Eoin Clerkin at Karwendel mountain

Thanks for visting my academic homepage. Its primary aim is to provide free online access to completed and published work. For questions or issues, you're welcome to contact me using the postal or electronic mail addresses below.



Contact details:

Postal Address:   TU Darmstadt S410 R410, FNB, Dynamics & Vibrations Group, Dolivostraße 15, Darmstadt 64283, Germany.

Email Address:   first-name <at> surname <dot> biz




Lecturing/Teaching:

[MSc. Summer Semester 2017]   "Vibrations in continous mechanical systems" at the Dept. of Mechanical Engineering, TU Darmstadt.
For more info, see our course webpage here




Institute Homepages:

Dynamics and Vibrations Group
Fachgebeit Numerische Berechnungsverfahren im Maschinenbau

Funding Logos:





Ph.D. Tree:

To demonstrate my German credentials to my colleagues, here's part of my Ph.D. tree from the excellent website phdtree.org. Of the names here, 15 (62%) are German.





List of Publications

  1. "Robust Damping in Self-Excited Mechanical Systems"
  2. Dominic Jekel, Eoin Clerkin, and Peter Hagedorn

    GAMM: March 7th-11th, 2016 Braunschweig, Germany.
    PAMM: Volume 16, Issue 1 October 2016 pages 695-696

    A technique to optimize the stability of a general mechanical system is outlined. The method relies on decomposing the damping matrix into several component matrices, which may have some special structure or physical relevance. An optimization problem can then be formulated where the ratio of these are varied to either stabilize or make more stable the equilibrium state subject to sensible constraints. For the purpose of this study, we define a system to be more stable if its eigenvalue with largest real part is as negative as possible. The technique is demonstrated by applying it to an introduced non-dimensionalized variant of a known minimal wobbling disc brake model. In this case, it is shown to be beneficial to shift some damping from the disc to the pins for a system optimized for stability.
    abstract    slides    fulltext     website


  3. "Dynamical systems, time-periodic mechanical systems, and Floquet theory."
  4. Eoin Clerkin
    Seminar presentation to Applied Mechanics
    TU Darmstadt, Germany
    July 7th, 2016

    Coupled systems of second order differential equations naturally arise in applied mechanics and mechanical engineering as the equations of motion for a mechanical device. For many engineering applications, as the avoidance of instabilities is sought, after a suitable canonical choice of coordinates and possible linearization around a central equilibrium, Lypunouv stability is determined via the eigenvalue of the Jacobian with maximal real part. This spectral stability test is well ingrained in the engineering industry with many commercial software packages focused on efficiently applying the technique computationally to systems of large degree. However in practise, application of the technique is often applied naively without due consideration for the limiting criteria.

    This presentation will address second order linear differential equations with time-periodic coefficients which often arise as the equations of motion for systems involving, e.g. rotors. Paradigmatic examples have been studied in-depth by the dynamics and vibrations group of TU Darmstadt over several years and some on-going projects will be summarised. It will be stressed that the above stability test is not applicable in these cases and emphasised that Floquet theory is the appropriate approach to determine stability. In this case, time-periodicity is removed by a suitable coordinate transformation as specified by Floquet, with the eigenvalue of the monodromy matrix with largest absolute value, known as the maximal Floquet multiplier, determining stability. As a parameter is varied, e.g. the rotor speed, a bifurcation occurs and the system becomes unstable if a Floquet multiplier crosses the unit circle. Qualitatively different transitory dynamics results depending on whether the critical multiplier occurs at 1, -1, a multiple of 1, or as part of a complex conjugate pair. In addition, symmetries in the equation of motion can limit the type of bifurcations permitted and thereby the resultant dynamics.

