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This paper is devoted to the study of two-dimensional hyperbolic partial differential telegraph equation. Converting the PDE to an ODE yields exact solution to this problem. Then, using first-order finite difference techniques, we obtain approximate numerical solutions. The numerical solution’s error analysis is provided. The stability estimates of finite difference schemes, as well as some numerical tests to check the correctness with regard to the precise solution are provided. [ABSTRACT FROM AUTHOR]

In digital the detection techniques, the half adder is a component of electronic systems that performs calculations faster than the other logic gates. This article focusses on an all-optical half adder logic gate using a two-dimensional T-shaped photonic crystal waveguide and silicon in an air medium. The half adder design is predicated on the concept of constructive (in-phase) and destructive (out-of-phase) interferences. The high-intensity output is achieved by carefully selecting the lattice constant, rod radius and refractive index of the half adder structure. The effectiveness of the half adder is investigated using finite-difference time-domain and plane-wave expansion techniques at 1.55 µm wavelength. The suggested structure features a minimal size of 8.4 µm × 8.4 µm. For this structure, the CARRY has a greater contrast ratio of 18.96 dB and SUM of 8.7 dB, as expressed by the results. SUM and CARRY have bit rates of 28.5 Tbps and 23.8 Tbps, respectively. The proposed circuit's primary objective is to be compact and to have a high contrast ratio. [ABSTRACT FROM AUTHOR]

In this paper, numerical solution of partial differential equations of the so-called hyperbolic telegraph, which has different applications in many fields such as engineering and physics, is investigated. The numerical solutions of telegraph equation defined by Caputo fractional derivative and by Atangana–Baleanu fractional derivative are obtained by Dufort–Frankel difference scheme method. It is important to investigate the solution of this equation defined by these two fractional derivatives and to compare these solutions. Studying this problem for the derivatives of different fractional order makes this problem different from previous studies. The originality of this problem is illustrated by initially considering two types of problems with both the Caputo and Atangana–Baleanu fractional derivatives. In addition, the approximate solution of these two problems with the Dufort–Frankel difference scheme method and their comparison indicate the originality of this study. Difference schemes are constructed for this equation defined by Caputo and Atangana–Baleanu fractional derivatives. Stability estimates are given for this difference scheme method. The error analysis is calculated by comparing the exact solutions of these two problems, which are defined by both Caputo and Atangana–Baleanu fractional derivatives. Present results show that this method is effective and suitable for these equations defined by Caputo and Atangana–Baleanu fractional derivative. From the simulations obtained using the Matlab program, it can be seen that the Dufort–Frankel difference scheme method is suitable for both types of problems and has approximate solutions close to the exact solution. [ABSTRACT FROM AUTHOR]

A new singularly P-Stable two-step algorithm of economical type with zero phase–lag and its derivative is produced in this paper. We symbolized the new scheme as LOWPFTECON2STEP. We apply the new algorithm to problems in Chemistry. The new algorithm achieves a 10th algebraic order using four function evaluations per step. For this reason, is called economical. [ABSTRACT FROM AUTHOR]

A new phase-fitting singularly P-Stable economical two–step method (which is symbolized as PHAFITECON2STEP) is produced in this paper. The newly introduced method has eliminated phase-lag and its derivatives up to order seven and can be applied to initial or boundary value problems with oscillating and/or periodical solutions. The new method is applied to problems in Quantum Chemistry. We call the newly produced method economical since to achieve the highest possible algebraic order, uses the minimum number of function evaluations per step. [ABSTRACT FROM AUTHOR]

In order to solve the general multidimensional perturbed oscillatory system y ′ ′ + Ω y = f (y , y ′) with K ∈ R d × d , the order conditions for the ERKN (extended Runge–Kutta–Nyström) methods and some effective ERKN methods were presented in the literature. These methods integrate exactly the multidimensional unperturbed oscillator y ′ ′ + Ω y = 0 . In this paper, we analyze the stability of ERKN methods for general oscillatory second-order initial value problems whose right-hand-side functions depend on both y and y ′ . Based on the linear test model y ′ ′ (t) + ω 2 y (t) + μ y ′ (t) = 0 with μ < 2 ω , further discussion and analysis on the linear stability of ERKN methods for general oscillatory problems are presented. A new conception of α -stability region is proposed to investigate how well the numerical methods respect the damping rate of the general oscillatory systems. It gains more insight to the numerical methods when applied to the systems involving y ′ . Numerical experiments are carried out to show the significance of the theory. [ABSTRACT FROM AUTHOR]

