Computer Simulation of Ordering and Atom Clustering in Aging Binary Al-Li Alloy

Ordering and atom clustering in aging binary Al-Li alloy has been investigated by computer simulation through calculating the long range order (Iro.) parameter and composition deviation order parameter from single-site occupation probabilities of Li atom. The results show that when the alloy lies in metastable region in the phase diagram ordering and atom clustering occur simultaneously. As the composition of the alloy increases ordering occurs earlier than atom clustering gradually. When the alloy lies in instable region atom clustering takes place after the congruent ordering completes. It has also been found that the incubation period of the phase transformation is shortened as the composition increases.

Observation and computer simulation of multicomponent chemical short-range order (MCSRO) for the bulk metallic glasses

The atomic configuration of chemical short-range order (CSRO) for the Zr-base metallic glasses was investigated by using nano-diffraction and high resolution transmission electronic microscopy (HRTEM) technology with a beam size of 0.5 nm. It is il- lustrated that the pattern of atomic configuration of CSRO might have various compound counterparts because of the chemical inter- action of bonding atoms. Some atomic configuration of MCSRO is similar to the icosahedral structure with 10-fold symmetry of very weak spots. In deed, the nano-beam technology could clearly detect the evolution of atomic configuration in nanometer scale during the transformation from the metallic melt to the primary crystallization. The local atomic configuration of CSRO is also investigated by molecular dynamics simulation (MD) for the Zr2Ni compound in a wider temperature range. The CSRO in the melt could be pic- torially demonstrated as distorted coordination polyhedron of the compound structure and/or the structure similar to cubo-octahedron analogs. The MD simulation illustrates that the atomic packing of long-range order disappears just above the melting point, but the chemical interaction of bonding atoms still exists that leads to form the various CSRO with the atomic configuration similar to stable or metastable unit cell of Zr2Ni compound. The icosahedral polyhedron became more abundance as the overheating temperature was raised.

Atomic Scale Computer Simulation for Early Precipitation Process of Ni75Al6Vi9 Alloy

The atomic scale computer simulation for initial precipitation mechanism of Ni75Al6V19 alloy was carried out for the first time by employing the microscopic diffusion equation. The initial precipitation process was invest igated throughsimulating the atomic pictures and calculating the order parameters of the two kinds of ordered phases. Simulationresults show that the γ′ordered phase precipitated earlier than θ ordered phase by congruent ordering+spinodal decomposition mechanism and thus produced a nonstoicheometric γ′ single ordered phase. Then, the nonstoichiometricθ phase precipitated by a non-classical nucleation and growth mechanism at the APBS of γ′ phase.

Local chemical ordering and its impact on radiation damage behavior of multi-principal element alloys

Multi-principal element alloys(MPEAs)have attracted much attention as future nuclear materials due to their extraordinary radiation resistances.In this work,we have elucidated the development of local chemical orderings(LCOs)and their influences on radiation damage behavior in the typical CrFeNi MPEA by hybrid-molecular dynamics and Monte Carlo simulations.It was found that considerable LCOs consist-ing of the Cr-Cr and Ni-Fe short-range orders existed in the ordered configuration with optimized system energy.Through modeling the accumulation cascades up to 1000 recoils,we revealed that the size of de-fect clusters and dislocation loops is smaller in the ordered configuration than those in the random one,although the former formed more Frenkel pairs(i.e.,self-interstitials and vacancies).In addition,the dis-tribution of dislocation loops is relatively more dispersed in the ordered configuration,and the stair-rod dislocations related to irradiation swelling are also smaller,implying that the existence of LCOs is con-ducive to enhancing radiation damage tolerance.To understand the underlying mechanism,the effects of LCOs on the formation and evolution of defects and radiation resistance were discussed from the aspects of atomic bonding,migration path,and energy of defect diffusion,which provides theoretical guidance for the design of MPEAs with enhanced radiation resistance.

