A Proper Time Integration with Split Stepping for the Explicit Free-Surface Modeling

Errors due to split time stepping are discussed for an explicit free–surface ocean model. In commonly used split time stepping, the way of time integration for the barotropic momentum equation is not compatible with that of the baroclinic one. The baroclinic equation has three–time–level structure because of leapfrog scheme. The barotropic one, however, has two–time–level structure when represented in terms of the baroclinic time level, on which the baroclinic one is integrated. This incompatibility results in the splitting errors as shown in this paper. The proper split time stepping is therefore proposed in such a way that the compatibility is kept between the barotropic and baroclinic equations. Its splitting errors are shown extremely small, so that it is particularly relevant to long–term integration for climate studies. It is applied to a free–surface model for the North Pacific Ocean.

Multidimensional Numerical Simulation of Glow Discharge by Using the N-BEE-Time Splitting Method

In this work, a new numerical technique is proposed for the resolution of a fluid model based on three Boltzmann moments. The main purpose of this technique is to calculate electric and physical properties in the non-equilibrium electric discharge at low pressure. The transport and Poisson＇s equations form a self-consistent model. This equation system is written in cylindrical coordinates following the geometric shape of a plasma reactor. Our transport equation system is discretized using the finite volume approach and resolved by the N-BEE explicit scheme coupled to the time splitting method. This programming structure reduces computation time considerably. The 2D code is carried out and tested by comparing our results with those found in literature.

Profiling elite male 100-m sprint performance:The role of maximum velocity and relative acceleration

Purpose:This study aimed to determine the accuracy of a 4 split time modelling method to generate velocity-time and velocity-distance variables in elite male 100-m sprinters and subsequently to assess the roles of key sprint parameters with respect to 100-m sprint performance.Additionally,this study aimed to assess the differences between faster and slower sprinters in key sprint variables that have not been assessed in previous work.Methods:Velocity-time and velocity-distance curves were generated using a mono-exponential function from 4 split times for 82 male sprinters during major athletics competitions.Key race variables-maximum velocity,the acceleration time constant(τ),and percentage of velocity lost(vLoss)-were derived for each athlete.Athletes were divided into tertiles,based on 100-m time,with the first and third tertiles considered to be the faster and slower groups,respectively,to facilitate further analysis.Results:Modelled split times and velocities displayed excellent accuracy and close agreement with raw measures(range of mean bias was-0.2%to 0.2%,and range of intraclass correlation coefficients(ICCs)was 0.935 to 0.999)except for 10-m time(mean bias was 1.6%±1.3%,and the ICC was 0.600).The 100-m sprint performance time and all 20-m split times had a significant near-perfect negative correlation with maximum velocity(r≥-0.90)except for the 0 to 20-m split time,where a significantly large negative correlation was found(r=-0.57).The faster group had a significantly higher maximum velocity andτ(p<0.001),and no significant difference was found for vLoss(p=0.085).Conclusion:Coaches and researchers are encouraged to utilize the 4 split time method proposed in the current study to assess several key race variables that describe a sprinter’s performance capacities,which can be subsequently used to further inform training.

Modeling Thermodynamics of Smart Cut Process

A thermodynamic model of hydrogen induced silicon surface layer splitting with the help of an oxidized silicon wafer bonded is proposed.Wafer splitting is the result of lateral growth of hydrogen blisters in the entire implanted hydrogen region during annealing.The blister growth rate depends on the effective activation energies of both hydrogen complex dissociation and hydrogen diffusion.The hydrogen blister radius was studied as the function of annealing time,annealing temperature and implantation dose.The critical radius was obtained according to the Griffith energy condition.The time required for wafer splitting at the cut temperature was calculated in accordance with the growth of hydrogen blisters.

