arXiv subjects

G. P. Tsironis

Publications and source records attributed to G. P. Tsironis.

At least 55 records · Page 3Linked to original sources

arXiv2014

Stochastic metastability by spontaneous localization

Nonequilibrium, quasi-stationary states of a one-dimensional "hard" $ϕ^4$ deterministic lattice, initially thermalized to a particular temperature, are investigated when brought into contact with a stochastic thermal bath at lower temperature. For lattice initial temperatures sufficiently higher than those of the bath, energy localization through the formation of nonlinear excitations of the breather type during the cooling process occurs. These breathers keep the nonlinear lattice away from thermal equilibrium for relatively long times. In the course of time some breathers are destroyed by fluctuations, allowing thus the lattice to reach another nonequilibrium state of lower energy. The number of breathers thus reduces in time; the last remaining breather, however, exhibits amazingly long life-time demonstrated by extensive numerical simulations using a quasi-symplectic integration algorithm. For the single-breather states we have calculated the lattice velocity distribution unveiling non-gaussian features describable in a closed functional form. Moreover, the influence of the coupling constant on the life-time of a single breather has been explored. The latter exhibits power-law behaviour as the coupling constant approaches the anticontinuous limit.

cond-mat.stat-mech↗

arXiv2014

Enhanced surface plasmon polariton propagation induced by active dielectrics

We present numerical simulations for the propagation of surface plasmon polaritons in a dielectric-metal-dielectric waveguide using COMSOL multiphysics software. We show that the use of an active dielectric with gain that compensates metal absorption losses enhances substantially plasmon propagation. Furthermore, the introduction of the active material induces, for a specific gain value, a root in the imaginary part of the propagation constant leading to infinite propagation of the surface plasmon. The computational approaches analyzed in this work can be used to define and tune the optimal conditions for surface plasmon polariton amplification and propagation.

cond-mat.mtrl-sci↗

arXiv2014

Small-world networks of optical fiber lattices

We use a simple dynamical model and explore coherent dynamics of wavepackets in complex networks of optical fibers. We start from a symmetric lattice and through the application of a Monte-Carlo criterion we introduce structural disorder and deform the lattice into a small-world network regime. We investigate in the latter both structural (correlation length) as well as dynamical (diffusion exponent) properties and find that both exhibit a rapid crossover from the ordered to the fully random regime. For a critical value of the structural disorder parameter $ρ\approx 0.25$ transport changes from ballistic to sub-diffusive due to the creation strongly connected local clusters and channels of preferential transport in the small world regime.

physics.optics↗

arXiv2014

${\cal PT}-$Symmetric Dimers with Time-Periodic Gain/Loss Function

${\mathcal PT}-$symmetric dimers with a time-periodic gain/loss function in a balanced configuration where the amount of gain equals that of loss are investigated analytically and numerically. Two prototypical dimers in the linear regime are investigated: a system of coupled classical oscillators, and a Schrödinger dimer representing the coupling of field amplitudes; each system representing a wide class of physical models. Through a thorough analysis of their stability behaviour, we find that turning on the coupling parameter in the classical dimer system, leads initially to decreased stability but then to re-entrant transitions from the exact to the broken ${\mathcal PT}-$phase and vice versa, as it is increased beyond a critical value. On the other hand, the Schrödinger dimer behaves more like a single oscillator with time-periodic gain/loss. In addition, we are able to identify the conditions under which the behaviour of the two dimer systems coincides and/or reduces to that of a single oscillator.

cond-mat.other↗

arXiv2014

Wide-Band Tuneability, Nonlinear Transmission, and Dynamic Multistability in SQUID Metamaterials

Superconducting metamaterials comprising rf SQUIDs (Superconducting QUantum Interference Devices) have been recently realized and investigated with respect to their tuneability, permeability and dynamic multistability properties. These properties are a consequence of intrinsic nonlinearities due to the sensitivity of the superconducting state to external stimuli. SQUIDs, made of a superconducting ring interrupted by a Josephson junction, possess yet another source of nonlinearity, which makes them widely tuneable with an applied dc dlux. A model SQUID metamaterial, based on electric equivalent circuits, is used in the weak coupling approximation to demonstrate the dc flux tuneability, dynamic multistability, and nonlinear transmission in SQUID metamaterials comprising non-hysteretic SQUIDs. The model equations reproduce the experimentally observed tuneability patterns, and predict tuneability with the power of an applied ac magnetic magnetic field. Moreover, the results indicate the opening of nonlinear frequency bands for energy transmission through SQUID metamaterials, for sufficiently strong ac fields.

