Band 69, Heft 10-11

This paper deals with a mathematical model describing the inward solidification of a melt of phase change material within a container of different geometrical configuration like slab, circular cylinder or sphere under the most generalized boundary conditions. The thermal and physical properties of melt and solid are assumed to be identical. To solve this mathematical model, the finite difference scheme is used to convert the problem into an initial value problem of vector matrix form and further, solving it using the Legendre wavelet Galerkin method. The results thus obtained are analyzed by considering particular cases when one might impose either a constant=time varying temperature or a constant=time varying heat flux or a constant heat transfer coefficient on the surface. The whole analysis is presented in dimensionless form. The effect of variability of shape factor, condition posed at the boundary, Stefan number, Predvoditelev number, Kirpichev number, and Biot number on dimensionless temperature and solid-layer thickness are shown graphically. Furthermore, a comparative study of time for complete solidification is presented.

A novel fractal image coding algorithm based on domain blocks sorting strategies and modified no search scheme is proposed in this paper. On one hand, in order to improve the encoding time, a modified no search (MNS) scheme is adopted. Firstly, the image is divided into blocks of different size utilizing an adaptive quadtree partition method. Secondly, one finds the location of the best matching domain block using the MNS scheme for the range blocks, whose sizes are larger than the preset minimum value. Thirdly, the types of the range block and domain block are computed employing the proposed approach, and then the corresponding computation of mean square error (MSE) is determined. The computation of the MSE is reduced and the encoding phase speeds up. On the other hand, the range blocks with the minimal sizes are encoded applying the proposed domain blocks sorting (DBS) method. Contrast experiment results show that the proposed algorithm can obtain good quality of the reconstructed images and shorten the encoding time significantly.

The nonlinear Schrödinger (NLS) equation appears in fluid mechanics, plasma physics, etc., while the Hirota equation, a higher-order NLS equation, has been introduced. In this paper, a higher-order Hirota system is investigated, which describes the wave propagation in an erbium-doped nonlinear fiber with higher-order dispersion. By virtue of the Darboux transformation and generalized Darboux transformation, multi-soliton solutions and higher-order rogue-wave solutions are derived, beyond the published first-order consideration.Wave propagation and interaction are analyzed: (i) Bell-shape solitons, bright- and dark-rogue waves are found; (ii) the two-soliton interaction is elastic, i. e., the amplitude and velocity of each soliton remain unchanged after the interaction; (iii) the coefficient in the system affects the direction of the soliton propagation, patterns of the soliton interaction, distance, and direction of the first-order rogue-wave propagation, as well as the range and direction of the second-order rogue-wave interaction.

A new computing model on the volume dependence of the product αK T of the thermal expansion coefficient α and the isothermal bulk modulus K T is proposed straightforward in this paper. Based on this revised formula, the volume dependence of Grüneisen parameter, entropy, Anderson-Grüneisen parameter, and first pressure derivative of bulk modulus, respectively, are thus investigated. The calculated results agree well with the previous work for magnesium oxide, sodium chloride, lithium, sodium, and potassium.

In this manuscript, the fractional transmission line with losses is presented. The order of the Caputo derivative is considered as 0 < β ≤ 1 and 0 < γ ≤ 1 for the fractional equation in space and time domain, respectively. Two cases are solved, with fractional spatial and fractional temporal derivatives, and also numerical simulations were carried out, where there are taken both derivatives in simultaneous form. Two parameters σ x and σ t are introduced and a physical relation between these parameters is reported. Solutions in space and time are given in terms of the Mittag-Leffler functions. The classic cases are recovered when β and γ are equal to 1.

In this paper, we consider a wave equation with space variable coefficients. Due to physical considerations, a distributed delay damping is acted on the part of the boundary. Under suitable assumptions, we prove the exponential stability of the energy based on the use of Riemannian geometry method, the perturbed energy argument, and some observability inequalities. From the applications point of view, our results may provide some qualitative analysis and intuition for the researchers in fields such as engineering, biophysics, and mechanics. And the method is rather general and can be adapted to other evolution systems with variable coefficients (e. g. elasticity plates) as well.

An analysis is carried out to study magnetohydrodynamic (MHD) flow and heat transfer of two immiscible fluids in an inclined channel. The channel is filled with couple stress fluid in one region and a viscous fluid in the other region. The viscous fluid is assumed to be electrically conducting. The governing equations are modelled using the fully developed flow conditions. A closed form solutions of velocity and the temperature profiles are obtained by using perturbation method. The physical interpretation of the emerging parameters of interest on the velocity and temperature distributions are shown through graphs and discussed in detail.

The local angular distortion and spin Hamiltonian parameters (g factors g || , g ⊥ and the hyperfine structure constants) for the trigonal Co 2+ center in MgCl 2 are theoretically studied by diagonalizing the 6×6 energy matrix of ground 4 T 1 state for a trigonally distorted octahedral 3d 7 cluster. Based on the cluster approach, the contributions from the admixtures of various J (= 1/2;3/2;5/2) states and the ligand orbital and spin-orbit coupling interactions are taken into account in a uniform way. The local impurity-ligand bond angle in the Co 2+ center is found to be about 3.44° larger than the host metal-ligand bond angle in the pure crystal due to substitution of smaller Mg 2+ by bigger Co 2+ , inducing a further compressed ligand octahedron. The calculated spin Hamiltonian parameters using the above local angular distortion are in good agreement with the experimental data. The present studies on the local structure and the spin Hamiltonian parameters for Co 2+ in MgCl 2 are tentatively extended to a more general case by comparing the relevant impurity behaviours for Co 2+ in various trigonal environments.

