Superstatistics as the statistics of quasi-equilibrium states: Application to fully developed turbulence

In non-equilibrium states, currents are produced by irreversible processes that take a system toward the equilibrium state, where the current vanishes. We demonstrate, in a general setting, that a superstatistics arises when the system relaxes to a (stationary) quasi-equilibrium state instead, where only the \textit{mean} current vanishes because of fluctuations. In particular, we show that a current with Gaussian white noise takes the system to a unique class of quasi-equilibrium states, where the superstatistics coincides with Tsallis escort $q$-distributions. Considering the fully developed turbulence as an example of such quasi-equilibrium states, we analytically deduce the power-law spectrum of the velocity structure functions, yielding a correction to the log-normal model which removes its shortcomings with regard to the decreasing higher order moments and the Novikov inequality, and obtain exponents that agree well with the experimental data.Comment: To appear in Phys. Rev. E (2011

Superselection from canonical constraints

The evolution of both quantum and classical ensembles may be described via the probability density P on configuration space, its canonical conjugate S, and an_ensemble_ Hamiltonian H[P,S]. For quantum ensembles this evolution is, of course, equivalent to the Schroedinger equation for the wavefunction, which is linear. However, quite simple constraints on the canonical fields P and S correspond to_nonlinear_ constraints on the wavefunction. Such constraints act to prevent certain superpositions of wavefunctions from being realised, leading to superselection-type rules. Examples leading to superselection for energy, spin-direction and `classicality' are given. The canonical formulation of the equations of motion, in terms of a probability density and its conjugate, provides a universal language for describing classical and quantum ensembles on both continuous and discrete configuration spaces, and is briefly reviewed in an appendix.Comment: MiKTex 2.3, no figures, minor clarifications, to appear in J. Phys.

Berry effect in acoustical polarization transport in phononic crystals

We derive the semiclassical equations of motion of a transverse acoustical wave packet propagating in a phononic crystal subject to slowly varying perturbations. The formalism gives rise to Berry effect terms in the equations of motion, manifested as the Rytov polarization rotation law and the polarization-dependent Hall effect. We show that the formalism is also applicable to the case of non-periodic inhomogeneous media, yielding explicit expressions for the Berry effect terms.Comment: To appear in JETP Let

One-loop approximation of Moller scattering in Krein-space quantization

It has been shown that the negative-norm states necessarily appear in a covariant quantization of the free minimally coupled scalar field in de Sitter spacetime [1,2]. In this processes ultraviolet and infrared divergences have been automatically eliminated [3]. A natural renormalization of the one-loop interacting quantum field in Minkowski spacetime ($\lambda\phi^4$) has been achieved through the consideration of the negative-norm states defined in Krein space. It has been shown that the combination of quantum field theory in Krein space together with consideration of quantum metric fluctuation, results in quantum field theory without any divergences [4]. Pursuing this approach, we express Wick's theorem and calculate M{\o}ller scattering in the one-loop approximation in Krein space. The mathematical consequence of this method is the disappearance of the ultraviolet divergence in the one-loop approximation.Comment: 10 page

Macroscopic effects of the spectral structure in turbulent flows

Two aspects of turbulent flows have been the subject of extensive, split research efforts: macroscopic properties, such as the frictional drag experienced by a flow past a wall, and the turbulent spectrum. The turbulent spectrum may be said to represent the fabric of a turbulent state; in practice it is a power law of exponent \alpha (the "spectral exponent") that gives the revolving velocity of a turbulent fluctuation (or "eddy") of size s as a function of s. The link, if any, between macroscopic properties and the turbulent spectrum remains missing. Might it be found by contrasting the frictional drag in flows with differing types of spectra? Here we perform unprecedented measurements of the frictional drag in soap-film flows, where the spectral exponent \alpha = 3 and compare the results with the frictional drag in pipe flows, where the spectral exponent \alpha = 5/3. For moderate values of the Reynolds number Re (a measure of the strength of the turbulence), we find that in soap-film flows the frictional drag scales as Re^{-1/2}, whereas in pipe flows the frictional drag scales as Re^{-1/4} . Each of these scalings may be predicted from the attendant value of \alpha by using a new theory, in which the frictional drag is explicitly linked to the turbulent spectrum. Our work indicates that in turbulence, as in continuous phase transitions, macroscopic properties are governed by the spectral structure of the fluctuations.Comment: 6 pages, 3 figure

Chemical constituents of sea buckthorn (Hippophae rhamnoides L.) fruit in populations of central Alborz Mountains in Iran

Background and objectives: Hippophae rhamnoides L. known as sea buckthorn is a deciduous medicinal shrub belonging to Elaeagnaceae family. In this study, the most important chemical constituents of sea buckthornwere evaluated in wild populations of central Alborz Mountains in Iran during the growth season of 2014 and 2015. Methods: Phytochemical analysis of fruit pulp and seed oil traits was performed using different methods of chromatography such as spectrophotometry, HPLC and GC. Results: Based on the results of combined analysis of variance, significant (p≤0.01) difference ranges between populations were found in respect to fruit dry weight (21.32 to 32.03%), total phenolic compounds (20.78 to 34.60 mg/g), extractable tannin (1.99 to 5.74 mg/g), glucose (38.14 to 110.70 mg/g), total carotenoids (0.80 to 1.17 mg/g), lycopene (0.13 to 0.20 mg/g), β-carotene (0.18 to 0.26 mg/g), total flavonoids (0.98 to 2.80 mg/g), total soluble solids (TSS) (11.85 to 31.50%), vitamin C (1.47 to 8.96 mg/g), seed oil content (4.51 to 7.91%), and two major unsaturated fatty acids including linoleic acid (28.71 to 37.44%) and linolenic acid (21.52 to 28.28%). Factor analysis based on principal component analysis (PCA) revealed most important traits with the highest correlation factor such as vitamin C, carbohydrates, TSS, fruit dry weight (FDW), and tannin for the first component. Conclusion: content of vitamin C was the main variable in chemical constituents for effective detection of original wild populations of central Alborz Mountains. Accordingly, sea buckthorn populations were divided into four main clusters and groups with high diversity based on their chemical compositions

