G. P. Tsironis

Publications (55)73.67 Total impact

• Article: Multistability and Self-Organization in Disordered SQUID Metamaterials

  N. Lazarides, G. P. Tsironis
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  ABSTRACT: Planar arrays of magnetoinductively coupled rf SQUIDs belong to the emergent class of superconducting metamaterials that encompass the Josephson effect. SQUID metamaterials acquire their electromagnetic properties from the resonant characteristics of their constitutive elements, i.e., the individual rf SQUIDs, which consist of a superconducting ring interrupted by a Josephson junction. We investigate the response of a two-dimensional SQUID metamaterial to frequency variation of an applied alternating magnetic field in the presence of disorder, arising from critical current fluctuations of the Josephson elements; in effect, the resonance frequencies of individual SQUIDs are distributed randomly around a mean value. Bistability is observed in the total current-frequency curves both in ordered and disordered SQUID metamaterials; moreover, bistability is favoured by disorder through the improvement of synchronization between SQUID oscillators. Relatively weak disorder widens significantly the bistability region by helping the system to self-organize itself and leads to nearly homogeneous states that change smoothly with varying frequency. Moreover, the total current of the metamaterial is enhanced compared with that of uncoupled SQUIDs, through the synergetic action of coupling and synchronization. Multistability of nearly homogeneous states allows the metamaterial to exhibit different magnetic responses corresponding to different values of the magnetic permeability. At low power of the incident field, high-current states exhibit extreme diamagnetic properties corresponding to negative magnetic permeability in a narrow frequency region.
  04/2013;
• Article: Gain-Driven Discrete Breathers in PT-Symmetric Nonlinear Metamaterials.

  N Lazarides, G P Tsironis
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  ABSTRACT: We introduce a one-dimensional parity-time- (PT-)symmetric nonlinear magnetic metamaterial consisting of split-ring dimers having both gain and loss. When nonlinearity is absent we find a transition between an exact to a broken PT phase; in the former, the system features a two band gapped spectrum with shape determined by the gain and loss coefficients as well as the interunit coupling. In the presence of nonlinearity, we show numerically that as a result of the gain and dissipation matching a novel type of long-lived stable discrete breathers can form below the lower branch of the band with no attenuation. In these localized modes the energy is almost equally partitioned between two adjacent split rings on the one with gain and the other one with loss.
  Physical Review Letters 02/2013; 110(5):053901. · 7.37 Impact Factor
• Article: Extreme events in two dimensional disordered nonlinear lattices

  A. Maluckov, N. Lazarides, G. P. Tsironis, Lj. Hadzievski
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  ABSTRACT: Spatiotemporal complexity is induced in a two dimensional nonlinear disordered lattice through the modulational instability of an initially weakly perturbed excitation. In the course of evolution we observe the formation of transient as well as persistent localized structures, some of which have extreme magnitude. We analyze the statistics of occurrence of these extreme collective events and find that the appearance of transient extreme events is more likely in the weakly nonlinear regime. We observe a transition in the extreme events recurrence time probability from exponential, in the nonlinearity dominated regime, to power law for the disordered one.
  04/2012;
• Source

  Available from: Serge Aubry

  Article: Discrete nonlinear Schrödinger breathers in a phonon bath

  K.Ø. Rasmussen, S. Aubry, A.R. Bishop, G.P. Tsironis
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  ABSTRACT: We study the dynamics of the discrete nonlinear Schrödinger lattice initialized such that a very long transitory period of time in which standard Boltzmann statistics is insufficient is reached. Our study of the nonlinear system locked in this non-Gibbsian state focuses on the dynamics of discrete breathers (also called intrinsic localized modes). It is found that part of the energy spontaneously condenses into several discrete breathers. Although these discrete breathers are extremely long lived, their total number is found to decrease as the evolution progresses. Even though the total number of discrete breathers decreases we report the surprising observation that the energy content in the discrete breather population increases. We interpret these observations in the perspective of discrete breather creation and annihilation and find that the death of a discrete breather cause effective energy transfer to a spatially nearby discrete breather. It is found that the concepts of a multi-frequency discrete breather and of internal modes is crucial for this process. Finally, we find that the existence of a discrete breather tends to soften the lattice in its immediate neighborhood, resulting in high amplitude thermal fluctuation close to an existing discrete breather. This in turn nucleates discrete breather creation close to a already existing discrete breather. PACS. 63.70.+h Statistical mechanics of lattice vibrations and displacive phase transitions - 63.20.Pw Localized modes - 63.20.Ry Anharmonic lattice modes
  Physics of Condensed Matter 04/2012; 15(1):169-175. · 1.53 Impact Factor
• Source

  Available from: ArXiv

  Article: Optical surface modes in the presence of nonlinearity and disorder.

