Abstract. We present the computation of the elementary solutions of the Dirac equation, in the sense of Hadamard, and the subsequent evaluation of the vacuum polarization, worked out by Titeica, in four papers, published in the early forties of the previous century. Even if the quantum electrodynamics has chosen, about ten years later, a different evolution, Titeica's papers, which produced results confirmed by subsequent researches, remain valuable and interesting, from a historical perspective.

Abstract. Brans-Dicke theory in its original form can explain the radiation and matter dominated eras with a constant Brans-Dicke scalar field and the explanation of dark energy requires a nonvanishing potential term for the scalar field in the action. Within the framework of Jordan-Brans-Dicke theory where we take the scalar field as the Jordan field with a standard kinetic term and no mass term, we find the same radiation dominated solution as given by Einstein cosmology. On the other hand, by adding a mass term for the scalar field to the action, the radiation dominated solution is modified. We make an expansion in increasing powers of the scale size. This is valid for small scale sizes. We show that this expansion describing the early radiation dominated era also gives the late time dark energy dominated era in the Friedmann equation.

Abstract. We revisit the geodesic equations for both special and general relativity from the perspective of the field equations for a fermion field. Complete agreement with the known results is obtained. As an application of this method we compute the electromagnetic potentials created by a point like charge in the Minkowski space. The method can have applications in studying the electromagnetic potentials or other dynamical issues associated to a point like particle charged or not in both special or general relativity.

Abstract. We describe the quantum steering in a Gaussian system, consisting of two bosonic modes, each one being placed in its own thermal bath. The study is given in the framework of the theory of open systems based on completely positive quantum dynamical semigroups. The evolution of the system is given in terms of the covariance matrix formalism, using the Kossakowski-Lindblad master equation. We determine the time evolution of quantum steering in terms of the temperatures and dissipation coefficients of the thermal baths, frequencies of the modes, average thermal photon numbers and squeezing parameter of the modes. We also compare the dynamics of quantum steering with the time evolution of quantum entanglement in the considered system.

Abstract. To date, water waves are actively studied. On a (2+1)-dimensional generalized variable-coefficient Boiti-Leon-Pempinelli system for water waves, our scaling transformations and symbolic computation bring about a set of the heteroB¨acklund transformations, while our symbolic computation results in a set of the similarity reductions, with respect to the horizontal velocity and elevation of the water wave, relying on the variable coefficients.

Abstract. This work is devoted to find the reliable numerical solution of an epidemic model with constant vaccination strategy. For this purpose, a structure preserving numerical scheme called the Grünwald-Letnikov nonstandard finite difference scheme is designed. The proposed technique retains all the important properties of the continuous epidemic model like boundedness, positivity, and stability. This behavior of the proposed numerical scheme is validated mathematically and graphically. The role of the vaccination in controlling the disease dynamics in the population is verified through numerical simulations. The stability of the system under discussion is also examined at the disease free equilibrium point and the endemic equilibrium point. Finally, the outcome of this study is furnished with concluding remarks and future directions of research.

Abstract. Duffing systems are a pattern for illustrating various physical processes and dynamical systems. These systems can be accurately modeled by fractionalorder equations. In this paper, we present a numerical method to examine the behavior of fractionally damped Duffing equation via hybrid functions. We accomplish numerical simulations to demonstrate the efficiency and reliability of this technique. The obtained results show that the method provides a fast convergence and it has a good computational accuracy.

Abstract. The Susceptible-Infected-Recovered (SIR) epidemic model is extensively used for the study of the spread of infectious diseases. Even that the exact solution of the model can be obtained in an exact parametric form, in order to perform the comparison with the epidemiological data a simple but highly accurate representation of the time evolution of the SIR compartments would be very useful. In the present paper we obtain a series representation of the solution of the SIR model by using the Laplace-Adomian Decomposition Method to solve the basic evolution equation of the model. The solutions are expressed in the form of infinite series. The series representations of the time evolution of the SIR compartments are compared with the exact numerical solutions of the model. We find that there is a good agreement between the Laplace-Adomian semianalytical solutions containing only three terms, and the numerical results.

