Finite Difference Schemes for Time-Space Fractional Diffusion Equations in One-and Two-Dimensions

In this paper,finite difference schemes for solving time-space fractional diffusion equations in one dimension and two dimensions are proposed.The temporal derivative is in the Caputo-Hadamard sense for both cases.The spatial derivative for the one-dimensional equation is of Riesz definition and the two-dimensional spatial derivative is given by the fractional Laplacian.The schemes are proved to be unconditionally stable and convergent.The numerical results are in line with the theoretical analysis.

TIME-SPACE CONCEPT FOR PRECISION MEASUREMENT

The transformation between time and space is discussed. To improve real-time response speed of intelligent measuring system, the concept of exchanging program execution time with more circuitry is presented working in cycle mode. Displacement measuring by magnification is achieved with period measurement by magnification. To change the condition that traditional precision measurement depends on machining precision greatly, the concept of measuring space with time and theory of time-space coordinate transformation are proposed. Guided by the idea of measuring space with time, differential frequency measurement system and time grating displacement sensor are developed based on the proposed novel methods. And high-precision measurement is achieved without high-precision manufacture, which embeds the remarkable characteristics of low cost but high precision to the devices. Experiment and test results conform the validity of the proposed time-space concept.

Adaptive time-space resource and waveform control for collocated MIMO radar with simultaneous multi-beam

Collocated multiple input multiple output(MIMO)radar,which has agile multi-beam working mode,can offer enhanced multiple targets tracking(MTT)ability.In detail,it can illuminate different targets simultaneously with multi-beam or one wide beam among multi-beam,providing greater degree of freedom in system resource control.An adaptive time-space resource and waveform control optimization model for the collocated MIMO radar with simultaneous multi-beam is proposed in this paper.The aim of the proposed scheme is to improve the overall tracking accuracy and meanwhile minimize the resource consumption under the guarantee of effective targets detection.A resource and waveform control algorithm which integrates the genetic algorithm(GA)is proposed to solve the optimization problem.The optimal transmitting waveform parameters,system sampling period,sub-array number,binary radar tracking parameterχ_i(t_k),transmitting energy and multi-beam direction vector combination are chosen adaptively,where the first one realizes the waveform control and the latter five realize the timespace resource allocation.Simulation results demonstrate the effectiveness of the proposed control method.

Adaptive resource management for multi-target tracking in co-located MIMO radar based on time-space joint allocation

Compared with the traditional phased array radar, the co-located multiple-input multiple-output(MIMO) radar is able to transmit orthogonal waveforms to form different illuminating modes, providing a larger freedom degree in radar resource management. In order to implement the effective resource management for the co-located MIMO radar in multi-target tracking,this paper proposes a resource management optimization model,where the system resource consumption and the tracking accuracy requirements are considered comprehensively. An adaptive resource management algorithm for the co-located MIMO radar is obtained based on the proposed model, where the sub-array number, sampling period, transmitting energy, beam direction and working mode are adaptively controlled to realize the time-space resource joint allocation. Simulation results demonstrate the superiority of the proposed algorithm. Furthermore, the co-located MIMO radar using the proposed algorithm can satisfy the predetermined tracking accuracy requirements with less comprehensive cost compared with the phased array radar.

A Time-Space Optimal Parallel Sorting on a Hypercube

In this paper we discuss a parallel sorting algorithm on a hypercube. Its time complexity is O(n logn/p) +O(n). Here, P is the number of processors available and n, the amount of items to be sorted. Take the problem of time-space optimization into consideration, when P≤ O(log n), this algorithm is both timespace optimal and cost optimization. But this means only speedup is O(P) and it is not linear speedup. Therefore, we further discuss relevant parallel efficiency problems.

