Numerical Simulation of Electromagnetic Waves Scattering by Discrete Exterior Calculus

We show how to construct discrete Maxwell equations by discrete exterior calculus. The new scheme has many virtues compared to the traditional Yee＇s scheme： it is a multisymplectic scheme and keeps geometric properties. Moreover, it can be applied on triangular mesh and thus is more adaptive to handle domains with irregular shapes. We have implemented this scheme on a Java platform successfully and our experimental results show that this scheme works well.     

Numerical Solution of the Three-Dimensional Helmholtz Equation

We apply the homotopy analysis method to solve the nonhomogeneous multidimensional partial differential equation model problem. The analytic solutions are calculated in terms of convergent series with easily computable components. The nonhomogeneous problem is quickly solved by observing the self-canceling ＂noise＂ terms whose sum vanishes in the limit. Numerical results clearly reveal the complete reliability and efficiency of the proposed algorithm.     

Transmission Frequency Properties of Elastic Waves along a Hetero-Phononic Crystal Waveguide

We investigate the propagation properties of hetero-phononic crystal waveguides by the improved eigen-mode matching theory, which can be used at same time to calculate both the transmission （reflection） coefficient and band structure. The numerical results show that the transmission frequency range is the same as the common range for two uniform waveguides composing the hereto-system, and the gap of any composite waveguide is also the gap of the hetero-phononic crystals waveguide.     

Numerical Analysis and Comparison of Three Metal-Oxide-Type Super-Resolution Near Field Structures

Based on the Fresnel-Kirchhoff diffraction theory, we build up a Gaussian diffraction model of metal-oxide-type super-resolution near field structure （super-liENS）, which can describe far field optical properties. The spectral contrast induced by refractive index and the structural changes in AgOg, PtOx and PdOz thin films, which are the key functional layers in super-RENS, are studied by using this model. Comparison results indicate that the spectral contrast depends intensively on the laser-induced distribution and change of the refractive index in the metal-oxide films. The readout mechanism of the metal-oxide-type super-RENS optical disc is further clarified. This Gaussian diffraction model can be used as a simple and effective method for choosing proper active materials in super-RENS.     

Mechanisms of small clusters production by short and ultra-short laser ablation

The mechanisms involved into the formation of clusters by pulsed laser ablation are studied both numerically and experimentally. To facilitate the model validation by comparison with experimental results, the time and length scales of the simulation are considerably increased. This increase is achieved by using a combination of molecular dynamics (MD) and the direct simulation Monte Carlo (DSMC) methods. The combined MD-DSMC model is then used to compare the relative contribution of the two channels of the cluster production by laser ablation: (i) direct cluster ejection upon the laser-material interaction, and (ii) collisional sticking and aggregation in the ablated gas flow. Calculation results demonstrate that both of these mechanisms play a role. The initial cluster ejection provides cluster precursors thus eliminating the three-body collision bottleneck in the cluster growth process. The presence of clusters thus facilitates the following collisional condensation and evaporation processes. The rates of these processes become considerable, leading to the modification of not only the plume cluster composition, but also the dynamics of the plume expansion. Calculation results explain several recent experimental findings.     

Synthesis of nanoclusters by nanosecond laser ablation: Direct simulation Monte Carlo modelling

Collisional processes leading to the formation of nanoparticles in a laser-ablated plume are numerically simulated with the aid of an atomistic-level model based on direct simulation Monte Carlo (DSMC) method. The formation of nanoparticles in nanosecond laser ablation of a mono-atomic target is investigated in the presence of an inert background gas. The DSMC procedure is modified in order to account for numerous plume species and to describe several reactions (i.e., recombination/dissociation, sticking, evaporation) taking place in the plume and affecting the size and spatial distribution of the produced nanoclusters. Calculation results allow us to visualize the nanoparticles and to correlate their space distributions with plume dynamics. In addition, cluster size distributions are investigated at different pressures. The effects of the background gas on cluster formation within the plume are furthermore shown.     