    A robust and efficient technique for calculating the Floquet multipliers numerically is therefore vital to understand realistic engineering models. Large stiff systems cause particular problems in obtaining reliable and accurate approximations of the monodromy matrix. For example, the computational cost of the direct integration method grows exponentially with size of the system as one is required to integrate over the period for each degree of freedom. Other, less well known, techniques exist which can make some computational savings by skipping monodromy matrix calculation and obtaining Floquet multipliers indirectly.


    edital    abstract    slides   



  5. "Analytical Methods in Nonlinear Dynamics"
  6. Peter Hagedorn and Eoin Clerkin
    IUTAM Procedia: Vol 19 p1-4 (March 2016)

    Preface: for the IUTAM proceedings.

    Nonlinear dynamics is a fascinating rapidly growing field in research and applications. Almost everywhere in nature one encounters beautiful dynamical phenomena which are challenging to understand. New phenomena have been found in physical experiments and in extensive numerical simulations. Engineering problems currently being investigated are for example self-excited vibrations of rotor systems, dynamics of wind turbines, granular dynamics, fluid-structure interaction, vibro-impacts, elastic waves in nonlinear media and many other fields. Numerics and algorithmic tools can however only be effective when joined with qualitative insight to understand the underlying generic mechanisms. A wealth of analytical and semi-analytical methods and techniques are available for the investigation of nonlinear systems. Many of them are classical, such as perturbation theory, others are of more recent origin. Examples of analytical methods for the investigation of ordinary and partial differential equations, which commonly arise in the context of nonlinear oscillations, are center manifold and normal form theory, nonlinear normal mode analysis and embedding techniques, such as Carleman linearization, among others. The major challenges are for example the study of bifurcations, the estimation of basins of attraction and the detection of chaotic behavior. The methods have to be adapted to different systems which may have slow and fast dynamics, as well as discontinuities yielding stiff differential equations.

    fulltext     website


  7. "Mutually Coupled Semiconductor Lasers in Photonic Integrated Circuits"
  8. F.M. Dubois, E. Sooudi, R. N. Sheehan, E. Clerkin, M. Yang, J.K. Alexander, H. Yang, and F.H. Peters
    "Photonics Ireland" at The Maryborough House Hotel, Douglas, Cork.
    2nd to 4th September, 2015

    Abstract:  We report on the analysis of dynamics of mutually coupled semiconductor lasers in photonic integrated circuits. Slotted Fabry Perot (SFP) lasers were integrated via waveguide sections of varying lengths to analyse the stability and properties of CW output, for use in advanced modulation formats.

    poster    website


  9. "Two Semiconductor Lasers Weakly Coupled Lasers"
  10. E. Clerkin and A. Amann
    "Institute of Physics Spring Meeting" at Clarion Hotel, Lapps Quay, Cork.
    23rd March, 2015

    Abstract: We theoretically investigate two laser diodes weakly coupled via a small amount of each laser's light entering the cavity of the other after a moderate delay. Using a well known rate equation description, eight stable dynamical states are categorised namely in-phase and anti-phase one-colour states, symmetry and symmetry broken undamped relaxation oscillations, symmetric and symmetry-broken quasi-periodic states, and symmetric and symmetry-broken chaotic dynamics.

    Using a recently published method to remove singularities from the laser rate equations, it was possible to make a bifurcation diagram by varying the coupling strength and coupling phase. The extent of each dynamical state in terms of this parameter space is ascertained and the bifurcation transitions between them are studied. The Lyapunov exponent is calculated and used to delimit chaotic regions on the bifurcation diagram. Several routes to chaos are present and several areas of multi-stabilities are observed.


    poster   


  11. "Closely Coupled Lasers: Dynamics & Applications"
  12. Eoin J. Clerkin
    Thesis: 3rd July 2014 (Ph.D. in Physics)
    Viva Voce: 19th September 2014: Physics Department University College Cork at Tyndall National Institute in Cork.