Modeling of Surface Waves in a Fluid Saturated Poro-Elastic Medium under Initial Stress Using Time-Space Domain Higher Order Finite Difference Method

In this present context, mathematical modeling of the propagation of surface waves in a fluid saturated poro-elastic medium under the influence of initial stress has been considered using time dependent higher order finite difference method (FDM). We have proved that the accuracy of this finite-difference scheme is 2M when we use 2nd order time domain finite-difference and 2M-th order space domain finite-difference. It also has been shown that the dispersion curves of Love waves are less dispersed for higher order FDM than of lower order FDM. The effect of initial stress, porosity and anisotropy of the layer in the propagation of Love waves has been studied here. The numerical results have been shown graphically. As a particular case, the phase velocity in a non porous elastic solid layer derived in this paper is in perfect agreement with that of Liu et al. (2009).

SLC Method and Earthquakes' Clustering Features in Time-Space in the Top Area of the Kunlun-Altun-Arc

By using the SLC(Single-Link Cluster)method,this study worked in three respects:(a)set up three-dimensional(3-D)SLC software that can deal with a large catalogue of earthquakes and analyze the characteristics of earthquakes’ clustering and scattering in time-space:(b)defined several parameters to describe the distinguishing feature for the SLC frame and developed a technique to calculate the 3-D SLC frames and these parameters with gradual time-sliding,and inspected their variations with time,especially before large events; and(c)by using these means,treated the earthquake catalogue in the top area of the Kunlun-Altun-Arc as well as some valuable results that had been obtained.

FULL TIME-SPACE GOVERNANCE STRATEGY AND TECHNOLOGY FOR CROPLAND NON-POINT POLLUTION CONTROL IN CHINA

Ensuring food safety while reducing agricultural non-point source pollution is quite challenging,especially in developing and underdeveloped countries.Effective systematic strategies and comprehensive technologies need to be developed for agricultural non-point source pollution control at the watershed scale to improve surface water quality.In this review,a proposal is made for a full time-space governance strategy that prioritizes source management followed by endpoint water pollution control.The 4R chain technology system is specifically reviewed,including source reduction,process retention,nutrient reuse and water restoration.The 4R chain technology system with the full time-space governance strategy was applied at the scale of an administrative village and proved to be a feasible solution for reducing agricultural non-point source pollution in China.In the future,a monitoring system needs to be established to trace N and P transport.Additionally,new smart fertilizer and intelligent equipment need to be developed,and relevant governance standards and supportive policies need to be set to enhance the efficacy of agricultural non-point source pollution control.

Can Time-Space Compression Promote Urban Economic Growth?Evidence from China’s High-speed Rail Projects

This paper studies the effect of high-speed rail(HSR)on urban economic growth using a panel data comprising 285 Chinese cities in 2007-2017.Combining the endogenous growth model with a difference-in-difference analysis,we extend the horse-mass theory to explain how China may use HSR to avoid the so-called middle-income trap.The paper also examines the efficient boundaries of HSR and simultaneously studies HSR timespace compression as well as the city neighboring ejfects on economic growth.It is found that HSRs efficient boundaries are within the range of 200-1,200 km for provincial capitals and 50-300 km for prefecture-level cities.HSR stimulates economic growth by approximately 0.6 percent,and the neighboring effect accounts for one-quarter of economic growth.Three policy implications are drawn:(i)China needs tofurther reduce the travel times between the inland provincial cities and Beijing,Shanghai or Guangzhou;(ii)China should build a denser HSR network to maximize its economic impact on the vast majority of cities;(Hi)China needs to develop some powerful economic growth centers in the inland areas to lead the development of their neighboring cities.

