Figure 10 - uploaded by Albert John Sievers
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Laser manipulation of an ILM in an array with hard anharmonicity. (a) Experimental observation of a laser-induced ILM hopping event. Periodic horizontal white lines are images of stationary cantilevers. The dark ILM location is centered at site 73 and the white laser spot is located at site 76. The laser spot is placed nearby a locked ILM and then the IR laser power is gradually increased. When an ILM hops away from the laser spot, it is accompanied by wave-packet emission, as labeled by A and B. Reflected waves from the edges are seen to the right of C and the left of D. The canted white lines are guides to eye of the traveling waves. The speed of these waves are 16.3×103,12.8×103,16.2×103, and 12.3×103(p∕sec) for A,B,C, and D, respectively, where p is the cantilever pitch. An ILM is stable at shorter cantilever sites (odd numbered sites in this figure). When one hops onto such a site its lateral momentum produces an oscillation that decays with time. (b) Successive manipulation of the ILM. The images are constructed from a number of chronologically ordered pictures. The two arrows at sites 105 and 78 indicate the initial locations of the laser spot and the ILM, respectively. The darkest stripe in each frame corresponds to a highly excited ILM. The white rectangles identify the heating laser spot, which produces a linear impurity mode. As the laser spot approaches, the ILM is repelled and hops away. When the laser spot is far removed, the ILM remains fixed as shown in the frames around 10, 40, and 52. When the laser power is low, it can pass through the ILM without interaction (around frame 23). At the last frame, the ILM was pushed against an impurity site near the end of the array, and disappeared.
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It has been known for some time that nonlinearity and discreteness play important roles in many branches of condensed-matter physics as evidenced by the appearance of domain walls, kinks, and solitons. A recent discovery is that localized dynamical energy in a perfect nonlinear lattice can be stabilized by the lattice discreteness. Intrinsic locali...
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Citations
... Discrete breather (DB) [1,2], which is a time-periodic spatially localized excitation, has been one of the most intriguing nonlinear phenomena over past decades, because it provides a means for energy concentration and transport in waveguides [3], polaronic materials [4], long biological molecules [5], and other settings [6]. The DB emerges due to the interplay between the nonlinearity and discreteness of the system, and supported by diverse nonlinear lattice media, such as arrays of micromechanical cantilevers [7], coupled Josephson junctions [8,9], optical waveguides [10][11][12][13][14][15], antiferromagnets [16,17], Bose-Einstein condensates (BECs) [18][19][20][21][22], and Tonks-Girardeau [23,24] or superfluid fermionic [25,26] gases fragmented and trapped in deep optical lattices (OL), as well as some dissipative systems [27,28]. ...
It is widely believed that the discrete breather (DB) can only be created when the nonlinearity is strong in nonlinear systems. However, we here establish that this belief is incorrect. In this work, we systemically investigate the generation of DBs induced by coupling of the defects and nonlinearity for Bose-Einstein condensates in dissipative optical lattices. The results show that, only in a clean lattice is strong nonlinearity a necessary condition for generating of DB; whereas, if the lattice has a defect, the DBs can also be discovered even in weak nonlinearity, and its generation turns out to be controllable. In addition, we further reveal a critical interval of the defect in weak nonlinearity, within which DBs can be found, while outside DBs do not exist. Furthermore, we also explore the impact of multiple defects on the generation of DBs, and analyze the underlying physical mechanisms of these interesting phenomena. The results not only have the potential to be used for more precise engineering in the DB experiments, but also suggest that the DB may be ubiquitous since the defects and dissipation are unavoidable in real physics.
... wave-matter interaction through localized modes [1][2][3] is essential for achieving improved sensitivity [4][5][6][7][8][9][10], nonlinearity [11][12][13], and emission rate [14], which lays the foundation of many applications requiring high quality (Q) factors including lasers [15][16][17], biosensors [18,19], vortex generators [20][21][22], and other compact devices [23][24][25][26]. The localization of waves can be achieved in various ways such as topological states [1,2,27,28], in-gap defect modes [29,30], Anderson localization [31,32], nonlinearity [33][34][35], and the acoustic black hole effect [36][37][38], etc. An alternative way for energy "trapping" or "isolation," referred to as bound state in the continuum (BIC), rests on the mismatch between a localized state and all nearby extended states, which features complete suppression of radiation in an open environment. ...
