Intrinsic Localized Modes Research Articles

Bright and Dark ILSM in a bilinear and biquadratic antiferromagnetic spin lattice

In the semiclassical limit, we investigate the intrinsic localized spin-wave modes (ILSM) in an antiferromagnetic spin system with bilinear, biquadratic and D-M interactions. Derivation of the nonlinear Schrödinger equation for the coherent-state amplitude involves the introduction of the multiple scale approximation paired with a quasi discreteness approximation. Consequently, we discover that the oscillatory frequency of the Bright–Dark stationary type ILSM’s can appear below the linear spin wave spectrum and the Bright–Dark type kink lies below the upper of the linear spin-wave spectrum. The effect of the interaction parameters in the system is also examined.

Stringlet excitation model of the boson peak.

The boson peak (BP), a low-energy excess in the vibrational density of states over the Debye contribution, is often identified as a characteristic of amorphous solid materials. Despite decades of efforts, its microscopic origin still remains a mystery. Recently, it has been proposed, and corroborated with simulations, that the BP might stem from intrinsic localized modes involving one-dimensional (1D) string-like excitations ("stringlets"). We build on a theory originally proposed by Lund that describes the localized modes as 1D vibrating strings, but we specify the stringlet size distribution to be exponential, as observed in simulations. We provide an analytical prediction for the BP frequency ωBP in the temperature regime well below the observed glass transition temperature Tg. The prediction involves no free parameters and accords quantitatively with prior simulation observations in 2D and 3D model glasses based on inverse power law potentials. The comparison of the string model to observations is more uncertain when compared to simulations of an Al-Sm metallic glass material at temperatures well above Tg. Nonetheless, our stringlet model of the BP naturally reproduces the softening of the BP frequency upon heating and offers an analytical explanation for the experimentally observed scaling with the shear modulus in the glass state and changes in this scaling in simulations of glass-forming liquids. Finally, the theoretical analysis highlights the existence of a strong damping for the stringlet modes above Tg, which leads to a large low-frequency contribution to the 3D vibrational density of states, observed in both experiments and simulations.

Intrinsically localized modes of bilinear FPU chains: Analytical study

Present study concerns the analysis of stationary intrinsically localized modes emerging in bilinear and symmetric Fermi–Pasta–Ulam chains. Each element of the chain is coupled to its nearest neighbors through identical and symmetric (tension/compression) bilinear springs. The intrinsically localized modes are the time-periodic, localized vibration states which are manifested by the extreme energy localization on one and two bonds of the chain for bond - centered and site - centered symmetries, respectively. Approximate and exact analytical solutions of intrinsic localized modes are derived for the infinite as well as the finite chains, correspondingly. The derived analytical approximations allow to describe explicitly the amplitude wave profiles of these special localized states as well as to establish their zones of existence in the space of system parameters. In the second part of the study, we derive the exact analytical solutions for the same type of site- and bond- centered intrinsically localized modes supported by the finite bilinear Fermi–Pasta–Ulam chains and analyze their stability properties using Fillipov method.

Shift manipulation of intrinsic localized mode in ac driven Klein Gordon lattice

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.

An artificial intelligence approach to design periodic nonlinear oscillator chains under external excitation with stable damped solitons

In this paper, an artificial intelligence approach is developed to create a metamodel of damped solitons in periodic nonlinear oscillator chains under external excitation. Unlike resonators subjected to parametric excitation, chains subjected exclusively to external excitation do not have known analytical solutions for Intrinsic Localized Modes (ILMs) when damping is pondered. The proposed metamodel is a quick design tool of nonlinear damped periodic structures describing effectively the behavior of solitonic solutions, demonstrating a computational cost considerably lower than that of the Newton method. The results of this work highlight the potential of ANN regression models in the description of physical phenomena represented by the Nonlinear Schrödinger Equation when damping is considered.

