The set of equations for magnetohydrodynamic (MHD) waves in a shear flow is
consecutively derived. The proposed scenario involves the presence of a
self-sustained turbulence and magnetic field. In ...the framework of
Langevin--Burgers approach the influence of the turbulence is described by an
additional external random force in the MHD system. Kinetic equation for the
spectral density of the slow magnetosonic (Alfvenic) mode is derived in the
short wavelength (WKB) approximation. The results show a pressing need for
conduction of numerical Monte Carlo (MC) simulations with a random driver to
take into account the influence of the long wavelength modes and to give a more
precise analytical assessment of the short ones. Realistic MC calculations for
the heating rate and shear stress tensor should give an answer to the
perplexing problem for the missing viscosity in accretion disks and reveal why
the quasars are the most powerful sources of light in the universe. The planned
MC calculations can be incorporated in global models for accretion disks and
also in all other physical conditions where there is a shear flow in a
magnetized turbulent plasma. It is supposed that the heating mechanism by
Alfven waves absorption is common for many kinds of space plasmas from solar
corona to active galactic nuclei and the solution of these longstanding puzzles
deserves active interdisciplinary research. The work is illustrated by
numerical calculations and by exact solutions for the time dependence of the
magnetic field given by the Heun function.
The set of equations for magnetohydrodynamic (MHD) waves in a shear flow is consecutively derived. The proposed scenario involves the presence of a self-sustained turbulence and magnetic field. In ...the framework of Langevin--Burgers approach the influence of the turbulence is described by an additional external random force in the MHD system. Kinetic equation for the spectral density of the slow magnetosonic (Alfvenic) mode is derived in the short wavelength (WKB) approximation. The results show a pressing need for conduction of numerical Monte Carlo (MC) simulations with a random driver to take into account the influence of the long wavelength modes and to give a more precise analytical assessment of the short ones. Realistic MC calculations for the heating rate and shear stress tensor should give an answer to the perplexing problem for the missing viscosity in accretion disks and reveal why the quasars are the most powerful sources of light in the universe. The planned MC calculations can be incorporated in global models for accretion disks and also in all other physical conditions where there is a shear flow in a magnetized turbulent plasma. It is supposed that the heating mechanism by Alfven waves absorption is common for many kinds of space plasmas from solar corona to active galactic nuclei and the solution of these longstanding puzzles deserves active interdisciplinary research. The work is illustrated by numerical calculations and by exact solutions for the time dependence of the magnetic field given by the Heun function.
Abstract
Several generalizations of the well-known fluid model of Braginskii (1965) are considered. We use the Landau collisional operator and the moment method of Grad. We focus on the 21-moment ...model that is analogous to the Braginskii model, and we also consider a 22-moment model. Both models are formulated for general multispecies plasmas with arbitrary masses and temperatures, where all of the fluid moments are described by their evolution equations. The 21-moment model contains two “heat flux vectors” (third- and fifth-order moments) and two “viscosity tensors” (second- and fourth-order moments). The Braginskii model is then obtained as a particular case of a one ion–electron plasma with similar temperatures, with decoupled heat fluxes and viscosity tensors expressed in a quasistatic approximation. We provide all of the numerical values of the Braginskii model in a fully analytic form (together with the fourth- and fifth-order moments). For multispecies plasmas, the model makes the calculation of the transport coefficients straightforward. Formulation in fluid moments (instead of Hermite moments) is also suitable for implementation into existing numerical codes. It is emphasized that it is the quasistatic approximation that makes some Braginskii coefficients divergent in a weakly collisional regime. Importantly, we show that the heat fluxes and viscosity tensors are coupled even in the linear approximation, and that the fully contracted (scalar) perturbations of the fourth-order moment, which are accounted for in the 22-moment model, modify the energy exchange rates. We also provide several appendices, which can be useful as a guide for deriving the Braginskii model with the moment method of Grad.
