Two-dimensional mobile breather scattering in a hexagonal crystal lattice

We describe, for the first time, the full 2D scattering of long-lived breathers in a model hexagonal lattice of atoms. The chosen system, representing an idealized model of mica, combines a Lennard-Jones interatomic potential with an "egg-box" harmonic potential well surface. We investigate the dependence of breather properties on the ratio of the well depths associated to the interaction and on-site potentials. High values of this ratio lead to large spatial displacements in adjacent chains of atoms and thus enhance the two dimensional character of the quasi-one-dimensional breather solutions. This effect is further investigated during breather-breather collisions by following the constrained energy density function in time for a set of randomly excited mobile breather solutions. Certain collisions lead to 60$^\circ$ scattering, and collisions of mobile and stationary breathers can generate a rich variety of states.Comment: 4 pages, 5 figure

WO3 as Additive for Efficient Photocatalyst Binary System TiO2/WO3

The financial support provided by Scientific Research Project for Students and Young Researchers No. SJZ/2018/9 implemented at the Institute of Solid State Physics, University of Latvia is greatly acknowledged. Institute of Solid State Physics, University of Latvia as the Center of Excellence has received funding from the Euro-pean Union’s Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART².Two different methods of synthesis of TiO2/WO3 heterostructures were carried out with the aim to increase photocatalytic activity. In this study, anodic TiO2 nanotube films were synthesized by electrochemical anodization of titanium foil. WO3 particles were applied to anodic Ti/TiO2 samples in two different ways-by electrophoretic deposition (EPD) and insertion during the anodization process. Structural and photocatalytic properties were compared between pristine TiO2 and TiO2 with incorporated WO3 particles. Raman mapping was used to character-ise the uniformity of EPD WO3 coating and to determine the structural composition. The study showed that deposition of WO3 onto TiO2 nanotube layer lowered the band gap of the binary system compared to pristine TiO2 and WO3 influence on photo-electrochemical properties of titania. The addition of WO3 increased charge carrier dynamics but did not increase the measured photo-current response. As the WO3 undergoes a phase transition from monoclinic to orthorhombic at approximately 320 proper sequence WO3 deposition could be beneficial. It was observed that secondary heat treatment of WO3 lowers the photocurrent. © 2021 A. Knoks et al., published by Sciendo. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.Scientific Research Project for Students and Young Researchers No. SJZ/2018/9; Institute of Solid State Physics, University of Latvia as the Center of Excellence has received funding from the Euro-pean Union’s Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART²

Nonlinear propagating localized modes in a 2D hexagonal crystal lattice

In this paper we consider a 2D hexagonal crystal lattice model first proposed by Marin, Eilbeck and Russell in 1998. We perform a detailed numerical study of nonlinear propagating localized modes, that is, propagating discrete breathers and kinks. The original model is extended to allow for arbitrary atomic interactions, and to allow atoms to travel out of the unit cell. A new on-site potential is considered with a periodic smooth function with hexagonal symmetry. We are able to confirm the existence of long-lived propagating discrete breathers. Our simulations show that, as they evolve, breathers appear to localize in frequency space, i.e. the energy moves from sidebands to a main frequency band. Our numerical findings contribute to the open question of whether exact moving breather solutions exist in 2D hexagonal layers in physical crystal lattices.Comment: Both this paper and arXiv 1408.6853 discuss similar models with the same on-site potential. This paper has a Lennard-Jones interparticle potential, 1408.6853 has a piecewise polynomial function. The latter favours the existence of long-lived kinks, and much of 1408.6853 is given to a study of these. Both models support long-lived breathers, and the present paper concentrates on such solution