Experimental study of intrinsic localized mode mobility in a cyclic, balanced, 1D nonlinear transmission line.

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.

Quasi discreteness analysis of a two dimensional ferromagnetic spin system

By introducing bilinear and anisotropic interactions in a model based on a square lattice of ferromagnetism, we learn about the influence of excitations with nonlinearity in intrinsic localized modes (ILMS) and modulational instability. Equations of motion are constructed in the semi-classical limit by pairing Glauber’s coherent state representation with the Dyson-Maleev form of spin operators. A Cubic Nonlinear Schrödinger (CNLS) equation is obtained using an intensive method of quasi-discreteness analysis mixed with a method of multiple scales. We also analyze the bright envelope solitons and intrinsically localized modes using a Sine-Cosine function approach. Stability conditions are obtained using Modulational Instability analysis.

Discrete breathers in square lattices from delocalized nonlinear vibrational modes.

Standing and moving discrete breathers (or equally, intrinsic localized modes) in a square β-Fermi-Pasta-Ulam-Tsingou lattice are obtained by applying localizing functions to the delocalized nonlinear vibrational modes (DNVMs) found earlier by Ryabov and Chechin. The initial conditions used in our study do not correspond to exact spatially localized solutions, but make it possible to obtain long-lived quasibreathers. The approach employed in this work can easily be used to search for quasibreathers in three-dimensional crystal lattices, for which DNVMs with frequencies outside the phonon spectrum are known.

Propagating intrinsic localized mode in a cyclic, dissipative, self-dual one-dimensional nonlinear transmission line.

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 equationsof 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.

Intrinsic localized modes in polymers and hyperconductors

The history of the experimental study of nonlinear lattice excitations in layered silicate materials, when exposed to swift particles of appreciable momentum is described briefly. For brevity, and because of the difficulty of studying the structure of the lattice excitations, the term quodon was adopted to reflect their ballistic and quasione-dimensional propagative nature. Quodons in muscovite were observed experimentally. Eventually, it was deduced that the lattice excitations were carrying an electric charge. This led to the prediction of hyperconductivity (HC) in which charge is carried ballistically by neutral, mobile lattice excitations in absence of a driving electromotive force and at any temperature. HC was later observed experimentally. For practical applications of HC, it is necessary to encase the HC material in an insulating sheath. This focused attention on the behavior of insulating materials in the presence of quodons. These could enter the sheath by direct contact with the HC material or by the impact of the swift particles. It was found that quodons can exist and propagate in many different materials, perhaps all, but their behavior can vary dramatically. This universality and charge neutrality, together with their unexpected existence in the excellent insulator polytetrafluoroethylene, probably accounts for the delay in finding evidence of their existence.

Splitting Methods for Semi-Classical Hamiltonian Dynamics of Charge Transfer in Nonlinear Lattices

We propose two classes of symplecticity-preserving symmetric splitting methods for semi-classical Hamiltonian dynamics of charge transfer by intrinsic localized modes in nonlinear crystal lattice models. We consider, without loss of generality, one-dimensional crystal lattice models described by classical Hamiltonian dynamics, whereas the charge (electron or hole) is modeled as a quantum particle within the tight-binding approximation. Canonical Hamiltonian equations for coupled lattice-charge dynamics are derived, and a linear analysis of linearized equations with the derivation of the dispersion relations is performed. Structure-preserving splitting methods are constructed by splitting the total Hamiltonian into the sum of Hamiltonians, for which the individual dynamics can be solved exactly. Symmetric methods are obtained with the Strang splitting of exact, symplectic flow maps leading to explicit second-order numerical integrators. Splitting methods that are symplectic and conserve exactly the charge probability are also proposed. Conveniently, they require only one solution of a linear system of equations per time step. The developed methods are computationally efficient and preserve the structure; therefore, they provide new means for qualitative numerical analysis and long-time simulations for charge transfer by nonlinear lattice excitations. The properties of the developed methods are explored and demonstrated numerically considering charge transport by mobile discrete breathers in an example model previously proposed for a layered crystal.