Boolean satisfiability problems are an important benchmark for questions about complexity, algorithms, heuristics, and threshold phenomena. Recent work on heuristics and the satisfiability threshold ...has centered around the structure and connectivity of the solution space. Motivated by this work, we study structural and connectivity-related properties of the space of solutions of Boolean satisfiability problems and establish various dichotomies in Schaefer's framework. On the structural side, we obtain dichotomies for the kinds of subgraphs of the hypercube that can be induced by the solutions of Boolean formulas, as well as for the diameter of the connected components of the solution space. On the computational side, we establish dichotomy theorems for the complexity of the connectivity and $st$-connectivity questions for the graph of solutions of Boolean formulas. Our results assert that the intractable side of the computational dichotomies is PSPACE-complete, while the tractable side--which includes but is not limited to all problems with polynomial-time algorithms for satisfiability--is in P for the $st$-connectivity question, and in coNP for the connectivity question. The diameter of components can be exponential for the PSPACE-complete cases, whereas in all other cases it is linear; thus, diameter and complexity of the connectivity problems are remarkably aligned. The crux of our results is an expressibility theorem showing that in the tractable cases, the subgraphs induced by the solution space possess certain good structural properties, whereas in the intractable cases, the subgraphs can be arbitrary.
To find the correlations between the parameters of iron homeostasis, inflammatory activity and autoimmune disorders in rheumatoid arthritis (RA).
The present study included 114 patients with RA and ...42 healthy controls. We determined the parameters of iron homeostasis: serum iron, total iron binding capacity (TIBC), ferritin and soluble transferrin receptor (sTfR), the parameters of inflammatory activity: C-reactive protein (CRP), interleukin-6 (IL-6) and prohepcidin, and the parameters of autoimmune disorders: rheumatoid factor (RF), anti-cyclic citrullinated peptide (antiCCP) antibodies and DAS 28.
The levels of sTfR, CRP, IL-6 and prohepcidin were significantly higher in RA patients than those in the controls and the level of serum iron was significantly lower in RA than that in the control group. Unlike the controls, in RA, there was a significant positive correlation of sTfR with the parameters of inflammatory activity (IL-6, prohepcidin, ESR) and with the parameters of autoimmune disorders (DAS 28, RF, antiCCP). A negative correlation of serum iron with sTfR was found only in RA patients. Prohepcidin positively correlated with the parameters of inflammation (CRP, ESR) and with the parameters for evaluation of autoimmune disorders (DAS 28 and RF) in the RA group.
Our study shows that the simultaneous determination of the two parameters sTfR and prohepcidin is most informative for evaluation of the changes in iron homeostasis in RA. The increase of both parameters provides information for tissue iron deficiency (assessed by the level of sTfR), caused by the inflammation when prohepcidin is expressed.
To find the correlations between the parameters of iron homeostasis, inflammatory activity and autoimmune disorders in rheumatoid arthritis (RA).
The present study included 114 patients with RA and ...42 healthy controls. We determined the parameters of iron homeostasis: serum iron, total iron binding capacity (TIBC), ferritin and soluble transferrin receptor (sTfR), the parameters of inflammatory activity: C-reactive protein (CRP), interleukin-6 (IL-6) and prohepcidin, and the parameters of autoimmune disorders: rheumatoid factor (RF), anti-cyclic citrullinated peptide (antiCCP) antibodies, and DAS 28.
The levels of sTfR, CRP, IL-6 and prohepcidin were significantly higher in RA patients than those in the controls and the level of serum iron was significantly lower in RA than that in the control group. Unlike the controls, in RA, there was a significant positive correlation of sTfR with the parameters of inflammatory activity (IL-6, prohepcidin, ESR) and with the parameters of autoimmune disorders (DAS 28, RF, antiCCP). A negative correlation of serum iron with sTfR was found only in RA patients. Prohepcidin positively correlated with the parameters of inflammation (CRP, ESR) and with the parameters for evaluation of autoimmune disorders (DAS 28 and RF) in the RA group.
Our study shows that the simultaneous determination of the two parameters sTfR and prohepcidin is most informative in evaluating the changes in iron homeostasis in RA. The increase of both parameters provides information for tissue iron deficiency (assessed by the level of sTfR), caused by the inflammation when prohepcidin is expressed.
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