Constructing a highly localized wave field by means of bound states in the continuum (BICs) promotes enhanced wave-matter interaction and offers approaches to high-sensitivity devices. Elastic waves can carry complex polarizations and thus differ from electromagnetic waves and other scalar mechanical waves in the formation of BICs, which is yet to be fully explored and exploited. Here, we report the investigation of local resonance modes supported by a Lamb waveguide side-branched with two pairs of resonant pillars and show the emergence of two groups of elastic BICs with different polarizations or symmetries. Particularly, the two groups of BICs exhibit distinct responses to external perturbations, based on which a label-free sensing scheme with enhanced-sensitivity is proposed. Our study reveals the rich properties of BICs arising from the complex wave dynamics in elastic media and demonstrates their unique functionality for sensing and detection.
... 4,5 By now they are frequently encountered in a variety of practical and theoretical contexts with the later mainly concerned with their onsite vibrations and stability. Actually such studies go back to the very first work on intrinsic modes by Sato et al. 6,7 or Campbell et al., 8 a highly localized stationary excitation induced in an anharmonic lattice, from where it evolved into complex and electro-mechanical entities supporting rich dynamics (see Refs. 9-15 for a very partial sample of these efforts). ...
... The non-local central differences approximation of the spatial operator is equivalent to the physical representation of a mass-spring lattice with the closest neighbor interaction. Since x = x/ B √ η and x = B, Fig. 2, the non-dimensional step x is fully dictated by the intersite coupling parameter η, which, in turn, can be largely tailored by design (η between 0.0265 and 0.13 was reported in Ref. 13, and η ≈ 1 was used in Ref. 7). Robust propagation of a "flaton" in a discrete lattice, case-4, with η = 4 and, consequently, x = 1/2 is illustrated in Fig. 31, where several time snapshots for each of the half arrays, Fig. 7, are shown (for the arrays considered in Ref. 13, σ = 1, see Ref. 20). ...
We introduce and study both analytically and numerically a class of microelectromechanical chains aiming to turn them into transmission lines of solitons. Mathematically, their analysis reduces to the study of a spatially one-dimensional nonlinear Klein–Gordon equation with a model dependent onsite nonlinearity induced by the electrical forces. Since the basic solitons appear to be unstable for most of the force regimes, we introduce a stabilizing algorithm and demonstrate that it enables a stable and persisting propagation of solitons. Among other fascinating nonlinear formations induced by the presented models, we mention the “meson”: a stable square shaped pulse with sharp fronts that expands with a sonic speed, and “flatons”: flat-top solitons of arbitrary width.
... The dynamics of large arrays of coupled micro-or nanoelectromechanical (MEMS/NEMS) structural elements have been intensively studied theoretically and experimentally for more than two decades [1] (e.g., see reviews [2][3][4], see [5][6][7][8][9][10] for more recent contributions). Microand nanodevices manifest rich behavior and may serve as a convenient platform for investigation of exciting dynamic phenomena, such as parametric resonances (PR) [7,[11][12][13][14][15][16][17], intrinsic localized modes [4,18,19], pattern selection [20,21] and synchronization [8], to name just a few. ...
... The dynamics of large arrays of coupled micro-or nanoelectromechanical (MEMS/NEMS) structural elements have been intensively studied theoretically and experimentally for more than two decades [1] (e.g., see reviews [2][3][4], see [5][6][7][8][9][10] for more recent contributions). Microand nanodevices manifest rich behavior and may serve as a convenient platform for investigation of exciting dynamic phenomena, such as parametric resonances (PR) [7,[11][12][13][14][15][16][17], intrinsic localized modes [4,18,19], pattern selection [20,21] and synchronization [8], to name just a few. Within the applied physics and engineering communities, the interest in microscale arrays is motivated by their applicability as mass, chemical and biological multi-point sensors [5,9,10,[22][23][24][25][26], efficient band pass filters or active metamaterials. ...
... In most of the cases, the MEMS arrays are realized as assemblies of cantilevered or double clamped beams, attached at their ends to a thin flexible plate (an "overhang") serving as a source of the elastic coupling [4,26]. In these devices, both the onsite (OS) and intersite (IS) stiffness, along with the OS and IS nonlinearities are of the mechanical nature, are fully dictated by design and cannot be varied (stiffness tuning using an integrated piezoelectric actuator was reported in [19,27]; stiffness modulation by laser was explored in [28]). ...
