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EN
Thermodynamic properties of ternary Al-Ni-Pt system, such as ^{ex}G_{AlNiPt}, μ_{Al(AlNiPt)}, μ_{Ni(AlNiPt)}, and μ_{Pt(AlNiPt)} at 1373 K were predicted on the basis of thermodynamic properties of binary systems included in the investigated ternary system. The idea of predicting ^{ex}G_{AlNiPt} values was regarded as calculation of values of ^{ex}G function inside a certain area (a Gibbs triangle) unless all boundary conditions, that is values of ^{ex}G on all legs of the triangle are known (^{ex}G_{AlNi}, ^{ex}G_{AlPt}, ^{ex}G_{NiPt}). This approach is contrary to finding the function value outside a certain area, if the function value inside this area is known. ^{ex}G and L_{ijk} ternary interaction parameters in the Muggianu extension of the Redlich-Kister formalism are calculated numerically using the Mathematica program. The accepted values of the third component concentration x_{x} differed from 0.01 to 0.1 mol fraction. Values of L parameters in the Redlich-Kister formula vary for different x_{x} values, the ^{0}L_{AlNiPt} value in particular. Values of thermodynamic functions: ^{ex}G_{AlNiPt}, μ_{Al(AlNiPt)}, μ_{Ni(AlNiPt)} and μ_{Pt(AlNiPt)} do not differ significantly for different x_{x} values. The choice of x_{x} value does not influence the accuracy of calculations.
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The paper deals with the ways of finding an electrical conductivity tensor of a plane and anisotropically conductive sample. On the basis of the analysis of currents flowing through the electrodes at vertices of a rectangular sample, we derived specific electrical conductivity tensor calculation formula. The novelty of the present article is the use of the rectangular shape sample with arbitrarily directed sides in respect of the principal axes of the tensor. The influence of values of electrode lengths and the tensor components on the accuracy of these formulae is investigated. An iterative algorithm of increase of precision of calculating the tensor's components is presented.
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Simulations of blue and green laser diodes with InGaN quantum wells are presented. In this study, a particular emphasis on efficiency and optical power of the structures was placed. Effect of the aluminum content in an electron blocking layer on the electron overflow and efficiency is discussed. Substantial decrease of efficiency of laser diodes is reported for low aluminum levels. It is also shown that polarization charges existing in AlInGaN heterostructures grown on GaN polar direction and low ionization degree of magnesium acceptors lead to high resistance of these devices. These effects hinder the carriers from reaching an active region and consequently they impose high operating voltages.
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Simulation of Radiation Effects in SiO₂/Si Structures

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The space-time evolution of electric charge induced in the dielectric layer of simulated metal-insulator-semiconductor structures due to irradiation with X-rays is discussed. The system of equations used as a basis for the simulation model is solved iteratively by the efficient numerical method. The obtained simulation results correlate well with the respective data presented in other scientific publications.
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The paper deals with the ways of finding an electrical conductivity tensor of a plane and anisotropically conductive sample. Application of the Van der Pauw method to investigate the conductivity of anisotropically conductive media makes the basis of research. Several models of distribution of the electric field potential are presented, their merits and demerits are discussed, and the necessary physical measurements are indicated. On the basis of these models, the respective calculation expressions of the specific conductivity tensor are derived and algorithms for their realization and error calculation are developed.
EN
In this paper, we attempt to display effective numerical simulations of shock wave propagating represented by the Burgers equations known as a significant mathematical model for turbulence. A high order hybrid approximation based on seventh order weighted essentially non-oscillatory finite difference together with the sixth order finite difference scheme implemented for spatial discretization is presented and applied without any transformation or linearization to the Burgers equation and its modified form. Then, the produced system of first order ordinary differential equations is solved by the MacCormack method. The efficiency, accuracy and applicability of the proposed technique are analyzed by considering three test problems for several values of viscosity that can be caused by the steep shock behavior. The performance of the method is measured by some error norms. The results are in good agreement with the results reported previously, and moreover, the suggested approximation relatively comes to the forefront in terms of its low cost and easy implementation.