In this work, a numerical model is developed for a rapid computation of eddy currents in composite materials, adaptable for both carbon fiber reinforced polymers (CFRPs) for NDT applications and multifilamentary high temperature superconductive (HTS) tapes for AC loss evaluation. The proposed model is based on an integro-differential formulation in terms of the electric vector potential in the frequency domain. The high anisotropy and the nonlinearity of the considered materials are easily handled in the frequency domain.

A new finite difference method with eliminated phase-lag and its derivatives is introduced for the numerical approximation of differential equations in Chemistry. [ABSTRACT FROM AUTHOR]

In this research, we propose and analyse a two-dimensional photonic crystal having L-shaped bend waveguide to realise a negligible bending loss, nonlinearity and confinement loss at the signal of 1.31 μm and 1.55 μm. The proposed waveguide comprises 9 × 9 circular dielectric rods of silicon with air as background material. Further, finite-difference time-domain method is employed for analysing electric field distribution in order to realise effective area as well as high transmission characteristics of the proposed waveguide. Moreover, numerical formulations are used for simulation of bending loss, nonlinearity and confinement loss in the waveguide with suitable structure parameters (diameter of circular rods, nature of the material, lattice spacing). Again, simulation results revealed that ultra-low bending loss of 0.72 × 10−7 dB/m and 0.93 × 10−7 dB/m is experienced by the waveguide at wavelengths 1.31 μm and 1.55 μm, respectively, for 10 nm diameter of the circular rod, whereas a feeble nonlinearity of 0.085 W−1 km−1 and 0.072 W−1 km−1 is also asserted in the same. Furthermore, simulation outcomes proclaimed a negligible confinement loss of 5.7 × 10−11 and 4.8 × 10−11 for the said wavelengths. Finally, this article discloses that the projected silicon-based photonic crystal waveguide appears to be an apt candidate as optical interconnects for application in photonic integrated circuits. [ABSTRACT FROM AUTHOR]

High-level algebra-algorithmic software tools for automated design of parallel code in the OpenMP environment are developed for the purpose of both producing efficient parallel code and increasing the performance of program developers. Application of the tools is illustrated with an example of a problem in atmosphere circulation modeling, represented as a service belonging to an Internet portal providing meteorological forecasting services. Results of execution of the parallel weather forecasting program on multiprocessor platforms are given.

In this paper a four stages twelfth algebraic order symmetric two-step method with vanished phase-lag and its first, second, third, fourth and fifth derivatives is developed for the first time in the literature. For the new proposed method: (1) we will study the phase-lag analysis, (2) we will present the development of the new method, (3) the local truncation error (LTE) analysis will be studied. The analysis is based on a test problem which is the radial time independent Schrödinger equation, (4) the stability and the interval of periodicity analysis will be presented, (5) stepsize control technique will also be presented, (6) the examination of the accuracy and computational cost of the proposed algorithm which is based on the approximation of the Schrödinger equation.

From various types of scintillating materials lutetium-yttrium oxyorthosilicate (LYSO) has the highest luminosity and the greatest potential of application in high-energy radiation detectors. Due to the small critical angle of total internal reflection the enhancement of the extraction of light outside a scintillator is a challenge. We study numerically the influence of the effective refractive index layer on the transmittance of LYSO crystal. It is possible to realize such layer by sub-wavelength patterning of crystal surface using for example focused ion beam. The enhancement of transmittance of LYSO crystal up to 100% as well as the possibility to tune the positions of transmittance maxima have been shown. [ABSTRACT FROM AUTHOR]

