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Subject = Dynamical Systems;
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Displaying Results 1  13 of 13 on page 1 of 1
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A Stochastic Model for Wind Turbine Power Quality using a Levy Index Analysis of Wind Velocity Data
(2011)
Blackledge, Jonathan; Coyle, Eugene; Kearney, Derek
A Stochastic Model for Wind Turbine Power Quality using a Levy Index Analysis of Wind Velocity Data
(2011)
Blackledge, Jonathan; Coyle, Eugene; Kearney, Derek
Abstract:
The power quality of a wind turbine is determined by many factors but timedependent variation in the wind velocity are arguably the most important. After a brief review of the statistics of typical wind speed data, a non Gaussian model for the wind velocity is introduced that is based on a Levy distribution. It is shown how this distribution can be used to derive a stochastic fractional diusion equation for the wind velocity as a function of time whose solution is characterised by the Levy index. A Levy index numerical analysis is then performed on wind velocity data for both rural and urban areas where, in the latter case, the index has a larger value. Finally, an empirical relationship is derived for the power output from a wind turbine in terms of the Levy index using Betz law.
https://arrow.dit.ie/engscheleart/146
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Basins of attraction in nonsmooth models of gear rattle
(2018)
MASON, JOANNA F.; PIIROINEN, PETRI T.; WILSON, R. EDDIE; HOMER, MARTIN E.
Basins of attraction in nonsmooth models of gear rattle
(2018)
MASON, JOANNA F.; PIIROINEN, PETRI T.; WILSON, R. EDDIE; HOMER, MARTIN E.
Abstract:
This paper is concerned with the computation of the basins of attraction of a simple one degreeoffreedom backlash oscillator using celltocell mapping techniques. This analysis is motivated by the modeling of order vibration in geared systems. We consider both a piecewiselinear stiffness model and a simpler infinite stiffness impacting limit. The basins reveal rich and delicate dynamics, and we analyze some of the transitions in the system's behavior in terms of smooth and discontinuityinduced bifurcations. The stretching and folding of phase space are illustrated via computations of the grazing curve, and its preimages, and manifold computations of basin boundaries using DsTool (Dynamical Systems Toolkit).
http://hdl.handle.net/10379/12673
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Decision landscapes: visualizing mousetracking data
(2018)
Zgonnikov, A.; Aleni, A.; Piiroinen, P. T.; O'Hora, Denis; di Bernardo, M.
Decision landscapes: visualizing mousetracking data
(2018)
Zgonnikov, A.; Aleni, A.; Piiroinen, P. T.; O'Hora, Denis; di Bernardo, M.
Abstract:
Computerized paradigms have enabled gathering rich data on human behaviour, including information on motor execution of a decision, e.g. by tracking mouse cursor trajectories. These trajectories can reveal novel information about ongoing decision processes. As the number and complexity of mousetracking studies increase, more sophisticated methods are needed to analyse the decision trajectories. Here, we present a new computational approach to generating decision landscape visualizations based on mousetracking data. A decision landscape is an analogue of an energy potential field mathematically derived from the velocity of mouse movement during a decision. Visualized as a threedimensional surface, it provides a comprehensive overview of decision dynamics. Employing the dynamical systems theory framework, we develop a new method for generating decision landscapes based on arbitrary number of trajectories. This approach not only generates threedimensional illustration of decision l...
http://hdl.handle.net/10379/14522
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Dynamical Analysis of Scalar Field Cosmologies with Spatial Curvature
(2016)
Gosenca, Mateja; Coles, Peter
Dynamical Analysis of Scalar Field Cosmologies with Spatial Curvature
(2016)
Gosenca, Mateja; Coles, Peter
Abstract:
We explore the dynamical behaviour of cosmological models involving a scalar field (with an exponential potential and a canonical kinetic term) and a matter fluid with spatial curvature included in the equations of motion. Using appropriately defined parameters to describe the evolution of the scalar field energy in this situation, we find that there are two extra fixed points that are not present in the case without curvature. We also analyse the evolution of the effective equationofstate parameter for different initial values of the curvature.
