Stars creating a gravitational repulsion

In the framework of the Theory of General Relativity, models of stars with an unusual equation of state $\rho c^20$ where $\rho$ is the mass density and $P$ is the pressure, are constructed. These objects create outside themselves the forces of gravitational repulsion. The equilibrium of such stars is ensured by a non-standard balance of forces. Negative mass density, acting gravitationally on itself, creates an acceleration of the negative mass, directed from the center. Therefore in the absence of pressure such an object tends to expand. At the same time, the positive pressure, which falls just like in ordinary stars from the center to the surface, creates a force directed from the center. This force acts on the negative mass density, which causes acceleration directed the opposite of the acting force, that is to the center of the star. This acceleration balances the gravitational repulsion produced by the negative mass. Thus, in our models gravity and pressure change roles: the negative mass tends to create a gravitational repulsion, while the gradient of the pressure acting on the negative mass tends to compress the star. In this paper, we construct several models of such a star with various equations of state.Comment: 6 pages, 4 figure

Topology of quasiperiodic functions on the plane

The article describes a topological theory of quasiperiodic functions on the plane. The development of this theory was started (in different terminology) by the Moscow topology group in early 1980s. It was motivated by the needs of solid state physics, as a partial (nongeneric) case of Hamiltonian foliations of Fermi surfaces with multivalued Hamiltonian function. The unexpected discoveries of their topological properties that were made in 1980s and 1990s have finally led to nontrivial physical conclusions along the lines of the so-called geometric strong magnetic field limit. A very fruitful new point of view comes from the reformulation of that problem in terms of quasiperiodic functions and an extension to higher dimensions made in 1999. One may say that, for single crystal normal metals put in a magnetic field, the semiclassical trajectories of electrons in the space of quasimomenta are exactly the level lines of the quasiperiodic function with three quasiperiods that is the dispersion relation restricted to a plane orthogonal to the magnetic field. General studies of the topological properties of levels of quasiperiodic functions on the plane with any number of quasiperiods were started in 1999 when certain ideas were formulated for the case of four quasiperiods. The last section of this work contains a complete proof of these results. Some new physical applications of the general problem were found recently.Comment: latex2e, 27 pages, 7 figure

Hydrodynamic Flow as Congruence of Geodesic Lines in Riemannian Space-Time

It is shown that small elements of perfect fluid in adiabatic processes move along geodesic lines of a Riemannian space-time.Comment: 5 pages, Latex. Final versio

The electrification of spacecraft

Physical and applied aspects of the electrification of space vehicles and natural celestial objects are discussed, the factors resulting in electrification of spacecraft are analyzed, and methods of investigating various phenomena associated with this electrification and ways of protecting spacecraft against the influence of static electricity are described. The booklet is intended for the general reader interested in present day questions of space technology

Efficiency at maximum power of thermally coupled heat engines

We study the efficiency at maximum power of two coupled heat engines, using thermoelectric generators (TEGs) as engines. Assuming that the heat and electric charge fluxes in the TEGs are strongly coupled, we simulate numerically the dependence of the behavior of the global system on the electrical load resistance of each generator in order to obtain the working condition that permits maximization of the output power. It turns out that this condition is not unique. We derive a simple analytic expression giving the relation between the electrical load resistance of each generator permitting output power maximization. We then focuse on the efficiency at maximum power (EMP) of the whole system to demonstrate that the Curzon-Ahlborn efficiency may not always be recovered: the EMP varies with the specific working conditions of each generator but remains in the range predicted by irreversible thermodynamics theory. We finally discuss our results in light of non-ideal Carnot engine behavior.Comment: 11 pages, 7 figure