Calculation of the anomalous exponents in the rapid-change model of passive scalar advection to order ε3\varepsilon^{3}

The field theoretic renormalization group and operator product expansion are applied to the model of a passive scalar advected by the Gaussian velocity field with zero mean and correlation function \propto\delta(t-t')/k^{d+\eps}. Inertial-range anomalous exponents, identified with the critical dimensions of various scalar and tensor composite operators constructed of the scalar gradients, are calculated within the $\varepsilon$ expansion to order $\varepsilon^{3}$ (three-loop approximation), including the exponents in anisotropic sectors. The main goal of the paper is to give the complete derivation of this third-order result, and to present and explain in detail the corresponding calculational techniques. The character and convergence properties of the $\varepsilon$ expansion are discussed; the improved ``inverse'' $\varepsilon$ expansion is proposed and the comparison with the existing nonperturbative results is given.Comment: 34 pages, 5 figures, REVTe

Anomalous scaling, nonlocality and anisotropy in a model of the passively advected vector field

A model of the passive vector quantity advected by a Gaussian time-decorrelated self-similar velocity field is studied; the effects of pressure and large-scale anisotropy are discussed. The inertial-range behavior of the pair correlation function is described by an infinite family of scaling exponents, which satisfy exact transcendental equations derived explicitly in d dimensions. The exponents are organized in a hierarchical order according to their degree of anisotropy, with the spectrum unbounded from above and the leading exponent coming from the isotropic sector. For the higher-order structure functions, the anomalous scaling behavior is a consequence of the existence in the corresponding operator product expansions of ``dangerous'' composite operators, whose negative critical dimensions determine the exponents. A close formal resemblance of the model with the stirred NS equation reveals itself in the mixing of operators. Using the RG, the anomalous exponents are calculated in the one-loop approximation for the even structure functions up to the twelfth order.Comment: 37 pages, 4 figures, REVTe

Определение концентрации холестерина и триглицеридов в экстраклеточных везикулах сыворотки крови с помощью коммерческих наборов

Exosomes and microvesicles, collectively referred to as small extracellular vesicles (sEV) are vesicles with an average size of about 100-150 nm. Currently, the role of sEV in various aspects of signaling in the body is being actively investigated; in addition, sEV can often serve as markers of various pathologies. The active study of the sEV composition is continuing. In this study we have demonstrated that in sEV it is possible to determine cholesterol and triglycerides concentration by using commercial kits designed for serum. The technique was tested on sEV from the blood of patients diagnosed with depression and on healthy volunteers. No differences were found in the concentration of cholesterol and triglycerides in mEV from the blood serum of depressed patients and the control group. The concentration of cholesterol and triglycerides in the samples is several times higher than the sensitivity threshold of the methods set by the manufacturer of the kits.Экзосомы и микровезикулы, совместно называемые малые экстраклеточные везикулы (мЭВ), представляют собой везикулы со средним размером около 100-150 нм. В настоящее время активно исследуется роль мЭВ в самых разных аспектах сигналинга в организме, кроме того, часто мЭВ могут служить маркерами разных патологий. Продолжается активное изучение состава мЭВ. В данной работе мы показали, что в мЭВ можно определить концентрацию холестерина и триглицеридов с помощью коммерческих наборов, предназначенных для сыворотки крови. Методика была опробована на мЭВ из крови пациентов с диагнозом депрессия и на здоровых добровольцах. Различий в концентрации холестерина и триглицеридов в мЭВ из сыворотки крови пациентов с депрессией и контрольной группы найдено не было. Концентрация холестерина и триглицеридов в образцах в несколько раз превосходит порог чувствительности методов, установленный производителем наборов

Anomalous exponents in the rapid-change model of the passive scalar advection in the order ϵ3\epsilon^{3}