Local chemical ordering coordinated thermal stability of nanograined high-entropy alloys

Nanograined(NG)materials often suffer from low thermal stability owing to the high volume fraction of grain boundaries(GBs).Herein,we investigate the possibility of utilizing local chemical ordering(LCO)for improving the thermal stability of NG FeCoNiCrMn highentropy alloys(HE As).NG HE As with two different grain sizes were considered.Tensile tests and creep test simulations were then performed to reveal the influence of LCO on the mechanical properties and thermal stability of NG HE As.After performing hybrid molecular dynamics and Monte Carlo simulations,Cr atoms were found to accumulate at GBs.By analyzing the atomic structure evolution during the deformation process,we found that the formation of LCO effectively stabilized the GBs and inhibited GB movement.In addition,dislocation nucleation from GBs and dislocation movement was also hindered.The inhibiting effect of LCO on GB movement and dislocation activity is more prominent than in the NG model with smaller grain sizes.The current simulation results suggest a possible strategy for enhancing the thermal stability of NG HEAs for service in a high-temperature environment.

Icosahedral medium-range order formed in Mg_(70)Zn_(30) metallic glass: a larger-scale molecular dynamics simulation

A larger-scale Mg70Zn30 alloy system including 100000 atoms has been simulated by using the molecular dynamics method to investigate the icosahedral medium-range order （IMRO） formed in the MgToZn30 metallic glass. It is found that the simulated pair distribution function of Mg70Zn30 metallic glass is in good agreement with the experimental results. The glass transition temperature Tg is near 450 K under the cooling rate of 1×10^12 K/s. The icosahedral local structures play a critical role in the formation of metallic glass, and they are the dominant local configurations in the Mg70Zn30 metallic glass. The IMRO in the Mg70Zn30 metallic glass is characterized by certain types of extended icosahedral clusters combined by intercross-sharing atoms in the form of chains or dendrites. The size distributions of these IMRO clusters present a magic number sequence of 19, 23, 25, 27, 29, 31, 33, 35, 37, 39,..., and the magic clusters can be classified into three types according to their compactness. The IMRO clusters grow rapidly in a low-dimensional way with cooling, but this growth is limited near Tg.

Unsplit-field higher-order nearly PML for arbitrary media in EM simulation

An unsplit-field higher order nearly perfectly matched layer(NPML)based on the auxiliary differential equation approach is introduced in three-dimensional finite-difference timedomain lattices.The proposed scheme has the advantage of both the NPML scheme and the higher order concept in terms of the improved absorbing performance and considerable computational efficiency.By incorporating with the generalized material independent concept,the proposed implementation is indepen dent of the material’s type.Thus,it has the advantages of terminating arbitrary media without changing the updated equations in the PML regions.Its effectiveness and efficiency is further demonstrated through numerical examples.

NUMERICAL SIMULATION OF METHANE-AIR TURBULENT JET FLAME USING A NEW SECOND-ORDER MOMENT MODEL

A new second-order moment model for turbulent combustion is applied in the simulation of methane-air turbulent jet flame. The predicted results are compared with the experimental results and with those predicted using the well-known EBU-Arrhenius model and the original second-order moment model. The comparison shows the advantage of the new model that it requires almost the same computational storage and time as that of the original second-order moment model, but its modeling results are in better agreement with experiments than those using other models. Hence, the new second-order moment model is promising in modeling turbulent combustion with NOx formation with finite reaction rate for engineering application.

Chaos in fractional-order generalized Lorenz system and its synchronization circuit simulation

The chaotic behaviours of a fractional-order generalized Lorenz system and its synchronization are studied in this paper. A new electronic circuit unit to realize fractional-order operator is proposed. According to the circuit unit, an electronic circuit is designed to realize a 3.8-order generalized Lorenz chaotic system. Furthermore, synchronization between two fractional-order systems is achieved by utilizing a single-variable feedback method. Circuit experiment simulation results verify the effectiveness of the proposed scheme.

Ordered water monolayer on ionic model substrates studied by molecular dynamics simulations

The molecular behaviors of interfacial water molecules at the solid/liquid interface are of a fundamental significance in a diverse set of technical and scientific contexts,thus have drawn extensive attentions.On certain surfaces,the water monolayer may exhibit an ordered feature,which may result in the novel wetting phenomenon.In this article,based on the molecular dynamics simulations,we make a detailed structure analysis of the ordered water monolayer on ionic model surface with graphene-like hexagonal lattices under various charges and unit cell sizes.We carefully analyze the water density profiles and potential of mean force,which are the origin of the special hexagonal ordered water structures near the solid surface.The number of hydrogen bonds of the ordered water monolayer near the solid surface is carefully investigated.

