



Volume 73, Number 2, 2021 




THEORETICAL, MATHEMATICAL, AND COMPUTATIONAL PHYSICS 






A short presentation of Titeica’s papers on positron theory
S. MARCULESCU
Rom. Rep. Phys. 73, 107 (2021)
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. 




Corrections to standard radiation dominated universe in JordanBransDicke cosmology
M. ARIK, L. AMON SUSAM
Rom. Rep. Phys. 73, 108 (2021)
Abstract. BransDicke theory in its original form can explain the
radiation and matter dominated eras with a constant BransDicke scalar field and the explanation of dark energy requires
a nonvanishing potential term for the scalar field in the action. Within the framework of JordanBransDicke 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. 




Geodesics and electromagnetic potentials associated to a point like particle revisited
RENATA JORA
Rom. Rep. Phys. 73, 109 (2021)
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. 




Quantum steering of two bosonic modes in the tworeservoir model
MARINA CUZMINSCHI, AURELIAN ISAR
Rom. Rep. Phys. 73, 110 (2021)
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 KossakowskiLindblad 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. 




Scaling transformation, heteroBacklund transformation and similarity reduction on a (2+1)dimensional generalized variablecoefficient BoitiLeonPempinelli system for water waves
XINYI GAO, YONGJIANG GUO, WENRUI SHAN
Rom. Rep. Phys. 73, 111 (2021)
Abstract. To date, water waves are actively studied. On a (2+1)dimensional
generalized variablecoefﬁcient BoitiLeonPempinelli 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. 




Mathematical and numerical investigations of the fractionalorder epidemic model with constant vaccination strategy
ZAFAR IQBAL, MUHAMMAD AZIZ UR REHMAN, DUMITRU BALEANU, NAUMAN AHMED, ALI RAZA, MUHAMMAD RAFIQ
Rom. Rep. Phys. 73, 112 (2021)
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
GrünwaldLetnikov 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. 




Numerical behavior of nonlinear Duffing equations with fractional damping
L. TORKZADEH
Rom. Rep. Phys. 73, 113 (2021)
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. 




A simple computational approach to the susceptibleinfectedrecovered (SIR) epidemic model via the LaplaceAdomian decomposition method
TIBERIU HARKO, MAN KWONG MAK
Rom. Rep. Phys. 73, 114 (2021)
Abstract. The SusceptibleInfectedRecovered (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 LaplaceAdomian 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 LaplaceAdomian semianalytical solutions
containing only three terms, and the numerical results. 




Analysis of the random heat equation via approximate density functions
JULIA CALATAYUD, JUAN CARLOS CORTES
Rom. Rep. Phys. 73, 115 (2021)
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 ﬁnitedimensional
joint distributions. In this paper, the goal is to obtain approximations to the probability density function of the solution
(the ﬁrst ﬁnitedimensional 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. 




The semiimplicit approach for stochastic oscillators systems with multiplicative additive noises
K. NOURI
Rom. Rep. Phys. 73, 116 (2021)
Abstract. We develop a semiimplicit EulerMaruyama 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. 

OPTICS AND PHOTONICS, PLASMAS, LASER AND BEAM PHYSICS 






Localized structures in optical and matterwave media: a selection of recent studies
D. MIHALACHE
Rom. Rep. Phys. 73, 403 (2021)
Abstract. A survey of some recent theoretical and experimental studies on
localized structures that form and propagate in a broad class of optical and matterwave 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 threedimensional solitons propagating in carbon nanotubes, ultrashort fewcycle optical pulses,
localized structures that form in fractional systems, rogue waves in scalar, vectorial, and multidimensional nonlinear systems, and
solitons and vortices in matterwave media. 




Ultrashort optical pulses in photonic crystal with superlattice and defects
Y.V. DVUZHILOVA, I.S. DVUZHILOV, N.N. KONOBEEVA, M.B. BELONENKO
Rom. Rep. Phys. 73, 404 (2021)
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. 




Controlling rotational temperature of molecular beam by using terawatt femtosecond pump pulse
ABDURROUF
Rom. Rep. Phys. 73, 405 (2021)
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. 

CONDENSED AND SOFT MATTER PHYSICS 






Critical behavior of an anharmonic nanoscopic solid
VICTOR BARSAN
Rom. Rep. Phys. 73, 501 (2021)
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 onsite quantum quartic oscillators,
interacting with their nearest neighbors by elastic forces. The critical equation of the orderdisorder 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. 




