Numerical Investigations on the Resonance Errors of Multiscale Discontinuous Galerkin Methods for One-Dimensional Stationary Schrödinger Equation

In this paper,numerical experiments are carried out to investigate the impact of penalty parameters in the numerical traces on the resonance errors of high-order multiscale discontinuous Galerkin(DG)methods(Dong et al.in J Sci Comput 66:321–345,2016;Dong and Wang in J Comput Appl Math 380:1–11,2020)for a one-dimensional stationary Schrödinger equation.Previous work showed that penalty parameters were required to be positive in error analysis,but the methods with zero penalty parameters worked fine in numerical simulations on coarse meshes.In this work,by performing extensive numerical experiments,we discover that zero penalty parameters lead to resonance errors in the multiscale DG methods,and taking positive penalty parameters can effectively reduce resonance errors and make the matrix in the global linear system have better condition numbers.

Prediction of one-dimensional CrN nanostructure as a promising ferromagnetic half-metal

Searching for one-dimensional(1D)nanostructure with ferromagnetic(FM)half-metallicity is of significance for the development of miniature spintronic devices.Here,based on the first-principles calculations,we propose that the 1D CrN nanostructure is a FM half-metal,which can generate the fully spin-polarized current.The ab initio molecular dynamic simulation and the phonon spectrum calculation demonstrate that the 1D CrN nanostructure is thermodynamically stable.The partially occupied Cr-d orbitals endow the nanostructure with FM half-metallicity,in which the half-metallic gap(?s)reaches up to 1.58 eV.The ferromagnetism in the nanostructure is attributed to the superexchange interaction between the magnetic Cr atoms,and a sizable magnetocrystalline anisotropy energy(MAE)is obtained.Moreover,the transverse stretching of nanostructure can effectively modulate?s and MAE,accompanied by the preservation of half-metallicity.A nanocable is designed by encapsulating the CrN nanostructure with a BN nanotube,and the intriguing magnetic and electronic properties of the nanostructure are retained.These novel characteristics render the 1D CrN nanostructure as a compelling candidate for exploiting high-performance spintronic devices.

Size effect on light propagation modulation near band edges in one-dimensional periodic structures

Periodic photonic structures can provide rich modulation in propagation of light due to well-defined band structures.Especially near band edges,light localization and the effect of near-zero refractive index have attracted wide attention.However,the practically fabricated structures can only have finite size,i.e.,limited numbers of periods,leading to changes of the light propagation modulation compared with infinite structures.Here,we study the size effect on light localization and near-zero refractive-index propagation near band edges in one-dimensional periodic structures.Near edges of the band gap,as the structure's size shrinks,the broadening of the band gap and the weakening of the light localization are discovered.When the size is small,an added layer on the surface will perform large modulation in the group velocity.Near the degenerate point with Dirac-like dispersion,the zero-refractive-index effects like the zero-phase difference and near-unity transmittance retain as the size changes,while absolute group velocity fluctuates when the size shrinks.

A Dugdale-Barenblatt model for elliptical orifice problem with asymmetric cracks in one-dimensional orthorhombic quasicrystals

By means of Muskhelishvili’s method and the technique of generalized conformal mapping,the physical plane problems are transformed into regular mathematical problems in quasicrystals(QCs).The analytical solution to an elliptical orifice problem with asymmetric cracks in one-dimensional(1D)orthorhombic QCs is obtained.By using the Dugdale-Barenblatt model,the plastic simulation at the crack tip of the elliptical orifice with asymmetric cracks in 1D orthorhombic QCs is performed.Finally,the size of the atomic cohesive force zone is determined precisely,and the size of the atomic cohesive force zone around the crack tip of an elliptical orifice with a single crack or two symmetric cracks is obtained.

