| 11. |
- Johnson, Tomas, 1979-, et al.
(författare)
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A note on the convergence of parametrised non-resonant invariant manifolds
- 2011
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Ingår i: Qualitative Theory of Dynamical Systems. - : Springer Science and Business Media LLC. - 1575-5460 .- 1662-3592. ; 10:1, s. 107-121
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Tidskriftsartikel (refereegranskat)abstract
- Truncated Taylor series representations of invariant manifolds are abundant in numerical computations. We present an aposteriori method to compute the convergence radii and error estimates of analytic parametrisations of non-resonant local invariant manifolds of a saddle of an analytic vector field, from such a truncated series. This enables us to obtain local enclosures, as well as existence results, for the invariant manifolds.
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| 12. |
- Johnson, Tomas, 1979-
(författare)
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A Quartic System with Twenty-Six Limit Cycles
- 2011
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Ingår i: Experimental Mathematics. - : Informa UK Limited. - 1058-6458 .- 1944-950X. ; 20:3, s. 323-328
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Tidskriftsartikel (refereegranskat)abstract
- We construct a planar quartic system and demonstrate that it has at least 26 limit cycles. The vector field is symmetric and integrable, but non-Hamiltonian. The proof is based on a verified computation of zeros of pseudo-Abelian integrals, together with the symmetry properties.
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| 13. |
- Johnson, Tomas, 1979-, et al.
(författare)
-
A rigorous study of possible configurations of limit cycles bifurcating from a hyper-elliptic Hamiltonian of degree five
- 2009
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Ingår i: Dynamical systems. - : Informa UK Limited. - 1468-9367 .- 1468-9375. ; 24:2, s. 237-247
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Tidskriftsartikel (refereegranskat)abstract
- We consider a hyper-elliptic Hamiltonian of degree five, chosen from a generic set of parameters, and study what configurations of limit cycles can bifurcate from the corresponding differential system under quartic perturbations. Perturbations of Lienard type are considered separately. Several different configurations with seven (four) limit cycles, bifurcating from the given system for general (Lienard type) quartic perturbations, are constructed. We also discuss how to construct perturbations yielding a given configuration, and how to validate the correctness of such a candidate perturbation.
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| 14. |
- Johnson, Tomas, 1979-, et al.
(författare)
-
An improved lower bound on the number of limit cycles bifurcating from a Hamiltonian planar vector field of degree 7
- 2010
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Ingår i: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. - : World Scientific Publishing. - 0218-1274. ; 20:5, s. 1451-1458
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Tidskriftsartikel (refereegranskat)abstract
- The limit cycle bifurcations of a Z(2) equivariant planar Hamiltonian vector field of degree 7 under Z(2) equivariant degree 7 perturbation is studied. We prove that the given system can have at least 53 limit cycles. This is an improved lower bound for the weak formulation of Hilbert's 16th problem for degree 7, i.e. on the possible number of limit cycles that can bifurcate from a degree 7 planar Hamiltonian system under degree 7 perturbation.
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| 15. |
- Johnson, Tomas, 1979-, et al.
(författare)
-
An improved lower bound on the number of limit cycles bifurcating from a quintic Hamiltonian planar vector field under quintic perturbation
- 2010
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Ingår i: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. - : World Scientific Publishing. - 0218-1274. ; 20:1, s. 63-70
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Tidskriftsartikel (refereegranskat)abstract
- The limit cycle bifurcations of a equivariant quintic planar Hamiltonian vector field under equivariant quintic perturbation is studied. We prove that the given system can have at least 27 limit cycles. This is an improved lower bound on the possible number of limit cycles that can bifurcate from a quintic planar Hamiltonian system under quintic perturbation.
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| 16. |
- Johnson, Tomas, 1979-, et al.
(författare)
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Automated computation of robust normal forms of planar analytic vector fields
- 2009
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Ingår i: Discrete and continuous dynamical systems. Series B. - : American Institute of Mathematical Sciences (AIMS). - 1531-3492 .- 1553-524X. ; 12:4, s. 769-782
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Tidskriftsartikel (refereegranskat)abstract
- We construct an auto-validated algorithm that calculates a close to identity change of variables which brings a general saddle point into a normal form. The transformation is robust in the underlying vector field, and is analytic on a computable neighbourhood of the saddle point. The normal form is suitable for computations aimed at enclosing the flow close to the saddle, and the time it takes a trajectory to pass it. Several examples illustrate the usefulness of this method.