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Soliton evolution in spatially extended Josephson junction is studied for three types of ad hoc structural potentials describing tunnelling magnetic flux vortices; symmetric, ratchet and double-well. Setting from the inline geometry of the junction, the soliton dynamics could be modelled by the perturbed sine-Gordon equation. Numerical solutions of the latter equation yielded the soliton waves of the fluxon phase, for boundary conditions imposed on the system upon variation of the dispersion parameter α. It has been found that a change in the soliton waveform and intensity occurs as α goes higher, in dependence on the functional of the potential and its symmetry properties. For ratchet and double-well potential at α=0.5, a time-dependent forcing has been found to endorse the balance between dispersion and nonlinearity, jointly with enhancing the stability of the soliton wave. The McLoughlin-Scott perturbation theory has been adopted to show that the system conserves energy due to the delicate balance between nonlinearity and dispersion, so that the soliton keeps robust as it temporally evolves.
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Acta Physica Polonica A
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2018
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vol. 133
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issue 6
1465-1469
EN
In this work, the aim is to discuss the relative importance of the driving parameters of the diffusion of innovation under competition. As a case study the competitive existence of Android and iOS operating systems are modeled in the context of an extended Bass model. The chosen model consists of two coupled differential equations. Each differential equation has the same form of the well known Bass equation with an extra term which represents the effect of the existence of the competitor. Since the smartphone sales and usage are globally well documented, publicly available global smartphone market share and sales data are used to determine the model parameter values. The smartphone global market share data spans 28 quarters starting from the first quarter of 2009. The distribution of the market share in the first quarter has been used as the initial values of the competing operating systems. A minimization process obtains the free parameters (six in total) of the differential equations. The values of the parameters are fixed by minimizing the difference between the solution of Bass equation and the smartphone global market share data. The parameter values of iOS and Android operating systems indicate that, on the worldwide scale, the adaptation of new ideas/products the dominantly led by the personal interactions. In fact, through social networks, information flow is immense, and individuals rely on the information obtained directly from a trusted individual. Publicity parameter values indicate that very rarely decision of an individual is formed by only the mass media or publicity. On the contrary, to the publicity parameter, it is observed that the existence of a competitor has a considerable effect on the sales of both parties.
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Photonic Liquid Crystal Fibers with Polymers

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Photonic liquid crystal fibers with polymers constitute a new solution based on liquid crystals and microstructured polymer optical fibers opening up new areas in innovative sensing and photonic devices applications. Compared with their silica-based microstructured fibers, it is easier to fabricate exotic microstructured polymer optical fibers by extrusion or drilling at low temperature; their nonlinearity is potentially stronger, the range of available polymers that may be drawn is more diverse and the biocompatibility of polymers is often better. Liquid crystals due to their attractive properties i.e., the high birefringence, high electro-optic and thermo-optic effects are a very good candidate for microstructured polymer optical fiber infiltration to obtain tunable all-in-fiber innovative photonic devices. The paper will discuss basic properties and possible applications of the polymer photonic liquid crystal fibers that will arise from their high optical tunability with external and internal factors. Current research effort is directed towards two main solutions: photonic crystal fibers and microstructured polymer optical fiber-based structures, both infiltrated with liquid crystals of tailored optical properties.
EN
This paper presents an optimal boundary temperature control of thermal stresses in a plate, based on time-conformable fractional heat conduction equation. The aim is to find the boundary temperature that takes thermal stress under control. The fractional Laplace and finite Fourier sine transforms are used to obtain the fundamental solution. Then the optimal control is held by successive iterations. Numerical results are depicted by plots produced by MATLAB codes.
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Coherence of spins of electrons confined in III-V quantum dots is strongly affected by their hyperfine interaction with the nuclei. In this paper an introduction to this subject is presented. Some theoretical approaches to the problem will be outlined. Most attention will be given to the quasi-static bath approximation, to the cluster expansion theories of dephasing due to the nuclear dynamics induced by the dipolar interactions (spectral diffusion), and to the effective Hamiltonian based theory of dephasing due to hyperfine-mediated interactions. The connections between the theoretical results and various experiments will be emphasized.
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vol. 125
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issue 6
1275-1279
EN
This paper considers the problem of finding the temperature field in two-layer metallic materials heated by a moving source of radiation. It describes developed by the authors numerical method for solving the problem of heating a two-layer plate by a moving axially symmetric surface heat source with regard to the function of distribution of the power density of the beam for which the program of computation in C^{++} was implemented. The calculation results were used for selecting the optimal parameters (speed and power density of the source) of modifying radiation of protective powder coatings on steel substrates.
