In the present paper, we are considering a spatially-flat Friedmann-Robertson-Walker cosmological model, fueled with stiff matter and dust, treated as non-interacting ideal fluid sources. By solving the corresponding Friedmann equation with a non-zero cosmological constant, we are deriving the scale function and the fundamental cosmological parameters. Within a thermodynamic approach, the general form of the Equation of State is obtained, together with the explicit dependence of the energy density and pressure on temperature.

The mixed Chen-Lee-Liu derivative nonlinear Schrödinger (CLL-NLS) equation can be considered as the simplest model to approximate the dynamics of weakly nonlinear and dispersive waves, taking into account the self-steepening effect (SSE). The latter effect arises as a higher-order correction of the nonlinear Schrödinger (NLS) equation, which is known to describe the dynamics of pulses in nonlinear fiber optics, and constitutes a fundamental part of the generalized NLS equation. Similar effects are described within the framework of the modified NLS equation, also referred to as the Dysthe equation, in hydrodynamics. In this work, we derive fundamental and higher-order solutions of the CLL-NLS equation by applying the Darboux transformation. Exact expressions of non-vanishing solitons at boundaries, breathers, and a hierarchy of rogue wave solutions are presented. In addition, we discuss the localization properties of such rogue waves, by characterizing their length and width. In particular, we describe how the localization properties of first-order NLS rogue waves can be modified by taking into account the SSE, presented in the CLL-NLS equation. This is illustrated by use of an analytical and a graphical method. The results may motivate similar analytical studies, extending the family of the reported rogue wave solutions as well as possible experiments in several nonlinear dispersive media, confirming these theoretical results.

The purpose of this study is to investigate a combination between the homotopy analysis method and finite differences for the numerical resolution of coupled two-dimensional Burgers’ equation. The performance of the proposed technique is successfully verified. The application shows very good agreement of the two convergence regions for absolute and relative errors. This fact is important in case the exact solution is unknown.

In this paper, a numerical method based on the hybrid of the quasi-linearization method (QLM) and the collocation method is suggested for solving well-known nonlinear Lane-Emden-type equations as singular initial value problems, which model many phenomena in mathematical physics and astrophysics. First, by using the QLM method, the nonlinear ordinary differential equation is converted into a sequence of linear differential equations, and then the linear equations by the fractional order of rational Bernoulli collocation (FRBC) method on the semi-infinite interval $[0, \infty)$ are solved. This method reduces the solution of these problems to the solution of a system of algebraic equations. Computational results of several problems are presented to demonstrate the viability and powerfulness of the method. Further, the fractional order of rational Bernoulli functions has also been used for the first time. The first zeros of standard Lane-Emden equation and the approximations of $y(x)$ for Lane-Emden-type equations are given with unprecedented accuracy.

In this paper, a new space-time spectral algorithm is constructed to solve the generalized Hirota-Satsuma coupled Korteweg-de Vries (GHS-C-KdV) system of time-fractional order. The present algorithm consists of applying the collocation-spectral method in conjunction with the operational matrix of fractional derivative for the double Jacobi polynomials, which will be employed as a basis function for the spectral solution. The main characteristic behind this approach is that such problems will reduce to those of solving algebraic systems of equations that greatly simplifying the problem. For ensuring the accuracy and efficiency of the presented algorithm, we apply it to find the approximate solutions of two specific problems, namely, a homogeneous form of the GHS-C-KdV system and a inhomogeneous GHS-C-KdV system.

The macroscopic quantum self-trapping (MQST) of two-component Bose-Einstein condensates (BECs) with two- and three-body interactions is studied. For the undamped case, a high modulating frequency causes a monotonic increase in the number of localized atoms in one well. Decreasing the modulating frequency changes this monotonic increasing trend and lead to an oscillating appearance of MQST in the two wells. But a weak damping changes this oscillating behavior and keep the MQST in one well after a transient process. The parametric resonance is also observed in the time-evolution of the population imbalance.

Analytic expression for the nonsequential transition rate in a linearly polarized laser field has been found, based on the adiabatic Landau-Dykhne approach. The formula involves electron-electron correlation through the mechanism of collective tunneling. The formula fails for a “knee” structure, but improves agreement with experimental results in the range of higher laser field intensities. A brief discussion on the dependence of the nonsequential transition rate on the laser pulse shape and wavelength was made.

In standard optical fibers, combined effects of dispersion and nonlinearity can generate critical effects of localization of energy, which are potentially harmful for the transmission of data. Using the nonlinear Schrödinger equation as the universal transmission model, we establish the existence of ultrashort light pulses, in the form of breathers on top of the continuous-wave (CW) background, and of structural discontinuities (SDCs), in the form of jumps of the breathers’ phase and group velocities (i.e., the SDC is a variety of an optical shock). We produce exact analytical solutions, which demonstrate that, passing the SDC point, the breathers are converted into rogue waves (RWs), which is a potentially penalizing nonlinear effect in optical telecommunications. On the other hand, numerical simulations demonstrate that the modulational instability of the underlying CW effectively replaces the abrupt transition by a smooth one, and makes the breathers and RWs strongly unstable close to the SDC point. This dynamical scenario, which may be effectively controlled by a frequency shift of the optical signal from the CW background, opens a way to mitigate the strong nonlinear effects. On the other hand, we also consider possibilities to stabilize the RWs, for their possible use in other settings.

