Abstract. We present a multi-parameter family of rational solutions to the complex Korteweg-de Vries equations. This family of solutions includes particular cases with high-amplitude peaks at the centre, as well as a multitude of cases in which higher-order rogue waves are partially split into lower-order fundamental components. We present an empirically-found symmetry that introduces a parameter controlling the splitting of the rogue wave components into multi-peak solutions, and allows for nonsingular solutions at higher order.

Abstract. The Gardner equation is used as a generic model for internal waves and other phenomena. We find interesting structures revealed by rational solutions of this equation. We show the benefit of using the Hirota method to give simple forms, which are then used to generate the solutions. These forms are of lower order than the polynomials in the solutions themselves. Patterns and powers of these polynomials are discussed. A brief study of the poles of each solution elucidates the structure of various rogue wave solutions and allows us to gain understanding and insight regarding the features of such rogue waves. These solutions provided here have numerous applications in internal ocean waves and dusty-type plasmas.

Abstract. In this paper, we present a new approach for solving equations of motion for the dynamics of charged particles moving under the action of electromagnetic field along with additional influence of the Joule effect. A new type of solving procedure is implemented here for the equations of motion of the charged particle, determined by the Lorentz force, and additionally taking into account the Joule effect. Meanwhile, the system of equations of motion has been successfully explored with respect to the existence of an analytical way for the presentation of the solution. Last but not least, we obtain the solutions in a form of a spiral-type motion. As a main result of this study, the equations of motion are reduced to a system of two nonlinear ordinary differential equations of first order (with regard to time t) for two unknown functions: 1) w(t) (angular velocity of spiral rotation) and 2) ξ(t) (spiral factor of motion for a charged particle). Moreover, the approximated solutions have been also obtained under appropriate simplifying assumptions.

Abstract. In many physical problems, positivity is one of the most prevalent and imperative attribute of diverse mathematical models such as concentration of chemical reactions, population dynamics etc. However, the numerical discretization of dynamical systems that illustrate negative values may lead to meaningless solutions and sometimes to their divergence. The main objective of this work is to develop positivity preserving numerical schemes for the two-dimensional autocatalytic reaction diffusion Brusselator model. Two explicit finite difference (FD) schemes are proposed to solve numerically the two-dimensional Brusselator system. The proposed methods are the non-standard finite difference (NSFD) scheme and the unconditionally positivity preserving scheme. These numerical methods retain the positivity of the solution and the stability of the equilibrium point. Both proposed numerical schemes are compared with the forward Euler explicit FD scheme. The stability and consistency of all schemes are proved analytically and then verified by numerical simulations.

Abstract. Very often in an experiment the access to a measuring apparatus is very limited. We investigate a possible effective description of a quantum system, when an experimenter has access to an experimental apparatus described by a POVM, and has no information about the quantum system under study. A coarse graining CPTP map is introduced, that maps the state of the quantum system into a compressed effective state, from which one obtains the same measurement statistics.

Abstract. The configuration of a commercial TW-class femtosecond laser amplifier and measurement techniques used for laser pulse characterization are described. Designed laser modules and new laser system layout for upgrading this sub-TW femtosecond laser system to a multi-TW laser system are presented. A fourpass Ti:sapphire amplifier was designed to amplify the chirped pulses from 15 mJ up to 220 mJ energy. A vacuum compressor, with two-diffraction gratings, was designed for amplified pulses temporal compression. Considering 30 nm bandwidth input pulses with ideal Fourier transform limit (FTL) duration of 31.4 fs, 1.05 times FTL pulses can be obtained by the compensation of the chirped pulse amplifier phase dispersion in the compressor. Some experiments based on the upgraded multi-TW Ti:sapphire laser are proposed, such as spectral broadening for post-compression, laser induced damage threshold measurements using femtosecond pulses, and coherent combination of ultrashort pulses.