    Abstract: The dynamics of two mutually coupled identical single-mode semi-conductor lasers are theoretically investigated. For small separation and large coupling between the lasers, symmetry-broken one-colour states are shown to be stable. In this case the light output of the lasers have significantly different intensities whilst at the same time the lasers are locked to a single common frequency. For intermediate coupling we observe stable two-colour states, where both single-mode lasers lase simultaneously at two optical frequencies which are separated by up to 150 GHz. For low coupling but possibly large separation, the frequency of the relaxation oscillations of the free-running lasers defines the dynamics. Chaotic and quasi-periodic states are identified and shown to be stable. For weak coupling undamped relaxation oscillations dominate where each laser is locked to three or more odd number of colours spaced by the relaxation oscillation frequency. It is shown that the instabilities that lead to these states are directly connected to the two colour mechanism where the change in the number of optical colours due to a change in the plane of oscillation.

    At initial coupling, in-phase and anti-phase one colour states are shown to emerge from "on" uncoupled lasers using a perturbation method. Similarly symmetry-broken one-colour states come from considering one free-running laser initially "on" and the other laser initially "off". The mechanism that leads to a bi-stability between in-phase and anti-phase one-colour states is understood. Due to an equivariant phase space symmetry of being able to exchange the identical lasers, a symmetric and symmetry-broken variant of all states mentioned above exists and is shown to be stable. Using a five dimensional model we identify the bifurcation structure which is responsible for the appearance of symmetric and symmetry-broken one-colour, symmetric and symmetry-broken two-colour, symmetric and symmetry-broken undamped relaxation oscillations, symmetric and symmetry-broken quasi-periodic, and symmetric and symmetry-broken chaotic states. As symmetry-broken states always exist in pairs, they naturally give rise to bi-stability. Several of these states show multi-stabilities between symmetric and symmetry-broken variants and among states.

    Three memory elements on the basis of bi-stabilities in one and two colour states for two coupled single-mode lasers are proposed. The switching performance of selected designs of optical memory elements is studied numerically.

    cora


  13. "Multi-stabilities and symmetry-broken one-colour and two-colour states in closely coupled single-mode lasers"
  14. E.Clerkin, S.O'Brien, A.Amann
    Physical Review E 89.3 (March 2014): 032919.

    Abstract: We theoretically investigate the dynamics of two mutually coupled identical single-mode semi-conductor lasers. For small separation and large coupling between the lasers, symmetry-broken one-colour states are shown to be stable. In this case the light output of the lasers have significantly different intensities while at the same time the lasers are locked to a single common frequency. For intermediate coupling we observe stable symmetry-broken two-colour states, where both lasers lase simultaneously at two optical frequencies which are separated by up to 150 GHz. Using a five dimensional model we identify the bifurcation structure which is responsible for the appearance of symmetric and symmetry-broken one-colour and two-colour states. Several of these states give rise to multi-stabilities and therefore allow for the design of all-optical memory elements on the basis of two coupled single-mode lasers. The switching performance of selected designs of optical memory elements is studied numerically.

    fulltext


  15. "Photonic Devices: All Optical Components using Closely Coupled Lasers"
  16. E. Clerkin, E.P. O'Reilly, and A. Amann
    Photonics Ireland conference hosted at Wellington Park Hotel for Queen's University Belfast.
    4th September 2013
    abstract   slides


  17. "Symmetry-broken states in closely coupled single-mode lasers"
  18. 15th August 2013
    Eoin Clerkin, Stephen O'Brien, and Andreas Amann
    Technische Universität Berlin, Germany.
    slides


  19. "When a photon eats an electron"
  20. E. Clerkin and A. Amann
    "Workshop on Slow-Fast Dynamics: Theory, Numerics, Application to Life and Earth Sciences" at Universitat Autonoma de Barcelona.
    Bellaterra, 3rd to 7th June, 2013

    Abstract: Over the last three decades, laser dynamics has provided physical demonstrations for many fascinating theoretical non-linear phenomena. Lasers subject to feedback, electrical modulation or optical injection were extensively studied by systems of low dimensional ordinary differential equations. These systems are similar to a predator-prey model, whereby the photons act as a predator which feeds off carriers which are continually pumped. In addition, as there are several orders of magnitude difference between lifetimes of a photon and a carrier, the physics within lasers are a paradigmatic example of a slow-fast system.