Robust Damage Detection and Localization Under Complex Environmental Conditions Using Singular Value Decomposition-based Feature Extraction and One-dimensional Convolutional Neural Network

Ultrasonic guided wave is an attractive monitoring technique for large-scale structures but is vulnerable to changes in environmental and operational conditions(EOC),which are inevitable in the normal inspection of civil and mechanical structures.This paper thus presents a robust guided wave-based method for damage detection and localization under complex environmental conditions by singular value decomposition-based feature extraction and one-dimensional convolutional neural network(1D-CNN).After singular value decomposition-based feature extraction processing,a temporal robust damage index(TRDI)is extracted,and the effect of EOCs is well removed.Hence,even for the signals with a very large temperature-varying range and low signal-to-noise ratios(SNRs),the final damage detection and localization accuracy retain perfect 100%.Verifications are conducted on two different experimental datasets.The first dataset consists of guided wave signals collected from a thin aluminum plate with artificial noises,and the second is a publicly available experimental dataset of guided wave signals acquired on a composite plate with a temperature ranging from 20℃to 60℃.It is demonstrated that the proposed method can detect and localize the damage accurately and rapidly,showing great potential for application in complex and unknown EOC.

Analysis of Dynamical Behavior of One-Dimensional Real Maps: An Executable Dynamical Programming Software Approach

The dynamical behavior of real-world phenomena is implausible graphically due to the complexity of mathematical coding. The present article has mainly focused on some one-dimensional real maps’ dynamical behavior irrespective of using coding. In continuation, linear, quadratic, cubic, higher-order, exponential, logarithmic, and absolute value maps have been used to scrutinize their dynamical behavior, including the characteristics of the orbit of points. Dynamical programming software (DPS.exe) will be proposed as a new technique to ascertain the dynamical behavior of said maps. Thus, a mathematician can automatically determine one-dimensional real maps’ dynamical behavior apart from complicated programming code and analytical solutions.

Thermal-induced interfacial behavior of a thin one-dimensional hexagonal quasicrystal film

In this paper,we investigate the interfacial behavior of a thin one-dimensional(1D)hexagonal quasicrystal(QC)film bonded on an elastic substrate subjected to a mismatch strain due to thermal variation.The contact interface is assumed to be nonslipping,with both perfectly bonded and debonded boundary conditions.The Fourier transform technique is adopted to establish the integral equations in terms of interfacial shear stress,which are solved as a linear algebraic system by approximating the unknown phonon interfacial shear stress via the series expansion of the Chebyshev polynomials.The expressions are explicitly obtained for the phonon interfacial shear stress,internal normal stress,and stress intensity factors(SIFs).Finally,based on numerical calculations,we briefly discuss the effects of the material mismatch,the geometry of the QC film,and the debonded length and location on stresses and SIFs.

The Conflict between Individuals and Society in Seize the Day

This paper explores the existential problem in Seize the Day-the conflict between individuals and society in modern society.With a brief introduction of Saul Bellow and the novel,the paper emphasizes the analysis of the conflict and the sources of the conflict.Besides,Saul Bellow uses many rhetorical devices to intensify the conflict.The analysis of these rhetorical devices is beneficial for us to interpret and understand the true meaning of the novel.Through the study of Bellow’s vision and the novel’s metaphorical meaning,we may find an effective solution to the conflict that our human being is involved in,and realize the social values of this novel.

“社会”与Society的中英语义差别对比分析

翻译过程中,中英文同一组词的语义不对等问题引起语义学者兴趣,而高频互译的“社会”与society这组词在译者与读者视角下语义对等性极强,由此语义差别研究较少且研究空间较大。该文研究该组词的字典释义,对比探究两者的语义不对等性,归纳语义差别背后原因。研究发现,“社会”和society存在语义不对等;“社会”一词包含“社交”和“公共”两大含义,而society一词对应其中“社交”之意,表现出一定的不对等性。

Combinations of Transportation Policies to Promote BRT Usage Using Artificial Society Model

Various transportation systems have been developed in recent years.In this study,an artificial society model is developed to examine the combination of transportation policies in urban areas.In this model,each trip maker selects the primary and terminal transportation modes.An artificial society model is applied to the southeastern region of Osaka City,Japan.The effects of introducing BRT(bus rapid transit,primary transportation)and on-demand buses(terminal transportation)are investigated.The results confirm that BRT is used by a certain number of users.An increase in the use of BRT will increase the amount of walking,thus resulting in a healthy city.However,on-demand buses are rarely used as terminal transportation.Additionally,the development of bicycle parking stations near BRT stops is shown to be effective in the northern section of the BRT route.