While dealing in [1] with the supersymmetry of a tridiagonal Hamiltonian H , we have proved that its partner Hamiltonian H (+) also has a tridiagonal matrix representation in the same basis and that the polynomials associated with the eigenstates expansion of H (+) are precisely the kernel polynomials of those associated with H . This formalism is here applied to the case of the Morse oscillator which may have a finite discrete energy spectrum in addition to a continuous one. This completes the treatment of tridiagonal Hamiltonians with pure continuous energy spectrum, a pure discrete one, or a spectrum of mixed discrete and continous parts. [ABSTRACT FROM AUTHOR]

The methodology and results of a detailed four-element lens optimization analysis based on electron trajectory numerical simulations are presented for a hemispherical deflector analyzer (HDA), whose entry aperture size is determined by the injection lens itself and is therefore virtual. Trajectory calculations were performed using both the boundary-element method (BEM) and the finite-difference method (FDM) and results from these two different approaches were benchmarked against each other, to probe and confirm the accuracy of our results. Since the first and last electrode are held at fixed potentials, the two intermediate adjustable lens electrode voltages were varied over the entire available voltage space in a direct, systematic, brute-force approach, while minima in beam spot size on the 2-D position sensitive detector (PSD) at the exit of the HDA were investigated using a beam shaping approach. Lens voltages demonstrating improved energy resolution for the combined lens/HDA/PSD spectrograph system were sought with and without pre-retardation. The optimal voltages were then tested experimentally on the modeled HDA system using a hot-wire electron gun. The measured energy resolution was found to be in good overall agreement with our simulations, particularly at the highest resolution (∼0.05%) working conditions. These simulations also provide a detailed insight to the distinctive trajectory optics and positions of the first and second image planes, when the PSD has to be placed some distance away from the HDA exit plane, and is therefore not at the ideal optics conjugate image position. The substantial time savings afforded over usual trial-and-error experimentation should make this type of make-do simulation approach attractive to experimentalists. [ABSTRACT FROM AUTHOR]

In this work, we propose an efficient method to investigate optical properties as well as their dependence on geometrical parameters in InAs/InAlAs quantum wires. The used method is based on the coordinate transformation and the finite difference method. It provides sufficient accuracy, stability and flexibility with respect to the size and shape of the quantum wire. The electron and hole energy levels as well as their corresponding wave functions are investigated for different shape of quantum wires. The optical transition energies, the emission wavelengths and the oscillator strengths are also studied. [ABSTRACT FROM AUTHOR]

Polarization properties of apertureless-type scanning near-field optical microscopy (a-SNOM) were measured experimentally and were also analyzed using a finite-difference time-domain (FDTD) simulation. Our study reveals that the polarization properties in the a-SNOM are maintained and the a-SNOM works as a wave plate expressed by a Jones matrix. The measured signals obtained by the lock-in detection technique could be decomposed into signals scattered from near-field region and background signals reflected by tip and sample. Polarization images measured by a-SNOM with an angle resolution of 1° are shown. FDTD analysis also reveals the polarization properties of light in the area between a tip and a sample are p-polarization in most of cases. [ABSTRACT FROM AUTHOR]

In this article, an implementation of an efficient numerical method for solving the system of coupled nonlinear fractional diffusion equations (NFDEs) is introduced. The proposed system has many applications, such as porous media and plasma transport. The fractional derivative is described in the Caputo sense. The method is based upon a combination between the properties of the Legendre approximations and finite difference method (FDM). The proposed method reduces NFDEs to a system of ordinary differential equations that are solved using FDM. Special attention is given to the study of the convergence analysis and deducing the upper bound of the error of the resulting approximate solution. A numerical example is given to show the validity and the accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

This paper describes two new techniques which give improved exponential finite difference solutions of Burgers' equation. These techniques are called implicit exponential finite difference method and fully implicit exponential finite difference method for solving Burgers' equation. As the Burgers' equation is nonlinear, the scheme leads to a system of nonlinear equations. At each time-step, Newton's method is used to solve this nonlinear system. The results are compared with exact values and it is clearly shown that results obtained using both the methods are precise and reliable. [ABSTRACT FROM AUTHOR]

