLinked to original sources

arXiv2011

Analytical and numerical studies of creation probabilities of hierarchical trees

We consider the creation conditions of diverse hierarchical trees both analytically and numerically. A connection between the probabilities to create hierarchical levels and the probability to associate these levels into a united structure is studied. We argue that a consistent probabilistic picture requires the use of deformed algebra. Our consideration is based on the study of the main types of hierarchical trees, among which both regular and degenerate ones are studied analytically, while the creation probabilities of Fibonacci, scale-free and arbitrary trees are determined numerically.

cond-mat.stat-mech↗

arXiv2010

Statistical field theories deformed within different calculi

Within framework of basic-deformed and finite-difference calculi, as well as deformation procedures proposed by Tsallis, Abe, and Kaniadakis to be generalized by Naudts, we develop field-theoretical schemes of statistically distributed fields. We construct a set of generating functionals and find their connection with corresponding correlators for basic-deformed, finite-difference, and Kaniadakis calculi. Moreover, we introduce pair of additive functionals, whose expansions into deformed series yield both Green functions and their irreducible proper vertices. We find as well formal equations, governing by the generating functionals of systems which possess a symmetry with respect to a field variation and are subjected to an arbitrary constrain. Finally, we generalize field-theoretical schemes inherent in concrete calculi in the Naudts spirit.

cond-mat.stat-mech↗

arXiv2010

Suppression of oscillations by Levy noise

We find analytical solution of pair of stochastic equations with arbitrary forces and multiplicative Lévy noises in a steady-state nonequilibrium case. This solution shows that Lévy flights suppress always a quasi-periodical motion related to the limit cycle. We prove that difference between stochastic systems driven by Lévy and Gaussian noises is that the Lévy variation $ΔL\sim(Δt)^{1/α}$ with the exponent $α<2$ is much less than the Gaussian one $ΔW\sim(Δt)^{1/2}$ in the $Δt\to 0$ limit. Moreover, this difference is shown to remove the problem of the calculus choice because related addition to the physical force is of order $(Δt)^{2/α}\llΔt$.

cond-mat.stat-mech↗

arXiv2009

Self-organization of quasi-equilibrium stationary condensation in accumulative ion-plasma devices

We consider both theoretically and experimentally self-organization process of quasi-equilibrium steady-state condensation of sputtered substance in accumulative ion-plasma devices. The self-organization effect is shown to be caused by self-consistent variations of the condensate temperature and the supersaturation of depositing atoms. On the basis of the phase-plane method, we find two different types of the self-organization process to be possible. Experimental data related to aluminum condensates are discussed to confirm self-organization nature of quasi-equilibrium steady-state condensation process.

cond-mat.stat-mech↗

arXiv2009

Noise induced oscillations in non-equilibrium steady state systems

We consider effect of stochastic sources upon self-organization process being initiated with creation of the limit cycle. General expressions obtained are applied to the stochastic Lorenz system to show that departure from equilibrium steady state can destroy the limit cycle at certain relation between characteristic scales of temporal variation of principle variables. Noise induced resonance related to the limit cycle is found to appear if the fastest variations displays a principle variable, which is coupled with two different degrees of freedom or more.

cond-mat.stat-mech↗

arXiv2009

Self-similarity degree of deformed statistical ensembles

We consider self-similar statistical ensembles with the phase space whose volume is invariant under the deformation that squeezes (expands) the coordinate and expands (squeezes) the momentum. Related probability distribution function is shown to possess a discrete symmetry with respect to manifold action of the Jackson derivative to be a homogeneous function with a self-similarity degree $q$ fixed by the condition of invariance under $(n+1)$-fold action of the dilatation operator related. In slightly deformed phase space, we find the homogeneous function is defined with the linear dependence at $n=0$, whereas the self-similarity degree equals the gold mean at $n=1$, and $q\to n$ in the limit $n\to\infty$. Dilatation of the homogeneous function is shown to decrease the self-similarity degree $q$ at $n>0$.

cond-mat.stat-mech↗

arXiv2008

Complexity of hierarchical ensembles

Within the framework of generalized combinatorial approach, complexity is determined as a disorder measure for hierarchical statistical ensembles related to Cayley trees possessing arbitrary branching and number of levels. With strengthening hierarchical coupling, the complexity is shown to increase monotonically to the limit value that grows with tree branching. In contrast to the temperature dependence of thermodynamic entropy, the complexity is reduced by the variance of hierarchical statistical ensemble if the branching exponent does not exceed the gold mean. Time dependencies are found for both the probability distribution over ensemble states and the related complexity. The latter is found explicitly for self-similar ensemble and generalized for arbitrary hierarchical trees.

cond-mat.stat-mech↗

arXiv2007

Multifractal spectrum of phase space related to generalized thermostatistics

We consider a self-similar phase space with specific fractal dimension $d$ being distributed with spectrum function $f(d)$. Related thermostatistics is shown to be governed by the Tsallis formalism of the non-extensive statistics, where the non-additivity parameter is equal to ${\barτ}(q)\equiv 1/τ(q)>1$, and the multifractal function $τ(q)= qd_q-f(d_q)$ is the specific heat determined with multifractal parameter $q\in [1,\infty)$. In this way, the equipartition law is shown to take place. Optimization of the multifractal spectrum function $f(d)$ derives the relation between the statistical weight and the system complexity. It is shown the statistical weight exponent $τ(q)$ can be modeled by hyperbolic tangent deformed in accordance with both Tsallis and Kaniadakis exponentials to describe arbitrary multifractal phase space explicitly. The spectrum function $f(d)$ is proved to increase monotonically from minimum value $f=-1$ at $d=0$ to maximum one $f=1$ at $d=1$. At the same time, the number of monofractals increases with growth of the phase space volume at small dimensions $d$ and falls down in the limit $d\to 1$.