Based on the dipole response of neutron-rich nuclear systems obtained within a transport model which relies on two coupled Vlasov equations for protons and neutrons, respectively, we determine the contribution to polarizability of the pygmy dipole mode. We employ two different density parameterizations of the symmetry energy and investigate the effect of isospin and mass on the pygmy contribution to polarizability.

Previously [1] it was shown that for a configuration of two protons and two neutrons in the $g_{9/2}$ shell, there is a certain degeneracy that occurs when the quadrupole–quadrupole ($QQ$) interaction is used to obtain wave functions. We here show three other examples of such degenerate $T = 0$, $T = 2$ pairs. More importantly, we note a peculiarity of the $T = 0$ partner in the original example $(g_{9/2}$ , $J = 4$, $T = 0)$. Also we point out that degeneracies can be confusing and steps can be taken to remove them.

Starting from the $\Lambda^{0}_{b} \to p^+ K^− \gamma$ decay, we study the $\Lambda^{0}_{b} \to \Lambda^* (p^+ K^−) \gamma$ decay, with the intermediary resonances being treated in the helicity formalism. A specific algorithm is presented which transforms a sample of events generated for the $S$-wave decay $\Lambda^{0}_{b} \to p^+ K^− \gamma$ by adding twelve intermediary resonances $\Lambda^{*} \to p^+ K^−$ . This information is introduced using weights depending on the mass hypothesis and spin configuration of each resonance. The method allows fast Monte Carlo (MC) sample generation for efficiency and systematic uncertainties determination in future LHCb measurements involving $b$-hadron radiative decays. MC samples are produced for head-on proton-proton collisions at 8 TeV using PYTHIA 8.1 in the default and a LHCb specific configuration. The kinematics of the $\Lambda_{b}^{0}$ decay in the presence of a complex resonance structure is investigated.

The Ca₂Fe_1-xNi_xMoO₆ perovskites with $x \le 0.2$ crystallize in a monoclinic P2₁/n-type structure. The lattice parameters increase parallelly with the nickel content. The perovskites are ferrimagnetically ordered, the saturation magnetization decreasing as result of nickel substitution. The reciprocal susceptibilities show non-linear temperature dependences. Assuming a two sublattices model, the distribution of ions, their valence states as well as the exchange interactions parameters between and inside magnetic sublattices were determined. These values are discussed in correlation with perovskite compositions.

Thin ZnS_xSe_1-x films on glass substrates have been obtained by thermal evaporation. Electrodes from In or other materials have been deposited on thin films, and the temperature dependence of electrical conductivity was investigated during a series of successive cycles of heating and cooling performed at a rate of 6 K/min in a temperature interval from 300 K to 500 K. The measurements demonstrated that the energy of thermal activation at low temperatures (∆E₂ = 0.13–0.43 eV) is much lower as compared to that measured at high temperatures (∆E₁ = 0.43–1.89 eV). It was found that in both ranges of low and high temperatures the thermal activation energy increases with increasing the sulfur content in thin films. It was demonstrated that at low temperatures the dominant mechanism of electrical conduction is of Mott-type.

Treatment the sewage sludge is a major problem in preserving a clean environment. In this study we develop a model that allows the prediction of the net power consumption at the stirring of sludge proceeding from wastewater treatment. Its novelty consists in describing the mixing power not only as a function of Reynolds number and some geometrical dimensions ratios but also as a function on the fluid’s consistency, expressed as the dry matter fraction in the sludge.

11-days old plantlets developed from barley seeds exposed to homogenous 50 Hz magnetic field (1 ÷ 5 mT) for 22 hours, showed decreased level of chlorophyll a while the content of chlorophyll b was significantly increased with enhanced magnetic energy doses. The nucleic acids levels were increased in comparison to the control.

This work proposed marker associations for the differentiation of some organic vegetable types (salads, tomatoes, potatoes, cabbages, garlic and leek) from vegetables obtained through conventional agricultural practices. For this purpose, a number of 30 organic and 15 conventional vegetables samples were analyzed from isotopic and elemental point of view. Thus, the best differentiation markers, for these two categories, were found for each vegetable type. Another aim of this study was the differentiation of vegetables grown in greenhouses from those produced in field. For this purpose, the best differentiation elements prove to be: δ¹³C, Ni, Mo, Cd and Pb.

The scope of this paper is to put a case for lithological mapping of the limestone used in the Neolithic architecture of Malta to establish, through a comparative analysis, the provenance of the building fabric utilised in the erection of such monumental buildings. In this study, rock samples from the same lithology were assessed through destructive and non-destructive physico-mechanical, textural, chemical and mineralogical analytical techniques, to determine the principal characteristics of the limestone.

Pigments used in 1853 by famous Romanian painter Gh. Tattarescu for oil mural painting and icons-iconostasis of Church St. Constantine and Helena located in Măgurele, Ilfov County analyzed using a portable X-Ray Fluorescence spectrometer are discussed. The chemical element predominant in all spectra for the red areas is mercury suggesting the pigment is cinnabar (HgS - mercury sulfide). In pink areas we detected Hg together with Pb, which means cinnabar was mixed with lead white – (PbCO₃)₂$\cdot$Pb(OH)₂. Yellow pigment was made from a mixture of chrome-yellow (PbCrO₄) and ochre (Fe based yellow ochre – Fe₂O₃$\cdot$H₂O, – hydrated iron oxide). In a blue area (an iron-based pigment – very probably Prussian blue – Fe₇(CN)₁₈$\cdot$H₂O) we detected the presence of zinc suggesting a late repainting with zinc white (ZnO) on the original lead white layer.