cond-mat.mes-hall↗

arXiv2013

SQUID Metamaterials: Tuneability and Multistability

An overview of several dynamic properties of SQUID metamaterials is given in the presence of both constant and alternating magnetic field. The total current as a function of the driving frequency exhibits hysteretic effects which are favored by low levels of disorder. Multistability in the current states leads to multiple magnetic responses with different value of magnetic permeability. SQUID metamaterials exhibit wide-band tuneability which is periodic with the applied constant magnetic field; the numerical calculations reproduce fairly well recent experimental results. Current work also reveals the possibility for wave transmission through nonlinear bands, which is briefly discussed.

cond-mat.mes-hall↗

arXiv2013

Extreme Events in Nonlinear Lattices

The spatiotemporal complexity induced by perturbed initial excitations through the development of modulational instability in nonlinear lattices with or without disorder, may lead to the formation of very high amplitude, localized transient structures that can be named as extreme events. We analyze the statistics of the appearance of these collective events in two different universal lattice models; a one-dimensional nonlinear model that interpolates between the integrable Ablowitz-Ladik (AL) equation and the nonintegrable discrete nonlinear Schrödinger (DNLS) equation, and a two-dimensional disordered DNLS equation. In both cases, extreme events arise in the form of discrete rogue waves as a result of nonlinear interaction and rapid coalescence between mobile discrete breathers. In the former model, we find power-law dependence of the wave amplitude distribution and significant probability for the appearance of extreme events close to the integrable limit. In the latter model, more importantly, we find a transition in the the return time probability of extreme events from exponential to power-law regime. Weak nonlinearity and moderate levels of disorder, corresponding to weak chaos regime, favour the appearance of extreme events in that case.

cond-mat.dis-nn↗

arXiv2013

Nonlinear Localization in Metamaterials

Metamaterials, i.e., artificially structured ("synthetic") media comprising weakly coupled discrete elements, exhibit extraordinary properties and they hold a great promise for novel applications including super-resolution imaging, cloaking, hyperlensing, and optical transformation. Nonlinearity adds a new degree of freedom for metamaterial design that allows for tuneability and multistability, properties that may offer altogether new functionalities and electromagnetic characteristics. The combination of discreteness and nonlinearity may lead to intrinsic localization of the type of discrete breather in metallic, SQUID-based, and ${\cal PT}-$symmetric metamaterials. We review recent results demonstrating the generic appearance of breather excitations in these systems resulting from power-balance between intrinsic losses and input power, either by proper initialization or by purely dynamical procedures. Breather properties peculiar to each particular system are identified and discussed. Recent progress in the fabrication of low-loss, active and superconducting metamaterials, makes the experimental observation of breathers in principle possible with the proposed dynamical procedures.

cond-mat.mtrl-sci↗

arXiv2013

Multistability and Self-Organization in Disordered SQUID Metamaterials

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.

cond-mat.mes-hall↗

arXiv2013

Gain-Driven Discrete Breathers in PT-Symmetric Nonlinear Metamaterials

We introduce a one dimensional parity-time (PT)-symmetric nonlinear magnetic metamaterial consisted 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 inter-unit coupling. In the presence of nonlinearity we show numerically that as a result of the gain/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.