Abstract. A fiber-based plasmonic sensor with three layers is studied and the analytical method based on Bessel functions is applied to calculation of the loss, figure of merit, and amplitude and power sensitivities for the HE₁₂ mode in a resonant interaction with a TM₀₁ mode. In this method, the electromagnetic field is represented by a Bessel function J of the first kind in the core region (SiO₂), a linear combination of the Hankel functions H₁ and H₂ in the TiO₂/PSS (poly(styrene sulfonate)) region, and a modified Bessel function K of the second kind in the analyte region. The values of the effective indices calculated by using finite element method are in agreement with our analytical method. The results and subsequent analysis indicate that the full width at half maximum (FWHM) of the loss and maximum value of the loss P for HE₁₂ mode in resonant interaction with a TM₀₁ mode tend to decrease when the radius of the fiber core is increased. In addition, the shift δλ_res towards longer wavelengths of the maximum loss P for an increase Δn_a of the analyte refractive index by 0.001 RIU, the figure of merit FOM, and the maximum of the amplitude S_A and power S_P sensitivities increase with fiber core radius. In the angular integration method, the power loss PL and the corresponding angle θ are increasing when the thickness d₂ of the lossy layer and the refractive index n_a of the analyte layer are increased. Also, the power loss PL increases and the corresponding angle θ decreases when the wavelength λ is increased.

Abstract. An antireflection coating structure comprised of metal (copper) nanoparticles over silicon nitride has been numerically investigated. The structure is embedded between semi-infinite vacuum and silicon substrate and a TE plane polarized wave is incident on the proposed structure. The permittivity of all the involved materials in the proposed structure is wavelength dependent. Numerical results are presented to show the effects of the incidence angle, the wavelength, and the structure parameters on the reflection coefficient. The antireflection coating structure and the obtained results could be useful for design of future solar cells and optical sensors.

Abstract. In this study, we have demonstrated the efficiency improvement of a four-layer structure solar cell model based on conductive nanoparticle materials. New artificial conductive nanoparticles have been used to optimize the efficiency of solar cells and to overcome some limitations of the efficiency of conventional solar cells structures. The antireflection coating structure has been proposed where conductive nanoparticles (CNPs) film layer and TiO₂ layer are sandwiched between a glass cover layer and a silicon substrate. The transmittance and reflectance are derived and computed by using the transfer matrix method and are obtained numerically for different values of unit cell sizes and gap widths of the CNPs. The nanoparticles dimensions have been adjusted leading to approximately 100% light transmission and the current density to be about 80 mA/cm².

Abstract. We study families of optical solitons that form in three different types of nonlinear media with parity-time-symmetric mixed linear-nonlinear lattice potentials. The considered optical nonlinearities have the forms of Kerr law, quadratic-cubic law, and anti-cubic law. We obtain various types of exact soliton solutions with the help of the inverse engineering technique. Under diverse physical conditions, we give the explicit expressions for dark, bright, and singular soliton solutions.

Abstract. The theoretical investigation of propagation of few-cycle transverse acoustic solitons in a cubic paramagnetic crystal placed in an external magnetic field and in a field of static deformation is carried out. The self-consistent system of nonlinear equations for the spin variables and relative deformation of the acoustic pulse is derived. This system generalizes the system of the reduced Maxwell–Bloch equations, well-known in nonlinear optics, and occurs to be also integrable by the inverse scattering transformation method. The soliton and breather solutions of the obtained system are investigated in detail. It is revealed that the properties of the solitons and breathers depend on the ratio between the frequencies of the Zeeman and quadrupole Stark splittings of the effective spins of the paramagnet. If the Zeeman splitting exceeds the Stark one, then the short-living pulse of the deformation field, whose dynamics is similar to that of rogue waves, can be formed under the collision of two solitons having different polarities. In the opposite case, the soliton collision does not lead to the appearance of such pulse of the deformation field. Here, the duration of the soliton is limited from below by the minimal value at which the profile of relative deformation has a rectangular shape.

Abstract. Stress and strain always occur in the root canal dentin during endodontic instrumentation. Subsequently dentinal microcracks formation and propagation may be observed, with the potential of generating vertical root fractures. This study aims to a theoretical determination of the stress state by modeling these processes of dentinal stress development during straight root canals shaping using finite element analysis and ANSYS software.