The driven cavity turbulent flow with porous walls: Energy transfer, dissipation, and time-space correlations

The energy transfer and dissipation as well as the turbulent structures in a lid-driven cavity flow with porous walls are investigated via the lattice Boltzmann method, with direct numerical simulation (DNS) for an isothermal incompressible flow for which the Reynolds number (Re) is 50 000. A generalized Navier-Stokes equation with the Brinkman-Forchheimer-extended Darcy model is implemented, in which the presence of permeable walls is taken into account. This study focuses on the modulations of the flow field due to porous walls, by comparing with the results from the cavity flow bounded with smooth walls. Firstly, we derived the exact expression of the kinetic energy dissipation rate in a cavity to study the budget balance of the induced and dissipated kinetic energy. By decomposing the total kinetic energy dissipation into the componential contributions of the viscous and porous medium layer, we found that the kinetic energy dissipated in the thin porous layer occupies 37% of the total driven lid-induced kinetic energy in the present parameters. Then we found that the time-averaged kinetic energy, turbulent kinetic energy (TKE), as well as the strength of the large-scale energy-containing eddy, and secondary eddies are significantly attenuated. Furthermore, it is found that the momentum and kinetic energy transfer near the corners are vastly decreased. Finally, the space-time velocity correlation functions are also provided to examine the decorrelation property of small eddies by means of convection and distortion motions in the cavity turbulent field.

Multiple time-space scale atmosphere-ocean interactions and improvement of Zebiak-Cane model

In a real climate system there are multiple time-space scale atmosphere-ocean interactions, ranging from the planetary scale and basin scale to local air-sea interactions. The Zebiak-Cane (ZC) model with one-level atmosphere described only local air-sea interaction process. Thus the planetary scale Hadley cell and Walker cell anomalies should be introduced in the model. Including the planetary scale Hadley cell anomaly in the model improved the prediction skill. It showed that the improved model provided satisfactory prediction of the equatorial eastern Pacific SST anomaly with lead time of 9-10 months not only for 1970-1991 but also for 1992-1995.

Complex time－space spreading and focal mechanism of the 1989 Batang earthquake swarm （M_s＝6．7）

On the basis of field observations, the complex time-space spreading pattern and focal mechanism of the 1989Batang earthquake swarm are studied in this paper. The fault motions of the epicenter area are analysed bythe leveling survey before and after strong events. From the given simplified focal mechanical model of theswarm,the process of fracture indicates that swarm strong ruptures are associated with the spreading and thevirgation of the barrier of irregularen en echelon source fault system.

Application of the Improved Kudryashov Method to Solve the Fractional Nonlinear Partial Differential Equations

Our purpose of this paper is to apply the improved Kudryashov method for solving various types of nonlinear fractional partial differential equations. As an application, the time-space fractional Korteweg-de Vries-Burger (KdV-Burger) equation is solved using this method and we get some new travelling wave solutions. To acquire our purpose a complex transformation has been also used to reduce nonlinear fractional partial differential equations to nonlinear ordinary differential equations of integer order, in the sense of the Jumarie’s modified Riemann-Liouville derivative. Afterwards, the improved Kudryashov method is implemented and we get our required reliable solutions where the results are justified by mathematical software Maple-13.

Nonlinear Waves on Localized and Periodic Backgrounds with Time-Space Modulation

We present one family of general analytical solutions for the generalized nonlinear Schr?dinger equation with time-space modulation via the method of a combination of the Darboux transformation and similarity transformation. Nonlinear waves on different localized and periodic backgrounds depending on the corresponding nonlinearity modulations are obtained. In particular, we demonstrate the existence and property of localized modes on a doubleperiodic background under a special designed optical lattice potential. Our results may raise the possibility of related experiments and potential applications in nonlinear optics and Bose–Einstein condensates.

A NON－INCREMENTAL TIME－SPACE ALGORITHM FOR NUMERICAL SIMULATION OF FORMING PROCESS

A non-incremental time-space algorithm is proposed for numerical. analysis of forming process with the inclusion of geometrical, material, contact-frictional nonlinearities. Unlike the widely used Newton-Raphson counterpart, the present scheme features an iterative solution procedure on entire time and space domain. Validity and feasibility of foe present scheme are further justiced by the numerical investigation herewith presented.

