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1
Content available remote Embedded Solitons and Conservation Law with χ^{(2)} and χ^{(3)} Nonlinear Susceptibilities
100%
Savescu M. , Kara A. , Kumar S. , Krishnan E. , Zaka Ullah M. , Moshokoa S. , Zhou Q. , Biswas A.
Acta Physica Polonica A
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2017
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tom 131
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nr 2
297-303
EN
This paper studies embedded solitons that are confined to continuous spectrum, with χ^{(2)} and χ^{(3)} nonlinear susceptibilities. Bright and singular soliton solutions are obtained by the method of undetermined coefficients. Subsequently, the Lie symmetry analysis and mapping method retrieves additional solutions to the model such as shock waves, singular solitons, cnoidal waves, and several others. Finally, a conservation law for this model is secured through the Lie symmetry analysis.
2
Content available remote Nonlinear self-adjointness and invariant solutions of a 2D Rossby wave equation
100%
Cimpoiasu R. , Constantinescu R.
Open Physics
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2014
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tom 12
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nr 2
81-89
EN
The paper investigates the nonlinear self-adjointness of the nonlinear inviscid barotropic nondivergent vorticity equation in a beta-plane. It is a particular form of Rossby equation which does not possess variational structure and it is studied using a recently method developed by Ibragimov. The conservation laws associated with the infinite-dimensional symmetry Lie algebra models are constructed and analyzed. Based on this Lie algebra, some classes of similarity invariant solutions with nonconstant linear and nonlinear shears are obtained. It is also shown how one of the conservation laws generates a particular wave solution of this equation.
3
Content available remote Balance errors in numerical solutions of shallow water equations
88%
Gąsiorowski D.
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2007
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tom Vol. 11, No 4
329-340
EN
An analysis of the conservative properties of shallow water equations is presented, focused on the consistency of their numerical solution with the conservation laws of mass and momentum. Two different conservative forms are considered, solved by an implicit box scheme. Theoretical analysis supported with numerical experiments is carried out for a rectangular channel and arbitrarily assumed flow conditions. The improper conservative form of the dynamic equation is shown not to guarantee a correct solution with respect to the conservation of momentum. Consequently, momentum balance errors occur in the numerical solution. These errors occur when artificial diffusion is simultaneously generated by a numerical algorithm.
4
Content available remote Conservation laws and associated Lie point symmetries admitted by the transient heat conduction problem for heat transfer in straight fins
75%
Ndlovu P. , Moitsheki R.
Open Physics
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2013
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tom 11
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nr 8
984-994
EN
Some new conservation laws for the transient heat conduction problem for heat transfer in a straight fin are constructed. The thermal conductivity is given by a power law in one case and by a linear function of temperature in the other. Conservation laws are derived using the direct method when thermal conductivity is given by the power law and the multiplier method when thermal conductivity is given as a linear function of temperature. The heat transfer coefficient is assumed to be given by the power law function of temperature. Furthermore, we determine the Lie point symmetries associated with the conserved vectors for the model with power law thermal conductivity.
5
On some problems in mathematical modeling of turbulent flow
75%
Burnat M. , Moszyński K.
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2007
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tom Vol. 48, no 3-4
171-192
EN
The paper presents a new, rather elementary mathematical model of turbulent fluid flow with intensive self-mixing. The flow is described in this model by the (in general non-invertible) mappings Φt,t0 : ω -->S(t, t0,ω), ω, S ⊂ R³, t > t0, such that ◛ ∩ ω² = ∅ in general not implies S(t, to, ◛) ∩ S(t, t0, ω²) = ∅. This modeling allows a new approach to certain problems of turbulent flow. For example, there are possibilities of describing the unpredictable explosions of turbulence in a calm, laminar flow.
6
Content available remote Connecting Euler and Lagrange systems as nonlocally related systems of dynamical nonlinear elasticity
75%
Bluman G. , Ganghoffer J. F.
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2011
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tom Vol. 63, nr 4
363-382
EN
Nonlocally related systems for the Euler and Lagrange systems of twodimensional dynamical nonlinear elasticity are constructed. Using the continuity equation, i.e., conservation of mass of the Euler system to represent the density and Eulerian velocity components as the curl of a potential vector, one obtains the Euler potential system that is nonlocally related to the Euler system. It is shown that the Euler potential system also serves as a potential system of the Lagrange system. As a consequence, a direct connection is established between the Euler and Lagrange systems within a tree of nonlocally related systems. This extends the known situation for one-dimensional dynamical nonlinear elasticity to two spatial dimensions.
7
Content available remote Komplementarność fizycznych i chemicznych praw zachowania w aspekcie układów elektrolitycznych
63%
Michałowski T.
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2007
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tom [Z] 61, 7-8
625-640
EN
The charge, concentration and electron balances are closely related to other, more elementary rules of conservation of a matter in a closed system, separated from the environment by diathermal walls. The conservation rules can be formulated for the elements, electrons and protons. Among others, the generalised electron balance (GEB) concept presented and applied in some author's papers [1-7, 14-16] is derived from the elementary rules of conservation and exemplified by some batch and dynamic (titration) systems of a different degree of complexity. Some elementary rules of conservation are interdependent. This interdependency of the resulting balances and formulation of the set of independent relationships will be considered with the help of some examples, where the complex nature of the system, exemplified by the formation of aqua-complexes by both ionic and neutral species, will also be taken into account. Among others, the dynamic system is exemplified by titration of KIO_3 + HCl + H_2SeO_3 + HgCl_2 with ascorbic acid (C6H8O6). The degree of complexity of this system is evidenced by more than 40 equilibrium constants involved in the related balances.
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