We analyse the spectral content and parametric resonant dynamics of an array of elastically and electrostatically coupled interdigitated micro cantilevers assembled into two identical half-arrays. In this uncommon arrangement, within each of the half-arrays, the beams are coupled only elastically. The half-arrays are intercoupled only electrostatically, through fringing fields. First, by using the reduced order (RO) model, we analyse the voltage-dependent evolution of the eigenvalues and the eigenvectors of the equivalent mass-spring system, starting from the small two, three and four beams arrays and up to large beams assemblies. We show that at the coupling voltages below a certain critical value, the shape of the eigenvectors, the frequencies of the veering and of the crossing are influenced by the electrostatic coupling and can be tuned by the voltage. Next, by implementing the assumed modes techniques we explore the parametric resonant behavior of the array. We show that in the case of the sub critical electrostatic coupling the actuating voltages required to excite parametric resonance in the damped system can be lower than in a strongly coupled array. The results of the work may inspire new designs of more efficient resonant sensors.
... Achieving such exact adjustment is challenging, even in computational experiments. Moreover, it is exceedingly difficult to achieve this when conducting any physical experiments, particularly in situations where breather-like objects emerge spontaneously [14][15][16][17]. The cause for this phenomenon can be attributed to energy dissipation [17]. ...
... Moreover, it is exceedingly difficult to achieve this when conducting any physical experiments, particularly in situations where breather-like objects emerge spontaneously [14][15][16][17]. The cause for this phenomenon can be attributed to energy dissipation [17]. In general, the potential presence of discrete breathers can act as an indicator of the nonlinearity of the crystal lattice, which in turn may be a cause for various phenomena such as spontaneous localization, effective mass, and energy transport, as discussed in references [18][19][20][21][22]. ...
This study examines the mechanism of nonlinear supratransmission (NST), which involves the transfer of disturbance to discrete media at frequencies not supported by the structure. We considered a model crystal with A3B stoichiometry. The investigation was carried out using atomistic modeling through molecular dynamics. The interatomic interaction was determined by a potential obtained through the embedded atom method, which approximates the properties of the Pt3Al crystal. The effect of NST is an important property of many discrete structures. Its existence requires the discreteness and nonlinearity of the medium, as well as the presence of a forbidden zone in its spectrum. This work focuses on the differences in the NST effect due to the anisotropy of crystallographic directions. Three planes along which the disturbance caused by NST propagated were considered: (100), (110), and (111). It was found that the intensity of the disturbance along the (100) plane is an order of magnitude lower than for more densely packed directions. Differences in the shape of solitary waves depending on the propagation direction were shown. Moreover, all waves can be described by a single equation, being a solution of the discrete variational equations of macroscopic and microscopic displacements, with different parameters, emphasizing the unified nature of the waves and the contribution of crystal anisotropy to their properties. Studying the NST phenomenon is essential due to numerous applications of the latter, such as implications in information transmission and signal processing. Understanding how disturbances propagate in discrete media could lead to advancements in communication technologies, data storage, and signal amplification where the earlier mentioned ability to describe it with analytical equations is of particular importance.
... Properties of strongly localized excitations in 1D nonlinear transmission lines (NLTLs) have been reviewed over the last 30 years, from a variety of perspectives. [3][4][5][6][7][8][9][10][11] One use of a continuous, balanced NLTL can be as a pulse sharpener and/or a pulse compressor, due to the faster propagation of the high amplitude part Chaos ARTICLE pubs.aip.org/aip/cha of a pulse than for the low amplitude part, and, thus, a shock wave is generated. 12 Such practical applications have been studied utilizing both continuous and discrete transmission lines. ...
Mobile intrinsic localized modes (ILMs) in balanced nonlinear capacitive-inductive cyclic transmission lines are studied by experiment, using a spatiotemporal driver under damped steady-state conditions. Without nonlinear balance, the experimentally observed resonance between the traveling ILM and normal modes of the nonlinear transmission line generates lattice drag via the production of a lattice backwave. In our experimental study of a balanced running ILM in a steady state, it is observed that the fundamental resonance can be removed over extended, well-defined driving frequency intervals and strongly suppressed over the complete ILM driving frequency range. Because both of these nonlinear capacitive and inductive elements display hysteresis our observation demonstrates that the experimental system, which is only partially self-dual, is surprisingly tolerant, regarding the precision necessary to eliminate the ILM backwave. It appears that simply balancing the cell dual nonlinearities makes the ILM envelope shape essentially the same at the two locations in the cell, so that the effective lattice discreteness seen by the ILM nearly vanishes.
... It includes generation, annihilation, and spatial position manipulation of ILMs. These manipulation has been investigated numerically and experimentally [19,27]. Based on the results, we are going to focus on the spatial position manipulation. ...