Hungry and Angry Society: Implications for Sustainable Development in Nigeria

Hunger is a physiological need,but the production and consumption of adequate and balanced food is a function of social forces.At every point,social,political,and economic processes intervene,for better or(more common)for worse.Food is one fundamental need of human beings for survival.But in Nigeria there is widespread food shortage and hunger.Development scholars have put forward reasons why poverty,hunger persists in the country,from the platitudes about population growth,inadequate implementation of agricultural policies,and neglect of agriculture,bad leadership,corruption,and the issue of distribution.Nigeria is richly blessed with arable land and citizens eager to unlock its food potentials.Unfortunately,this is far from being realized as the country depends on foreign countries for food,a situation that is tragic and sad.She spends about$10 billion a year importing food and agricultural products,the majority of which are wheat,rice,poultry,fish,and consumer-oriented foods.The pressure on the exchange rate results in devaluation-triggered inflation and food costs that fly up beyond the grasp of people at the bottom of the ladder as it is now is one of the negative repercussions of high food importation bills.Examining the effects of hunger is one of this paper’s key concerns and goals,and anger crisis for achieving sustainable development in the country using the Frustration-Aggression Theory,The Relative Deprivation and Political Economy Approach as guide.

Controlled Growth of One-Dimensional Oxide Nanomaterials

This article reviews the recent developments in the controlled growth of one-dimensional （1D） oxide nanomaterials, including ZnO, SnO2, In203, Ga203, SiOx, MgO, and Al203. The growth of 2D oxide nanomaterials was carried out in a simple chemical vapor transport and condensation system. This article will begin with a survey of nanotechnology and 1D nanomaterials achieved by many researchers, and then mainly discuss on the controlled growth of ID oxide nanomaterials with their morphologies, sizes, compositions, and microstructures controlled by altering experimental parameters, such as the temperature at the source material and the substrate, temperature gradient in the tube furnace, the total reaction time, the heating rate of the furnace, the gas flow rate, and the starting material. Their roles in the formation of various morphologies are analyzed and discussed. Finally, this review will be concluded with personal perspectives on the future research directions of this area.

One-Dimensional (1D) ZnS Nanomaterials and Nanostructures

One-dimensional （1D） nanomaterials and nanostructures have received much attention due to their potential interest for understanding fundamental physical concepts and for applications in constructing nanoscale electric and optoelectronic devices. Zinc sulfide （ZnS） is an important semiconductor compound of Ⅱ-Ⅵ group, and the synthesis of 1D ZnS nanomaterials and nanostructures has been of growing interest owing to their promising application in nanoscale optoelectronic devices. This paper reviews the recent progress on 1D ZnS nanomaterials and nanostructures, including nanowires, nanowire arrays, nanorods, nanobelts or nanoribbons, nanocables, and hierarchical nanostructures etc. This article begins with a survey of various methods that have been developed for generating 1D nanomaterials and nanostructures, and then mainly focuses on structures, synthesis, characterization, formation mechanisms and optical property tuning, and luminescence mechanisms of 1D ZnS nanomaterials and nanostructures. Finally, this review concludes with personal views towards future research on 1D ZnS nanomaterials and nanostructures.

The interaction between a screw dislocation and a wedge-shaped crack in one-dimensional hexagonal piezoelectric quasicrystals

Based on the fundamental equations of piezoelasticity of quasicrystal material,we investigated the interaction between a screw dislocation and a wedge-shaped crack in the piezoelectricity of one-dimensional hexagonal quasicrystals.Explicit analytical solutions are obtained for stress and electric displacement intensity factors of the crack,as well as the force on dislocation.The derivation is based on the conformal mapping method and the perturbation technique.The influences of the wedge angle and dislocation location on the image force are also discussed.The results obtained in this paper can be fully reduced to some special cases already available or deriving new ones.

