A new hypothesis of sunspot formation

The process of sunspot formation is considered with the account of heat effects. According to the Le Chatelier principle, a local overheating must precede to the cooling of solar surface in the places of sunspot formation. The sunspot dynamics is a process close to the surface nucleate-free boiling in a thin layer with formation of bubbles (or craters), so we focus on the analogy between these two processes. Solar spots and surface nucleate-free boiling in a thin layer have similarities in formation conditions, results of impact on the surface were they have been formed, periodicity, and their place in the hierarchy of self-organization in complex systems. The difference is in the working medium and method of channelling of extra energy from the overheated surface -for boiling process, the energy is forwarded to generation of vapor, and in sunspots the solar energy is consumed to formation of a strong magnetic field. This analogy explains the problem of a steady brightness (temperature) of a spot that is independent of the spot size and other characteristics.Comment: 10 pages in LaTeX, 5 figures (JPEG

Microscopic Theory for Emission of Elementary Excitations into He II from a Heated Solid

I develop here the microscopic quantum theory for description of creation of phonons and rotons in superfluid helium by a solid heater. Starting with correct transfer Hamiltonian describing a coupling between the solid and liquid $^4$He the probabilities of transformation of a single phonon in the solid into i) single helium phonon, ii) two helium phonons, and iii) single helium roton are found out. All the obtained expressions account for different polarizations of phonons in the solid. The heat transfer associated with single phonon and single roton channels are calculated. Particularly, the obtained expression for heat flux via the single phonon channel calculated in the framework of present microscopic theory exactly coincides with the well known Khalatnikov formula obtained initially in the framework of acoustic-mismatch theory. The impossibility of direct creation of R$^{(-)}$ rotons becomes clear in the used framework due to accurate account of the boundary conditions at the solid -- liquid helium interface, which is in agreement with recent experimental results.Comment: 13 pages, 4 eps figure

Lagrangian subspaces, delta-matroids and four-term relations

Finite order invariants (Vassiliev invariants) of knots are expressed in terms of weight systems, that is, functions on chord diagrams satisfying the four-term relations. Weight systems have graph analogues, so-called $4$-invariants of graphs, i.e. functions on graphs that satisfy the four-term relations for graphs. Each $4$-invariant determines a weight system. The notion of weight system is naturally generalized for the case of embedded graphs with an arbitrary number of vertices. Such embedded graphs correspond to links; to each component of a link there corresponds a vertex of an embedded graph. Recently, two approaches have been suggested to extend the notion of $4$-invariants of graphs to the case of combinatorial structures corresponding to embedded graphs with an arbitrary number of vertices. The first approach is due to V.~Kleptsyn and E.~Smirnov, who considered functions on Lagrangian subspaces in a $2n$-dimensional space over $\mathbb{F}_2$ endowed with a standard symplectic form and introduced four-term relations for them. On the other hand, the second approach, the one due to Zhukov and Lando, suggests four-term relations for functions on binary delta-matroids. In this paper, we prove that the two approaches are equivalent

Relaxation times hierarchy in two-component quasiparticle gas

A quasiparticle description of various condensed media is a very popular tool in study of their transport and thermodynamic properties. I present here a microscopic theory for the description of diffusion processes in two-component gas of quasiparticles with arbitrary dispersion law and statistics. Particularly, I analyze the role of interaction within each subsystem (i.e. between identical quasiparticles) in relaxation of the whole system. The approach for solution of such kinetic problem allows to study the most important limiting cases and to clarify their physical sense. Classical results for diffusion coefficient of light particles in a massive gas (Lorentz model) and of massive particles in a light gas (Rayleigh model) are obtained directly from the general solution without using artificial approaches, as it was done earlier. This particularly provide a possibility to generalize these popular models on quasiparticle systems.Comment: 10 pages, REVTe