Abstract. In this paper we study the randomized heat equation with homogeneous boundary conditions. The diffusion coefficient is assumed to be a random variable and the initial condition is treated as a stochastic process. The solution of this randomized partial differential equation problem is a stochastic process, which is given by a random series obtained via the classical method of separation of variables. Any stochastic process is determined by its finite-dimensional joint distributions. In this paper, the goal is to obtain approximations to the probability density function of the solution (the first finite-dimensional distributions) under mild conditions. Since the solution is expressed as a random series, we perform approximations to its probability density function. Several illustrative examples are shown.

Abstract. We develop a semi-implicit Euler-Maruyama method to study stochastic oscillators systems with multiplicative additive noises. Two test problems including the stochastic Langevin oscillator equation with two additive noises and the coupled Van der Pol oscillator with additive noise have been used to examine the reliability and efficiency of the numerical approach.

Abstract. A survey of some recent theoretical and experimental studies on localized structures that form and propagate in a broad class of optical and matter-wave media is presented. The article is structured as a resource paper that overviews a large series of theoretical and experimental works in diverse physical contexts: linear and nonlinear light bullets, two- and three-dimensional solitons propagating in carbon nanotubes, ultrashort few-cycle optical pulses, localized structures that form in fractional systems, rogue waves in scalar, vectorial, and multidimensional nonlinear systems, and solitons and vortices in matter-wave media.

Abstract. In this paper, we study the propagation of ultrashort optical pulses in superlattice with defects, placed in a photonic crystal. The dependence of the pulse transmission coefficient both on the parameters of the defect (depth and size) and on the parameters of the photonic crystal (depth and modulation period of the refractive index) is analyzed.

Abstract. We propose a method to control the rotational temperature of a molecular beam exposed to intense femtosecond pump pulses. In practice, we solve the Schrödinger equation, obtain the molecular wave function, calculate the rotational energy and extract the corresponding rotational temperature. This paper investigates the role of peak intensity, pulse duration and pulse separation on increase of the rotational temperature, both in the classical and in the quantum approaches. The method enables us to control the dynamics of the rotational energy, calculate the increase of temperature accordingly, and draw limiting conditions in which the classical approach prevails.

Abstract. The paper presents a toy model of phase transition in an anharmonic solid. The starting point of our study is a 2D or 3D rectangular lattice of on-site quantum quartic oscillators, interacting with their nearest neighbors by elastic forces. The critical equation of the order-disorder transition is obtained using the theory of dielectric susceptibility. To obtain a mathematically tractable model, the quartic potential - a symmetric, two well potential - is replaced by a similar, but more workable one - a rectangular symmetric two well potential. For energies and wave functions corresponding to the lowest states, we obtain accurate analytical approximations, which lead to a simple critical equation. It gives the critical temperature as a function of the ”anharmonicity” of potential. Similar toy models can be obtained using other workable, two well potentials. Applications in nanophysics are briefly discussed.

Abstract. Our work contributes to a better understanding of interfacial processes that lead to Ag and Au metal nanoparticle dissolution by repetitive oxidative steps. According to literature studies, the adsorption of an electron donor (nucleophile) such as I^- to a metal nanoparticle raises the Fermi energy of the electrons, and consequently, an electron is transferred from the nanoparticle to an electrophilic species such as O₂. As a result, a metal cation is formed at the surface of the nanoparticle and subsequently dissolved into the solution; such repetitive processes lead to the complete dissolution of the nanoparticle. In this study, we show a remarkably simple method to increase the chemisorption rate of I^- by generating additional adsorption active sites via Mg²⁺ adsorbed ions (adions) and consequently increasing the dissolution rate of metallic Ag nanoparticles (AgNPs). Thus, an increase of the dissolution rate by 57% was estimated when supplementing the Ag colloidal solution with I^- and Mg²⁺, compared to the case when adding only I^-. In addition, the significant increase in the chemisorption rate of I^-, mediated by Mg²⁺ adions, leads to a 16% faster decrease in AgNPs radius, due to their dissolution, as probed by UV-Vis spectroscopy and by surface-enhanced Raman scattering (SERS). Further, electron density increase in single Au nanoparticles (AuNPs) due to partial charge transfer from chemisorbed I^- ions, and subsequent AuNP dissolution, were tracked through single particle dark-field scattering.

Abstract. The paper aims to obtain and study two types of magnetorheological materials based on silicone rubber obtained by adding different magnetic materials as well as checking their thermal stability in the presence and in the absence of a magnetic field. The influence of magnetic field on the thermal stability is studied by thermoanalytical techniques: TG/DTG/HF and spectroscopic techniques FTIR-UATR. Thermal degradation of materials is also analyzed using the non-isothermal kinetic methods proposed by Friedman, Flynn-Wall-Ozawa, Kissinger-Akahira-Sunose and also by modified nonparametric kinetic (NPK) methods.