Phytochemical and growth responses of Mentha piperita

The biostimulant products are able to improve quality and quantity of medicinal plants. The comparative effects of biostimulants foliar spraying on peppermint (Mentha piperita L.) were investigated. These studies were done on the basis of randomized complete blocks design in 3 replicates during 2015. In field conditions, the highest leaves and stems dry weight by 400 mg/l chitosan (CH) + 400 mg/l citric acid (CA), essential oil content by 200 mg/l chitosan + 400 mg/l humic acid (HA) + 400 mg/l citric acid and menthol content in 200 mg/l chitosan + 800 mg/l humic acid + 400 mg/l citric acid were observed. In greenhouse conditions, the best results of those mentioned parameters were obtained by 400 mg/l chitosan + 800 mg/l humic acid + 400 mg/l citric acid, 800 mg/l humic acid and 400 mg/l chitosan + 400 mg/l humic acid + 400 mg/l citric acid, respectively.Produkty biostymulujące mają właściwości podnoszące jakość i plon roślin leczniczych. Porównanie efektów spryskiwania biosymulatorami liści mięty pieprzowej. Badanie przeprowadzono w 2015 r. metodą wybranych losowo kompletnych bloków w trzech powtórzeniach. W warunkach polowych najwyższy plon suchej masy łodyg i liści otrzymano przy zastosowaniu 400 mg/l chitosanu (CH) + 400 mg/l kwasu cytrynowego (CA), zawartość olejku eterycznego przy użyciu 200 mg/l chitosanu + 400 mg/l kwasu humusowego (HA) + 400 mg/l kwasu cytrynowego oraz zawartość mentolu przy zastosowaniu 200 mg/l chitosanu + 800 mg/l kwasu humusowego + 400 mg/l kwasu cytrynowego. W warunkach szklarniowych najlepsze wyniki powyższych parametrów uzyskano, stosując odpowiednio 400 mg/l chitosanu + 800 mg/l kwasu humusowego + 400 mg/l kwasu cytrynowego, 800 mg/l kwasu humusowego oraz 400 mg/l chitosanu + 400 mg/l kwasu humusowego + 400 mg/l kwasu cytrynowego.Stosowanie dolistne efektywnych biostymulantów może podnieść jakość i plon mięty pieprzowej

Odpowiedź biochemiczna i wzrost Mentha piperita po dolistnym podaniu biostymulatorów w warunkach szklarniowych i polowych

The biostimulant products are able to improve quality and quantity of medicinal plants. The comparative effects of biostimulants foliar spraying on peppermint (Mentha piperita L.) were investigated. These studies were done on the basis of randomized complete blocks design in 3 replicates during 2015. In field conditions, the highest leaves and stems dry weight by 400 mg/l chitosan (CH) + 400 mg/l citric acid (CA), essential oil content by 200 mg/l chitosan + 400 mg/l humic acid (HA) + 400 mg/l citric acid and menthol content in 200 mg/l chitosan + 800 mg/l humic acid + 400 mg/l citric acid were observed. In greenhouse conditions, the best results of those mentioned parameters were obtained by 400 mg/l chitosan + 800 mg/l humic acid + 400 mg/l citric acid, 800 mg/l humic acid and 400 mg/l chitosan + 400 mg/l humic acid + 400 mg/l citric acid, respectively.Produkty biostymulujące mają właściwości podnoszące jakość i plon roślin leczniczych. Porównanie efektów spryskiwania biosymulatorami liści mięty pieprzowej. Badanie przeprowadzono w 2015 r. metodą wybranych losowo kompletnych bloków w trzech powtórzeniach. W warunkach polowych najwyższy plon suchej masy łodyg i liści otrzymano przy zastosowaniu 400 mg/l chitosanu (CH) + 400 mg/l kwasu cytrynowego (CA), zawartość olejku eterycznego przy użyciu 200 mg/l chitosanu + 400 mg/l kwasu humusowego (HA) + 400 mg/l kwasu cytrynowego oraz zawartość mentolu przy zastosowaniu 200 mg/l chitosanu + 800 mg/l kwasu humusowego + 400 mg/l kwasu cytrynowego. W warunkach szklarniowych najlepsze wyniki powyższych parametrów uzyskano, stosując odpowiednio 400 mg/l chitosanu + 800 mg/l kwasu humusowego + 400 mg/l kwasu cytrynowego, 800 mg/l kwasu humusowego oraz 400 mg/l chitosanu + 400 mg/l kwasu humusowego + 400 mg/l kwasu cytrynowego.Stosowanie dolistne efektywnych biostymulantów może podnieść jakość i plon mięty pieprzowej