We study the nonlinear Schrödinger equation with a $\mathcal{PT}$-symmetric potential. Using a hydrodynamic formulation and connecting the phase gradient to the field amplitude, allows for a reduction of the model to a Duffing or a generalized Duffing equation. This way, we can obtain exact soliton solutions existing in the presence of suitable $\mathcal{PT}$ symmetric potentials, and study their stability and dynamics. We report interesting new features, including oscillatory instabilities of solitons and (nonlinear) $\mathcal{PT}$-symmetry breaking transitions, for focusing and defocusing nonlinearities.

The link between the perturbed defocusing nonlinear Schrödinger (NLS) equation and the perturbed Korteweg-de Vries (KdV) equation is established using a multiple scales expansion method. Unlike previous studies, we use the idea of a background function, and a simple change in the independent variables, to transform the perturbed NLS in a way such that multiple scales can be directly applied. Different perturbations are examined to include any possible case for the background function.

We show through detailed numerical investigations and supporting variational results that the ground state of a cigar-shaped Bose-Einstein condensate with a Gaussian-shaped radially inhomogeneous scattering length has a density profile akin to that of a coaxial cable. Monitoring the transition from homogeneous to inhomogeneous scattering lengths, we show numerically the formation of a local minimum in the density profile of the ground state positioned where the scattering length reaches its maximum.

The spin precession of a Dirac particle in monotonically increasingly boosted coordinates is calculated using torsion gravity (teleparallel theory of gravity). Also, we find the vector and the axial-vector parts of the torsion tensor.

The purpose of the present work is to obtain new analytical solutions to the relativistically corrected Kompaneets equation describing the photon spectrum in magnetar's magnetosphere. In the assumption of stationarity, the solutions, expressed in terms of Heun Triconfluent functions, can be employed to compute the photons density as a function of the dimensionless frequency.

Evaluation of exact analytical solution for flow to a well, under the assumptions made in its development commonly requires large amounts of computation time and can produce inaccurate results for selected combinations of parameters. Large computation times occur because the solution involves the infinite series. Each term of the series requires evaluation of exponentials and Bessel functions, and the series itself is sometimes slowly convergent. Inaccuracies can result from lack of computer precision or from the use of improper methods of numerical computation. This paper presents a computationally efficient and an accurate new methodology in differential quadrature analysis of diffusivity equation to overcome these difficulties. The methodology would overcome the difficulties in boundary conditions implementations of second order partial differential equations encountered in such problems. The weighting coefficients employed are not exclusive, and any accurate and efficient method such as the generalized differential quadrature method may be used to produce the method’s weighting coefficients. By solving finite and infinite boundary condition in diffusivity equation and by comparing the results with those of existing solutions and/or those of other methodologies, accuracy, convergences, reduction of computation time, and efficiency of the methodology are asserted.

A semi-analytical solution based on a Jacobi-Gauss-Lobatto collocation (J-GLC) method is proposed and developed for the numerical solution of the spatial variable for two nonlinear coupled Klein-Gordon (KG) partial differential equations. The general Jacobi-Gauss-Lobatto points are used as collocation nodes in this approach. The main characteristic behind the J-GL-C approach is that it reduces such problems to solve a system of ordinary differential equations (SODEs) in time. This system is solved by diagonally-implicit Runge-Kutta-Nyström scheme. Numerical results show that the proposed algorithm is efficient, accurate, and compare favorably with the analytical solutions.

The determination of the physical and mechanical properties or mineralogical composition of mortars from heritage buildings is often difficult to realize because the possibility of extracting samples is reduced, being necessary a large number collected from different area of structural and nonstructural elements (piers, walls, etc.). This study analyzes a few mortar samples taken from an existing building and compared with a Portland cement mortar made in laboratory. It was used thin sections analysis as destructive investigation method and X-ray diffractions as non-destructive analytical technique in order to compare the mineralogical content of the investigated mortars.

The present paper gives a short description of the deterministic Point-by-Point model of prompt emission in fission. The model can provide almost all quantities characterizing the fission fragments and the prompt neutron and gamma rays emission. During the time, the Point-by-Point model was successfully applied to many spontaneous and neutron induced fissioning systems as ²⁵²Cf(SF), ^236-244Pu(SF), ^244,248Cm(SF), ^{233,234,235,236,238}U(n,f), ²³⁹Pu(n,f), ²³⁷Np(n,f), ^231-233Pa(n,f), ²³²Th(n,f), being validated by the excellent description of all existing experimental data.

A proton exchange membrane fuel cell, also known as polymer electrolyte membrane fuel cell (PEMFC), becomes in the last decade a prime candidate for applications in power systems, submarines and aerospace. The single-cell PEMFC consists of a carbon plate, a gas diffusion layer (GDL), a catalyst layer for each of the anode and the cathode sides, as well as a PEM membrane at the center. This model of the fuel cell, created from Electrochemistry Module of Comsol Multiphysics software package uses current balances, mass transport equations (Maxwell-Stefan diffusion for reactants, water and nitrogen gas) and momentum transport (Darcy’s law for the gas flows) to simulate a PEM fuel cell’s behavior. Darcy’s velocity field at GDL channels, water diffusive flux, current density distributions at anode catalyst electrode and membrane electrolyte potential distribution across the length of the cell for three models of PEM cell models (different from the point of view of membrane width) were computed in order to investigate the cell model performance.