Field theoretic renormalization group is applied to the Kraichnan model of a passive scalar advected by the Gaussian velocity field with the covariance $- <{\bf v}(t,{\bf x}){\bf v}(t',{\bf x'})> \propto\delta(t-t')|{\bf x}-{\bf x'} |^{\epsilon}$. Inertial-range anomalous exponents, related to the scaling dimensions of tensor composite operators built of the scalar gradients, are calculated to the order $\epsilon^{3}$ of the $\epsilon$ expansion. The nature and the convergence of the $\epsilon$ expansion in the models of turbulence is are briefly discussed.Comment: 4 pages; REVTeX source with 3 postscript figure

Anomalous scaling of a passive scalar in the presence of strong anisotropy

Field theoretic renormalization group and the operator product expansion are applied to a model of a passive scalar field, advected by the Gaussian strongly anisotropic velocity field. Inertial-range anomalous scaling behavior is established, and explicit asymptotic expressions for the n-th order structure functions of scalar field are obtained; they are represented by superpositions of power laws with nonuniversal (dependent on the anisotropy parameters) anomalous exponents. In the limit of vanishing anisotropy, the exponents are associated with tensor composite operators built of the scalar gradients, and exhibit a kind of hierarchy related to the degree of anisotropy: the less is the rank, the less is the dimension and, consequently, the more important is the contribution to the inertial-range behavior. The leading terms of the even (odd) structure functions are given by the scalar (vector) operators. For the finite anisotropy, the exponents cannot be associated with individual operators (which are essentially ``mixed'' in renormalization), but the aforementioned hierarchy survives for all the cases studied. The second-order structure function is studied in more detail using the renormalization group and zero-mode techniques.Comment: REVTEX file with EPS figure

Two-Loop Calculation of the Anomalous Exponents in the Kazantsev--Kraichnan Model of Magnetic Hydrodynamics

The problem of anomalous scaling in magnetohydrodynamics turbulence is considered within the framework of the kinematic approximation, in the presence of a large-scale background magnetic field. Field theoretic renormalization group methods are applied to the Kazantsev-Kraichnan model of a passive vector advected by the Gaussian velocity field with zero mean and correlation function $\propto \delta(t-t')/k^{d+\epsilon}$. Inertial-range anomalous scaling for the tensor pair correlators is established as a consequence of the existence in the corresponding operator product expansions of certain "dangerous" composite operators, whose negative critical dimensions determine the anomalous exponents. The main technical result is the calculation of the anomalous exponents in the order $\epsilon^2$ of the $\epsilon$ expansion (two-loop approximation).Comment: Presented in the Conference "Mathematical Modeling and Computational Physics" (Stara Lesna, Slovakia, July 2011

Dynamic structure factor of the Ising model with purely relaxational dynamics

We compute the dynamic structure factor for the Ising model with a purely relaxational dynamics (model A). We perform a perturbative calculation in the $\epsilon$ expansion, at two loops in the high-temperature phase and at one loop in the temperature magnetic-field plane, and a Monte Carlo simulation in the high-temperature phase. We find that the dynamic structure factor is very well approximated by its mean-field Gaussian form up to moderately large values of the frequency $\omega$ and momentum $k$. In the region we can investigate, $k\xi \lesssim 5$, $\omega \tau \lesssim 10$, where $\xi$ is the correlation length and $\tau$ the zero-momentum autocorrelation time, deviations are at most of a few percent.Comment: 21 pages, 3 figure

Transverse spin effects in hadron-pair production from semi-inclusive deep inelastic scattering

First measurements of azimuthal asymmetries in hadron-pair production in deep-inelastic scattering of muons on transversely polarised ^6LiD (deuteron) and NH_3 (proton) targets are presented. The data were taken in the years 2002-2004 and 2007 with the COMPASS spectrometer using a muon beam of 160 GeV/c at the CERN SPS. The asymmetries provide access to the transversity distribution functions, without involving the Collins effect as in single hadron production. The sizeable asymmetries measured on the NH_ target indicate non-vanishing u-quark transversity and two-hadron interference fragmentation functions. The small asymmetries measured on the ^6LiD target can be interpreted as indication for a cancellation of u- and d-quark transversities.Comment: 13 pages, 4 figures, updated to the published versio