  M I Molina, N Lazarides, G P Tsironis
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  ABSTRACT: We investigate numerically the effect of the competition of disorder, nonlinearity, and boundaries on the Anderson localization of light waves in finite-size, one-dimensional waveguide arrays. Using the discrete Anderson-nonlinear Schrödinger equation, the propagation of the mode amplitudes up to some finite distance is monitored. The analysis is based on the calculated localization length and the participation number, two standard measures for the statistical description of Anderson localization. For relatively weak disorder and nonlinearity, a higher disorder strength is required to achieve the same degree of localization at the edge than in the interior of the array, in agreement with recent experimental observations in the linear regime. However, for relatively strong disorder and/or nonlinearity, this behavior is reversed and it is now easier to localize an excitation at the edge than in the interior.
  Physical Review E 01/2012; 85(1 Pt 2):017601. · 2.26 Impact Factor
• Source

  Available from: ArXiv

  Article: Strain-induced interface reconstruction in epitaxial heterostructures

  N. Lazarides, V. Paltoglou, P Maniadis, G. P. Tsironis, C. Panagopoulos
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  ABSTRACT: We investigate in the framework of Landau theory the distortion of the strain fields at the interface of two dissimilar ferroelastic oxides that undergo a structural cubic-to-tetragonal phase transition. Simple analytical solutions are derived for the dilatational and the order parameter strains that are globally valid over the whole of the heterostructure. The solutions reveal that the dilatational strain exhibits compression close to the interface which may in turn affect the electronic properties in that region.
  05/2011;
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  Available from: ArXiv

  Article: Driven linear modes: Analytical solutions for finite discrete systems

  N. Lazarides, G. P. Tsironis
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  ABSTRACT: We have obtained exact analytical expressions in closed form, for the linear modes excited in finite and discrete systems that are driven by a spatially homogeneous alternating field. Those modes are extended for frequencies within the linear frequency band while they are either end-localized or end-avoided for frequencies outside the linear frequency band. The analytical solutions are resonant at particular frequencies, which compose the frequency dispersion relation of the finite system.
  02/2010;
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  Available from: arxiv.org

  Article: Bulk and surface magnetoinductive breathers in binary metamaterials.

  M I Molina, N Lazarides, G P Tsironis
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  ABSTRACT: We investigate theoretically the existence of bulk and surface discrete breathers in a one-dimensional magnetic metamaterial comprised of a periodic binary array of split-ring resonators; the two types of resonators used have different resonant frequencies caused by unequal slit sizes. We use the rotating-wave approximation and construct several types of breather excitations both for the energy-conserving as well as dissipative-driven case; we corroborate these approximate results trough numerically exact computations. We demonstrate that discrete breathers can appear spontaneously in the dissipative-driven system as a result of a fundamental instability.
  Physical Review E 10/2009; 80(4 Pt 2):046605. · 2.26 Impact Factor
• Source

  Available from: Aleksandra Maluckov

  Article: Extreme events in discrete nonlinear lattices.

  A Maluckov, Lj Hadzievski, N Lazarides, G P Tsironis
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  ABSTRACT: We perform statistical analysis on discrete nonlinear waves generated through modulational instability in the context of the Salerno model that interpolates between the integrable Ablowitz-Ladik (AL) equation and the nonintegrable discrete nonlinear Schrödinger equation. We focus on extreme events in the form of discrete rogue or freak waves that may arise as a result of rapid coalescence of discrete breathers or other nonlinear interaction processes. We find power law dependence in the wave amplitude distribution accompanied by an enhanced probability for freak events close to the integrable limit of the equation. A characteristic peak in the extreme event probability appears that is attributed to the onset of interaction of the discrete solitons of the AL equation and the accompanied transition from the local to the global stochasticity monitored through the positive Lyapunov exponent of a nonlinear map.
  Physical Review E 03/2009; 79(2 Pt 2):025601. · 2.26 Impact Factor
• Article: Left-handed metamaterials with saturable nonlinearity.

  A Maluckov, Lj Hadzievski, N Lazarides, G P Tsironis
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  ABSTRACT: The left-handed properties of metamaterials with saturable nonlinearity are analyzed with respect to their electromagnetic response as a function of externally varying parameters. We demonstrate that the response of the medium is strongly affected by the saturation of the nonlinear effects. The last can be exploited to modulate the amplitude or tune the frequency of the response. Moreover, the existence of bistability regions in large parts of the external parameter space allows for switching between different magnetization states, with either positive or negative response. The stability issue of multiple possible states is addressed through modulational instability analysis of plane wave envelopes in each of those states.
  Physical Review E 04/2008; 77(4 Pt 2):046607. · 2.26 Impact Factor
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  Available from: uoc.gr

  Article: Magnetoinductive breathers in metamaterials.