    Here we consider two identical mutually coupled single mode laser diodes in the small delay limit. We introduce a five-dimensional model which overcomes singularities encountered in conventional reduced models. These new coordinates allowed us to study the dynamical features using a bifurcation diagram, obtained by varying the coupling strength and the coupling phase between the lasers. Analysis reveals a large region of multi-stability which is organised by three co-dimension two bifurcations.

    The dynamics in the multi-stable region is a direct consequence of the slow-fast nature of the system. Both symmetric and symmetry-broken two colour states exists, where the magnitude of the each laser's electric field, the fast variable, oscillates at a frequency which is too high for the carriers, the slow variable. In these states the intensity of the single mode lasers are constant with two optical frequencies. Due to the Z2 symmetry of being able to exchange both lasers, symmetry-broken states always exist in pairs. When stable regions of symmetry-broken and symmetric states overlap, this creates regions of tri-stability.

    Finally with new knowledge of the slow-fast dynamical behaviour, bifurcation boundaries, and multi-stabilities, we purpose several all optical memory element and all optical logic gate designs.

    poster    website


  21. "Mechanism for multi-stability in coupled lasers"
  22. Eoin Clerkin, Stephen O'Brien, and Andreas Amann
    Conference title Dynamical Days Europe in Gothenburg, Sweden.
    6th September 2012

    Abstract:  Multistability and synchronisation are phenomena, which play an important role in many nonlinear dynamical systems. Often their underlying origins are higher order co-dimension bifurcations and are therefore of broad interest.

    Here we consider a simple system of two identical mutually coupled single mode laser diodes in the small delay limit. By varying the coupling strength and the coupling phase we observe a number of distinct regions of multistability.

    In particular it is shown that a symmetry-broken state is stable for large coupling. In this case the intensity of each laser is significantly different, but the lasers are synchronised (locked) to the same optical frequency. As the system is invariant under the exchange of the lasers, a complimentary symmetry-broken state exists and is stable. Both symmetry broken states coexist with a stable symmetric state for which both lasers are mutually locked and emit light at equal intensity and frequency. This creates a region of tristability between locked states.

    For weaker coupling the intensities of the symmetry broken states oscillate with a new frequency leading to an extensive region of bistability between limit cycles.

    The observed phenomena are explained by a five dimensional model. This model uses a set of coordinates which avoids the singularities encountered in conventional phase-amplitude models. A bifurcation analysis reveals that the multistability is organised by three co-dimension two bifurcations.

    slides


  23. "Synchronisation & symmetry-breaking in closely coupled lasers"
  24. Eoin Clerkin, Stephen O'Brien, Nicholas Blackbeard, Finbarr O'Callaghan, Eoin O'Reilly, Andreas Amann.
    Workshop titled "Resonance and Synchronisation" at the Lorentz Centre, Leiden, The Netherlands.
    20th to 24th August 2012
    slides    website


  25. "Mutually Coupled Single Mode Lasers"
  26. E. Clerkin, S O'Brien, E.P. O'Reilly and A.Amann
    Photonics Ireland conference hosted by Dublin City University in Malahide.
    7th - 9th September 2011

    We present a new approach to a previously studied problem [1,2]. Two lasers are mutually coupled via a small percentage of each lasers light entering the other after a delay. Any minuscule change in the distance between the two lasers would results in a large change in the phase of incoming light. The input phase therefore becomes a free (sweep) parameter. This infinite dimensional problem is modelled with a modified version of the Lang-Kobayashi equations [3].

    The problem can be made finite dimensional by assuming an infinite speed of light. To reduce the dimensions further we take the relative phase difference between the lasers and so constant frequency waves (phasors) become the fixed points of the system. Standard fixed point analysis is conducted. Solutions with different inversions (carrier densities) in the two lasers are shown to be unstable for non-detuned lasers. Solutions with the same inversions have outputs which are either in-phase or anti-phase. These solutions are stable for a range of the free parameter.

