| 1. |
- Banerjee, M., et al.
(författare)
-
Stabilizing Role of Nonlocal Interaction on Spatio-temporal Pattern Formation
- 2016
-
Ingår i: Mathematical Modelling of Natural Phenomena. - : EDP Sciences. - 0973-5348 .- 1760-6101. ; 11:5, s. 103-118
-
Tidskriftsartikel (refereegranskat)abstract
- Here we study a spatio-temporal prey-predator model with ratio-dependent functional response and nonlocal interaction term in the prey growth. For a clear understanding of the effect of nonlocal interaction on the resulting stationary and non-stationary patterns, we consider the nonlocal interaction term in prey growth only to describe the nonlocal intra-specific competition due to limited resources for the prey. First we obtain the patterns exhibited by the basic model in the absence of nonlocal interaction and then explore the effect of nonlocal interaction on the resulting patterns. We demonstrate the stabilizing role of nonlocal interaction as it induces stationary pattern from periodic and chaotic regimes with an increase in the range of nonlocal interaction. The existence of multiple branches of stationary solutions, bifurcating from homogeneous steady-state as well as non-stationary patterns, is illustrated with the help of numerical continuation technique.
|
|
| 2. |
- Ghoreyshi, M., et al.
(författare)
-
Automated CFD Analysis for the Investigation of Flight Handling Qualities
- 2011
-
Ingår i: Mathematical Modelling of Natural Phenomena. - : EDP Sciences. - 0973-5348 .- 1760-6101. ; 6:3, s. 166-188
-
Tidskriftsartikel (refereegranskat)abstract
- Physics based simulation is widely seen as a way of increasing the information about aircraft designs earlier in their definition, thus helping with the avoidance of unanticipated problems as the design is refined. This paper reports on an effort to assess the automated use of computational fluid dynamics level aerodynamics for the development of tables for flight dynamics analysis at the conceptual stage. These tables are then used to calculate handling qualities measures. The methodological questions addressed are a) geometry and mesh treatment for automated analysis from a high level conceptual aircraft description and b) sampling and data fusion to allow the timely calculation of large data tables. The test case used to illustrate the approaches is based on a refined design passenger jet wind tunnel model. This model is reduced to a conceptual description, and the ability of this geometry to allow calculations relevant to the final design to be drawn is then examined. Data tables are then generated and handling qualities calculated.
|
|
| 3. |
- Gustafsson, Björn, 1947-, et al.
(författare)
-
Finite term relations for the exponential orthogonal polynomials*
- 2020
-
Ingår i: Mathematical Modelling of Natural Phenomena. - : EDP SCIENCES S A. - 0973-5348 .- 1760-6101. ; 15
-
Tidskriftsartikel (refereegranskat)abstract
- The exponential orthogonal polynomials encode via the theory of hyponormal operators a shade function g supported by a bounded planar shape. We prove under natural regularity assumptions that these complex polynomials satisfy a three term relation if and only if the underlying shape is an ellipse carrying uniform black on white. More generally, we show that a finite term relation among these orthogonal polynomials holds if and only if the first row in the associated Hessenberg matrix has finite support. This rigidity phenomenon is in sharp contrast with the theory of classical complex orthogonal polynomials. On function theory side, we offer an effective way based on the Cauchy transforms of to decide whether a (d + 2)-term relation among the exponential orthogonal polynomials exists; in that case we indicate how the shade function g can be reconstructed from a resulting polynomial of degree d and the Cauchy transform of g. A discussion of the relevance of the main concepts in Hele-Shaw dynamics completes the article.
|
|
| 4. |
- Iantchenko, Alexei, et al.
(författare)
-
Schrödinger Operator on the Zigzag Half-Nanotube in Magnetic Field
- 2010
-
Ingår i: Mathematical Modelling of Natural Phenomena. - : EDP Sciences. - 0973-5348 .- 1760-6101. ; 5:4 Spectral problems. Issue dedicated to the memory of M. Birman, s. 175-197
-
Tidskriftsartikel (refereegranskat)abstract
- We consider the zigzag half-nanotubes (tight-binding approximation) in a uniform magnetic field which is described by the magnetic Schrödinger operator with a periodic potential plus a finitely supported perturbation. We describe all eigenvalues and resonances of this operator, and theirs dependence on the magnetic field. The proof is reduced to the analysis of the periodic Jacobi operators on the half-line with finitely supported perturbations.
|
|
| 5. |
- Ibragimov, Nail, et al.
(författare)
-
Applications of Lie Group Analysis to Mathematical Modelling in Natural Sciences
- 2012
-
Ingår i: Mathematical Modelling of Natural Phenomena. - : EDP SCIENCES. - 0973-5348 .- 1760-6101. ; 7:2, s. 52-65
-
Tidskriftsartikel (refereegranskat)abstract
- Today engineering and science researchers routinely confront problems in mathematical modeling involving solutions techniques for differential equations. Sometimes these solutions can be obtained analytically by numerous traditional ad hoc methods appropriate for integrating particular types of equations. More often, however, the solutions cannot be obtained by these methods, in spite of the fact that, e.g. over 400 types of integrable second-order ordinary differential equations were summarized in voluminous catalogues. On the other hand, many mathematical models formulated in terms of nonlinear differential equations can successfully be treated and solved by Lie group methods. Lie group analysis is especially valuable in investigating nonlinear differential equations, for its algorithms act here as reliably as for linear cases. The aim of this article is, from the one hand, to provide the wide audience of researchers with the comprehensive introduction to Lie's group analysis and, from the other hand, is to illustrate the advantages of application of Lie group analysis to group theoretical modeling of internal gravity waves in stratified fluids.
|
|
| 6. |
- Ibragimov, Nail, et al.