Abstract: For a detailed description of the excitation energy of the fission fragments, that is used to evaporate neutrons and emit γ-rays, realistic nuclear shapes at scission are necessary. It is shown that the nuclear shapes around the scission point, along the main fission mode, are well described by Cassini ovals with only two parameters: α (elongation) and α1 (mass asymmetry). This shape parametrization is used in an attempt to solve, in the case of the low-energy fission of 236U, the puzzle of the energy balance at scission. The deformation energy liberated during the neck rupture (αi=0.985 → αf =1.001)and the extra def deformation energy of the fragments immediately after scission are calculated as a function of eachdef fragment mass A. This allows us to estimate the excitation energy for each fragment pair as well as its partition among the light and the heavy fragment and compare with data extracted from measured prompt neutron and γ-ray multiplicities. The Coulomb repulsion of the fission fragments immediately after scission is also calculated as a function of their mass ratio and compared with experimental total fragment kinetic energies. [Copyright &y& Elsevier]

Abstract: The nuclear dissipation, i.e. the conversion of collective energy into intrinsic energy is investigated in the frame of quantum mechanics. Using appropiate numerical procedures, we follow the motion of individual nucleons according to the time-dependent Schr̈odinger equation with time-dependent potential. In particular we study the transition from the saddle to the scission point during the low energy fission of 236U. Different rates T of change of the nuclear shape along this path were considered. The overlap integrals between the static solutions of the bi-dimensional Schr̈odinger equation and the time-dependent wave packets yield the transition probabilities and hence the singleparticle excitations during the saddle-to-scission descent. Using the numerical solutions other relevant pre-scission properties have been evaluated as well. [Copyright &y& Elsevier]

In this study, we present a new and very accurate numerical method to approximate the Fisher's-type equations. Firstly, the spatial derivative in the proposed equation is approximated by a sixth-order compact finite difference (CFD6) scheme. Secondly, we solve the obtained system of differential equations using a third-order total variation diminishing Runge-Kutta (TVD-RK3) scheme. Numerical examples are given to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

We study the invariance, exact solutions, conservation laws, and double reductions of the nonlinear Schrödinger equation with damping and driving terms. The underlying equation is used to model a variety of resonant phenomena in nonlinear dispersive media, inter alia. For the purpose of our analysis, the complex equation is construed as a system of two real partial differential equations. [ABSTRACT FROM AUTHOR]

The shape of nanostructure array is one of the important parameters for the nanobiosensor applications. In this paper, we focus on the optical properties of silver pentagram nanostructure arrays based on localized surface plasmon resonance (LSPR). This novel nanostructure array has more hot spots than the tradition nanostructure array. Finite-difference and time-domain (FDTD) method was used to design the suitable structure parameters and the localized electric field distribution on the surface of the nanostructures is also explored too. According to the design results, we fabricated the regularly silver pentagram nanostructure array distributed on the surface of the glass substrate using focused ion beam (FIB) nanofabrication method. The calculated and experiment results show that the pentagram nanostructure array can be realized easily by FIB method. The nanostructure array has potential application for the high sensitivity nanobiosensor in the future. [ABSTRACT FROM AUTHOR]

Abstract: A quartic spline based remapping algorithm is developed and illustrative tests of it are presented herein. To ensure mass conservation, the scheme solves an integral form of the transport equation rather than the differential form. The integrals are computed from reconstructed quartic splines with mass conservation constraints. For higher dimensions, this remapping can be used within a standard directional splitting methodology or within the flow-dependent cascade splitting approach. A high-order grid and sub-grid based monotonic filter is also incorporated into the overall scheme. This filter is independent of the underlying spline representation adopted here, and is of more general application. [Copyright &y& Elsevier]

Abstract: The Klein–Gordon equation is a Lorentz invariant equation of motion for spinless particles. We propose a real space split operator method for the solution of the time-dependent Klein–Gordon equation with arbitrary electromagnetic fields. Split operator methods for the Schrödinger equation and the Dirac equation typically operate alternately in real space and momentum space and, therefore, require the computation of a Fourier transform in each time step. However, the fact that the kinetic energy operator in the two-component representation of the Klein–Gordon equation is a nilpotent operator, that is , allows us to implement the split operator method for the Klein–Gordon equation entirely in real space. Consequently, the split operator method for the Klein–Gordon equation does not require the computation of a Fourier transform and may be parallelized efficiently by domain decomposition. [Copyright &y& Elsevier]