Abstract. The treatment of chronic wounds is one of the main therapeutic and economic problems of contemporary medicine. Photobiomodulation (PBM) stands out among the contemporary methods of wound treatment. The photobiostimulation effects of 660 nm laser irradiance on chronic wound were investigated. Effects of low-level laser on cytokines concentrations in the serum were evaluated using immunosorbent assay kits. Histological studies conducted here showed that application of PBM therapy accelerates wound repair during early stages of healing. Application of PBM therapy facilitated the reduction of inflammation and faster wound healing.

Abstract. This paper provides activity concentrations of ⁴⁰K, ²³⁸U, ²²⁶Ra, ²³²Th, and ¹³⁷Cs in samples of cultivated soil, hay, cow milk, cheese, mushrooms, and mosses collected at Mt. Maljen, Serbia, during 2018 and 2019. The average contents of ⁴⁰K (435 ± 33 Bq/kg), ²³⁸U (42 ± 5 Bq/kg), ²²⁶Ra (42 ± 4 Bq/kg) and ²³²Th (47 ± 4 Bq/kg) in the soil are slightly higher than the global means. Radiation hazard index is less than one. ¹³⁷Cs is detected in soil (3.1 – 111 Bq/kg), hay (4.6 – 9.4 Bq/kg), cow milk (2.0 ± 0.2 Bq/kg), cheese (1.7 ± 0.2 Bq/kg), mushrooms (26 ± 2 Bq/kg), and mosses (21 ± 2 Bq/kg). Investigated dairy products are safe for consumption.

Abstract. Metals concentrations of Cr, Ni, Co, Cu, Zn, Cd, and Pb in nettle (Urtica dioica) and soil samples, collected in April 2019 from several villages around Targoviste City, were determined. The samples were collected in the springtime (April 2019) when it is considered that the plants have reached the maturity and because inhabitants pick nettles for their purposes or sell them in markets to other consumers as well. This study revealed that concentrations of Cr, Ni, Co, Cu, Zn, Cd, and Pb in soil samples collected in April 2019 were higher than the alert level established by Romanian legislation. In the same time, Cd and Pb contents were higher than maximum admitted levels (established by Romanian Order no. 975/1998) and the daily intake values for Cr, Co, Cu, Cd, and Pb were higher than reference doses (recommended by USEPA) in all analyzed samples. The obtained results can extend understanding of the human risks of heavy metals in soil and fresh leaves and stem of nettle regarding the consumption and medical purposes. Also, this study will provide insights into pollution levels, concerning human health risk.

Abstract. In circular (and elliptical) polarization the electric E and magnetic H fields rotate, i.e. are in motion at a constant rate in the appropriate plane as the electromagnetic (EM) wave propagates. In technical literature there is a dual approach to the rotation of the vector E for circularly polarized waves, depending on the position of an "observer's eye" in relation to the direction of the wave propagation. There are non-identical traditions and agreements regarding right-hand and left-hand polarization between specialists from different area of knowledge as well as the preferences of individual scientists. For example, in radar astronomy, the "observer's eye" is positioned against EM waves spreading from a wave source towards the "observer's eye". In optics the "observer's eye" may be located on the side of the wave source and sees the wave propagating away from the "observer's side". The contrast approach can be partly explained by differences in measurement techniques in separate areas of science. This ambiguity in the approach to the circular polarization definitions may also complicate the educational process. Here we analyse the definitions of terms related to the circularly polarized waves which are recommended for use in IEEE standards and definitions applying in scientific papers. It should be noted that usually approaches are correct, the problem arises only when the location of the observer's eye is not fixed in space.

Abstract. Given the spectacular technological developments in recent years, teaching high school physics should be tailored to generate the competencies required by nowadays labor market. In order to achieve the learning objectives of a modern high school physics lessons, chalk and board are no longer adequate alternatives. Effective teaching methods and strategies involve hands-on science activities, as well as integrated content implemented using today’s technological developments. The real physics experiments presented in this paper suggest a change in the way of teaching some physics lessons by using smartphone applications (Apps): teaching the light absorption (Beer-Lambert's law) and Color Detect using the Phyphox App (Physical Phone Experiment), as well as determining the acceleration in free fall circumstances by means of Phyphox App, too. This manner of tackling a physics lesson emphasizes the integrated content approach, as knowledge of physics, mathematics and computing is simultaneously needed in order to confront these experiments.