  M Eleftheriou, N Lazarides, G P Tsironis
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  ABSTRACT: The existence and stability of discrete breathers (DBs) in one- and two-dimensional magnetic metamaterials (MMs), which consist of periodic arrangements (arrays) of split-ring resonators (SRRs), are investigated numerically. We consider different configurations of the SRR arrays, which are related to the relative orientation of the SRRs in the MM, in both one and two spatial dimensions. In the latter case we also consider anisotropic MMs. Using standard numerical methods we construct several types of linearly stable breather excitation in both Hamiltonian and dissipative MMs (dissipative breathers). The study of stability in both cases is performed using standard Floquet analysis. In both cases we find that the increase of dimensionality from one to two spatial dimensions does not destroy the DBs, which may also exist in the case of moderate anisotropy (in two dimensions). In dissipative MMs, the dynamics is governed by a power balance between the mainly Ohmic dissipation and driving by an alternating magnetic field. In that case it is demonstrated that DB excitation locally alters the magnetic response of MMs from paramagnetic to diamagnetic. Moreover, when the frequency of the applied field approaches the SRR resonance frequency, the magnetic response of the MM in the region of the DB excitation may even become negative (extremely diamagnetic).
  Physical Review E 03/2008; 77(3 Pt 2):036608. · 2.26 Impact Factor
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  Available from: arxiv.org

  Article: Dissipative discrete breathers in rf SQUID metamaterials

  N. Lazarides, G. P. Tsironis, M. Eleftheriou
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  ABSTRACT: The existence and stability of dissipative discrete breathers (DDBs) in rf superconducting quantum interference device (SQUID) arrays in both one and two dimensions is investigated numerically. In an rf SQUID array, the nonlinearity which is intrinsic to each SQUID due to the presence of the Josephson junction (on-site nonlinearity), along with the weak coupling of each SQUID to its nearest neighbors through magnetic forces, result in the appearance of discrete breathers. We analyze several discrete breather excitations, both in one and two dimensions, which are subjected to unavoidable losses. These losses, however, are counter-balanced by an external flux source leading to linearly stable discrete breather structures up to relatively large coupling parameters. We show that DDB excitations may locally alter the magnetic response of array from paramagnetic to diamagnetic or vice versa, and that they are not destroyed by increasing the dimensionality. Comment: 9 pages, 13 figures, submitted to Nonlinear Phenomena in Complex Systems
  12/2007;
• Source

  Available from: ArXiv

  Article: Magnetoinductive breathers in magnetic metamaterials

  M. Eleftheriou, N. Lazarides, G. P. Tsironis
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  ABSTRACT: The existence and stability of discrete breathers (DBs) in one-dimensional and two-dimensional magnetic metamaterials (MMs), which consist of periodic arrangem ents (arrays) of split-ring resonators (SRRs), is investigated numerically. We consider different configurations of the SRR arrays, which are related to the relative orientation of the SRRs in the MM, both in one and two spatial dimensions. In the latter case we also consider anisotropic MMs. Using standard numerical methods we construct several types of linearly stable breather excitations both in Hamiltonian and dissipative MMs (dissipative breathers). The study of stability in both cases is performed using standard Floquet analysi s. In both cases we found that the increase of dimensionality from one to two spatial dimensions does not destroy the DBs, which may also exist in the case of moderate anisotropy (in two dimensions). In dissipative MMs, the dynamics is governed by a power balance between the mainly Ohmic dissipation and driving by an alternating magnetic field. In that case it is demonstrated that DB excitation locally alters the magnetic response of MMs from paramagnetic to diamagnetic. Moreover, when the frequency of the applied field approaches the SRR resonance frequency, the magnetic response of the MM in the region of the DB excitation may even become negative (extreme diamagnetic). Comment: 12 pages 15 figures
  09/2007;
• Source

  Available from: arxiv.org

  Article: Self-focusing and envelope pulse generation in nonlinear magnetic metamaterials.