    After a forward-shift of the input phase, the constant phase (balanced) solutions are shown to lose stability via a pitchfork bifurcation. This joins the in-phase and anti-phase via mixed phase (unbalanced) solutions which confirms analytically a principle result of [2] in the zero delay limit. Back-shifted, it loses stability via a Hopf bifurcation. A limit cycle is born which after a further small change in input phase undergoes a pitchfork bifurcation of limit cycles. Analytically expressions for these fixed and critical points are obtained. The results are then transferred back to the infinite dimensional problem by noting parametric similarities between the finite and infinite cases. To have a continuous transition between these two cases all eigenvalues must remain unchanged for at least a finite increase in delay. We obtain transferred results for the Hopf and pitchfork bifurcations. New bifurcations of two saddle-nodes exist for relatively small delay. These effect the stability of the phasors as the delay is increased. Complete analytical expressions are obtained for this. This work may have interesting applications utilizing bi-stabilities in limit cycles.

    REFERENCES
    [1] Harmutt Erzgraeber, Bernd Krauskopf, Lenstra Daan Compound laser modes of mutually delay-coupled lasers. SIAM J. Applied Dynamical Systems Vol 5 No 1 pp 30-65
    [2] A. Gravrieldes, V. Kovanis, T. Erneux Analytical stability boundaries for a semicondictor laser subject to optical injection Optics Communcations 136 (1997) 253-256
    [3] R. Lang and K. Kobayashi External optical feedback effects on semiconductor injection laser properties. IEEE J. Quantum Electron., (1980) pp. 347-353

    poster    website


  27. "The Youngest Stellar Clusters Associated with Massive Protostellar Candidates"
  28. MSN. Kumar, E. Keto, E. Clerkin
    Astronomy & Astrophysics, Vol.449, Iss.3, April III (2006), pp.1033-1041.

    Abstract: We theoretically investigate the dynamics of two mutually coupled identical single-mode semi-conductor lasers. For small separation and large coupling between the lasers, symmetry-broken one-colour states are shown to be stable. In this case the light output of the lasers have significantly different intensities while at the same time the lasers are locked to a single common frequency. For intermediate coupling we observe stable symmetry-broken two-colour states, where both lasers lase simultaneously at two optical frequencies which are separated by up to 150 GHz. Using a five dimensional model we identify the bifurcation structure which is responsible for the appearance of symmetric and symmetry-broken one-colour and two-colour states. Several of these states give rise to multi-stabilities and therefore allow for the design of all-optical memory elements on the basis of two coupled single-mode lasers. The switching performance of selected designs of optical memory elements is studied numerically.



    fulltext


  29. "A 2MASS study of candidate precursors to UCHII regions"
  30. Eoin James Clerkin
    Thesis: (MSc in Astronomy) April 2004
    12th July 2004   Viva Voce: Centro da Astrofisica de Universidade do Porto, Rua da Estrella, Portugal.

    Abstract: We report on the identification of 54 embedded clusters around 217 massive protostellar candidates of which 34 clusters are new detections. The embedded clusters are identified as stellar surface density enhancements in the 2 μm All Sky Survey (2MASS) data. Because the clusters are all associated with massive stars in their earliest evolutionary stage, the clusters should also be in an early stage of evolution. Thus the properties of these clusters should reflect properties associated with their formation rather than their evolution. For each cluster, we estimate the mass, the morphological type, the photometry and extinction. The clusters in our study, by their association with massive protostars and massive outflows, reinstate the notion that massive stars begin to form after the first generation of low mass stars have completed their accretion phase. Further, the observed high gas densities and accretion rates at the centers of these clusters is consistent with the hypothesis that high mass stars form by continuing accretion onto low mass stars.

    edital    fulltext    website




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last updated: 2017-01-24