arXiv subjects

Jānis Bajārs

Publications and source records attributed to Jānis Bajārs.

6 recordsLinked to original sources

arXiv2026

Localization region detection with directionality estimation in a two-dimensional hexagonal crystal lattice model

This work is devoted to data-driven identification of discrete breathers in numerical simulations of a two-dimensional crystal lattice using locally sampled wave data. Different lattice wave datasets are considered, with data collected from regions of different shapes and sizes defined by the lattice particles in mechanical equilibrium. Specifically, in addition to regions with a regular hexagonal shape, one- and quasi-one-dimensional regions reflecting the quasi-one-dimensionality of discrete breathers in two-dimensional hexagonal crystal lattices are proposed. To improve numerical efficiency, dataset dimensionality is reduced using Principal Component Analysis, and highly accurate Support Vector Machine classifiers are trained to distinguish between linear and nonlinear wave data. The obtained classifiers, together with the sliding window method, are applied to detect localization regions in two-dimensional hexagonal crystal lattice numerical simulations. High-precision algorithms for detected localization region segmentation and localized wave directionality estimation within the detected regions are further proposed, and their performance is evaluated. The presented methods are successfully applied to detect localized waves and their collision regions, as well as their directionality, performing a numerical study of stationary and traveling two-dimensional discrete breather interactions. Qualitatively better results are obtained when considering wave-data collection regions respecting the quasi-one-dimensional nature of two-dimensional discrete breathers in the hexagonal crystal lattice model.

nlin.PS↗

arXiv2025

Thermal lifetime of breathers

In this article, we explore the lifetime of localized excitations in nonlinear lattices, called breathers, when a thermalized lattice is perturbed with localized energy delivered to a single site. We develop a method to measure the time it takes for the system to approach equilibrium based on a single scalar quantity, the participation number, and deduce the value corresponding to thermal equilibrium. We observe the time to achieve thermalization as a function of the energy of the excited site. We explore a variety of different physical system models. The result is that the lifetime of breathers increases exponentially with the breather energy for all the systems. This increase becomes observable when this energy is larger than approximately ten times the local average thermal energy. These results may provide a method to detect the existence of breathers in real systems.

cond-mat.stat-mech↗

arXiv2024

A semiclassical model for charge transfer along ion chains in silicates

It has been observed in fossil tracks and experiments in the layered silicate mica muscovite the transport of charge through the cation layers sandwiched between the layers of tetrahedra-octahedra-tetrahedra. A classical model for the propagation of anharmonic vibrations along the cation chains has been proposed based on first principles and empirical functions. In that model, several propagating entities have been found as kinks or crowdions and breathers, both with or without wings, the latter for specific velocities and energies. Crowdions are equivalent to moving interstitials and transport electric charge if the moving particle is an ion, but they also imply the movement of mass, which was not observed in the experiments. Breathers, being just vibrational entities, do not transport charge. In this work, we present a semiclassical model obtained by adding a quantum particle, electron or hole to the previous model. We present the construction of the model based on the physics of the system. In particular, the strongly nonlinear vibronic interaction between the nuclei and the extra electron or hole is essential to explain the localized charge transport, which is not compatible with the adiabatic approximation. The formation of vibrational localized charge carriers breaks the lattice symmetry group in a similar fashion to the Jahn-Teller Effect, providing a new stable dynamical state. We study the properties and the coherence of the model through numerical simulations from initial conditions obtained by tail analysis and other means. We observe that although the charge spreads from an initial localization in a lattice at equilibrium, it can be confined basically to a single particle when coupled to a chaotic quasiperiodic breather. This is coherent with the observation that experiments imply that a population of charge is formed due to the decay of potassium unstable isotopes.

cond-mat.mtrl-sci↗

arXiv2023

Locally-symplectic neural networks for learning volume-preserving dynamics

We propose locally-symplectic neural networks LocSympNets for learning the flow of phase volume-preserving dynamics. The construction of LocSympNets stems from the theorem of the local Hamiltonian description of the divergence-free vector field and the splitting methods based on symplectic integrators. Symplectic gradient modules of the recently proposed symplecticity-preserving neural networks SympNets are used to construct invertible locally-symplectic modules. To further preserve properties of the flow of a dynamical system LocSympNets are extended to symmetric locally-symplectic neural networks SymLocSympNets, such that the inverse of SymLocSympNets is equal to the feed-forward propagation of SymLocSympNets with the negative time step, which is a general property of the flow of a dynamical system. LocSympNets and SymLocSympNets are studied numerically considering learning linear and nonlinear volume-preserving dynamics. We demonstrate learning of linear traveling wave solutions to the semi-discretized advection equation, periodic trajectories of the Euler equations of the motion of a free rigid body, and quasi-periodic solutions of the charged particle motion in an electromagnetic field. LocSympNets and SymLocSympNets can learn linear and nonlinear dynamics to a high degree of accuracy even when random noise is added to the training data. When learning a single trajectory of the rigid body dynamics locally-symplectic neural networks can learn both quadratic invariants of the system with absolute relative errors below 1%. In addition, SymLocSympNets produce qualitatively good long-time predictions, when the learning of the whole system from randomly sampled data is considered. LocSympNets and SymLocSympNets can produce accurate short-time predictions of quasi-periodic solutions, which is illustrated in the example of the charged particle motion in an electromagnetic field.

math-ph↗

arXiv2022

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 onedimensional 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.

cond-mat.mtrl-sci↗

arXiv2022

Frequency-momentum representation of moving breathers in a two dimensional hexagonal lattice

We study nonlinear excitations propagating in a hexagonal layer which is a model for the cation layer of silicates. We consider their properties in the frequency-momentum or $ω-k$ representation, extending the theory on pterobreathers in their moving frame for the first time to two dimensions. It can also be easily extended to three dimensions. Exact traveling waves in the $ω-k$ representation are within {\em resonant} planes, each plane corresponding in the moving frame to a single frequency. These frequencies are integer multiples of a frequency called the fundamental frequency. A breather is within a resonant plane called the breather plane and has a single frequency in the moving frame. The intersection of the resonant planes with the phonon surfaces produce co-traveling wings with a small set of frequencies. The traveling waves obtained by perturbing the system consist of a breather and a soliton traveling together and are quasi-exact. These traveling waves can be used as seeds to obtain exact traveling waves, also formed by a breather and a soliton. The wings do exist but they are usually very small.

nlin.PS↗