Numerical Investigation of Noise Enhanced Stability Phenomenon in a Time-Delayed Metastable System

The transient properties of a time-delayed metastable system subjected to the additive white noise are investigated by means of the stochastic simulation method. The noise enhanced stability phenomenon （NES） can be observed in this system and the effect of the delay time on the NES shows a critical behaviour, i.e., there is a critical value of the delay time Tc ≈1, above which the time delay enhances the NES effect with the delay time increasing and below which the time delay weakens the NES effect as the delay time increases.     

A New Numerical Approach to Evaluate Variation of Electric Field Strength at the End of Particle Trajectory in Nuclear Track Detectors

A geometrical model for an electrochemical etching （ECE） track in a dielectric detector is defined and a primaxy programme is written to generate the track. The generated track is transformed to an M× N matrix of primary voltages. Using a numerical method, the matrix of final voltages is computed, and using another numerical approach, the electric field strengths in the elements of detector volume are computed. The final field strength at the end of particle trajectory is obtained. The results of our numerical computation show that there are exact correlations between the field strength at the end of particle trajectory and the parameters of track under ECE. It is found that although two traditional models of Mason and Smythe in dielectrics can be partly applied for short and long tracks, none of them are able to explain the behaviour of field strength in a ‘general case＇. Furthermore, we find that there is an expressive relationship between the field strength and the incidence angle of impacted particle, while the mentioned traditional models are not able to explain this effect.     

Kinetics of Nitrogen Indiffusion in Czochralski Silicon Annealed in Nitrogen Ambient

By means of low-temperature （10 K） Fourier transform infrared absorption spectroscopy, the kinetics of nitrogen indiffusion in Czochralski （CZ） silicon annealed at 1150-1250℃ in nitrogen ambient is investigated. Moreover, the nitrogen diffusivities in CZ silicon at elevated temperatures deduced herein are in good agreement with those previously obtained in float-zone silicon, thus leading to the conclusion that the nitrogen indiffusion in CZ silicon at elevated temperatures is via nitrogen pairs.     

Coupled modes of the torsion pendulum

The coupling of the swing modes of a torsion pendulum to the torsional mode has been solved analytically. Our solution provides a clear explanation of why a magnetic damper is effective in suppressing unwanted modes in most gravitational experiments. The analytic solution also shows that the amplitude of the mode coupling is greatest at the lowest frequencies. This explains why mode coupling at the lowest frequency is all that is observed in the experiments reported here.     

Simulation of Electromagnetic Wave Logging Response in Deviated Wells Based on Vector Finite Element Method

The vector finite element method of tetrahedral elements is used to model 3D electromagnetic wave logging response. The tangential component of the vector field at the mesh edges is used as a degree of freedom to overcome the shortcomings of node-based finite element methods. The algorithm can simulate inhomogeneous media with arbitrary distribution of conductivity and magnetic permeability. The electromagnetic response of well logging tools are studied in dipping bed layers with the borehole and invasion included. In order to simulate realistic logging tools, we take the transmitter antennas consisting of circular wire loops instead of magnetic dipoles. We also investigate the apparent resistivity of inhomogeneous formation for different dip angles.     

SIMS investigation of gettering centres produced by phosphorus MeV ion implantation

The ion implantation is a well-known standard procedure in electronic device technology for precise and controlled introduction of dopants into silicon. Damages caused by implantation act as effective gettering zones, collecting unwanted metal impurities. In this work, the consequences of high-energy ion implantation into silicon and of subsequently annealing were analysed by means of secondary ion mass spectrometry (SIMS). The differences in impurities gettering behaviour were studied in dependence of the implantation dose and annealing time at T = 900 °C.     

Maintaining the stability of nonlinear differential equations by the enhancement of HPM

Homotopy perturbation method is an effective method to find a solution of a nonlinear differential equation. In this method, a nonlinear complex differential equation is transformed to a series of linear and nonlinear parts, almost simpler differential equations. These sets of equations are then solved iteratively. Finally, a linear series of the solutions completes the answer if the convergence is maintained. In this Letter, the need for stability verification is shown through some examples. Consequently, HPM is enhanced by a preliminary assumption. The idea is to keep the inherent stability of nonlinear dynamic, even the selected linear part is not.     

