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.

Viscoacoustic prestack reverse time migration based onthe optimal time-space domain high-order finite-difference method

Prestack reverse time migration （RTM） is an accurate imaging method ofsubsurface media. The viscoacoustic prestack RTM is of practical significance because itconsiders the viscosity of the subsurface media. One of the steps of RTM is solving thewave equation and extrapolating the wave field forward and backward; therefore, solvingaccurately and efficiently the wave equation affects the imaging results and the efficiencyof RTM. In this study, we use the optimal time-space domain dispersion high-order finite-difference （FD） method to solve the viscoacoustic wave equation. Dispersion analysis andnumerical simulations show that the optimal time-space domain FD method is more accurateand suppresses the numerical dispersion. We use hybrid absorbing boundary conditions tohandle the boundary reflection. We also use source-normalized cross-correlation imagingconditions for migration and apply Laplace filtering to remove the low-frequency noise.Numerical modeling suggests that the viscoacoustic wave equation RTM has higher imagingresolution than the acoustic wave equation RTM when the viscosity of the subsurface isconsidered. In addition, for the wave field extrapolation, we use the adaptive variable-lengthFD operator to calculate the spatial derivatives and improve the computational efficiencywithout compromising the accuracy of the numerical solution.

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.

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 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.

Performance Evaluation System of Pig Supply Chain Based on Time-Space Perspective and Balanced Score Card(BSC)

The overall structure of live pig supply chain was constructed based on theoretical study and practical investigation, and the performance evaluation sys- tem for supply chain was studied from two perspectives of time and space and balanced score card （BSC）. From the space perspective and BSC, the performance evaluation system composed of four primary indicators （financial dimension, customer dimension, internal business dimension and innovation/learning perspective） and 26 secondary indicators. From the time perspective and BSC, the system could be divided into four stages, including formation stage, development stage, matu- rity stage and recession stage, with a total of 30 indicators.

A "TIME-SPACE" RELATED DESIGN METHOD OF FREEZING WALL

Artificially ground freezing (AGF) is one of the main methods to establish temporary support for shaft sinking in unstable water bearing strata. Domde (1915) formula based on frozen soil strength has widely been used for designing freezing wall thickness. However, it can not ensure the stability of freezing wall, nor guarantee the safety of shaft construction as frozen depth increases in unstable water bearing strata. F A. Auld (1985, 1988)[1,2] presented a design method of freezing wall, which is on the basis of strength and stability, together with deformation of freezing wall. This paper, according to the practice in China, describes a "time -space" related design method for deep freezing wall. The method is based on "time-space" concept, which includes influence of excavation rate of advance, unsupported length of freezing wall and the sump state on inward deformation of freezing wall, and the allowable pipe deformation caused by inward deformation of freezing wall. Finally, successful application of this method to the large scale coal mine-Jining No. 2 Mine[3] in Shandong Province of China is presented. It saved much investment compared with F. A. Auld’s design for the same mine.

A traffic model of optical networks based on time-space complexity and traffic grooming

This paper researched the traffic of optical networks in time-space complexity,proposed a novel traf-fic model for complex optical networks based on traffic grooming,designed a traffic generator GTS(gener-ator based on time and space)with 'centralized+distributed' idea,and then made a simulation in Clanguage.Experiments results show that GTS can produce the virtual network topology which can changedynamically with the characteristic of scaling-free network.GTS can also groom the different traffic andtrigger them under real-time or scheduling mechanisms,generating different optical connections.Thistraffic model is convenient for the simulation of optical networks considering the traffic complexity.

Earthquake-Affected Time-Space Domain, Recurrence Interval and Effective Preparation Time of Earthquakes

The study shows that earthquake-affected time-space domain (ETSD), i.e. a time-space range in which strong earthquakes are unable to occur owing to the influence of a prior earthquake occurring, shows a hyperbolic margin curve in the t(time)-r(distance) coordinate plane, which has a maximum affected radius r 0 at t=0 and a maximum influence time t 0 (i.e. the in-situ recurrence interval of earthquakes) at r=0. Based on the time-distance distributions of posterior earthquakes relative to prior ones in the regions of North China, Northwest China, Qinghai-Xizang (Tibet) plateau and Southwest China, the optimized and 90%-confidence margin curves are estimated using optimization and statistical analysis methods. This indicates that the concept and method of ETSD with 3-dimension (time-distance-magnitudes) instead of those of “recurrence interval" with 1-dimension (time) or 2-dimension (time-magnitude) provides a new approach to understanding the fluctuation of seismic activities, estimating the effective earthquake-preparation time of potential hypocenters, and therefore improving the medium- and long-term prediction of strong earthquakes.

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.

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.

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.

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.