http://mural.maynoothuniversity.ie/12500/
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Dynamics of oneresonant biholomorphisms
(2013)
ZAITSEV, DMITRI
Dynamics of oneresonant biholomorphisms
(2013)
ZAITSEV, DMITRI
Abstract:
Our first main result is a construction of a simple formal normal form for holomorphic diffeomorphisms in Cn whose differentials have onedimensional family of resonances in the first m eigenvalues, m ? n (but more resonances are allowed for other eigenvalues). Next, we provide invariants and give conditions for the existence of basins of attraction. Finally, we give applications and examples demonstrating the sharpness of our conditions
http://hdl.handle.net/2262/64092
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Euler Equations on a SemiDirect Product of the Diffeomorphisms Group by Itself
(2011)
Escher, Joachim; Ivanov, Rossen; Kolev, Boris
Euler Equations on a SemiDirect Product of the Diffeomorphisms Group by Itself
(2011)
Escher, Joachim; Ivanov, Rossen; Kolev, Boris
Abstract:
The geodesic equations of a class of right invariant metrics on the semidirect product of two Diff(S) groups are studied. The equations are explicitly described, they have the form of a system of coupled equations of CamassaHolm type and possess singular (peakon) solutions. Their integrability is further investigated, however no compatible biHamiltonian structures on the corresponding dual Lie algebra are found.
https://arrow.dit.ie/scschmatart/125
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EulerPoincar´e equations for GStrands
(2014)
Holm, Darryl; Ivanov, Rossen
EulerPoincar´e equations for GStrands
(2014)
Holm, Darryl; Ivanov, Rossen
Abstract:
The Gstrand equations for a map R×R into a Lie group G are associated to a Ginvariant Lagrangian. The Lie group manifold is also the configuration space for the Lagrangian. The Gstrand itself is the map g(t,s):R×R→G, where t and s are the independent variables of the Gstrand equations. The EulerPoincar'e reduction of the variational principle leads to a formulation where the dependent variables of the Gstrand equations take values in the corresponding Lie algebra g and its coalgebra, g∗ with respect to the pairing provided by the variational derivatives of the Lagrangian. We review examples of different Gstrand constructions, including matrix Lie groups and diffeomorphism group. In some cases the Gstrand equations are completely integrable 1+1 Hamiltonian systems that admit soliton solutions.
https://arrow.dit.ie/scschmatcon/16
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GStrands
(2012)
Holm, Darryl; Ivanov, Rossen; Percival, James
GStrands
(2012)
Holm, Darryl; Ivanov, Rossen; Percival, James
Abstract:
A Gstrand is a map g(t,s): RxR > G for a Lie group G that follows from Hamilton's principle for a certain class of Ginvariant Lagrangians. The SO(3)strand is the Gstrand version of the rigid body equation and it may be regarded physically as a continuous spin chain. Here, SO(3)Kstrand dynamics for ellipsoidal rotations is derived as an EulerPoincar'e system for a certain class of variations and recast as a LiePoisson system for coadjoint flow with the same Hamiltonian structure as for a perfect complex fluid. For a special Hamiltonian, the SO(3)Kstrand is mapped into a completely integrable generalization of the classical chiral model for the SO(3)strand. Analogous results are obtained for the Sp(2)strand. The Sp(2)strand is the Gstrand version of the Sp(2) BlochIserles ordinary differential equation, whose solutions exhibit dynamical sorting. Numerical solutions show nonlinear interactions of coherent wavelike solutions in both cases. Diff(R)strand equ...
https://arrow.dit.ie/scschmatart/133
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Inverse scattering transform for the Degasperis–Procesi equation
(2010)
Constantin, Adrian; Ivanov, Rossen; Lenells, Jonatan
Inverse scattering transform for the Degasperis–Procesi equation
(2010)
Constantin, Adrian; Ivanov, Rossen; Lenells, Jonatan
Abstract:
We develop the Inverse Scattering Transform (IST) method for the Degasperis Procesi equation. The spectral problem is an sl(3) ZakharovShabat problem with constant boundary conditions and finite reduction group. The basic aspects of the IST such as the construction of fundamental analytic solutions, the formulation of a RiemannHilbert problem, and the implementation of the dressing method are presented.
https://arrow.dit.ie/scschmatart/53
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Multistate dynamical processes on networks: analysis through degreebased approximation frameworks
(2019)
Fennell, Peter G.; Gleeson, James P.
Multistate dynamical processes on networks: analysis through degreebased approximation frameworks
(2019)
Fennell, Peter G.; Gleeson, James P.
