Exploration of Traversable Wormholes Sustained by an Extra Spatial Dimension

The main goal of this paper is to determine the effect of an extra dimension on a traversable wormhole. Here an earlier study by the author [Phys. Rev. D 98, 064041 (2018)] is extended in several significant ways. To begin with, the extra spatial dimension is assumed to be time dependent, while the redshift and shape functions, as well as the extra dimension, are functions of both r and l, the respective radial and extra coordinates;the last of these is therefore a function of r, l, and t. The main objective is to determine the conditions that allow the throat of the wormhole to be threaded with ordinary matter (by respecting the null energy condition) and that the same conditions lead to a violation of the null energy condition in the fifth dimension, which is therefore responsible for sustaining the wormhole. The dependence of the extra dimension on l and t is subject to additional conditions that are subsequently analyzed in this paper. Finally, the extra dimension may be extremely small or even curled up.

Effect of Spatial Dimension and External Potential on Joule-Thomson Coefficients of Ideal Bose Gases

Based on the form of the n-dimensional generic power-law potential, the state equation and the heat capacity, the analytical expressions of the Joule-Thomson coefficient （3TC） for an ideal Bose gas are derived in n-dimensional potential. The effect of the spatial dimension and the external potential on the JTC are discussed, respectively. These results show that： （i） For the free ideal Bose gas, when n/s ≤ 2 （n is the spatial dimension, s is the momentum index in the relation between the energy and the momentum）, and T → Tc （Tc is the critical temperature）, the JTC can obviously improve by means of changing the throttle valve＇s shape and decreasing the spatial dimension of gases. （ii） For the inhomogeneous external potential, the discriminant △= [1 - y∏^ni=1（kT/εi）^1/tiГ（1/ti＋1）] （k is the Boltzmann Constant, T is the thermodynamic temperature, ε is the external field＇s energy）, is obtained. The potential makes the JTC increase when △ 〉 0, on the contrary, it makes the JTC decrease when A 〈△. （iii） In the homogenous strong external potential, the JTC gets the maximum on the condition of kTεi〈〈1.

Efficient Sparse-Grid Implementation of a Fifth-Order Multi-resolution WENO Scheme for Hyperbolic Equations

High-order accurate weighted essentially non-oscillatory(WENO)schemes are a class of broadly applied numerical methods for solving hyperbolic partial differential equations(PDEs).Due to highly nonlinear property of the WENO algorithm,large amount of computational costs are required for solving multidimensional problems.In our previous work(Lu et al.in Pure Appl Math Q 14:57–86,2018;Zhu and Zhang in J Sci Comput 87:44,2021),sparse-grid techniques were applied to the classical finite difference WENO schemes in solving multidimensional hyperbolic equations,and it was shown that significant CPU times were saved,while both accuracy and stability of the classical WENO schemes were maintained for computations on sparse grids.In this technical note,we apply the approach to recently developed finite difference multi-resolution WENO scheme specifically the fifth-order scheme,which has very interesting properties such as its simplicity in linear weights’construction over a classical WENO scheme.Numerical experiments on solving high dimensional hyperbolic equations including Vlasov based kinetic problems are performed to demonstrate that the sparse-grid computations achieve large savings of CPU times,and at the same time preserve comparable accuracy and resolution with those on corresponding regular single grids.

Raman spectra and structure study of silicate glasses and their liquids

Stress index of tetrahedron （SIT） was defined to describe the topological connectivities among various sili- con-oxygen tetrahedra （SiOT） in anionic clusters of binary silicate crystals, glasses, and melts. It was found that the value of SIT was well correlated with the wavenumber of Raman active symmetric stretching vibration of non-bridging oxygen of SiOT. The spatial fractional dimension of hyperfine structure was introduced while comparative analysis was made with the value of SIT. It can be concluded that the concepts of SIT, vibrational wavenumber, and spatial fractional dimension were inherently and holographically correlated and exhibit isomorphic representations of complex structure of binary silicates. Experimental Raman spectra of binary silicates with different alkali cations were investigated. It was demonstrated that alkali cations have little effect on the vibrational wavenumber of symmetric stretching of non-bridging oxygen （NBO） of SiOT, but remarkably affect its Raman active optical cross section, as was consensus resulted from ab initio calculation. It can also be concluded that the spatial fractional dimension of binary silicate is predominantly determined by the hyperfine structure of the anionic clusters and little affected by alkali cations, although the species of anionic clusters and their distributions were originally assigned by the content of alkali oxides. And Raman optical activity extinct effect of isolated SiOT at high basicity should be considered while being applied to quantitatively analysis.