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| 17. |
- Johnson, Tomas, 1979-
(författare)
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Computer-aided Computation of Abelian integrals and Robust Normal Forms
- 2009
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This PhD thesis consists of a summary and seven papers, where various applications of auto-validated computations are studied. In the first paper we describe a rigorous method to determine unknown parameters in a system of ordinary differential equations from measured data with known bounds on the noise of the measurements. Papers II, III, IV, and V are concerned with Abelian integrals. In Paper II, we construct an auto-validated algorithm to compute Abelian integrals. In Paper III we investigate, via an example, how one can use this algorithm to determine the possible configurations of limit cycles that can bifurcate from a given Hamiltonian vector field. In Paper IV we construct an example of a perturbation of degree five of a Hamiltonian vector field of degree five, with 27 limit cycles, and in Paper V we construct an example of a perturbation of degree seven of a Hamiltonian vector field of degree seven, with 53 limit cycles. These are new lower bounds for the maximum number of limit cycles that can bifurcate from a Hamiltonian vector field for those degrees. In Papers VI, and VII, we study a certain kind of normal form for real hyperbolic saddles, which is numerically robust. In Paper VI we describe an algorithm how to automatically compute these normal forms in the planar case. In Paper VII we use the properties of the normal form to compute local invariant manifolds in a neighbourhood of the saddle.
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| 18. |
- Johnson, Tomas, 1979, et al.
(författare)
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Efficient Simulation of Convective Ovens in Automotive Paintshops
- 2023
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Ingår i: Journal of Heat Transfer. - : ASME International. - 1528-8943 .- 0022-1481. ; 144:9
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Tidskriftsartikel (refereegranskat)abstract
- Heat transfer modeling of large industrial ovens such as those used in automotive paintshops is difficult due to the large and multiple scales and long curing times. The flow inside a convective oven is turbulent, and the process includes large temperature gradients. An efficient simulation requires a simplified and localized model of the heat transfer coupling. We present a novel method with three ingredients: localization using local Nusselt numbers of the oven nozzles, projection of Nusselt number profiles onto the target, and efficient conduction modeling on a coarse background mesh. The approach, which was developed in a research project together with the Swedish automotive industry, makes it possible to accurately simulate a curing oven with close to real-time performance. The simulation results are demonstrated to be in close agreement with measurements from automotive production.
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| 19. |
- Johnson, Tomas, 1979-, et al.
(författare)
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Enclosing all zeros of an analytic function : a rigorous approach
- 2009
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Ingår i: Journal of Computational and Applied Mathematics. - : Elsevier BV. - 0377-0427 .- 1879-1778. ; 228:1, s. 418-423
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Tidskriftsartikel (refereegranskat)abstract
- We present a method to find all zeros of an analytic function in a rectangular domain. The approach is based on finding guaranteed enclosures rather than approximations of the zeros. Well-isolated simple zeros are determined fast and with high accuracy. Clusters of zeros can in many cases be distinguished from multiple zeros by applying the argument principle to sufficiently high-order derivatives of the function. We illustrate the proposed method through five examples of varying levels of complexity.
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| 20. |
- Johnson, Tomas, 1979-
(författare)
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No elliptic islands for the universal area-preserving map
- 2011
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Ingår i: Nonlinearity. - : IOP Publishing. - 0951-7715 .- 1361-6544. ; 24:7, s. 2063-2078
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Tidskriftsartikel (refereegranskat)abstract
- A renormalization approach has been used in Eckmann et al (1982) and Eckmann et al (1984) to prove the existence of a universal area-preserving map, a map with hyperbolic orbits of all binary periods. The existence of a horseshoe, with positive Hausdorff dimension, in its domain was demonstrated in Gaidashev and Johnson (2009a). In this paper the coexistence problem is studied, and a computer-aided proof is given that no elliptic islands with period less than 18 exist in the domain. It is also shown that less than 1.5% of the measure of the domain consists of elliptic islands. This is proven by showing that the measure of initial conditions that escape to infinity is at least 98.5% of the measure of the domain, and we conjecture that the escaping set has full measure. This is highly unexpected, since generically it is believed that for conservative systems hyperbolicity and ellipticity coexist.
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