Abstract:
Multistate dynamical processes on networks, where nodes can occupy one of a multitude of discrete states, are gaining widespread use because of their ability to recreate realistic, complex behavior that cannot be adequately captured by simpler binarystate models. In epidemiology, multistate models are employed to predict the evolution of real epidemics, while multistate models are used in the social sciences to study diverse opinions and complex phenomena such as segregation. In this paper, we introduce generalized approximation frameworks for the study and analysis of multistate dynamical processes on networks. These frameworks are degreebased, allowing for the analysis of the effect of network connectivity structures on dynamical processes. We illustrate the utility of our approach with the analysis of two specific dynamical processes from the epidemiological and physical sciences. The approximation frameworks that we develop, along with opensource numerical solvers, provide a ...
http://hdl.handle.net/10344/7702
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Noise in nonsmooth dynamical systems
(2020)
Staunton, Eoghan J.
Noise in nonsmooth dynamical systems
(2020)
Staunton, Eoghan J.
Abstract:
This articlebased thesis comprises a collection of four articles, each of which constitutes a chapter, written and formatted in preprint manuscript form. The general aim underlying these articles is to understand how noise affects the dynamics of nonsmooth dynamical systems. Nonsmooth dynamical systems arise naturally when modelling systems in engineering and applied sciences and are characterised by sudden changes in system properties. Examples of naturally arising nonsmooth systems include mechanical systems involving impacts or friction, economic or sociological systems with decision thresholds, switching electronic systems and climate systems with sharp icecap boundaries. The dynamical systems resulting from these models exhibit several unique behaviours including new types of bifurcations called discontinuity induced bifurcations, which can be considered the hallmark of nonsmooth systems. A level of noise or randomness is also ubiquitous in realworld systems and has been sh...
http://hdl.handle.net/10379/15739
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Nonlinear wave interactions : beyond weak nonlinearity
(2020)
Walsh, Shane
Nonlinear wave interactions : beyond weak nonlinearity
(2020)
Walsh, Shane
Abstract:
An important aspect of the dynamics of nonlinear wave systems is the effect of finite amplitude phenomena — that is, phenomena which can only manifest beyond the limit of weak nonlinearity. The work in this thesis aims to bridge the gap between the phenomenology of finite amplitude effects in nonlinear wave systems and the existing theories describing these systems. We describe the phenomenon of precession resonance, a manifestly finite amplitude phenomenon characterised by a balance between the linear and nonlinear timescales of the system. We then investigate numerically the region of convergence of the normal form transformation to understand if precession resonance can be described with tools commonly used to study nonlinear wave systems. We find that the boundary of the region of convergence of the transformation closely matches the values which lead to precession resonance, giving us an understanding of where precession resonance lies with the general theory of wave turbulence...
http://hdl.handle.net/10197/11661
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On the (Non)Integrability of KdV Hierarchy with Selfconsistent Sources
(2011)
Gerdjikov, Vladimir; Grahovski, Georgi; Ivanov, Rossen
On the (Non)Integrability of KdV Hierarchy with Selfconsistent Sources
(2011)
Gerdjikov, Vladimir; Grahovski, Georgi; Ivanov, Rossen
Abstract:
Nonholonomic deformations of integrable equations of the KdV hierarchy are studied by using the expansions over the socalled “squared solutions” (squared eigenfunctions). Such deformations are equivalent to a perturbed model with external (selfconsistent) sources. In this regard, the KdV6 equation is viewed as a special perturbation of KdV. Applying expansions over the symplectic basis of squared eigenfunctions, the integrability properties of the KdV6 equation are analysed. This allows for a formulation of conditions on the perturbation terms that preserve its integrability. The perturbation corrections to the scattering data and to the corresponding actionangle (canonical) variables are studied. The analysis shows that although many nontrivial solutions of KdV6 can be obtained by the Inverse Scattering Transform (IST), there are solutions that in principle can not be obtained via IST. Thus the equation in general is not completely integrable.
https://arrow.dit.ie/scschmatart/62
Displaying Results 1  13 of 13 on page 1 of 1
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Institution
Dublin Institute of Technology (6)
Maynooth University (1)
NUI Galway (3)
Trinity College Dublin (1)
University College Dublin (1)
University of Limerick (1)
Item Type
Conference item (1)
Doctoral thesis (2)
Journal article (10)
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Peerreviewed (3)
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2020 (2)
2019 (1)
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2016 (1)
2014 (1)
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2012 (1)
2011 (3)
2010 (1)
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