Coupling Effect of Ion Channel Clusters on Calcium Signalling

Based on a modified intracellular Ca^2＋ model involving diffusive coupling of two calcium ion channel dusters, the effects of coupling on calcium signalling are numerically investigated. The simulation results indicate that the diffusive coupling of dusters together with internal noise determine the calcium dynamics of single duster, and for either homogeneous or heterogeneous coupled dusters, the synchronization of dusters, which is important to calcium signalling, is enhanced by the coupling effect.     

Self-consistent solution of cosmological radiation-hydrodynamics and chemical ionization

We consider a PDE system comprising compressible hydrodynamics, flux-limited diffusion radiation transport and chemical ionization kinetics in a cosmologically-expanding universe. Under an operator-split framework, the cosmological hydrodynamics equations are solved through the piecewise parabolic method, as implemented in the Enzo community hydrodynamics code. The remainder of the model, including radiation transport, chemical ionization kinetics, and gas energy feedback, form a stiff coupled PDE system, which we solve using a fully-implicit inexact Newton approach, and which forms the crux of this paper. The inner linear Newton systems are solved using a Schur complement formulation, and employ a multigrid-preconditioned conjugate gradient solver for the inner Schur systems. We describe this approach and provide results on a suite of test problems, demonstrating its accuracy, robustness, and scalability to very large problems.     

Differential transform method for solving linear and non-linear systems of partial differential equations

In this Letter, we propose a reliable algorithm to develop exact and approximate solutions for the linear and non-linear systems of partial differential equations. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and non-linear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Several illustrative examples are given to demonstrate the effectiveness of the present method.     

Deactivation of the boron–oxygen recombination center in silicon by illumination at elevated temperature

The boron–oxygen‐related recombination center responsible for the light‐induced degradation of solar cells made on boron‐doped oxygen‐contaminated silicon is deactivated by simultaneously annealing the silicon wafer in the temperature range 135–210 °C and illuminating it with white light. The recombination lifetime after deactivation is found to be stable under illumination at room temperature. The deactivation process is shown to be thermally activated with an activation energy of 0.7 eV. Based on the experimental findings, a defect reaction model is proposed explaining the deactivation of the boron–oxygen center. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Assessment of two analytical approaches in some nonlinear problems arising in engineering sciences

In this research, two powerful analytical methods are introduced to handle nonlinear good Boussinesq, heat transfer and coupled Burgers' equations. One is the homotopy-perturbation method (HPM) and the other is the variational iteration method (VIM). VIM is used to construct correction functionals using general Lagrange multipliers identified optimally via the variational theory. HPM converts a difficult problem into a simple one, which can be easily handled. The results attained in this paper confirm the idea that HPM and VIM are powerful mathematical tools and that they can be applied to a large class of linear and nonlinear problems arising in different fields of science and engineering.     

Propagation of Plasma Generated by Intense Pulsed Ion Beam Irradiation

Taking the calculation results based on the established two-dimensional ablation model of the intense-pulsed-ionbeam （IPIB） irradiation process as initial conditions, we build a two-dimensional hydrodynamic ejection model of plasma produced by an IPIB-irradiated metal titanium target into ambient gas. We obtain the conclusions that shock waves generate when the background pressure is around 133 mTorr and also obtain the plume splitting phenomenon that has been observed in the experiments.     

The positive charging effect of dielectric films irradiated by a focused electron beam

Space charge and surface potential profiles are investigated with numerical simulation for dielectric films of SiO₂ positively charged by a focused electron beam. By combining the Monte Carlo method and the finite difference method, the simulation is preformed with a newly developed comprehensive two-dimensional model including electron scattering, charge transport and trapping. Results show that the space charge is distributed positively, like a semi-ellipsoid, within a high-density region of electrons and holes, but negatively outside the region due to electron diffusion along the radial and beam incident directions. Simultaneously, peak positions of the positive and negative space charge densities shift outwards or downwards with electron beam irradiation. The surface potential, along the radial direction, has a nearly flat-top around the center, abruptly decreases to negative values outside the high-density region and finally increases to zero gradually. Influences of electron beam and film parameters on the surface potential profile in the equilibrium state are also shown and analyzed. Furthermore, the variation of secondary electron signal of a large-scale integration sample positively charged in scanning electron microscopic observation is simulated and validated by experiment.