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.     

Application of He's parameter-expansion method for oscillators with smooth odd nonlinearities

This Letter applies He's parameter-expansion method to oscillators with smooth nonlinearities. The method does not depend upon small parameter assumption, hence it is very better than the perturbation method. In parameter-expansion method the solution and unknown frequency of oscillation are expanded in a series by a bookkeeping parameter. By imposing the non-secularity condition at each order in the expansion the method provides different approximations to both the solution and the frequency of oscillation. One iteration step provides an approximate solution which is valid for the whole solution domain. The method can be easily extended to other nonlinear oscillations.     

Variational iteration method for solving the multi-pantograph delay equation

In this Letter, the variational iteration method is applied to solve the multi-pantograph delay equation. Sufficient conditions are given to assure the convergence of the method. Examples show that the method is effective.     

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.     

Generalized differential transform method to differential-difference equation

In this Letter, we generalize the differential transform method to solve differential-difference equation for the first time. Two simple but typical examples are applied to illustrate the validity and the great potential of the generalized differential transform method in solving differential-difference equation. A Padé technique is also introduced and combined with GDTM in aim of extending the convergence area of presented series solutions. Comparisons are made between the results of the proposed method and exact solutions. Then we apply the differential transform method to the discrete KdV equation and the discrete mKdV equation, and successfully obtain solitary wave solutions. The results reveal that the proposed method is very effective and simple. We should point out that generalized differential transform method is also easy to be applied to other nonlinear differential-difference equation.     

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.     

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.     

Efficient algorithms for discrete lattice calculations

We discuss algorithms for lattice-based computations, in particular lattice reduction, the detection of nearest neighbors, and the computation of clusters of nearest neighbors. We focus on algorithms that are most efficient for low spatial dimensions (typically d=2,3$d=2\text{,}3$) and input data within a reasonably limited range. This makes them most useful for physically oriented numerical simulations, for example of crystalline solids. Different solution strategies are discussed, formulated as algorithms, and numerically evaluated.     

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.     

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.     

Thermal Stability of Reliable Polycrystalline Zirconium Oxide for Nonvolatile Memory Application

Thermal stability of resistive switching of stoichiometric zirconium oxide thin films is investigated for high yielding nonvolatile memory application. The A1/ZrO2/AI cell fabricated in the conventional device process shows highly reliable switching behaviour between two distinct stable resistance states. The retention capabilities are also tested under various conditions and temperatures. The excellent performance of Ai/ZrO2/AI ceil can be explained by assuming that anode/ZrO2 interface exists and by conducting filament forming/rupture mechanism. The device failure is illustrated in terms of permanent conducting filaments formation.     

Polarity-Free Resistive Switching Characteristics of CuxO Films for Non-volatile Memory Applications

Resistive switching characteristics of CuxO films grown by plasma oxidation process at room temperature are investigated. Both bipolar and unipolar stable resistive switching behaviours are observed and confirmed by repeated current voltage measurements. It is found that the RESET current is dependent on SET compliance current. The mechanism behind this new phenomenon can be understood in terms of conductive filaments formation/rupture with the contribution of Joule heating.     

Solution of singular two-point boundary value problems using differential transformation method

In this Letter, we implemented relatively new, exact series method of solution known as the differential transform method for solving singular two-point boundary value problems. Several illustrative examples are given to demonstrate the effectiveness of the present method.     

Effect of modifying a methyl siloxane-based dielectric by a polymer thin film for pentacene thin-film transistors

We report on the fabrication of pentacene thin-film transistors (TFTs) utilizing a spun methyl siloxane-based spin-on-glass (SOG) dielectric and show that these devices can give a similar electrical performance as achieved by using pentacene TFTs with a silicon dioxide (SiO₂) dielectric. To improve the electrical performance of pentacene TFTs with the SOG dielectric, we employed a hybrid dielectric of an SOG/cross-linked poly-4-vinylphenol (PVP) polymer. The PVP film was deposited onto the spun SOG dielectric prior to pentacene evaporation, resulting in an improvement of the saturation field effect mobility (μ_sat) from 0.01 cm²/(V s) to 0.76 cm²/(V s). The good surface morphology and the matching surface energy of the SOG dielectric that was modified with the polymer thin film allow the optimized growth of crystalline pentacene domains whose nuclei are embedded in an amorphous phase.     

Generalized Synchronization of Time-Delayed Differential Systems

We establish two theorems for two time-delayed （chaotic） differential equation systems to achieve time-delayed generalized synchronization （TDGS）. The theorems uncover general forms of two TDGS systems via a prescribed differentiable transformation. Based on the theorems, we use two-coupled Ikeda equations as the driving system to construct TDGS driven systems via two prescribed transformations. Numerical simulations demonstrate the effectiveness of the proposed theorems. It may be expected that our theorems provide new tools for understanding and studying TDGS phenomena.     

Self-organized diffusion of congestion in complex networks

In this work, we propose and study a model for the diffusion of congestion in complex networks. According to the proposed model, the level of congestion on each node will be self-organized into the same value. The diffusion of congestion throughout various networks with different topologies is investigated analytically and by numerical tests. The flow fluctuations in complex networks are studied. We recover a power-law scaling relation between the standard deviation and mean flow, which is consistent with the previous studies. Finally, we extend our model by adding two constraints, which may be effective strategies for diffusing the local and the global congestion in complex networks, respectively.     

Improvement in piezoelectric effect of violet InGaN laser diodes

The laser performance of violet InGaN laser diodes is investigated numerically. The polarization-dependent properties, including overlap of electron and hole wavefunctions, threshold current, and slope efficiency, are studied through the use of step-like quantum well structure. Furthermore, the electron and hole wavefunctions, band diagrams, and emission wavelength are compared and analyzed. The simulation results show that the lowest threshold current and the highest slope efficiency are obtained when the step-like quantum well structure is designed as In_0.12Ga_0.88N (2.5 nm)-In_0.18Ga_0.82N (1 nm) or In_0.18Ga_0.82N (2.5 nm)-In_0.12Ga_0.88N (1 nm) for violet laser diodes due to sufficiently enhanced overlap of electron and hole wavefunctions.     

A New Cellular Automata Model Considering Finite Deceleration and Braking Distance

We present a new cellular automata model for one-lane traffic flow. In this model, we consider the driver prejudgment according to the state of the leading car. We also consider that the vehicle deceleration capability is finite and the braking distance of the high-speed running cars cannot be ignored, which is not considered in most models. Furthermore, comfortable driving is considered, too. Using computer simulations we obtain some basic qualitative results and the fundamental diagram of the proposed model. In comparison with the known models, we find that the fundamental diagram of the proposed model is more realistic than that of the known models.