Abstract:
Localization-delocalization transition in a discrete Anderson nonlinear Schr\"odinger equation with disorder is shown to be a critical phenomenon $-$ similar to a percolation transition on a disordered lattice, with the nonlinearity parameter thought as the control parameter. In vicinity of the critical point the spreading of the wave field is subdiffusive in the limit $t\rightarrow+\infty$. The second moment grows with time as a powerlaw $\propto t^\alpha$, with $\alpha$ exactly 1/3. This critical spreading finds its significance in some connection with the general problem of transport along separatrices of dynamical systems with many degrees of freedom and is mathematically related with a description in terms fractional derivative equations. Above the delocalization point, with the criticality effects stepping aside, we find that the transport is subdiffusive with $\alpha = 2/5$ consistently with the results from previous investigations. A threshold for unlimited spreading is calculated exactly by mapping the transport problem on a Cayley tree.

Abstract:
This study is concerned with destruction of Anderson localization by a nonlinearity of the power-law type. We suggest using a nonlinear Schr\"odinger model with random potential on a lattice that quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. For super-quadratic nonlinearity the borderline spreading corresponds to diffusion processes on finite clusters. We have proposed an analytical method to predict and explain such transport processes. Our method uses a topological approximation of the nonlinear Anderson model and, if the exponent of the power nonlinearity is either integer or half-integer, will yield the wanted value of the transport exponent via a triangulation procedure in an Euclidean mapping space. A kinetic picture of the transport arising from these investigations uses a fractional extension of the diffusion equation to fractional derivatives over the time, signifying non-Markovian dynamics with algebraically decaying time correlations.

Abstract:
In the present article, the new method of DNA extraction from fresh and herbarium leafs of grape to their subsequent sequencing was described

Abstract:
The concept of the generalized entropy is analyzed, with the particular attention to the definition postulated by Tsallis [J. Stat. Phys. 52, 479 (1988)]. We show that the Tsallis entropy can be rigorously obtained as the solution of a nonlinear functional equation; this equation represents the entropy of a complex system via the partial entropies of the subsystems involved, and includes two principal parts. The first part is linear (additive) and leads to the conventional, Boltzmann, definition of entropy as the logarithm of the statistical weight of the system. The second part is multiplicative and contains all sorts of multilinear products of the partial entropies; inclusion of the multiplicative terms is shown to reproduce the generalized entropy exactly in the Tsallis sense. We speculate that the physical background for considering the multiplicative terms is the role of the long-range correlations supporting the "macroscopic" ordering phenomena (e.g., formation of the "coarse-grained" correlated patterns). We prove that the canonical distribution corresponding to the Tsallis definition of entropy, coincides with the so-called "kappa" redistribution which appears in many physical realizations. This has led us to associate the origin of the "kappa" distributions with the "macroscopic" ordering ("coarse-graining") of the system. Our results indicate that an application of the formalism based on the Tsallis notion of entropy might actually have sense only for the systems whose statistical weights, Ω, are relatively small. (For the "coarse-grained" systems, the weight omega could be interpreted as the number of the "grains".) For large Ω (i.e., Ω -> ∞), the standard statistical mechanical formalism is advocated, which implies the conventional, Boltzmann definition of entropy as ln Ω.

Abstract:
The analysis of genetic polymorphisms of 12 autochthonous grape varieties grown in the National ampelographic collection of Russia (Anapa district of the Krasnodar region) through the study of allelic diversity at six microsatellite loci: VRZAG79, VVMD5, VVMD7, VVMD27, VRZAG62, VVS2 has been done. We have found that all native varieties have a unique set of allele. The assessment of genetic relationships varieties has been performed using cluster analysis. Data for DNA certification of the investigated genotypes of the grapes has also been obtained in the article

Abstract:
In the present article, we have described data of comparative ampelography of biometric evaluation of leaf parameters of the three table grapes: Preobragenie, Victor and Jubiley Novocherkasska, widespread in the amateur and farming areas of Russia and the Ukraine

Abstract:
In the present article, we have described data of comparative ampelography of biometric evaluation of leaf parameters of the three table grapes: Preobragenie, Victor and Jubiley Novocherkassk, widespread in the amateur and farming areas of Russia and the Ukraine. Showed results of molecular genetic analysis of DNA from these table grapes

Abstract:
The concept of percolation is combined with a self-consistent treatment of the interaction between the dynamics on a lattice and the external drive. Such a treatment can provide a mechanism by which the system evolves to criticality without fine tuning, thus offering a route to self-organized criticality (SOC) which in many cases is more natural than the weak random drive combined with boundary loss/dissipation as used in standard sand-pile formulations. We introduce a new metaphor, the e-pile model, and a formalism for electric conduction in random media to compute critical exponents for such a system. Variations of the model apply to a number of other physical problems, such as electric plasma discharges, dielectric relaxation, and the dynamics of the Earth's magnetotail.

Abstract:
The basic physics properties and simplified model descriptions of the paradigmatic "percolation" transport in low-frequency, electrostatic (anisotropic magnetic) turbulence are theoretically analyzed. The key problem being addressed is the scaling of the turbulent diffusion coefficient with the fluctuation strength in the limit of slow fluctuation frequencies (large Kubo numbers). In this limit, the transport is found to exhibit pseudochaotic, rather than simply chaotic, properties associated with the vanishing Kolmogorov-Sinai entropy and anomalously slow mixing of phase space trajectories. Based on a simple random walk model, we find the low-frequency, percolation scaling of the turbulent diffusion coefficient to be given by $D/\omega\propto Q^{2/3}$ (here $Q\gg 1$ is the Kubo number and $\omega$ is the characteristic fluctuation frequency). When the pseudochaotic property is relaxed the percolation scaling is shown to cross over to Bohm scaling. The features of turbulent transport in the pseudochaotic regime are described statistically in terms of a time fractional diffusion equation with the fractional derivative in the Caputo sense. Additional physics effects associated with finite particle inertia are considered.

Abstract:
In this chapter of the e-book "Self-Organized Criticality Systems" we summarize some theoretical approaches to self-organized criticality (SOC) phenomena that involve percolation as an essential key ingredient. Scaling arguments, random walk models, linear-response theory, and fractional kinetic equations of the diffusion and relaxation type are presented on an equal footing with theoretical approaches of greater sophistication, such as the formalism of discrete Anderson nonlinear Schr\"odinger equation, Hamiltonian pseudochaos, conformal maps, and fractional derivative equations of the nonlinear Schr\"odinger and Ginzburg-Landau type. Several physical consequences are described which are relevant to transport processes in complex systems. It is shown that a state of self-organized criticality may be unstable against a bursting ("fishbone") mode when certain conditions are met. Finally we discuss SOC-associated phenomena, such as: self-organized turbulence in the Earth's magnetotail (in terms of the "Sakura" model), phase transitions in SOC systems, mixed SOC-coherent behavior, and periodic and auto-oscillatory patterns of behavior. Applications of the above pertain to phenomena of magnetospheric substorm, market crashes, and the global climate change and are also discussed in some detail. Finally we address the frontiers in the field in association with the emerging projects in fusion research and space exploration.