A geometrical presentation of the surface mapping class group and surgery

We construct a tangle presentation of the mapping class group similar to a natural presentation of the braid group by geometrical braids. A relation between surgery and Heegard diagrams for 3-manifolds arising in this way and different applications are studied.Supported by Rotshild Fellowship     

Positons: Slowly Decreasing Analogues of Solitons

We present an introduction to positon theory, almost never covered in the Russian scientific literature. Positons are long-range analogues of solitons and are slowly decreasing, oscillating solutions of nonlinear integrable equations of the KdV type. Positon and soliton–positon solutions of the KdV equation, first constructed and analyzed about a decade ago, were then constructed for several other models: for the mKdV equation, the Toda chain, the NS equation, as well as the sinh-Gordon equation and its lattice analogue. Under a proper choice of the scattering data, the one-positon and multipositon potentials have a remarkable property: the corresponding reflection coefficient is zero, but the transmission coefficient is unity (as is known, the latter does not hold for the standard short-range reflectionless potentials).     

Dramatic role of critical current anisotropy on flux avalanches in MgB2 films

Anisotropic penetration of magnetic flux in MgB(2) films grown on vicinal sapphire substrates is investigated using magneto-optical imaging. Regular penetration above 10 K proceeds more easily along the substrate surface steps, the anisotropy of the critical current being 6%. At lower temperatures the penetration occurs via abrupt dendritic avalanches that preferentially propagate perpendicular to the surface steps. This inverse anisotropy in the penetration pattern becomes dramatic very close to 10 K where all flux avalanches propagate in the strongest pinning direction. The observed behavior is fully explained using a thermomagnetic model of the dendritic instability.     

Asymmetric zero-bias anomaly for strongly interacting electrons in one dimension

We study a system of one-dimensional electrons in the regime of strong repulsive interactions, where the spin exchange coupling J is small compared with the Fermi energy, and the conventional Tomonaga-Luttinger theory does not apply. We show that the tunneling density of states has a form of an asymmetric peak centered near the Fermi level. In the spin-incoherent regime, where the temperature is large compared to J, the density of states falls off as a power law of energy epsilon measured from the Fermi level, with the prefactor at positive energies being twice as large as that at the negative ones. In contrast, at temperatures below J the density of states forms a split peak with most of the weight shifted to negative epsilon.     

Model of a gas of solid particles with allowance for inelastic collisions

A study is made of the structure of the interaction region of a flow of solid particles with a surface (or another flow) in the case when the width of this region is much greater than the mean free path of the particles between collisions. The disperse phase is described by means of a model of an ideal non-heat-conducting gas of imperfectly elastic spherical particles. For simplicity, the influence of the carrier medium on the motion of the particles is ignored.     

Prediction of thermal explosion parameters for energetic materials on the basis of thermal analysis data

Results obtained in calculations of thermal ignition delay periods in a wide temperature range are in good agreement with published data for octogene samples in the form of a sphere 12.7 mm in diameter and cylindrical NEPE propellant samples with diameters of 20 to 80 mm. The kinetic parameters of the thermal decomposition of materials, used in the calculations, were obtained by the DSC method with the use of hermetically sealed crucibles and crucibles with perforated covers under a nitrogen pressure of 10 MPa at heating rates of 0.1 to 1.0 deg min^–1.     

Locally 2-fold symmetric manifolds are locally symmetric

A manifold is locally k-fold symmetric if for any point and any k-dimensional vector subspace tangent to this point, there exists a local isometry such that this point is a fixed point and the differential of the isometry restricted to that k-dimensional vector subspace is minus the identity. We show that for \(k \ge 2\), Riemannian, pseudoriemannian, and Finslerian locally k-fold symmetric manifolds are locally symmetric.     

Multigrid Models of Composite Materials of Irregular Structure with a Small Filling Ratio

This paper considers composites consisting of a set of typical composite multigrid finite elements whose structures are regular and different. Mean local errors are proposed for multigrid modeling of composites.     

Seepage from shallow channels and irrigation furrows

Two cases of two-dimensional steady seepage from broad channels and irrigation furrows through a layer of homogeneous isotropic soil into a highly permeable pressurized aquifer in the presence of soil capillarity are examined in the hydrodynamic formulation. A uniform method of solution in which the solution of the problem of seepage from an irrigation furrow can be obtained from the solution for a broad channel is given. The special and limiting cases studied in [1–3] and elsewhere are noted. Computer calculations are used to analyze the dependence of the rate of seepage from channels and irrigation furrows and the capillary spread on the profile and width of the channel or irrigation furrow, the thickness of the layer, the head and the capillarity of the soil.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 96–102, January–February, 1989.The authors are grateful to N. N. Verigin for valuable comments.