Data-driven intrinsic localized mode detection and classification in one-dimensional crystal lattice model

In this work we propose Support Vector Machine classification algorithms to classify one-dimensional crystal lattice waves from locally sampled data. Different learning datasets of particle displacements, momenta and energy density values are considered. Efficiency of the classification algorithms is further improved by two dimensionality reduction techniques: Principal Component Analysis and Locally Linear Embedding. Robustness of classifiers is investigated and demonstrated. Developed algorithms are successfully applied to detect localized intrinsic modes in three numerical simulations considering a case of two localized stationary breather solutions, a single stationary breather solution in noisy background and two mobile breather collision.

Experimental investigation of supertransmission for an intrinsic localized mode in a cyclic nonlinear transmission line.

In this experimental study of the nonlinear loss mechanism between traveling localized excitation and the underlying extended normal mode spectrum for a 1D lattice, three types of cyclic, electric, nonlinear transmission lines (NLTLs) are used. They are nonlinear capacitive, inductive, and capacitive+inductive NLTLs. To maintain a robust, steady-state traveling intrinsic localized mode (ILM), a traveling wave driver is used. The ILM loses energy because of a resonance between it and the extended NLTL modes. A wake field excitation is detected directly from ILM velocity experiments by the decrease in ILM speed and by the observation of the wake. Its properties are quantified via a two-dimensional Fourier map in the frequency-wavenumber domain, determined from the measured spatial-time voltage pattern. Simulations support and extend these experimental findings. We find for the capacitive+inductive NLTL configuration, when the two nonlinear terms are theoretically balanced, the wake excitation is calculated to become very small, giving rise to supertransmission over an extended driving frequency range.

A New Method to Control Intrinsic Localized Mode Using a Variable Magnetic Spring Structure

A special vibration mode called intrinsic localized mode (ILM) in a dispersed multi mass point-nonlinear spring system has been actively studied in solid-state physics and has a high application potential in engineering. Previous studies have only considered parameter-invariant systems; hence, active control of the excited ILM is not possible. Therefore, even though the phenomena are very interesting, there are no applications to devices. In this article, we propose a new paradigm of ILM by designing a dynamic nonlinear vibration system that can treat nonlinear spring properties in a variable manner depending on the applied current. By using variable spring characteristics, the localized vibration energy of the ILM can be freely transferred in unconventional way than before. The spring properties of the variable spring structure with applied current are investigated using finite element analysis. Then, numerical simulations in MATLAB show that the active control of the ILM is possible in a dynamic vibration system with variable spring characteristics.

Ballistic Charge Transport by Mobile Nonlinear Excitations

The developments in hyperconductivity, the loss‐free transmission of electric charge at room temperature and above, due to the ballistic transport of electric charge in crystals with quasi‐layered structure, are reported. The electric charge is carried by quodons, a type of mobile nonlinear intrinsic localized mode of lattice excitation observed as fossil tracks in layered silicates and recently by laboratory experiments. Here, ballistic means moving with minimal scattering or interaction with phonons. A test for hyperconductivity in solid materials is developed. It is based on the unique effect of short‐term continuation of transport of charge, by total internal reflection, after creation of quodons has ceased. This effect is called the slow‐quodon‐decay effect or SQD effect. So far, only layered silicates have been shown to exhibit hyperconductivity. New evidence is presented for hyperconductivity in chrysotile, a nonlayered silicate material with new results. Being a fibrous material, it is more flexible than the sheet mica phyllosilicates. It is found that quodons can also be created and carry charge in very different materials, such as polymers, but without showing hyperconductivity, because of the very short range and lifetime of quodons in those materials.