Tuning the potential of nanoelectrodes to maximum: Ag and Au nanoparticles dissolution by I^{} adsorption via Mg^{2+} adions
ANDREI STEFANCU, STEFANIA D. IANCU, VASILE COMAN, LOREDANA F. LEOPOLD, NICOLAE LEOPOLD
Rom. Rep. Phys. 73, 502 (2021)
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 O_{2}.
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 Mg^{2+} 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 Mg^{2+},
compared to the case when adding only I^{}. In addition, the significant increase in the chemisorption rate of I^{},
mediated by Mg^{2+} adions, leads to a 16% faster decrease in AgNPs radius, due to their dissolution, as probed by
UVVis spectroscopy and by surfaceenhanced 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 darkfield scattering. 




Study of thermal stability of some magnetorheological elastomers
M. BUNOIU, G. VLASE, I. BICA, M. BALASOIU, G. PASCU, T. VLASE
Rom. Rep. Phys. 73, 503 (2021)
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 FTIRUATR. Thermal degradation of materials is also analyzed
using the nonisothermal kinetic methods proposed by Friedman, FlynnWallOzawa, KissingerAkahiraSunose and also by modified
nonparametric kinetic (NPK) methods. 




Structural, morphological and optical behavior of Zn^{2+}:CeO_{2} nanoparticles annealed under Ar atmosphere
K. RAJESH, P. SAKTHIVEL, A. SANTHANAM, J. VENUGOBAL
Rom. Rep. Phys. 73, 504 (2021)
Abstract. Zndoped CeO_{2} nanoparticles were synthesized via coprecipitation
route. The asprepared nanoparticles were investigated through Xray diffraction, HRTEM, FESEM, EDX, UVvis, 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 redshifted due to Zndoping. Zn (2 wt[%]) doped CeO_{2} nanoparticles shown better
optical transmittance. The EDX and FTIR results ensured the presence of dopant. Photoluminescence results revealed the intensity of
redband emission was suppressed due to Znincorporation. Photocatalytic absorbance behavior was enhanced when Zn substituted in
CeO_{2} lattice. 




A simplified semiempirical potential for simulations of Li, Na, and K metals and binary alloys
GBENGA S. AGUNBIADE, TAIWO H. AKANDE, FADEKE MATTHEWOJELABI
Rom. Rep. Phys. 73, 505 (2021)
Abstract. The techniques involved in designing a simple and transferable
semiempirical potential for numerical simulations of Li, Na, and K metals and alloys with a minimal fitting have been put forward.
The embeddedatom method provides the most reliable and efficient semiempirical 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^{H}K^{G} and K^{H}Na^{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. 

ENVIRONMENTAL AND EARTH PHYSICS 






The geomagnetic field variations recorded in Vrancea zone during 20082013 and the seismic energy release
A. MIHAI, I.A. MOLDOVAN, V.E TOADER, M. RADULIAN
Rom. Rep. Phys. 73, 705 (2021)
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
intermediatedepth 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 seismoelectromagnetic
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 SouthEst 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 solarterrestrial 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. 




The analysis of earthquakes sequence generated in the Southern Carpathians, Orsova JuneJuly 2020 (Romania): seismotectonic implications
E. OROS, A. O. PLACINTA, I. A. MOLDOVAN
Rom. Rep. Phys. 73, 706 (2021)
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 aftershocks (M_{w} =
1.64.1) concentrated in the depth range 1421 km. The focal mechanisms are characterized by strikeslip faults and P axes oriented
N76^{o}E. The causative fault is dextral strikeslip oriented NESW, known as Cerna–Jiu Fault. The macroseismic data partially
match the intensities attenuation and conversion accelerationintensity relationships. 

PHYSICS EDUCATION 






Experimental study of biodegradable materials in environmental physics classes
S. VOINEA, C. NICHITA, I. ARMEANU, B. SOLOMONEA
Rom. Rep. Phys. 73, 903 (2021)
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. 




Acoustic resonators  a method for online study in determining the speed of sound in air
FABIOLA SANDA CHIRIACESCU, B. CHIRIACESCU, CRISTINA MIRON, C. BERLIC, V. BARNA
Rom. Rep. Phys. 73, 904 (2021)
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 closedend tube.
The experiment involved both video and sound recording, the files were afterward analyzed by using two free and opensource 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 longdistance studies. 





This is an electronic version of Volume 73 Number 2 2021