NUMERICAL SIMULATIONS OF EVOLUTIONS FROM WALL PULSE TO TURBULENT COHE RENT STRUCTURES

The high order compact d if ference method is developed for solving the perturbation equations based on Navi er Stokes equations, and is used in studying complex evolution processes from w all negative pulse to the turbulent coherent structure in the channel flow. Th is method contains three dimensional coupling difference scheme with high accur acy and high resolution, and the high order time splitting methods. Compared with the general spectral method, the method can be used to research turbule nt coherent structure under more general boundary conditions and in flow domains . In this paper, the generation and evolution of the turbulent coherent structur es ind uced by wall pulse in the channel flow are simulated, and the basic characterist ics and rules of the turbulent coherent structure are shown. Computational r esults indicate that a wall negative pulse is more convenient than the resonant three wave model.

Spectrum Efficiency Maximization for Cooperative Power Beacon-Enabled Wireless Powered Communication Networks

We consider a spectrum efficiency(SE)maximization problem for cooperative power beacon-enabled wireless powered communication networks(CPB-WPCNs),where each transmitter harvests en-ergy from multi-antenna power beacons(PBs)and transmits data to the corresponding receiver.For data transmission,both orthogonal transmission,i.e.,the time splitting(TS)mode,and non-orthogonal trans-mission,i.e.,the interference channel(IC)mode,are considered.Aiming to improve the system SE,the energy beamformers of PBs,the transmit power,and the transmit time duration of transmitters are jointly optimized.For the TS mode,the original non-convex problem is transformed into a convex opti-mization problem by means of variable substitution and semidefinite relaxation(SDR).The rank-one na-ture of this SDR is proved,and then a Lagrange-dual based fast algorithm is proposed to obtain the opti-mal solution with much lower complexity.For the IC mode,to conquer the strong non-convexity of the problem,a branch-reduce-and-bound(BRB)mono-tonic optimization algorithm is designed as a bench-mark.Furthermore,a low-complexity distributed suc-cessive convex approximation(SCA)algorithm is pre-sented.Finally,simulation results validate the perfor-mance of the proposed algorithms,achieving optimal-ity within only 1%∼2%computation time compared to the CVX solver in the TS mode and achieving 98%of the optimal performance in the IC mode.

Computational Methods for Three Coupled Nonlinear Schrödinger Equations

In this work, we will derive numerical schemes for solving 3-coupled nonlinear Schr&ouml;dinger equations using finite difference method and time splitting method combined with finite difference method. The resulting schemes are highly accurate, unconditionally stable. We use the exact single soliton solution and the conserved quantities to check the accuracy and the efficiency of the proposed schemes. Also, we use these methods to study the interaction dynamics of two solitons. It is found that both elastic and inelastic collision can take place under suitable parametric conditions. We have noticed that the inelastic collision of single solitons occurs in two different manners: enhancement or suppression of the amplitude.

Infragravity Waves Produced by Wave Groups on Beaches

The generation of low frequency waves by a single or double wave groups incident upon two Plane beaches with the slope of 1/40 and 1/100 is investigated experimentally and numerically. A new type of wave maker signal is used to generate the groups, allowing the bound long wave (set-down) to be included in the group. The experiments show that the low frequency wave is generated during breaking and propagation to the shoreline of the wave group. This process of generation and propagation of low frequency waves is simulated numerically by solving the short-wave averaged mass and momentum conservation equations. The computed and measured results are in good agreement. The mechanism of generation of low frequency waves in the surf zone is examined and discussed.

Decode-and-Forward Relay Based Bidirectional Wireless Information and Power Transfer

In this paper, we propose the decode-and-forward(DF) based bidirectional wireless information and power transfer(BWIPT) in two-hop relay systems, where the bidirectional relay can decode and forward information from the user to the access point(AP), and assist the wireless power transfer from the AP to the user. To maximize the information rate from the user to the AP, we derive the closed form expression of the optimal power splitting(PS) factor, and the time allocation scheme to obtain the optimal time switching(TS) factor. Simulation results show that for both PS and TS protocols, the proposed DF based bidirectional relay systems can improve the information rate as compared with the amplify-and-forward(AF) based bidirectional relay systems.