Mass recovery of carbonated fabrics of glass fibres after isothermal heating

Acknowledgement: Authors acknowledge financial support from Latvian National Program IMIS2Leaching of Na+ ions in sodium oxide (Na2O) and silica (SiO2) containing glass is well investigated mainly due to its weak weathering. The object of this study was naturally (at room conditions) leached, steady state product on surface of sodium oxide-silica-alumina (Al2O3) glass fibers (in fabric) in a form of shell of "glyed" trona crystals as a result of interaction of leached Na+ ions and H2O and CO2 from atmosphere. There are presented results of continued former investigation of mass loss by isothermal heating of fabric and mass recovery in different atmospheres during the first phase of adsorption (at least 0.25h) without changes of state of crystals obtained during preheating at different temperatures. There are observed two ways of decomposition of trona (Na3H (CO3)2•2H2O) with its beginning at about 55-570C and 73-750C. The regression analysis of mass restoring in different atmospheres indicates to simultaneous and exponential mass increase by physical adsorption of CO2 and H2O having the different parameters of exponents vs time. Decomposition of trona is discussed in terms of parameters of exponent vs preheating temperature.Institute of Solid State Physics, University of Latvia as the Center of Excellence has received funding from the European Union’s Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART

Modelling uncertainties in phase-space boundary integral models of ray propagation

A recently proposed phase-space boundary integral model for the stochastic propagation of ray densities is presented and, for the first time, explicit connections between this model and parametric uncertainties arising in the underlying physical model are derived. In particular, an asymptotic analysis for a weak noise perturbation of the propagation speed is used to derive expressions for the probability distribution of the phase-space boundary coordinates after transport along uncertain, and in general curved, ray trajectories. Furthermore, models are presented for incorporating geometric uncertainties in terms of both the location of an edge within a polygonal domain, as well as small scale geometric fluctuations giving rise to rough boundary reflections. Uncertain source terms are also considered in the form of stochastically distributed point sources and uncertain boundary data. A series of numerical experiments is then performed to illustrate these uncertainty models in two-dimensional convex polygonal domains

Geometric integration and thermostat methods for Hamiltonian systems

The research in this thesis is devoted to geometric numerical integration and thermostat methods for Hamiltonian ODEs and PDEs with applications in molecular dynamics and geophysical fluid dynamics

On the appearance of internal wave attractors due to an initial or parametrically excited disturbance

In this paper we solve two initial value problems for two-dimensional internal gravity waves. The waves are contained in a uniformly stratified, square-shaped domain whose sidewalls are tilted with respect to the direction of gravity. We consider several disturbances of the initial stream function field and solve both for its free evolution and for its evolution under parametric excitation. We do this by developing a structure-preserving numerical method for internal gravity waves in a two-dimensional stratified fluid domain. We recall the linearized, inviscid Euler–Boussinesq model, identify its Hamiltonian structure, and derive a staggered finite difference scheme that preserves this structure. For the discretized model, the initial condition can be projected onto normal modes whose dynamics is described by independent harmonic oscillators. This fact is used to explain the persistence of various classes of wave attractors in a freely evolving (i.e. unforced) flow. Under parametric forcing, the discrete dynamics can likewise be decoupled into Mathieu equations. The most unstable resonant modes dominate the solution, forming wave attractors

Transport of phase space densities through tetrahedral meshes using discrete flow mapping

Discrete flow mapping was recently introduced as an efficient ray based method determin- ing wave energy distributions in complex built up structures. Wave energy densities are transported along ray trajectories through polygonal mesh elements using a finite dimen- sional approximation of a ray transfer operator. In this way the method can be viewed as a smoothed ray tracing method defined over meshed surfaces. Many applications re- quire the resolution of wave energy distributions in three-dimensional domains, such as in room acoustics, underwater acoustics and for electromagnetic cavity problems. In this work we extend discrete flow mapping to three-dimensional domains by propagating wave energy densities through tetrahedral meshes. The geometric simplicity of the tetrahedral mesh elements is utilised to efficiently compute the ray transfer operator using a mixture of analytic and spectrally accurate numerical integration. The important issue of how to choose a suitable basis approximation in phase space whilst maintaining a reasonable computational cost is addressed via low order local approximations on tetrahedral faces in the position coordinate and high order orthogonal polynomial expansions in momentum space