Keldysh Institute of Applied Mathematics

About: Keldysh Institute of Applied Mathematics is a facility organization based out in Moscow, Russia. It is known for research contribution in the topics: Plasma & Computer science. The organization has 1843 authors who have published 3911 publications receiving 28977 citations. The organization is also known as: Federal State Institution of Science Institute of Applied Mathematics. Keldysh of the Russian Academy of Sciences.

Three-dimensional shapes of looped DNA

Abstract: The equilibrium shapes of a closed DNA are investigated by employing a model of a thin, homogeneous, isotropic, linearly elastic rod of circular cross section. An equilibrium configuration of such an initially straight and twisted rod, submitted to external forces and moments at its ends only, obeys equations identical to those governing the rotation of a symmetric gyrostat spinning about a fixed point in a gravitational field (the Kirchhoff analogy). To represent the equilibrium of the looped DNA, the model rod must be smoothly closed into a ring. The corresponding BVP results in a system of four nonlinear equations with respect to four parameters. The perturbation analysis and the parameter continuation approach are used to find nonplanar solutions. The conformation change is discussed for various values of parameters.

A multiwavelength analysis of a collection of short-duration GRBs observed between 2012 and 2015

Abstract: We investigate the prompt emission and the afterglow properties of short-duration gamma-ray burst (sGRB) 130603B and another eight sGRB events during 2012-2015, observed by several multiwavelength facilities including the Gran Canarias Telescope 10.4 m telescope. Prompt emission high energy data of the events were obtained by INTEGRAL-SPI-ACS, Swift-BAT, and Fermi-GBM satellites. The prompt emission data by INTEGRAL in the energy range of 0.1-10 MeV for sGRB 130603B, sGRB 140606A, sGRB 140930B, sGRB 141212A, and sGRB 151228A do not show any signature of the extended emission or precursor activity and their spectral and temporal properties are similar to those seen in case of other short bursts. For sGRB 130603B, our new afterglow photometric data constrain the pre-jet-break temporal decay due to denser temporal coverage. For sGRB 130603B, the afterglow light curve, containing both our new and previously published photometric data is broadly consistent with the ISM afterglow model. Modeling of the host galaxies of sGRB 130603B and sGRB 141212A using the LePHARE software supports a scenario in which the environment of the burst is undergoing moderate star formation activity. From the inclusion of our late-time data for eight other sGRBs we are able to: place tight constraints on the non-detection of the afterglow, host galaxy, or any underlying 'kilonova' emission. Our late-time afterglow observations of the sGRB 170817A/GW170817 are also discussed and compared with the sub-set of sGRBs.

Three-dimensional modeling of mass transfer in close binary systems with non-synchronous rotation

Abstract: We present the results of three-dimensional numerical simulations of mass transfer in semi-detached binary systems in which the mass-losing star is rotating The cases of aligned and misaligned non-synchronous rotation of the donor star are considered; the resulting flow patterns are compared to the synchronous case The main properties of the flow, such as the formation of an circumbinary envelope, the absence of a "hot spot" on the edge of the accretion disk, and the formation of a shock wave along the flow edge, are qualitatively similar to those obtained earlier For the case of misaligned, non-synchronous rotation, the behavior of the disk and surrounding matter in established flow regime reflects changes in the boundary conditions at the surface of the donor star; in other words, a "driven disk" model is realized in the calculations

Blow-up and critical exponents for parabolic equations with non-divergent operators: dual porous medium and thin film operators

Abstract: Our first basic model is the fully nonlinear dual porous medium equation with source $$u_{t} = {\left| {\Delta u} \right|}^{{m - 1}} \Delta u + u^{p} \quad in\;{\mathbb{R}}^{N} \times {\mathbb{R}}_{ + } ,\quad m > 1,\;\; p > 1,$$ for which we consider the Cauchy problem with given nonnegative bounded initial data u0. For the semilinear case m=1, the critical exponent \(p_{0} = 1 + \frac{2}{N}\) was obtained by H. Fujita in 1966. For p ∈(1, p0] any nontrivial solution blows up in finite time, while for p > p0 there exist sufficiently small global solutions. During last thirty years such critical exponents were detected for many semilinear and quasilinear parabolic, hyperbolic and elliptic PDEs and inequalities. Most of efforts were devoted to equations with differential operators in divergent form, where classical techniques associated with weak solutions and integration by parts with a variety of test functions can be applied. Using this fully nonlinear equation, we propose and develop new approaches to calculating critical Fujita exponents in different functional settings.