Simulation and characteristics analysis of a wavefield in a thermoelastic medium adopting the rotated staggered-grid pseudospectral method and L-S theory

The simulation of wave propagation in high-temperature media requires thermoelastic theory.In this paper,we apply the rotated-staggered-grid pseudo-spectral method(RSG-PSM)to solving thermoelastic governing equations based on L-S theory.A time splitting method is used to solve the stiffness problem of the equations,and we introduce the rotated staggered pseudo-spectral operator and centered pseudo-spectral operator to compute the first-order spatial derivatives and second-order spatial derivatives,respectively.In the case of the heterogeneous-medium model,the Crank-Nicolson explicit method is used instead of the pseudo-spectral method to compute the wavefield.The properties and propagation of the thermal coupled wavefield are discussed,and we compare the simulation results obtained using the pseudo-spectral method,staggered-grid pseudo-spectral method,and RSG-PSM.In the case of an isotropic homogeneous medium,we obtain stable and highly accurate results using the time splitting method combined with the RSG-PSM.However,the algorithm cannot be applied with a large time step when the thermal conductivity changes dramatically,and the algorithm is unstable when the reference temperature has a gradient distribution.The optimal combined application of the mesh generation mode and numerical algorithm is explored,laying a foundation for the extension of these methods to thermoporoelasticity,thermoviscoelasticity,and anisotropy.

An unconditionally energy stable finite difference scheme for a stochastic Cahn-Hilliard equation

In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation, is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional.For the non-stochastic case, we develop an unconditionally energy stable difference scheme which is proved to be uniquely solvable. For the stochastic case, by adopting the same splitting of the energy functional, we construct a similar and uniquely solvable difference scheme with the discretized stochastic term. The resulted schemes are nonlinear and solved by Newton iteration. For the long time simulation, an adaptive time stepping strategy is developed based on both first- and second-order derivatives of the energy. Numerical experiments are carried out to verify the energy stability, the efficiency of the adaptive time stepping and the effect of the stochastic term.

Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime

We present several numerical methods and establish their error estimates for the discretization of the nonlinear Dirac equation （NLDE） in the nonrelativistic limit regime, involving a small dimensionless parameter 0 〈 ε〈〈1 which is inversely proportional to the speed of light. In this limit regime, the solution is highly oscillatory in time, i.e., there are propagating waves with wavelength O（ ε^2） and O（1） in time and space, respectively. We begin with the conservative Crank-Nicolson finite difference （CNFD） method and establish rigorously its error estimate which depends explicitly on the mesh size h and time step τ- as well as the small parameter 0 〈 ε≤1 Based on the error bound, in order to obtain ＇correct＇ numerical solutions in the nonrelativistic limit regime, i.e., 0 〈 ε≤1 , the CNFD method requests the ε-scalability： τ- = O（ε3） and h = O（√ε）. Then we propose and analyze two numerical methods for the discretization of NLDE by using the Fourier spectral discretization for spatial derivatives combined with the exponential wave integrator and time- splitting technique for temporal derivatives, respectively. Rigorous error bounds for the two numerical methods show that their ε-scalability is improved to τ = O（ε2） and h = O（1） when 0 〈 ε 〈〈 1. Extensive numerical results are reported to confirm our error estimates.

Numerical Study of Quantized Vortex Interaction in theGinzburg-Landau Equation on Bounded Domains

In this paper,we study numerically quantized vortex dynamics and their interaction in the two-dimensional(2D)Ginzburg-Landau equation(GLE)with a dimensionless parameter#>0 on bounded domains under either Dirichlet or homogeneous Neumann boundary condition.We begin with a reviewof the reduced dynamical laws for time evolution of quantized vortex centers in GLE and show how to solve these nonlinear ordinary differential equations numerically.Then we present efficient and accurate numerical methods for discretizing the GLE on either a rectangular or a disk domain under either Dirichlet or homogeneous Neumann boundary condition.Based on these efficient and accurate numerical methods for GLE and the reduced dynamical laws,we simulate quantized vortex interaction of GLE with different#and under different initial setups including single vortex,vortex pair,vortex dipole and vortex lattice,compare them with those obtained from the corresponding reduced dynamical laws,and identify the cases where the reduced dynamical laws agree qualitatively and/or quantitatively as well as fail to agree with those from GLE on vortex interaction.Finally,we also obtain numerically different patterns of the steady states for quantized vortex lattices under the GLE dynamics on bounded domains.