Atomistic Simulation of Phase Transformation and Fracture in Ordered Intermetallics

A review of computer simulations carried out at our Center for Materials Simulation applied to stud- ying the different atomistic processes of fracture and displacive (martensitic) transformations is pres- ented.Since these processes can happen extremely rapidly and involve only a small number of atoms initially,they are ideally suited for molecular dynamics type simulations which can currently only span times of the order of one nanosecond and involve at most a million atoms.A method is also presented for simulating much larger samples for much longer times through the use of the Monte-Carlo technique combined with a Ginzburg-Landau free energy functional,where the rele- vant material parameters are determined from molecular dynamics runs on the same alloy system.A summary of studies on fracture simulations in the ordered intermetallics NiAI and RuAl is given,as well as a discussion of the observation and analysis of the heterogeneous nucleation of the martensitic transformation in NiAI which shows localized soft mode phenomena.It is concluded that computer simulations,whether of the atomistic molecular dynamics type or of the larger scale Monte-Carlo variety,are rapidly becoming of greater and greater use in understanding the properties of solids under a wide rancle of temperature and stress conditions.

Effects of notches on the order of flux-closure state formation in bi-rings by micromagnetic simulation

The effects of the number and the location of notches on the formation of flux-closure states in bi-rings with fields applied in the x direction （i.e., along the short axis direction of hi-rings） and y direction （i.e., along the long axis direction of bi-rings） are investigated using micromagnetic simulation. For the bi-rings with one notch and the bi-rings with two notches symmetric about y axis, the order of flux-closure state formation in each ring can be controlled. But the flux-closure state forms simultaneously in each ring for the bi-rings with two notches symmetric about x axis. For the bi-rings with two notches that are symmetric neither about x axis nor about y axis, only one ring can form a flux- closure state in the y-direction field and no fluxclosure state can be found in rings in the x-direction field. Therefore, logic states can be defined by controlling the order of flux-closure state formation, which can be utilized in future logic devices.

A second order volume of fluid (VOF) scheme for numerical simulation of 2-D breaking waves

Among all environmental forces acting on ocean structures and marine vessels, those resulting from wave impacts are likely to yield the highest loads. Being highly nonlinear, transient and complex, a theoretical analysis of their impact would be impossible without numerical simulations. In this paper, a pressure-split two-stage numerical algorithm is proposed based on Volume Of Fluid (VOF) methodology. The algorithm is characterized by introduction of two pressures at each half and full cycle time step, and thus it is a second-order accurate algorithm in time. A simplified second-order Godunov-type solver is used for the continuity equations. The method is applied to simulation of breaking waves in a 2-D water tank, and a qualitative comparison with experimental photo observations is made. Quite consistent results are observed between simulations and experiments. Commercially available software and Boundary Integral Method (BIM) have also been used to simulate the same problem. The results from present code and BIM are in good agreement with respect to breaking location and timing, while the results obtained from the commercial software which is only first-order accurate in time has clearly showed a temporal and spatial lag, verifying the need to use a higher order numerical scheme.

CRYSTAL STRUCTURE OF A LONG－PERIOD ORDERED PHASE IN Fe－C MARTENSITE AND COMPUTER SIMULATION OF ITS ELECTRON DIFFRACTION PATTERNS

Different structure models of a long-period ordered phase in Fe-C martenstie formed during aging have been checked by computer simulation of electron diffraction(ED) patterns based on these models.The results showed that the simulated ED pattern of γ'-FexC(Ⅱ) model proposed by the present authors is in good agreement with experimentally observed ED pattern.It was also confirmed that the incommensurate superperiod stems from the coexistence of several γ'-Fe_xC(H) phases with different superperiods.The Fe(144)C(24)(Fe6C) model proposed by Uwakweh et al.generated ED patterns remarkably different from the experimental ones.

Research on Order Quantity Simulation

The order quantity is often affected by various factors, so it is morevaluable to research the problem of evaluating the order quantity based on a less premise. In thispaper, a complicated order quantity problem is studied and an order quantity simulation system isestablished with the simulation software of ARENA. Finally, an example is given.