Abstract. Zn-doped CeO₂ nanoparticles were synthesized via co-precipitation route. The as-prepared nanoparticles were investigated through X-ray diffraction, HRTEM, FESEM, EDX, UV-vis, FTIR, photoluminescence, and photocatalytic measurements. Spherical shaped particle size was calculated (∼ 7 - 10 nm). FESEM picture depicts the surface morphology of samples. The optical band gap was red-shifted due to Zn-doping. Zn (2 wt[%]) doped CeO₂ nanoparticles shown better optical transmittance. The EDX and FTIR results ensured the presence of dopant. Photoluminescence results revealed the intensity of red-band emission was suppressed due to Zn-incorporation. Photocatalytic absorbance behavior was enhanced when Zn substituted in CeO₂ lattice.

Abstract. The techniques involved in designing a simple and transferable semi-empirical potential for numerical simulations of Li, Na, and K metals and alloys with a minimal fitting have been put forward. The embedded-atom method provides the most reliable and efficient semi-empirical atomic potentials used for various simulations. Here, this method is employed to study and theoretically reproduce some physical properties of materials, which are also gotten from the experiment and the ab initio calculations. To validate the suitability of this model, we optimally computed and reproduced the monovacancy formation energy and the elastic stiffness of these metals that comparably agree with the data from experiments. Additional properties like low index surface energies that were not used during fittings were computed. The obtained values reasonably agree with the data both from experiment and first principles. The little differences may be due to the inability to adequately determine the experimental values using Tyson’s estimation. Lastly, the six possible binary alloys of these metals were studied. Only two experimental sets of data are available at the moment for Na^HK^G and K^HNa^G, and our computed values are consistent with these data. Thus for a better and complete comparison, new experimental data are needed for other alloys.

Abstract. This paper discusses the use of ground magnetometer data to seismogenic zones and presents the relationship between anomalous geomagnetic variations and the occurrence of the intermediate-depth earthquakes. The present paper highlights the geomagnetic anomalies recorded at Muntele Rosu Seismological Observatory (MLR), between 2008 and 2013. To distinguish the global magnetic variations from possible seismo-electromagnetic anomalies presented in a seismic area like Vrancea zone, the data recorded on MLR were analyzed comparatively with the data recorded by the Surlari National Geomagnetic Observatory (SUA) which is located outside the Vrancea zone (150 km South-Est to Vrancea zone). Also, the geomagnetic indices taken from NOAA/Space Weather Prediction Center were plotted in order to separate these global variations caused by solar-terrestrial interaction. To highlight the relation between the geomagnetic anomalies and seismic activity of Vrancea zone, daily energy release, and total energy release calculations for each anomaly were performed.

Abstract. We present the study of the earthquakes sequence from 25 June to 6 July 2020 occurred in the western South Carpathians. The main shock had I_o = V^o MSK, M_w = 4.1, occurred at h = 16 km, was preceded by a foreshock (M_w = 3.2) and has 16 after-shocks (M_w = 1.6-4.1) concentrated in the depth range 14-21 km. The focal mechanisms are characterized by strike-slip faults and P axes oriented N76^oE. The causative fault is dextral strike-slip oriented NE-SW, known as Cerna–Jiu Fault. The macroseismic data partially match the intensities attenuation and conversion accelerationintensity relationships.

Abstract. The paper suggests an interdisciplinary laboratory, which can be used by the students in their experimental studies from the physics classes. For this purpose, the capacity of a natural absorbent to remove hydrocarbons from waters is analyzed by different methods. This absorbent based on Sphagnum moss is a biodegradable material with the main utility in environmental protection. The study of biodegradable materials can be performed by students with relatively simple tools, helping them to understand basic physical and chemical principles through experimentation.

Abstract. In this paper, we present an alternative experiment for measuring the speed of sound in air by finding the frequency and the wavelength of the stationary sound waves formed in a closed-end tube. The experiment involved both video and sound recording, the files were afterward analyzed by using two free and open-source computer software, namely Audacity and Kdenlive. The research described herein is intended for the students interested in emphasizing the learning of physics by inquirybased experiment, yet represents a viable alternative for developing long-distance studies.