Shift manipulation of intrinsic localized mode (ILM) is numerically discussed in an ac driven Klein Gordon lattice. Before the manipulation, we introduce the 2-degree of freedom nonlinear system, which is obtained by reducing the lattice. In the reduced system, two localized modes correspond to ILMs in the original system. These two localized modes are switched by changing a coupling constant adiabatically. Based on the result obtained in the reduced system, we numerically show that the shift manipulation of ILM is achieved, like a particle, by using an adiabatic change of coupling constant between the targeted sites in the lattice.
... A soliton is a solitary wave that behaves like a "particle", in that it satisfies the following conditions: (i) It must maintain its shape when it moves at constant speed and (ii) when a soliton interacts with another soliton, it emerges from the "collision" unchanged except possibly for a phase shift [14]. A breather is a localized wave that is periodic in time or space [15,16,17,18]. Bright-breathers are time periodic solutions with high amplitudes at localized regions in space that decay to zero outside of these regions (e.g., sech( ) cos (2 )), and are named such because in optics applications they would appear as a bright spot on a darker background. ...
This chapter discusses the development and implementation of algorithms based on Equation-Free/Dynamic Data Driven Applications Systems (EF/DDDAS) protocols for the computer-assisted study of the bifurcation structure of complex dynamical systems, such as those that arise in biology (neuronal networks, cell populations), multiscale systems in physics, chemistry and engineering, and system modeling in the social sciences. An illustrative example demonstrates the experimental realization of a chain of granular particles (a so-called engineered granular chain). In particular, the focus is on the detection/stability analysis of time-periodic, spatially localized structures referred to as "dark breathers". Results in this chapter highlight, both experimentally and numerically, that the number of breathers can be controlled by varying the frequency as well as the amplitude of an "out of phase" actuation, and that a "snaking" structure in the bifurcation diagram (computed through standard, model-based numerical methods for dynamical systems) is also recovered through the EF/DDDAS methods operating on a black-box simulator. The EF/DDDAS protocols presented here are, therefore, a step towards general purpose protocols for performing detailed bifurcation analyses directly on laboratory experiments, not only on their mathematical models, but also on measured data.
... Introduction.-Understanding the formation of oscillating localised structures known as 'breathers' is a fundamental problem in a wide variety of conservative and dissipative systems [1][2][3][4][5][6][7]. Breathers are known in optics [8], hydrodynamics [9], Bose-Einstein condensates [6], micromechanical arrays [10], and in the cavity optomechanics [11]. They provide a basis for more complicated formations-nonlinear superpositions of breathers that appear in many nonlinear phenomena of physical importance such as rogue wave events [12][13][14], breather molecules [15], chess-board-like patterns [16], breather turbulence [17], higher-order modulation instability (MI) [18,19], and the MI where small periodic modulation is additionally localised in transverse direction. ...
We developed an exact theory of the super-regular (SR) breathers of Manakov equations. We have shown that the vector SR breathers do exist both in the cases of focusing and defocusing Manakov systems. The theory is based on the eigenvalue analysis and on finding the exact links between the SR breathers and modulation instability. We have shown that in the focusing case the localised periodic initial modulation of the plane wave may excite both a single SR breather and the second-order SR breathers involving four fundamental breathers.
... Although a dissipative nonlinear transmission line (NLTL) is necessarily a nonconservative system, it is often used to compare experimental findings [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] with lattice solitons [18][19][20][21], discrete breathers [22][23][24], or intrinsic localized mode (ILM) [25][26][27][28][29][30] expectations. The properties of such strongly localized excitations in NLTLs have been described in a number of reviews [31][32][33][34][35][36][37][38][39][40]. A desired solitonlike property, such as the distortionless, free motion of a running energy pulse, is an important goal, but one impediment for the running ILM is the seemingly intrinsic backwave generated in the discrete nonlinear lattice [41][42][43][44]. ...
A well-known feature of a propagating localized excitation in a discrete lattice is the generation of a backwave in the extended normal mode spectrum. To quantify the parameter-dependent amplitude of such a backwave, the properties of a running intrinsic localized mode (ILM) in electric, cyclic, dissipative, nonlinear 1D transmission lines, containing balanced nonlinear capacitive and inductive terms, are studied via simulations. Both balanced and unbalanced damping and driving conditions are treated. The introduction of a unit cell duplex driver, with a voltage source driving the nonlinear capacitor and a synchronized current source, the nonlinear inductor, provides an opportunity to design a cyclic, dissipative self-dual nonlinear transmission line. When the self-dual conditions are satisfied, the dynamical voltage and current equations of motion within a cell become the same, the strength of the fundamental, resonant coupling between the ILM and the lattice modes collapses, and the associated fundamental backwave is no longer observed.