Abstract: Knowledge-based modeling of dust lifting behind shock waves is a prerequisite for realistic simulation of dust explosions. Mostly numerical simulations of this process focus on dusts consisting of monodisperse particles, while real dusts are polydisperse. This article investigates the effect on the lifting process of the dust being polydisperse with a log–normal distribution of particle sizes. The spatial distribution of the various sizes in the rising layer is studied, and statistical results for the rise, the collision frequency and the particle kinetic energy are compared for polydisperse and monodisperse dusts. It is shown that a layer consisting of polydisperse particles rises significantly faster than a one consisting of monodisperse particles, all other parameters being the same. [Copyright &y& Elsevier]

Abstract: Fractional order diffusion equations are viewed as generalizations of classical diffusion equations, treating super-diffusive flow processes. In this Letter, in order to solve the two-sided fractional advection–diffusion equation, the fractional Crank–Nicholson method (FCN) is given, which is based on shifted Grünwald–Letnikov formula. It is shown that this method is unconditionally stable, consistent and convergent. The accuracy with respect to the time step is of order . A numerical example is presented to confirm the conclusions. [Copyright &y& Elsevier]

In this article, we propose a numerical scheme to solve the Kac model of the Boltzmann equation for multiscale rarefied gas dynamics. Formally, this scheme is shown to be uniformly stable with respect to the Knudsen number, consistent with the fluid-diffusion limit for small Knudsen numbers, and with the Kac equation in the kinetic regime. Our approach is based on the micro–macro decomposition which leads to an equivalent formulation of the Kac model that couples a kinetic equation with macroscopic ones. This method is validated with various test cases and compared to other standard methods. [ABSTRACT FROM AUTHOR]

Abstract: Stable, accurate, divergence-free simulation of magnetized supersonic turbulence is a severe test of numerical MHD schemes and has been surprisingly difficult to achieve due to the range of flow conditions present. Here we present a new, higher order-accurate, low dissipation numerical method which requires no additional dissipation or local “fixes” for stable execution. We describe PPML, a local stencil variant of the popular PPM algorithm for solving the equations of compressible ideal magnetohydrodynamics. The principal difference between PPML and PPM is that cell interface states are evolved rather that reconstructed at every timestep, resulting in a compact stencil. Interface states are evolved using Riemann invariants containing all transverse derivative information. The conservation laws are updated in an unsplit fashion, making the scheme fully multidimensional. Divergence-free evolution of the magnetic field is maintained using the higher order-accurate constrained transport technique of Gardiner and Stone. The accuracy and stability of the scheme is documented against a bank of standard test problems drawn from the literature. The method is applied to numerical simulation of supersonic MHD turbulence, which is important for many problems in astrophysics, including star formation in dark molecular clouds. PPML accurately reproduces in three-dimensions a transition to turbulence in highly compressible isothermal gas in a molecular cloud model. The low dissipation and wide spectral bandwidth of this method make it an ideal candidate for direct turbulence simulations. [Copyright &y& Elsevier]

Abstract: A parallel dispersive finite-difference time-domain (FDTD) method for the modeling of three-dimensional (3-D) electromagnetic cloaking structures is presented in this paper. The permittivity and permeability of the cloak are mapped to the Drude dispersion model and taken into account in FDTD simulations using an auxiliary differential equation (ADE) method. It is shown that the correction of numerical material parameters and the slow switching-on of source are necessary to ensure stable and convergent single-frequency simulations. Numerical results from wideband simulations demonstrate that waves passing through a three-dimensional cloak experience considerable delay comparing with the free space propagations, as well as pulse broadening and blue-shift effects. [Copyright &y& Elsevier]