Acta Physica Polonica A
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2015
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vol. 128
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issue 2B
B-100-B-102
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Additive manufacturing technology is developed throughout the 1980's and 1990's. This technology makes the realization of mathematical models much easier. The challenge focused is here to fabricate real objects from very complex mathematical models by using a low-cost 3D fused deposition modeling desktop printer. Thus this brings the intangible mathematical expressions to life. In this study it is illustrated that complex mathematical expressions are not only numbers and symbols but also they are real life objects. In the examples, some mathematical functions such as Möbius strip, Schwartz functions and their boundary conditions are introduced and then digitally fabricated. This work shows that how complex functional mathematical models that cannot be manufactured with classical engineering methods or very difficult to produce can be fabricated by using a 3D FDM desktop printer.
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In this paper, some designed curves such as peak power, energy, pulse width, and a factor describing the pulse symmetry are generated. With these curves and expressions, one can design a passively Q-switched intracavity frequency-doubled laser and predict the pulse characteristics.
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Simulation of Langmuir-Blodgett Film Surface Stm Images

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The simulation of the STM image of a hydrocarbon tail of a fatty acid was carried out and compared to the experimental results. The simulation procedure includes calculations of the distribution of an isolated molecule electronic density by the extended Huckel-Hoffmann method. An agreement between the calculated and experimental STM images of closely packed Langmuir-Blodgett film of cobalt behenate on the graphite surface was observed. The weak interactions between the graphite surface and the adsorbed molecules constituting bi- and multilayer Langmuir-Blodgett films can be neglected in simulations of STM images.
EN
A computer-based numerical modelling of the adsorption process of gas phase metallic particles on the surface of a graphite substrate has been performed via the application of molecular dynamics simulation method. The simulation relates to an extensive STM-based experiment performed in this field, and reproduces part of the experimental results. Both two-body and many-body inter-atomic potentials have been employed. A Morse-type potential describing the metal-carbon interactions at the interface was specifically formulated for this modelling. Intercalation of silver in graphite has been observed as well as the correct alignments of monomers, dimers and two-dimensional islands on the surface.
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It is now possible to produce laser pulses with reproducible pulse shape and controlled carrier envelope phase. It is discussed how that can be explored in double ionisation studies. To this end we solve numerically the Schrödinger equation for a limited dimensionality model which nevertheless treats electron repulsion qualitatively correctly and allows to study correlation effects due to the Coulomb repulsion.
EN
In this paper we present our theoretical approach for the description of the light guidance in photonic liquid crystal fibers. In particular, we focus on the numerical methods allowing for a full implementation of the liquid crystals properties (i.e., including their optical anisotropy and molecular orientation), with a final target in characterizing photonic liquid crystal fibers with accessible computational effort. For this purpose suitable analytical formulae required for a full-vectorial description of the optical modes in photonic liquid crystal fibers have been derived. In addition, computational schemes allowing for numerical implementation of theoretical formulations (with the use of the finite-difference scheme) have been developed, validated and optimized. Their numerical convergence has been checked for different structures, as well as for different input parameters (e.g., grid-size). Obtained results have been compared to those analytically calculated, known from literature and/or got with use of commercial software. Moreover, the implemented schemes have been examined in accordance with experimental tests performed on the photonic liquid crystal fiber of interest.
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Suitable simulation approaches for the preliminary investigation of the electromagnetic metal forming process are presented. For this purpose an uncoupled (loose-coupled) simulation model is compared to a more rigorous sequential-coupled approach. As shown by examples, the connection between electromagnetic field and spatiotemporal evolution of the deformation of the workpiece cannot always be neglected to describe the electromagnetic forming process with adequate accuracy.
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Theoretical investigation of acoustic field in a tellurium two-coordinate deflector was carried out. We used angular spectrum method supported by consideration to boundary conditions in approximation of a given displacement to calculate spatial distribution of the acoustic field intensity. Volumetric illustration is presented for the acoustic beam launched from YZ face of the crystal. Cross-sections of the acoustic field generated from XZ face are also presented in the work. It is shown that the strong anisotropy of acoustic properties in the Te crystal leads to principally different structure of the two fields excited from the XZ and YZ crystal faces. The acoustic field excited from the XZ face may be considered as a simple beam with a relatively high divergence. On the other hand, the field generated from the YZ face looks like superposition of two beams with relatively low divergence. Ratio of intensities of the two beams generated by longitudinal piezotransducers is equal to the ratio predicted by analysis based by plane-wave theory.
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