Study on Mach stems induced by interaction of planar shock waves on two intersecting wedges

The properties of Mach stems in hypersonic corner flow induced by Mach interaction over 3D intersecting wedges were studied theoretically and numerically.A new method called ＂spatial dimension reduction＂ was used to analyze theoretically the location and Mach number behind Mach stems. By using this approach, the problem of 3D steady shock/shock interaction over 3D intersecting wedges was transformed into a 2D moving one on cross sections, which can be solved by shock-polar theory and shock dynamics theory. The properties of Mach interaction over 3D intersecting wedges can be analyzed with the new method,including pressure, temperature, density in the vicinity of triple points, location, and Mach number behind Mach stems.Theoretical results were compared with numerical results,and good agreement was obtained. Also, the influence of Mach number and wedge angle on the properties of a 3D Mach stem was studied.

A gas-kinetic theory based multidimensional high-order method for the compressible Navier–Stokes solutions

This paper presents a gas-kinetic theory based multidimensional high-order method for the compressible Naiver–Stokes solutions. In our previous study, a spatially and temporally dependent third-order flux scheme with the use of a third-order gas distribution function is employed.However, the third-order flux scheme is quite complicated and less robust than the second-order scheme. In order to reduce its complexity and improve its robustness, the secondorder flux scheme is adopted instead in this paper, while the temporal order of method is maintained by using a two stage temporal discretization. In addition, its CPU cost is relatively lower than the previous scheme. Several test cases in two and three dimensions, containing high Mach number compressible flows and low speed high Reynolds number laminar flows, are presented to demonstrate the method capacity.

On the inverse scattering transform in two spatial and one temporal dimensions

Some results and developments on the extension of the inverse scattering transform to solve non-linear evolution equations in one time and two space dimensions are described.

Design and experiment of variable rate orchard sprayer based on laser scanning sensor

During different growth periods,canopy size and density in orchards are variable,which need application conditions(flow rate and air flow)to be adjusted to match the canopy’s characteristics.In order to improve orchard sprayer’s automatic operating performance,an automatic variable-rate orchard sprayer(VARS)fixed with 40 electromagnetic valves and 8 brushless fans was developed based on the canopy’s spatial dimensions.Each solenoid valve and brushless motor can be individually adjusted in real-time through pulse width modulation(PWM)signals emitted by a control system to adjust each nozzle’s spout and fan rotation speed.A high-precision laser scanning sensor(light detecting and ranging,LIDAR)was adopted as the detector to measure the canopy volume using the variable rate algorithm principle.Field experiments were conducted in an apple orchard,and conventional air blast sprayer(CABS)and directed air-jet sprayer(DAJS)were tested as a comparison.Results showed that on average,46%less spraying solution was applied compared to conventional applications,while penetration rate was similar to DAJS.Normalized deposition in the canopy with variable application was higher than that of conventional applications,indicating that electronic sprayers are more efficient than conventional sprayers.It was also observed that VARS could significantly reduce off-target loss.The field experiment showed that the newly developed variable-rate sprayer can greatly reduce pesticide use and protect the environment for the orchard fruit production,and also provide a reference for design and performance optimization for plant protection machinery.

Changes in the size of China’s population over 70 years

Based on the data from China Statistical Yearbooks and China’s population cen-suses,this paper provides a systematic introduction to changes in the size of China’s population over the 70 years since the founding of the People’s Republic of China(PRC)in 1949.It analyzes population size and crude birth rate,crude death rate,natural increase rate and total fertility rate,all of which have an impact on popula-tion size in both the temporal and spatial dimensions.The paper divides China into sluggish Average Annual Growth Rate(AAGR)regions,recovering AAGR regions,and thriving AAGR regions.Challenges that may result from China’s demographic changes and strategies to address those challenges are discussed.