Abstract: Performing microstructure simulation of technical casting processes suffers from the strong interdependency between latent heat release due to local microstructure formation and heat diffusion on the macroscopic scale: local microstructure formation depends on the macroscopic heat fluxes and, in turn, the macroscopic temperature solution depends on the latent heat release, and therefore on the microstructure formation, in all parts of the casting. A self-consistent homoenthalpic approximation to this micro–macro problem is proposed, based on the assumption of a common enthalpy–temperature relation for the whole casting which is used for the description of latent heat production on the macroscale. This enthalpy–temperature relation is iteratively obtained by phase-field simulations on the microscale, thus taking into account the specific morphological impact on the latent heat production. This new approach is discussed and compared to other approximations for the coupling of the macroscopic heat flux to complex microstructure models. Simulations are performed for the binary alloy Al–3at%Cu, using a multiphase-field solidification model which is coupled to a thermodynamic database. Microstructure formation is simulated for several positions in a simple model plate casting, using a one-dimensional macroscopic temperature solver which can be directly coupled to the microscopic phase-field simulation tool. [Copyright &y& Elsevier]

Abstract: The model of the relativistic quantum particle in a homogeneous external field is proposed. This model is realized in the one-dimensional relativistic configurational x-space and is described by the finite-difference equation. The momentum p-space in our case is the one-dimensional Lobachevsky space. We have found the wave functions and propagator for the model under study in both x- and p-representations. [Copyright &y& Elsevier]

Abstract: A novel adaptive mesh refinement (AMR) strategy based on the moment-of-fluid (MOF) method for volume-tracking of evolving interfaces is presented. Moment-of-fluid method is a new interface reconstruction and volume advection method using volume fractions as well as material centroids. The mesh refinement criterion is based on the deviation of the actual centroid obtained by interface reconstruction from the reference centroid given by moment advection process. The centroid error indicator detects not only high curvature regions but also regions with complicated subcell structures like filaments. A new Lagrange+remap scheme is presented for advecting moments, which includes Lagrangian backtracking, polygon intersection-based remapping and forward tracking to define the material centroid. The effectiveness and efficiency of AMR-MOF method is demonstrated with classical test problems, such as Zalesak’s disk and reversible vortex problem. The comparison with previously published results for these problems shows the superior accuracy of the AMR-MOF method over other methods. In addition, two new test cases with severe deformation rates are introduced, namely droplet deformation and -shape deformation problems, for further demonstration of the capabilities of the AMR-MOF method. [Copyright &y& Elsevier]

Abstract: Although fabrication of photonic crystals improved over the last few years, intrinsic defects of the crystal lattice affect the experimentally measured spectral features. In order to compare experimental spectra with simulated photonic band structure, disorder effects are simulated by introduction of material absorption. By using the finite-difference time-domain (FDTD) method we were able in the past to obtain a good agreement between experimental and simulated transmission curves by taking in account the glass substrate. In this work we extend our analysis for reflectance curves of one, two and three-layered close-packed polystyrene spheres. We show that a key ingredient in simulating disorder effects is the introduction of fictional absorption for polystyrene. [Copyright &y& Elsevier]

The localized electromagnetic modes of the metallic Menger sponge fractal of stage three were studied by the finite-difference time-domain (FDTD) calculation and the linear combination of atomic orbitals (LCAO) analysis. In addition to the nearly ideal scaling property of the eigenfrequency, a wide distribution of the quality factor was found. An interpretation of the latter based on the idea of the symmetry-dependent escape time of the electromagnetic energy is given. [ABSTRACT FROM AUTHOR]

Abstract: Based on experimental results, the dynamic recrystallization mathematical models of 42CrMo steel were derived. The effects of strain rates on the strain/stress distribution and microstructural evolution in 42CrMo steel during hot upsetting process were simulated by integrating the thermo-mechanical coupled finite element model. The results show that the deformation of the specimen is inhomogeneous, and the degree of the deformation inhomogeneity decreases with the increase of strain rates. The distribution of the effective stress in the specimen is also inhomogeneous, and the locus of the maximum effective stress changes with the variations of strain rates. The dynamic recrystallization volume fraction decreases with the increase of strain rates. The distribution of the dynamic recrystallization grain is inhomogeneous in the deformed specimen, and the average dynamic recrystallization grain size decreases as the strain rate is increased. A good agreement between the predicted and experimental results confirmed that the derived dynamic recrystallization mathematical models can be successfully incorporated into the finite element model to predict the microstructural evolution in the hot upsetting process for 42CrMo steel. [Copyright &y& Elsevier]