A brief up-to-date survey of recent theoretical and experimental studies of the formation, stability and robustness of multidimensional localized structures in optics and Bose-Einstein condensate in a variety of physical settings is given.

The form in which the interpolated function given by the sampling theorem is generally used is a truncated version, due to the impossibility of taking in the infinite number of terms. However, in this paper we challenge this habit by introducing new functions, with a finite number of terms, some better approximating the original function and all having a circular character, necessary in Fourier computation for which the sampling theorem is mostly used. We use both integer and semi-integer sampling for generality. We also study both the cases of even and odd number of samples. We had in mind at all times the 2D sampling theorem for optics applications. However, for simplicity we worked in 1D. The generalization to 2D is straightforward.

One-dimensional extended fluid model of DC glow discharge in argon at low pressure is applied without and with Ar (³P₂) metastable state. The profiles of particle number densities, mean electron energy, potential and ionization source in the stationary state of glow discharge for 300V and 500V are presented.

Within present study we perform a computational analysis of the surface properties of the EF-hand calcium binding proteins (EFCaBPs), both at global and local levels. Among EFCaBPs there are calcium sensors involved in signal transduction processes and exhibiting extended spatial structures and calcium buffering proteins exhibiting compact structures. Structures superposition reflects higher structural similarity between extended forms, the compact ones being more divergent in good correlation with their sequence alignment. Surfaces of extended EFCaBPs present a smaller number of cavities but with larger volumes and areas than compact ones in correlation with their known biological functions. Surface electrostatic potential is higher for extended EFCaBPs, underlying the role of electrostatics repulsions in adopting their spatial structures and also the possible role in binding charged peptides.

A coherent light scattering experiment on Saccharomyces Cerevisia suspension with a concentration that covers four orders of magnitude was performed. The far field first order statistics was computed and the variation of the average contrast with the yeast particle concentration was analyzed. A fast procedure for monitoring the yeast concentration is suggested.

In this study, commercial fruit juices present on Romanian market were investigated, by mean of stable isotopes, in order to check their correct labeling. In order to detect the sugar addition, to investigated fruit juices, δ¹³C values of: whole juice, pulp and sugars were determined. Beside these, δ¹⁸O and δ²H values of fruit juices water were measured in order to differentiate directly press juices from juices obtained from concentrates by re-dilution. The interpretation of these results is based on the fact that authentic juices have elevated δ¹⁸O and δ²H content of water as compared to water from re-diluted products, which were made using tap water which is relatively, depleted in heavy oxygen and hydrogen isotopes.

Embedding of radioactive waste in Portland cement matrix is the most used method applied worldwide, but not all the radioactive waste types are compatible with the normal cement matrix because of negative effects of some chemical reactions developed during the hydrolysis and curing steps of cement paste. The radioactive aluminium, one of the as called “hazardous wastes” generated by the decommissioning of research nuclear reactor as VVR-S – IFIN-HH, or other nuclear techniques applications like irradiation/activation techniques, is a type of radioactive waste which can not be conditioned by this method, due to behaviour of the metallic aluminium in contact with normal cement products. The studies and preliminary results of the work presented in the present paper is part of a research project developed to identify a proper management of this special type of radioactive waste from the storage phase up to final disposal. To obtain a conditioning matrix for radioactive aluminium in accordance with the international disposal requirements and respecting the waste acceptance criteria of the National Radioactive Waste Repository – Baita-Bihor, is necessary to study new formulas of low basicity binding agents, in order to minimize the alkaline attack of cement hydrolysis products on metallic aluminium.

The paper shows a full 6 DOF modeling for a GRAD rocket in Earth’s non-inertial frame. For numerical purposes the modeling is limited to flat Earth approximation. The full motion equations are shown and all terms are explained together with the aerodynamics parameters for the entire flight envelope. Non-linear interpolation is used for aerodynamic coefficients and their derivatives. We present the typical dispersion factors due to rocket production inaccuracies, launch condition variability and atmospheric factors and their relative influence on a guidance implementation package.
Next we present a 6 DOF modeling with various step-like thrust-curves while maintain the same total impulse delivered by the original motor. The influence of the step size on the range of the GRAD rocket is investigated together with the dispersion influence. We show that significant range increase can be obtained while using the same propulsion unit with a step-like thrust-curve modification. We also investigate the influence of the step-like thrust-curve on dispersion of such a rocket and the technological possibilities to implement our solution.
In the last part of the paper we present a terminal guidance concept 122 mm rockets. A preliminary requirement for IMU units to be used for terminal guidance is shown together with the general guidance algorithm for several trajectories. Performance expectations are shown through the analysis of the IMU units performance as well as flight dynamics of the 122 mm rockets.

The paper presents the applicability of the magnitude coherence function as a powerful tool for investigating to what extent common activity is distributed across the frequency in pairs of financial time series. Relevant results obtained from the currencies active on the market and a possible interpretations using triadic schemes are presented. The application is a new and typical extension of physics models to finance and economics.