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The study of interhelical distances of helical pairs in protein molecules
No full textAbstract:
In this paper the study of interhelical distances in pairs of connected α-helices found in known proteins has been performed. A number of rules for selection of the helical pairs from a set of protein structures obtained from the Protein Data Bank (PDB) have been developed. The set of helical pairs has been analyzed for the purpose of classification and finding out the features of protein structural organization. A point model of a double-helix motif has been proposed. All pairs of connected helices were divided into three subsets according to the criterion of crossing of projections of the helices on parallel planes, which pass through the axes of the helices. In this work histograms of the distribution of all types of helical pairs are obtained depending on the interhelical distances. The statistical estimates of the interplanar and minimal distance distributions for helical pairs of various types belonging to different sets are presented.Note:
Research direction:Mathematical modelling in actual problems of science and technic
Construction of the return trajectory from the lunar parking orbit to the Earth’s atmosphere reentry point
No full textAbstract:
The practically useful algorithm for construction of the return trajectory from the lunar parking orbit to the Earth’s atmosphere reentry point using three-impulse maneuvering scheme for the three-body problem (the Earth, the Moon, the spacecraft) under non-central gravity field is presented. The algorithm provides fulfillment of the boundary conditions at the Earth’s atmosphere reentry point.Note:
Research direction:Theoretical and applied problems of mechanic
Normal form of a Hamiltonian system with a periodic perturbation
No full textAbstract:
Near a stationary solution we consider the Hamiltonian system with such perturbation, that the unperturbed Hamiltonian function is autonomous and the perturbation of the Hamiltonian function is periodic in time. First we remind the normal form of the autonomous Hamiltonian function. Second we describe the normal form of the periodic perturbation of the Hamiltonian function. It can always be reduced to the time independent Hamiltonian. It allows to compute the local families of periodic solutions to the initial system. The first approximations of some of these families are found by means of computation of the Newton polyhedron of the reduced normal form of Hamiltonian. We also discuss problems of the computer algebra arising in these computations.Note:
Research direction:Mathematical modelling in actual problems of science and technic
Statistical recognition of the dynamical systems with chaotic perturbation
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In this paper we consider a method of analyzing time series, generated by nonlinear dynamical systems with noise component in the form of perturbation. Noise filtering is carried out by evaluating the domain of density of the joint distribution function of values and its increments, depending on the fineness of the partitioning of the multidimensional histogram. Examples of different types of perturbations are given: additive noise, dimension perturbation, noise in the implementation of a dynamic system, random switching, injection of several processes.Note:
Research direction:Mathematical modelling in actual problems of science and technic
V.A. Yegorov, the first Works of Global modeling in Keldysh Institute of Applied Mathematics end the ecology’s problems of Ideas and Spiritual Processes in Society
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Analysis and modeling of global development in our country were started at the IAM of the AS of the USSR under the leadership of V.A. Yegorov in the early 1970s, investment management was firstly introduced to avoid catastrophe. This preprint is devoted to the history of these works, poorly covered in the literature. By analogy, it is made an attempt to discuss the issues of the dynamics and “ecology” of cultural and spiritual processes, supported by V.A. Yegorov.Note:
Research direction:Mathematical modelling in actual problems of science and technic
Regularization method for numerical modelling of a transport of pollutant in shallow water
No full textAbstract:
A new method for solving the passive scalar transport equation in the framework of hydrodynamic equations in the shallow water approximation is described. The method is similar in structure to the previously constructed quasi-gas-dynamic algorithm for the numerical simulation of compressible gas flows. Regularized equations and difference schemes based on them, including those for flows with an impurity source, are presented. Typical one-dimensional and two-dimensional test problems are considered. In conclusion, a generalization of the constructed approach for the numerical simulation of the passive scalar transport in the framework of the viscous incompressible fluid approximation is given.Note:
Research direction:Mathematical modelling in actual problems of science and technic
Euler and Navier–Stokes Equations as Self-Consistent Fields
No full textAbstract:
New kinetic equations are proposed from which the incompressible and compressible Euler and Navier–Stokes equations are derived by making an exact substitution. A class of exact solutions of the Navier–Stokes equation and the form of singularities for a gradient catastrophe are obtained.Note:
Research direction:Mathematical problems and theory of numerical method
Vlasov-Maxwell-Einstein Equation and Einstein Lambda
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Vlasov-Maxwell-Einstein equations are derived from classical action of Lorentz-Schwarzschild-Hilbert-Einstein. We need and get synchronization of times of different particles. On the basis of obtained results we analyze Einstein’s lambda and its connection with dark energy.Note:
Research direction:Theoretical and applied problems of mechanic
The basic property of the Jacobi integral for gravity assists maneuvers in the Solar system
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It is shown that the standard and bulky method of the general used revealing of the asymptotic velocity invariance during gravity assists maneuvers in the model of the circular restricted three body problem (RTBP), used in modern astrodynamics, can be significantly simplified. The refined forms of the Jacobi integral are presented, which allow, among others, to reveal the transparent relationship of the Jacobi integral and the patched conics method in a RTBP.Note:
Research direction:Theoretical and applied problems of mechanic
Verification of an entropic regularization method for discontinuous Galerkin schemes applied to hyperbolic equations
No full textAbstract:
In this work, methods of entropic correction in numerical schemes for hyperbolic equations are extensively overviewed. The variational method of entropic regularization in discontinuous Galerkin schemes is tested on the one-dimensional gasdynamic Einfeldt problem of two scattering rarefaction waves. Based on the results of this test, a simplified method of entropic regularization in discontinuous Galerkin schemes coupled with a slope limiter is proposed. The designed method is successfully verified on a number of Riemann problems for one-dimensional Euler equations.Note:
Research direction:Mathematical problems and theory of numerical method