Abstract: Scanning near-field optical microscopy (SNOM) achieves a resolution beyond the diffraction limit of conventional optical microscopy systems by utilizing subwavelength aperture probe scanning. A problem associated with SNOM is that the light throughput decreases markedly as the aperture diameter decreases. Apertureless scanning near-field optical microscopes obtain a much better resolution by concentrating the light field near the tip apex. However, a far-field illumination by a focused laser beam generates a large background scattering signal. Both disadvantages are overcome using the tip-on-aperture (TOA) approach, as presented in previous works. In this study, a finite difference time domain analysis of the degree of electromagnetic field enhancement is performed to verify the efficiency of TOA probes. For plasmon enhancement, silver is deposited on commercially available cantilevered SNOM tips with 20nm thicknesses. To form the aperture and TOA in the probes, electron beam-induced deposition and focused ion beam machining were applied at the end of the sharpened tip. The results show that cantilevered TOA probes were highly efficient for improvements of the resolution of optical and topological measurement of nanostructures. [Copyright &y& Elsevier]

Abstract: We consider natural convection of an incompressible fluid in a porous medium described by the planar Darcy equation. For some boundary conditions, Darcy problem may have non-unique solutions in form of a continuous family of steady states. We are interested in the situation when these boundary conditions are violated. The resulting destruction of the family of steady states is studied via computer experiments based on a mimetic finite-difference approach. Convection in a rectangular enclosure is considered under different perturbations of boundary conditions (heat sources, infiltration). Two scenario of the family of equilibria are found: the transformation to a limit cycle and the formation of isolated convective patterns. [Copyright &y& Elsevier]

Abstract: This paper investigates numerically the effects of tilted angle of the susceptor and the upper wall and of addition of a rib on the three-dimensional (3-D) flow structures and heat transfer characteristics in a model horizontal chemical vapor deposition (CVD) reactor with a circular heated disk which simulates a 12in wafer. The Grashof (Gr) and Reynolds (Re) numbers are kept constant at 8.13×104 and 100, respectively. Computed flow structures and thermal distributions indicate that as the tilted angle of the susceptor and the upper wall is increased from 0° to 9°, the sizes of transverse (return flow) and longitudinal rolls are reduced and the uniformity of heat flux distribution is improved, which would yield better film homogeneity during CVD processing. The retardation of the growth of thermal boundary layer leads to an increase of the heat flux and hence of the deposition rate. With placing a rib to the upper wall of the reactor, the heat flux on the susceptor is increased but it has a detrimental effect on the uniformity. [Copyright &y& Elsevier]

Abstract: The ground-state energies and wave functions for an electron in quantum well-wires (QWWs) with different shapes under the electric and magnetic fields are directly calculated using the finite difference method. It is shown that the method is able to calculate all energy states for any given QWW shape. Then, the ground-state binding energy of a hydrogenic impurity is found employing a variational method. The reliability of the results is tested against previous studies. The binding energy for QWWs consisting of the combinations of square and triangular well potential is obtained. [Copyright &y& Elsevier]

Abstract: A robust and stable numerical algorithm is developed for the hybrid method of particle-in-cell ions and Boltzmann distribution of electrons. A different approach to estimate the electron density reference and its proper potential reference is developed to overcome the problems of instability and divergence of previous approaches. The electron density reference is precisely calculated, the tolerance criterion is well-defined, and convergence is guaranteed by applying bi-section golden rule. To increase the rate of convergence, an external loop is incorporated with the bi-section golden rule to vary the brackets. The validity of the method is proved by comparing the simulated result with well-known analytical formula. The simulated sheath potential at a floating wall fit well to the analytic result. The collisionless ion kinetic energy acquired from the voltage difference between the pre-sheath and ion sheath does not violate the Bohm sheath criterion. For work that focuses on the plasma process at the ion sheath and not on the generation of plasma, this method saves simulation time by avoiding time consuming particle or kinetic model of electrons. The new approach reproduces the ion density profile at the ion sheaths region of a plasma with bi-Maxwellian electrons coupling with radio-frequency (RF) signal by introducing two Boltzmann relations to describe the cold and hot thermal electrons for the first time. [Copyright &y& Elsevier]