cond-mat.mtrl-sci↗

arXiv2013

PT-Symmetric Nonlinear Metamaterials and Zero-Dimensional Systems

A one dimensional, parity-time (${\cal PT}$)-symmetric magnetic metamaterial comprising split-ring resonators having both gain and loss is investigated. In the linear regime, the transition from the exact to the broken ${\cal PT}$-phase is determined through the calculation of the eigenfrequency spectrum for two different configurations; the one with equidistant split-rings and the other with the split-rings forming a binary pattern (${\cal PT}$ dimer chain). The latter system features a two-band, gapped spectrum with its shape determined by the gain/loss coefficient as well as the inter-element coupling. In the presense of nonlinearity, the ${\cal PT}$ dimer chain with balanced gain and loss supports nonlinear localized modes in the form of novel discrete breathers below the lower branch of the linear spectrum. These breathers, that can be excited from a weak applied magnetic field by frequency chirping, can be subsequently driven solely by the gain for very long times. The effect of a small imbalance between gain and loss is also considered. Fundamendal gain-driven breathers occupy both sites of a dimer, while their energy is almost equally partitioned between the two split-rings, the one with gain and the other with loss. We also introduce a model equation for the investigation of classical ${\cal PT}$ symmetry in zero dimensions, realized by a simple harmonic oscillator with matched time-dependent gain and loss that exhibits a transition from oscillatory to diverging motion. This behaviour is similar to a transition from the exact to the broken ${\cal PT}$ phase in higher-dimensional ${\cal PT}-$ symmetric systems. A stability condition relating the parameters of the problem is obtained in the case of piecewise constant gain/loss function that allows for the construction of a phase diagram with alternating stable and unstable regions.

nlin.PS↗

arXiv2012

Extreme events in two dimensional disordered nonlinear lattices

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.

nlin.AO↗

arXiv2011

Strain-induced interface reconstruction in epitaxial heterostructures

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.

cond-mat.str-el↗

arXiv2011

Optical surface modes in the presence of nonlinearity and disorder

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.

physics.optics↗

arXiv2011

Discrete nonlinear Schrödinger equation in complex networks

We investigate dynamical aspects of the discrete nonlinear Schrödinger equation (DNLS) in finite lattices. Starting from a periodic chain with nearest neighbor interactions, we insert randomly links connecting distant pairs of sites across the lattice. Using localized initial conditions we focus on the time averaged probability of occupation of the initial site as a function of the degree of complexity of the lattice and nonlinearity. We observe that selftrapping occurs at increasingly larger values of the nonlinearity parameter as the lattice connectivity increases, while close to the fully coupled network limit, localization becomes more preferred. For nonlinearity values above a certain threshold we find a reentrant localization transition, viz. localization when the number of long distant bonds is small followed by delocalization and enhanced transport at intermediate bond numbers while close to the fully connected limit localization reappears.

cond-mat.dis-nn↗

arXiv2011

Exact dynamics for fully connected nonlinear networks

We investigate the dynamics of the discrete nonlinear Schrödinger equation in fully connected networks. For a localized initial condition the exact solution shows the existence of two dynamical transitions as a function of the nonlinearity parameter, a hyperbolic and a trigonometric one. In the latter the network behaves exactly as the corresponding linear one but with a renormalized frequency.

nlin.SI↗

arXiv2011

Nonlinear magnetoinductive transmission lines

Power transmission in one-dimensional nonlinear magnetic metamaterials driven at one end is investigated numerically and analytically in a wide frequency range. The nonlinear magnetic metamaterials are composed of varactor-loaded split-ring resonators which are coupled magnetically through their mutual inductances, forming thus a magnetoiductive transmission line. In the linear limit, significant power transmission along the array only appears for frequencies inside the linear magnetoinductive wave band. We present analytical, closed form solutions for the magnetoinductive waves transmitting the power in this regime, and their discrete frequency dispersion. When nonlinearity is important, more frequency bands with significant power transmission along the array may appear. In the equivalent circuit picture, the nonlinear magnetoiductive transmission line driven at one end by a relatively weak electromotive force, can be modeled by coupled resistive-inductive-capacitive (RLC) circuits with voltage-dependent capacitance. Extended numerical simulations reveal that power transmission along the array is also possible in other than the linear frequency bands, which are located close to the nonlinear resonances of a single nonlinear RLC circuit. Moreover, the effectiveness of power transmission for driving frequencies in the nonlinear bands is comparable to that in the linear band. Power transmission in the nonlinear bands occurs through the linear modes of the system, and it is closely related to the instability of a mode that is localized at the driven site.

physics.class-ph↗

arXiv2010

Driven linear modes: Analytical solutions for finite discrete systems

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.

cond-mat.other↗