225 research outputs found
Lagrangian formalism and Noether-type theorems for second-order delay ODEs
The Lagrangian formalism for variational problem for second-order delay
ordinary differential equations (DODEs) is developed. The Noether-type operator
identities and theorems for DODEs of second order are presented. Algebraic
construction of integrals for DODEs based on symmetries are demonstrated by
examples
Invariant Finite-Difference Schemes for Cylindrical One-Dimensional MHD Flows with Conservation Laws Preservation
On the basis of the recent group classification of the one-dimensional
magnetohydrodynamics (MHD) equations in cylindrical geometry, the construction
of symmetry-preserving finite-difference schemes with conservation laws is
carried out. New schemes are constructed starting from the classical completely
conservative Samarsky-Popov schemes. In the case of finite conductivity,
schemes are derived that admit all the symmetries and possess all the
conservation laws of the original differential model, including previously
unknown conservation laws. In the case of a frozen-in magnetic field (when the
conductivity is infinite), various schemes are constructed that possess
conservation laws, including those preserving entropy along trajectories of
motion. The peculiarities of constructing schemes with an extended set of
conservation laws for specific forms of entropy and magnetic fluxes are
discussed.Comment: 29 pages; some minor fixes and generalizations + Appendix containing
an additional numerical schem
The model of development of creative potential of students in the system of additional art education
In the article the model of development of creative potential of students in the Children's school of arts in the discipline "Computer graphics"В статье рассматривается модель развития творческого потенциала обучающихся в Детской школе искусств по дисциплине «Компьютерная графика
One-dimensional MHD flows with cylindrical symmetry: Lie symmetries and conservation laws
A recent paper considered symmetries and conservation laws of the plane
one-dimensional flows for magnetohydrodynamics in the mass Lagrangian
coordinates. This paper analyses the one-dimensional magnetohydrodynamics flows
with cylindrical symmetry in the mass Lagrangian coordinates. The medium is
assumed inviscid and thermally non-conducting. It is modeled by a polytropic
gas. Symmetries and conservation laws are found. The cases of finite and
infinite electric conductivity need to be analyzed separately. For finite
electric conductivity we perform Lie group classification,
which identifies cases with additional symmetries. The
conservation laws are found by direct computation. For cases with infinite
electric conductivity variational formulations of the equations are considered.
Lie group classifications are obtained with the entropy treated as an arbitrary
element. A variational formulation allows to use the Noether theorem for
computation of conservation laws. The conservation laws obtained for the
variational equations are also presented in the original (physical) variables
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