This paper addresses the problem of stability and stabilization issue for a class of fuzzy nonlinear uncertain systems with discrete and distributed time delays. By utilizing a new Lyapunov-Krasovskii functional together with free weighting matrix approach, a new set of delay-dependent sufficient conditions are derived which makes the closed loop system robustly asymptotically stable. In particular, the parameter uncertainties are assumed to be norm bounded. Further, a state feedback controller is proposed to guarantee the robust stabilization for uncertain systems and subsequently the controller is constructed in terms of the solution to a set of linear matrix inequalities (LMI). The derived conditions are expressed in the form of linear matrix inequalities which can be efficiently solved via standard LMI toolbox. Further, two numerical examples are provided to demonstrate the effectiveness and less conservatism of the obtained results.

In terms of origin, the most important manganese deposits are sedimentary deposits which grow on the surface and/or fractures of the natural magnesite ore. They reveal various morphological characteristic according to their location in origin. Some of them may be fractal in appearance. Although several studies have been completed with regards to their growth mechanism, it may be safe to say that their cluster statistics and scaling properties have rarely been subject an academic scrutiny. Hence, the subject of this study has been designed to calculate cluster statistics of manganese deposits by first; transferring the images of manganese deposits into a computer and then scaling them with the help of software. Secondly, the root-mean square (rms) thickness (also called as expected value in systems), the number of particles, clusters and cluster sizes are computed by means of scaling method. In doing so it has been found that the rms thickness and the number of particles are in correlation, a result which is called as power-law behaviour, T~N -ε (the critical exponent is computed as ε = 1.743). It has also been found that the correlation between the number of clusters and their sizes are determined with the power-law behaviour n(s)~s -τ (the critical exponent t may vary between 1.054 and 1.321). Finally, the distribution functions of natural manganese clusters on the magnesite subtract have been determined. All that may point to the fact that the manganese deposits may be formed according to a Poisson distribution. The results found and the conclusion reached in this study may be used to compare various natural deposits in geophysics.

It is shown that cylindrical deuterium targets can be ignited with multi-mega-ampere GeV proton beams below the Alfvén limit and a small amount of tritium. The proton beams can be generated by discharging a magnetically insulated gigavolt capacitor. Surrounding the thermonuclear microexplosion with a thick layer of liquid hydrogen, heated to a ~ 10 5 K plasma by the thermalization of the fusion reaction neutrons, most of the energy released can be converted into electric energy by a magnetohydrodynamic generator.

The distribution of electric potential and space charge in a silicon nanowire has been investigated. First, a model of the nanowire is generated taking into consideration the geometry and physics of the nanowire. The physics of the nanowire was modelled by a set of partial differential equations (PDEs) which were solved using the finite element method (FEM). Comprehensive simulation experiments were performed on the model in order to compute the distribution of potential and space charge. We also determined, through simulation, how the characteristic of the nanowire is affected by its dimensions. The characterization of the resulting nanowire, calculated by COMSOL Multiphysics, shows different dimensions and their effect on space charge and electrical potential

The spin-Hamiltonian parameters (g factors g || , g ⊥ , and zero-field splittings b 0 2 , b 0 4 , b 4 4 , b 0 6 , b 4 6 ) of the 4f 7 Gd 3+ ion in the tetragonal phase of a BaTiO 3 crystal are calculated through the diagonalization (of energy matrix) method based on the one-electron crystal field mechanism. In the calculations, the crystal field parameters are estimated from the superposition model with the structural data of the studied crystal. It is found that by using three adjustable intrinsic parameters Ā k (R 0 ) (k=2, 4, 6) in the superposition model, the seven calculated spin-Hamiltonian parameters are in good agreement with the experimental values, suggesting that the diagonalization method based on one-electron crystal field mechanism is effective in the studies of spin-Hamiltonian parameters for 4f 7 ions in crystals.

30 keV 111m Cd and 50 keV 199m Hg beams from ISOLDE were used to implant on preformed targets of C 60 with a thickness of 1 mg cm -2 . Endofullerene compounds, viz. 111m Cd@C 60 and 199m Hg@C 60 formed during implantation were separated by filtration through micropore filter paper followed by solvent extraction. Dried samples of the endofullerene compounds were counted for the time differential perturbed angular correlation (TDPAC) measurement using the coincidence of the 151 - 245 keV cascade of 111m Cd and the 374 - 158 keV cascade of 199m Hg on a six LaBr 3 (Ce) detector system coupled with digital electronics. The results for 111m Cd@C 60 indicate a single static component (27%) and a fast relaxing component (73%), the latter implying that the cadmium atom moves rapidly inside the cage at room temperature. The quadrupole interaction frequency and asymmetry parameter of the cadmium atom occupying the static site in C 60 are w Q =8.21(36) Mrad s -1 and η = 0.41(9), respectively. The fast relaxation constant is 0.0031(4) ns -1 . Similarly, mercury atoms also exhibit a single static and a fast component. The static site has a quadrupole frequency w Q =283.0(12.4) Mrad s -1 and η =0 with a fraction of 30%. The fast relaxation constant is 0.045(8) ns -1 with a fraction of 70%, very similar to that of cadmium.