  I Kourakis, N Lazarides, G P Tsironis
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  ABSTRACT: The self-modulation of waves propagating in nonlinear magnetic metamaterials is investigated. Considering the propagation of a modulated amplitude magnetic field in such a medium, we show that the self-modulation of the carrier wave leads to a spontaneous energy localization via the generation of localized envelope structures (envelope solitons), whose form and properties are discussed. These results are also supported by numerical calculations.
  Physical Review E 07/2007; 75(6 Pt 2):067601. · 2.26 Impact Factor
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  Available from: users.physics.uoc.gr

  Article: rf superconducting quantum interference device metamaterials

  N. Lazarides, G. P. Tsironis
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  ABSTRACT: A rf superconducting quantum interference device (SQUID) array in an alternating magnetic field is investigated with respect to its effective magnetic permeability, within the effective medium approximation. This system acts as an inherently nonlinear magnetic metamaterial, leading to negative magnetic response, and thus negative permeability above the resonance frequency of the individual SQUIDs. Moreover, the permeability exhibits oscillatory behavior at low field intensities, allowing its tuning by a slight change of the intensity of the applied field.
  Applied Physics Letters 04/2007; 90(16):163501-163501-3. · 3.84 Impact Factor
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  Available from: arxiv.org

  Article: rf SQUID metamaterials

  N. Lazarides, G. P. Tsironis
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  ABSTRACT: An rf superconducting quantum interference device (SQUID) array in an alternating magnetic field is investigated with respect to its effective magnetic permeability, within the effective medium approximation. This system acts as an inherently nonlinear magnetic metamaterial, leading to negative magnetic response, and thus negative permeability, above the resonance frequency of the individual SQUIDs. Moreover, the permeability exhibits oscillatory behavior at low field intensities, allowing its tuning by a slight change of the intensity of the applied field. Comment: 3 pages, 4 figures, accepted by Applied Physics Letters, in production
  03/2007;
• Source

  Available from: arxiv.org

  Article: Discrete breathers in nonlinear magnetic metamaterials.

  N Lazarides, M Eleftheriou, G P Tsironis
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  ABSTRACT: Magnetic metamaterials composed of split-ring resonators or U-type elements may exhibit discreteness effects in THz and optical frequencies due to weak coupling. We consider a model one-dimensional metamaterial formed by a discrete array of nonlinear split-ring resonators where each ring interacts with its nearest neighbors. On-site nonlinearity and weak coupling among the individual array elements result in the appearance of discrete breather excitations or intrinsic localized modes, both in the energy-conserved and the dissipative system. We analyze discrete single and multibreather excitations, as well as a special breather configuration forming a magnetization domain wall and investigate their mobility and the magnetic properties their presence induces in the system.
  Physical Review Letters 11/2006; 97(15):157406. · 7.37 Impact Factor
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  Available from: arxiv.org

  Article: Thermal conductivity of a classical one dimensional spin-phonon system

  A. V. Savin, G. P. Tsironis, X. Zotos
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  ABSTRACT: We investigate the thermal conductivity of the classical Heisenberg spin chain coupled to a variety of phonon systems using a Green-Kubo approach as well as coupling to heat reservoirs. The decay of energy current correlations is power law or exponential, depending on the type of (an)harmonicity of the phonon system and the presence of a substrate. In particular, we find that coupling the spin system to displacements with an acoustic type harmonic inter-site potential leads to a diverging thermal conductivity. Adding a substrate, harmonic or periodic such as sine-Gordon, drives the system to diffusive behavior. With anharmonic potential without a substrate the generic transport is diffusive even for the integrable Toda potential, while for the FPU chain is ballistic. Comment: 4 pages, 4 figures
  05/2006;
• Article: Self-trapping and stationary properties of a generalized nonlinear Schrödinger equation dimer

  G Kalosakas, P Maniadis, G P Tsironis
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  ABSTRACT: We study a dimer system of a generalized discrete nonlinear Schrödinger equation that interpolates between the integrable Ablowitz-Ladic equation and the nonintegrable discrete nonlinear Schrödinger equation (DNLS). We find analytically and verify numerically the occurrence of selftrapping in the parameter space of the two nonlinearity coefficients. We also study the stationary solutions and discuss their stability properties.
  Physica Scripta 04/2006; 55(5):523. · 1.20 Impact Factor
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  Available from: uoc.gr

  Article: Exact Solution of a Generalized Nonlinear Schrödinger Equation Dimer

  P L Christiansen, P Maniadis, G P Tsironis
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  ABSTRACT: We present exact solutions for a nonlinear dimer system defined throught a discrete nonlinear Schrödinger equation that contains also an integrable Ablowitz–Ladik term. The solutions are obtained throught a transformation that maps the dimer into a double Sine–Gordon like ordinary nonlinear differential equation.
  Physica Scripta 03/2006; 57(2):192. · 1.20 Impact Factor