Internal Spatial Oscillations in a Single Trapped Bose--Einstein Condensate

I predict the existence of internal spatial currents in a {\it single} macroscopic quantum system, namely in trapped dilute-gas at sufficiently low temperatures, when a Bose-Einstein condensation occurs. The spatial profiles of the wavefunctions of low-lying states in such a system are different due to the inhomogeneity, caused by an asymmetry of external trapping potential. This is the reason for appearing of Josephson--like oscillations between atomic subsystems in different states including the ground state as well. Using a simple model for the wavefunctions of three low-lying states we demonstrate how essential this effect can be. The possible applications of the predicted effect are briefly discussed. Particularly, this effect opens the possibility to identify experimentally the low lying excited states of a system.Comment: 7 REVTeX pages, 4 ps figure

Continuum excitations of 26^{26}O in a three-body model: 0+0^+ and 2+2^+ states

The structure and decay dynamics for $0^+$ and $2^+$ continuum excitations of $^{26}$O are investigated in a three-body $^{24}$O+$n$+$n$ model. The validity of a simple approximation for the cross section profile for long-lived $2n$ emission is demonstrated. A sequence of three $0^+$ monopole ("breathing mode" type) excited states is predicted. These states could probably be interpreted as analogues of Efimov states pushed in the continuum due to insufficient binding. The calculated energies of the $2^+$ states are related to the excitation spectrum of $^{25}$O. We discuss the correlation between the predicted $^{26}$O spectrum and experimental observations.Comment: 9 pages, 8 figure

Confinement of Cosmic Rays in Dark Matter clumps

Some part of the relic Dark Matter is distributed in small-scale clumps which survived structure formation in inflation cosmological scenario. The annihilation of DM inside these clumps is a strong source of stable charged particles which can have a substantial density near the clump core. The streaming of the annihilation products from the clump can enhance irregularities in the galactic magnetic field. This can produce small scale variations in diffusion coefficient affecting propagation of Cosmic Rays.Comment: Contribution to the 30 ICRC, July 2007, Merida, Mexic

Hodograph Method and Numerical Integration of Two Hyperbolic Quasilinear Equations. Part I. The Shallow Water Equations

In paper [S.I. Senashov, A. Yakhno. 2012. SIGMA. Vol.8. 071] the variant of the hodograph method based on the conservation laws for two hyperbolic quasilinear equations of the first order is described. Using these results we propose a method which allows to reduce the Cauchy problem for the two quasilinear PDE's to the Cauchy problem for ODE's. The proposed method is actually some similar method of characteristics for a system of two hyperbolic quasilinear equations. The method can be used effectively in all cases, when the linear hyperbolic equation in partial derivatives of the second order with variable coefficients, resulting from the application of the hodograph method, has an explicit expression for the Riemann-Green function. One of the method's features is the possibility to construct a multi-valued solutions. In this paper we present examples of method application for solving the classical shallow water equations.Comment: 19 pages, 5 figure

Low-order models of 2D fluid flow in annulus

The two-dimensional flow of viscous incompressible fluid in the domain between two concentric circles is investigated numerically. To solve the problem, the low-order Galerkin models are used. When the inner circle rotates fast enough, two axially asymmetric flow regimes are observed. Both regimes are the stationary flows precessing in azimuthal direction. First flow represents the region of concentrated vorticity. Another flow is the jet-like structure similar to one discovered earlier in Vladimirov's experiments.Comment: 12 pages, 15 figure

Hodograph Method and Numerical Solution of the Two Hyperbolic Quasilinear Equations. Part III. Two-Beam Reduction of the Dense Soliton Gas Equations

The paper presents the solutions for the two-beam reduction of the dense soliton gas equations (or Born-Infeld equation) obtained by analytical and numerical methods. The method proposed by the authors is used. This method allows to reduce the Cauchy problem for two hyperbolic quasilinear PDEs to the Cauchy problem for ODEs. In some respect, this method is analogous to the method of characteristics for two hyperbolic equations. The method is effectively applicable in all cases when the explicit expression for the Riemann-Green function for some linear second order PDE, resulting from the use of the hodograph method for the original equations, is known. The numerical results for the two-beam reduction of the dense soliton gas equations, and the shallow water equations (omitting in the previous papers) are presented. For computing we use the different initial data (periodic, wave packet).Comment: 22 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:1503.0176