Solitons in nerve axons

An axon or nerve fiber is a long, slender projection of a nerve cell, or neuron, in vertebrates that typically conducts electrical impulse known as action potentials away from the nerve cell body. Axons are the cable-like protrusions of neurons which wire up the nervous system. These delicate structures frequently need to survive for a lifetime. Parallel polar, bundles of microtubules run beside axons to form their structural backbones and are acting as highways for life-sustaining transportation. In this paper, we investigate the excitations of soliton along axons that are governed by the Nerve Soliton (NS) model. The NS model of nerve axon is governed by the discrete nonlinear equation of motion derived using the finite difference method. We done modulational instability (MI) analysis for the discrete equation of motion with effect of damping force by using Rotating wave approximation (RWA). The inherent intrinsic localized wave modes were generated which is responsible for energy localization in the nerve axons.

Prediction and observation of intermodulation sidebands from anharmonic phonons in NaBr

A quantum Langevin model, similar to models used recently for optomechanics, was used to predict intermodulation phonon sidebands (IPS). Ab initio calculations of anharmonic phonons in rocksalt NaBr showed these spectral features as "many-body effects". Modern inelastic neutron scattering measurements on a crystal of NaBr at 300K revealed diffuse intensity at high phonon energy from a predicted upper IPS. The transverse optical (TO) part of the new features originates from phonon intermodulation between the transverse acoustic (TA) and TO phonons. The longitudinal optical (LO) spectral features originate from three-phonon coupling between the TA modes and the TO lattice modes. The partner lower IPS proves to be an "intrinsic localized mode". Interactions with the thermal bath broaden and redistribute the spectral weight of the IPS pair. These sidebands are a probe of anharmonicity and quantum noise, which originate from interactions between the phonons in NaBr.

Feasibility evaluation of new electric motors driven by intrinsic localized mode

Intrinsic localized mode (ILM) has been observed in various physical systems. In particular, electromagnetic ILM has been observed on an LC ladder circuit array. This paper focused on the electromagnetic ILM and aims to evaluate the feasibility of a new electric motor driven by the electromagnetic ILM numerically. First, we propose two types of nonlinear inductors with different geometries, and their magnetic saturation characteristics are clarified from the magnetic field analysis. Second, numerical simulations using the obtained parameters show that the moving velocity of a moving ILM varies with an initial voltage disturbance. Finally, we propose an inductor with permanent magnets placed on a surface of a rotor core, aiming to generate the electromagnetic ILM more efficiently. Numerical simulations show that the behavior of the moving ILM is affected by the rotational speed of the rotor.

Dynamics of solitons with periodic loops intrinsic localized modes and modulational instability in a quantum 2D nonlinear square Klein-Gordon chain

Abstract We investigate the effects of dispersion and nonlinearity interactions in view of generation of nonlinear intrinsic localized modes (ILMs) and modulational instability (MI) of a quantum 2D Klein-Gordon chain. For this, using Glauber’s coherent state representation and multiple-scale method, we find that the system supports nonlinear excitations referred to bright, dark radial symmetric and bright, dark bilateral symmetric line non-traveling and traveling ILMs. We also find that moving bright and radial solution are evolving like localized periodic loops, which is very interesting in this work. By means of linear stability approach, the instability criteria, threshold amplitude, instability areas showing the generation of bright ILMs predicted to be unstable and growth rate of unstable modes in the system are obtained. Numerical investigations are performed to support the analytical analysis, and an excellent agreement with the analytical results has been found.

A Novel Alternating Magnetic Field Generator Based on the Principle of Lattice Vibration in Crystals

Many researchers have been interested in a special vibrational mode called the intrinsic localized mode (ILM), which was found in solid-state physics. As a practical solution to use ILM, this article proposes a novel method of generating an alternating magnetic field which is completely different from the general three-phase alternating current method. An LC ladder circuit array is introduced to reproduce the ILM in an electrical system. Electromagnetic field analysis using the finite element method reveals that the ILM is able to transmit to the neighboring inductors at a constant velocity.