Analytical Solutions, Moments, and Their Asymptotic Behaviors for the Time-Space Fractional Cable Equation

Following the fractional cable equation established in the letter [B.I. Henry, T.A.M. Langlands, and S.L.Wearne, Phys. Rev. Lett. 100(2008) 128103], we present the time-space fractional cable equation which describes the anomalous transport of electrodiffusion in nerve cells. The derivation is based on the generalized fractional Ohm's law;and the temporal memory effects and spatial-nonlocality are involved in the time-space fractional model. With the help of integral transform method we derive the analytical solutions expressed by the Green's function; the corresponding fractional moments are calculated; and their asymptotic behaviors are discussed. In addition, the explicit solutions of the considered model with two different external current injections are also presented.

Model of Airflow Field on the Deck for Shipborne Helicopter Flight Dynamics Analysis

For the research of helicopter/ship dynamic interface,the method of combining steady flow and stochastic flow is adopted to establish a flow field model applied to the flight dynamics analysis of shipborne helicopter.The steady flow is calculated by computational fluid dynamics(CFD)method,while the stochastic flow is composed of the compensation velocity derived from ship motion and turbulence above the deck.The accuracy of the proposed flow field model is verified by comparing the helicopter response in the proposed flow field with the results calculated by US Army′s Military Specifications(MIL)model which is commonly used in engineering.Meanwhile,it also shows the proposed flow field model is more appliable to flight dynamics analysis of shipborne helicopter.On that the basis,ship deck flow field is simulated at different sea conditions by adjusting the wind speed on the deck,mother ship movement and shipboard turbulence,etc.And helicopter angular rate response is calculated.The results show that the difference of dynamic stability between helicopter′s roll and pitch leads to the facts that the influence of above factors on the helicopter′s roll angular rate response is greater than that of pitch angular rate,that the frequency and amplitude of mother ship roll motion are much greater than those of pitch motion,and that the disturbance caused by roll motion on the air has greater influence on the helicopter response.The shipboard turbulence is the main disturbance factor that influences helicopter flight stability and its intensity determines the amplitudes of angular rate response.

A STUDY ON CONTROLLABLE ANALOG DELAY LINE

This paper presents an analog delay line devised under the principle of an inventionof this country,the DYL integrated linear“AND-OR”gate.The analog delay line is distinguishedfor its features:simple in circuit structure,speedy in transmission,and capable of controlling thequantity of delay in the circuit by digital quantity.

Fractal and Fractional Diffusion Equations of Price Changing of Commodity

In this paper, three types of modeling of diffusion equations for price changing of commodity are studied. In which, the partial derivatives of price of commodity respected to time on the left hand side are integer-derivative, fractal derivative, and fractional derivative respectively;while just a second order derivative respected to space is considered on the right hand side. The solutions of these diffusion equations are obtained by method of departing variables and initial boundary conditions, by translation of variables, and by translation of operators. The definitions of order of commodity x and the distance between commodity?xi and xj are defined as [1]. Examples of calculation of price of pork, beef and mutton mainly due to price raising of pork in 2007-07 to 2008-02 inChina are given with same market data as [1]. Conclusion is made.

A time-space network based international transportation scheduling problem incorporating CO_2 emission levels

Environmental problems have received a great deal of attention in recent years.In particular,CO2 emissions worsen global warming and other environmental problems.The transport sector accounts for 20% of the total CO2 emissions.Therefore,the CO2 emission reduction of the transport sector is of great importance.In order to reduce emissions effectively,it is necessary to change the distribution and transportation processes.The purpose of this study is to minimize both the transportation costs and CO2 emissions during transportation.Our model considers a transportation scheduling problem in which loads are transported from an overseas production base to three domestic demand centers.The need for time-space networks arises naturally to improve the model.It is possible to know the distance carriers are moving,and also consider the timetables of carriers during transportation.Carrier choice,less-than carrier load,and domestic transportation among demand centers are considered as the three target areas to reduce CO2 emissions during the distribution process.The research model was formulated as a mixed integer programming (MIP) problem.It achieves cost reduction,and will contribute to improvement of the natural environment.