High-Order Discontinuous Galerkin Method for Hovering Rotor Simulations Based on a Rotating Reference Frame

An implicit higher ? order discontinuous Galerkin(DG) spatial discretization for the compressible Euler equations in a rotating frame of reference is presented and applied to a rotor in hover using hexahedral grids. Instead of auxiliary methods like grid adaptation,higher ? order simulations(fourth ? and fifth ? order accuracy) are adopted.Rigorous numerical experiments are carefully designed,conducted and analyzed. The results show generally excellent consistence with references and vigorously demonstrate the higher?order DG method's better performance in loading distribution computations and tip vortex capturing, with much fewer degrees of freedom(DoF). Detailed investigations on the outer boundary conditions for hovering rotors are presented as well. A simple but effective speed smooth procedure is developed specially for the DG method. Further results reveal that the rarely used pressure restriction for outlet speed has a considerable advantage over the extensively adopted vertical speed restriction.

AN INTEGRATION METHOD WITH FITTING CUBIC SPLINE FUNCTIONS TO A NUMERICAL MODEL OF 2ND-ORDER SPACE-TIME DIFFERENTIAL REMAINDER——FOR AN IDEAL GLOBAL SIMULATION CASE WITH PRIMITIVE ATMOSPHERIC EQUATIONS

In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the spherical coordinates.The Spline Model,which adopted the Navier-Stokes primitive equations and quasi-Lagrangian time-split integration scheme,provides an initial ideal case of global atmospheric circulation.In addition,considering the essentially non-linear atmospheric motions,the Spline Model could judge reasonably well simple points of any smoothed variable field according to its fitting spline curvatures that must conform to its physical interpretation.

Microscopic phase-field simulation of L1_2 and D0_(22) phases during the early precipitation process of Ni-Cr-Al alloys

The influence of temperature on the precipitation mechanism and sequence of L 12 and D022 phases during the early precipitation process of a Ni-15.Sat%Cr-14at%Al alloy was simulated based on the microscopic phase-field model. In the range from 873 to 1373 K, the precipitation mechanism transformed from spinodal decomposition to non-classic nucleation and growth; the incubation period prolonged gradually with increasing temperature. The volume fraction of L12 phases increased and that of D022 phases decreased. D022 phases disappeared at 1373 K, and finally single-phase L12 phases were formed.

Microscopic Phase-field Simulation of Competition Mechanism Between L12 and D022 Structure in Ni-Cr-Al Alloy

Simulations are performed on temporal evolution of atom morphology and ordering parameters of Ni-14.5 Cr-16.5 Al alloy during early precipitation process at different temperatures based on microscopic phase-field theory; the relationship between precipitation sequence and mechanism of L12 and D022 structure and precipitation temperature are illuminated. The nonstoichiometric ordered L12 phases appear first with congruent ordering＋spinodal decomposition mechanism which is then followed by precipitation of D022 phases at ordering domain boundaries of L12 phases by spinodal decomposition mechanism at 1073 K and 1223 K. The nonstoichiometric L12 phases transform to stoichiometric ordering phases gradually. The incubation period of L12 and D022 phases is shorter at 1073 K than that 1223 K, and growth speed is higher at 1073 K. At 1373 K, L12 and D022 phases appear simultaneously by non-classical nucleation and growth mechanism. After that the particles of D022 phases diminish and disappear gradually; L12 phases grow and single L12 phases are remained at last.

Pricing and Ordering Strategies of E-Retailers in Electronic Business Environments

It is becoming increasingly evident that in the future the Internet will host large numbers of software agents that aid or even act on behalf of companies and consumers to make decisions and carry out transactions. In this paper, we develop different pricing and ordering strategies with limited information requirements for e-retailers under the electronic business environment, and study the dynamics and performance of these strategies through multi-agent simulation. The results not only reproduce some phenomena in former literature, such as the "tacit collusion" and the cyclical price wars,but also generate new findings, for example, the "tacit collusion" does not always exist among hill-climbing e-retailers, and the cyclical price wars will be suppressed when e-retailers consider their competitors'strategies. The results show that in electronic business environments, to test different strategies and evaluate their performance by simulation before they are employed into practice is of great importance.