Geodesic plasma compressibility effects on the magnetic islands in a tokamak

It is shown that the stability of rotating magnetic islands in a tokamak plasma is affected by plasma compressibility related to the geodesic curvature in an inhomogeneous magnetic field. A robust contribution has been found to the Rutherford evolution equation. It is shown that the sign of the geodesic curvature contribution is opposite to the sign of the polarization term. It is suggested that this mechanism plays a crucial role in the stability of small scale magnetic islands.     

Submanifolds in five-dimensional pseudo-Euclidean spaces and four-dimensional FRW universes

Equations for submanifolds, which correspond to embeddings of the four-dimensional FRW universes in five-dimensional pseudo-Euclidean spaces, are presented in convenient form in general case. Several specific examples are considered.     

The construction of graph models for calculations of the properties of substitution isomers of basis structures on the basis of additivity of energy contributions

A method for the construction of additive models for calculations of the properties of substitution isomers of basis structures is described for the example of a series of X-substituted methylsilanes CH_{3 − k} X _k -SiH_{3 − l} X _l (where X = CH₃, F, Cl, …, k, l = 0, 1, 2, 3). The method is based on similarity of subgraphs in graphs of several molecules and the arrangement of polygonal numbers (triangular, tetrahedral) of the Pascal triangle. Parameters taking into account multiple nonvalence interactions (-C-Si<, >C-Si<, …) through two atoms along the molecular chain of an X-substituted methylsilane (X = CH₃) were for the first time explicitly included in the calculation scheme. Taking these interactions into account allows us to completely differentiate all the structural isomers of certain molecules and obtain numerical parameter values for predicting properties P under consideration in various approximations. Numerical calculations of Δ_f H _{g,298 K}^o were performed for 16 alkylsilanes (as X-substituted methylsilanes), including 7 compounds not studied experimentally.     

Field distribution along a longitudinally streamlined arc in a DC plasmatron

These measurements were made with potential probes and show that the voltage increases along the arc in the direction of gas flow. An explanation in terms of increase in temperature is proposed.Notation I arc current - G gas flow rate - E field strength - U potential - electrical conductivity - Q_c convective heat flux - heat-transfer factor - T mass-average temperature - F surface of unit length - dynamic viscosity - Ta arc temperature - N Nusselt number - thermal conductivity - d electrode diameter - d_a arc diameter - R Reynolds number - density deduced from T - W mean gas flow speed - S cross section of electrode - l distance along the axis from the inner electrode     

Newtonian limit in the stabilized Randall-Sundrum model

In the stabilized Randall-Sundrum model, we obtain and solve linearized equations of motion for gravitational and scalar fields in the case of matter on the brane. We find the Newtonian limit of an effective four-dimensional theory on branes with negative tension and explicitly isolate the radion field contribution. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 2, pp. 226–236, August, 2008.     

A stabilized warped brane world with equal gravity strengths on the branes

We discuss a stabilized brane world model with two branes, allowing a solution to the hierarchy problem due to the warped extra dimension and having a remarkable feature: the strength of gravitational interaction is of the same order on both branes, contrary to the case of the Randall-Sundrum model with a hierarchical difference of the gravitational strength on the branes. The solution also admits the existence of two branes with equal gravity strengths. The article is published in the original.     

Linearized gravity in the Randall-Sundrum model with stabilized distance between branes

We consider linearized gravity in the Randall-Sundrum model in which the distance between branes is stabilized by introducing the scalar Goldberger-Wise field. We construct the second variation Lagrangian for fluctuations of gravitational and scalar fields over the background solution and investigate its gauge invariance. We obtain, separate, and solve the corresponding equations of motion. For physical degrees of freedom, we obtain the effective four-dimensional Lagrangian describing the massless graviton, massive gravitons, and the set of massive scalar fields. We also find masses and coupling constants of these fields to the matter on the negative-tension brane. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 149, No. 3, pp. 339–353, December, 2006.