Abstract: Transparent boundary conditions (TBCs) are an important tool for the truncation of the computational domain in order to compute solutions on an unbounded domain. In this work we want to show how the standard assumption of ‘compactly supported data’ could be relaxed and derive TBCs for a generalized Schrödinger equation directly for the numerical scheme on the discrete level. With this inhomogeneous TBCs it is not necessary that the initial data lies completely inside the computational region. However, an increased computational effort must be accepted. [Copyright &y& Elsevier]

Abstract: We extend our finite difference time domain method for numerical solution of the Schrödinger equation to cases where eigenfunctions are complex-valued. Illustrative numerical results for an electron in two dimensions, subject to a confining potential , in a constant perpendicular magnetic field demonstrate the accuracy of the method. [Copyright &y& Elsevier]

Abstract: An immersed boundary method for the incompressible Navier–Stokes equations in irregular domains is developed using a local ghost cell approach. This method extends the solution smoothly across the boundary in the same direction as the discretization it will be used for. The ghost cell value is determined locally for each irregular grid cell, making it possible to treat both sharp corners and thin plates accurately. The time stepping is done explicitly using a second order Runge–Kutta method. The spatial derivatives are approximated by finite difference methods on a staggered, Cartesian grid with local grid refinements near the immersed boundary. The WENO scheme is used to treat the convective terms, while all other terms are discretized with central schemes. It is demonstrated that the spatial accuracy of the present numerical method is second order. Further, the method is tested and validated for a number of problems including uniform flow past a circular cylinder, impulsively started flow past a circular cylinder and a flat plate, and planar oscillatory flow past a circular cylinder and objects with sharp corners, such as a facing square and a chamfered plate. [Copyright &y& Elsevier]

Abstract: Computational science and engineering are dominated by field problems. Traditionally, engineering practice involves repeated iterations of shape design (i.e., shaping and modeling of material properties), simulation of the physical field, evaluation of the result, and re-design. In this paper, we propose a specific interpretation of the algebraic-topological formulation of field problems, which is conceptually simple, physically sound, computational effective and comprehensive. In the proposed approach, physical information is attached to an adaptive, full-dimensional decomposition of the domain of interest. Giving preeminence to the cells of highest dimension allows us to generate the geometry and to simulate the physics simultaneously. We will also demonstrate that our formulation removes artificial constraints on the shape of discrete elements and unifies commonly unrelated methods in a single computational framework. This framework, by using an efficient graph-representation of the domain of interest, unifies several geometric and physical finite formulations, and supports local progressive refinement (and coarsening) effected only where and when required. [Copyright &y& Elsevier]

Abstract: We present a new discrete Adomian decomposition method to approximate the theoretical solution of discrete nonlinear Schrödinger equations. The method is examined for plane waves and for single soliton waves in case of continuous, semi-discrete and fully discrete Schrödinger equations. Several illustrative examples and Mathematica program codes are presented. [Copyright &y& Elsevier]

Abstract: The influence of nonmagnetic central node defect on dynamical properties of regular square-shaped segment of magnetic dot array under the thermal activation is investigated via computer simulations. Using stochastic Landau–Lifshitz–Gilbert equation we simulate hysteresis and relaxation processes. The remarkable quantitative and qualitative differences between magnetic dot arrays with nonmagnetic central node defect and magnetic dot arrays without defects have been found. [Copyright &y& Elsevier]

Abstract: We report on the implementation of a scattering-type scanning near-field optical microscope based on a heterodyne detection scheme, which has the ability to record near-field optical images at multiple wavelengths simultaneously. It is used to map out local field distribution and to investigate the dispersion behavior of plasmon created by nanometer-scale metallic structures. It opens up an unprecedented opportunity to study nano-photonics. [Copyright &y& Elsevier]