cond-mat.stat-mech↗

arXiv2006

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.

cond-mat.stat-mech↗

arXiv2006

Hopf Bifurcation within Thermodynamic Representation

On base of Hamiltonian formalism, we show that Hopf bifurcation arrives, in the course of the system evolution, at creation of revolving region of the phase plane being bounded by limit cycle. A revolving phase plane with a set of limit cycles is presented in analogy with revolving vessel containing superfluid He$^4$. Within such a representation, fast varying angle is shown to be reduced to phase of complex order parameter whose module squared plays a role of action. Respectively, vector potential of conjugate field is reduced to relative velocity of movement of the limit cycle interior with respect to its exterior.

cond-mat.stat-mech↗

arXiv2006

Generalized thermostatistics based on multifractal phase space

We consider the self-similar phase space with reduced fractal dimension $d$ being distributed within domain $0 1$ of the multifractal function $τ(q)= qd(q)-f(d(q))$, being the specific heat, $q\in(1,\infty)$ is multifractal parameter. In this way, the equipartition law is shown to take place. Optimization of the multifractal spectrum $f(d)$ derives the relation between the statistical weight and the system complexity.

cond-mat.stat-mech↗

arXiv2006

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 $τ(q)$ 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 $f(d)$, determining the specific number of monofractals with reduced dimension $d$, is proved to increases monotonically from minimum value $f=-1$ at $d=0$ to maximum $f=1$ at $d=1$. The number of monofractals is shown to increase with growth of the phase space volume at small dimensions $d$ and falls down in the limit $d\to 1$.

cond-mat.stat-mech↗

arXiv2004

Phase transitions induced by noise cross-correlations

A general approach to consider spatially extended stochastic systems with correlations between additive and multiplicative noises subject to nonlinear damping is developed. Within modified cumulant expansion method, we derive an effective Fokker-Planck equation whose stationary solutions describe a character of ordered state. We find that fluctuation cross-correlations lead to a symmetry breaking of the distribution function even in the case of the zero-dimensional system. In general case, continuous, discontinuous and reentrant noise induced phase transitions take place. It is appeared the cross-correlations play a role of bias field which can induce a chain of phase transitions being different in nature. Within mean field approach, we give an intuitive explanation of the system behavior through an effective potential of thermodynamic type. This potential is written in the form of an expansion with coefficients defined by temperature, intensity of spatial coupling, auto- and cross-correlation times and intensities of both additive and multiplicative noises.

cond-mat.stat-mech↗

arXiv2003

Supersymmetry theory of microphase separation in homopolymer--oligomer mixtures

Mesoscopic structure of the periodically alternating layers of stretched homopolymer chains surrounded by perpendicularly oriented oligomeric tails is studied for the systems with both strong (ionic) and weak (hydrogen) interactions. We focus on the consideration of the distribution of oligomers along the homopolymer chains that is described by the effective equation of motion with the segment number playing the role of imaginary time. Supersymmetry technique is developed to consider associative hydrogen bonding, self--action effects, inhomogeneity and temperature fluctuations in the oligomer distribution. Making use of the self--consistent approach allows to explain experimentally observed temperature dependence of the structure period and the order--disorder transition temperature and period as functions of the oligomeric fraction for systems with different strength of bonding. A whole set of parameters of the model used is found for strong, intermediate and weak coupled systems being P4VP--(DBSA)$_x$, P4VP-(Zn(DBS)$_2$)$_x$ and P4VP--(PDP)$_x$, respectively. A passage from the formers to the latters shows to cause crucial decrease of the magnitude of both parameters of hydrogen bonding and self--action, as well as the order--disorder transition temperature.

cond-mat.soft↗

arXiv2002

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.

cond-mat.stat-mech↗

arXiv2002

Statistical theory of self--similar time series

Within Tsallis statistics, a picture 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. Predictability conditions of time series analysis are discussed in details on the basis of Van der Waals model. Maximal magnitude for time interval and minimal resolution scale of the value under consideration are found and analyzed in details. Time series statistics is shown to be governed by effective temperature being exponential measure of the fractal dimensionality of a phase space related to the time series.

cond-mat.stat-mech↗

arXiv2001

Structure evolution of Pd-Ta-H alloy In Edwards' thermodynamics representation

X-rays diffraction pictures time dependence of deformed alloy Pd-Ta being charged with hydrogen has been shown to be possibly caused by multi-pits character of energetic relief in the states space. Phenomenological model representing alloy structural evolution as a occasional roaming on minima of internal energy of non-ergodic system, has been offered in Lorenz synergetic scheme frames. Here, order parameters are the part of minima occupied by the system, conjugated field is considered to be Edwards entropy and control parameter is taken to be internal energy. Thermodynamics interpretation of Pd-Ta-H alloy evolution structure as a complex non-ergodic system is offered

cond-mat.mtrl-sci↗

arXiv2001

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.

cond-mat.stat-mech↗