(författare)
-
Bifurcation of Nonlinear Conservation Laws from the Classical Energy Conservation Law for Internal Gravity Waves in Cylindrical Wave Field
- 2013
-
Ingår i: Mathematical Modelling of Natural Phenomena. - : EDP Sciences. - 0973-5348 .- 1760-6101. ; 8:5, s. 119-130
-
Tidskriftsartikel (refereegranskat)abstract
- New conservation laws bifurcating from the classical form of conservation laws are constructed to the nonlinear Boussinesq model describing internal Kelvin waves propagating in a cylindrical wave field of an uniformly stratified water affected by the earth's rotation. The obtained conservation laws are different from the well known energy conservation law for internal waves and they are associated with symmetries of the Boussinesq model. Particularly, it is shown that application of Lie group analysis provide three infinite sets of nontrivial integral conservation laws depending on two arbitrary functions, namely a(t, theta),b(t, r) and an arbitrary function c(t, theta, r) which is given implicitly as a nontrivial solution of a partial differential equation involving a(t, theta) and b(t,r).
|
|
| 7. |
- Ibragimov, Nail H., et al.
(författare)
-
Nonlinear Whirlpools Versus Harmonic Waves in a Rotating Column of Stratified Fluid
- 2013
-
Ingår i: Mathematical Modelling of Natural Phenomena. - : EDP SCIENCES. - 0973-5348 .- 1760-6101. ; 8:1, s. 122-131
-
Tidskriftsartikel (refereegranskat)abstract
- Propagation of nonlinear baroclinic Kelvin waves in a rotating column of uniformly stratified fluid under the Boussinesq approximation is investigated. The model is constrained. by the Kelvin's conjecture saying that the velocity component normal to the interface between rotating fluid and surrounding medium (e.g. a seashore) is possibly zero everywhere in the domain of fluid motion, not only at the boundary. Three classes of distinctly different exact solutions for the nonlinear model are obtained. The obtained solutions are associated with symmetries of the Boussinesq model. It is shown that one class of the obtained solutions can be visualized as rotating whirlpools along which the pressure deviation from the mean state is zero, is positive inside and negative outside of the whirlpools. The angular velocity is zero at the center of the whirlpools and it is monotonically increasing function of radius of the whirlpools.
|
|
| 8. |
- Ibragimov, Nail H., et al.
(författare)
-
Symmetries and Conservation Laws of a Spectral Nonlinear Model for Atmospheric Baroclinic Jets
- 2014
-
Ingår i: Mathematical Modelling of Natural Phenomena. - : EDP SCIENCES S A.. - 0973-5348 .- 1760-6101. ; 9:5, s. 111-118
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper, we shall obtain the symmetries of the mathematical model describing spontaneous relaxation of eastward jets into a meandering state and use these symmetries for constructing the conservation laws. The basic eastward jet is a spectral parameter of the model, which is in geostrophic equilibrium with the basic density structure and which guarantees the existence of nontrivial conservation laws.
|
|
| 9. |
- Ibragimov, Nail, 1939-, et al.
(författare)
-
INVARIANT SOLUTIONS AND SHOCK ATMOSPHERIC WAVES IN A THIN CIRCULAR LAYER
- 2018
-
Ingår i: Mathematical Modelling of Natural Phenomena. - : EDP SCIENCES S A. - 0973-5348 .- 1760-6101. ; 13:2
-
Tidskriftsartikel (refereegranskat)abstract
- The objective of this paper is to investigate the nonlinear mathematical model describing equatorial waves from Lie group analysis point of view in order to understand the nature of shallow water model theory, which is associated to planetary equatorial waves. Such waves correspond to the Cauchy-Poisson free boundary problem on the nonstationary motion of a perfect incompressible fluid circulating around a solid circle of a large radius.
|
|
| 10. |
- Kavallaris, Nikos I., et al.
(författare)
-
A Time Discretization Scheme for a Nonlocal Degenerate Problem Modelling Resistance Spot Welding
- 2015
-
Ingår i: Mathematical Modelling of Natural Phenomena. - : EDP Sciences. - 0973-5348 .- 1760-6101. ; 10:6, s. 90-112
-
Tidskriftsartikel (refereegranskat)abstract
- In the current work we construct a nonlocal mathematical model describing the phase transition occurs during the resistance spot welding process in the industry of metallurgy. We then consider a time discretization scheme for solving the resulting nonlocal moving boundary problem. The scheme consists of solving at each time step a linear elliptic partial differential equation and then making a correction to account for the nonlinearity. The stability and error estimates of the developed scheme are investigated. Finally some numerical results are presented confirming the efficiency of the developed numerical algorithm.
|
|