Anti-plane problem of nano-cracks emanating from a regular hexagonal nano-hole in one-dimensional hexagonal piezoelectric quasicrystals

By constructing a new conformal mapping function, we study the surface effects on six edge nano-cracks emanating from a regular hexagonal nano-hole in one-dimensional (1D) hexagonal piezoelectric quasicrystals under anti-plane shear. Based on the Gurtin–Murdoch surface/interface model and complex potential theory, the exact solutions of phonon field, phason field and electric field are obtained. The analytical solutions of the stress intensity factor of the phonon field, the stress intensity factor of the phason field, the electric displacement intensity factor and the energy release rate are given. The interaction effects of the nano-cracks and nano-hole on the stress intensity factor of the phonon field, the stress intensity factor of the phason field and the electric displacement intensity factor are discussed in numerical examples. It can be seen that the surface effect leads to the coupling of phonon field, phason field and electric field. With the decrease of cavity size, the influence of surface effect is more obvious.

Synthesis and Photocatalytic Activity of One-Dimensional CdS@TiO_2 Core-Shell Hetero-structures

One-dimensional Cd S@TiO_2 core-shell heterostructures were fabricated via the hydrolysis of tetrabutyl titanate(TBT) on preformed Cd S nanowires. The as-prepared products were characterized by X-ray diffraction, transmission electron microscopy, selected area electron diffraction and diffuse reflectance spectroscopy techniques. Results demonstrated that the hydrolysis of TBT had a great influence on the morphology of the coated TiO_2 shell, resulting in the formation of TiO_2 nanoparticles and nanolayer-modified Cd S@TiO_2 heterostructures. Degradation of methylene blue using Cd S@TiO_2 core-shell heterostructures as photocatalysts under visible light irradiation was investigated. Comparative photocatalytic tests showed that the TiO_2 nanoparticles-modified heterostructure exhibited a superior activity due to the passivity of photogenerated charge carriers.

Exact analytic solutions for an elliptic hole with asymmetric collinear cracks in a one-dimensional hexagonal quasi-crystal

Using the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with asymmetric colfinear cracks in a one-dimensional hexagonal quasi-crystal is solved, and the exact analytic solutions of the stress intensity factors （SIFs） for mode Ⅲ problem are obtained. Under the limiting conditions, the present results reduce to the Griffith crack and many new results obtained as well, such as the circular hole with asymmetric collinear cracks, the elliptic hole with a straight crack, the mode T crack, the cross crack and so on. As far as the phonon field is concerned, these results, which play an important role in many practical and theoretical applications, are shown to be in good agreement with the classical results.

Analytical solution to one-dimensional consolidation in unsaturated soils

This paper presents an analytical solution of the one-dimensional consolidation in unsaturated soil with a finite thickness under vertical loading and confinements in the lateral directions. The boundary contains the top surface permeable to water and air and the bottom impermeable to water and air. The analytical solution is for Fredlund＇s one-dimensional consolidation equation in unsaturated soils. The transfer relationship between the state vectors at top surface and any depth is obtained by using the Laplace transform and Cayley-Hamilton mathematical methods to the governing equations of water and air, Darcy＇s law and Fick＇s law. Excess pore-air pressure, excess pore-water pressure and settlement in the Laplace-transformed domain are obtained by using the Laplace transform with the initial conditions and boundary conditions. By performing inverse Laplace transforms, the analytical solutions are obtained in the time domain. A typical example illustrates the consolidation characteristics of unsaturated soil from an- alytical results. Finally, comparisons between the analytical solutions and results of the finite difference method indicate that the analytical solution is correct.

Design of(GO/TiO2)N one-dimensional photonic crystal photocatalysts with improved photocatalytic activity for tetracycline degradation

(GO/TiO2)N(GO represents graphene oxide,and N represents the period number of alternate superposition of two dielectrics)onedimensional photonic crystal with different lattice constants was prepared via the sol–gel technique,and its transmission characteristics for photocatalysis were tested.The results show that the lattice constant,filling ratio,number of periodic layers,and incident angle had effects on the band gap.When the lattice constant,filling ratio,number of periodic layers,and incident angle were set to 125 nm,0.45,21,and 0°,respectively,a gap width of 53 nm appeared at the central wavelength(322 nm).The absorption peak of the photocatalyst at 357 nm overlapped the blue edge of the photonic band gap.A slow photon effect region above 96%reflectivity appeared.The degradation rate of tetracycline in(GO/TiO2)N photonic crystal was enhanced to 64%within 60 min.Meanwhile,the degradation efficiency of(GO/TiO2)N one-dimensional photonic crystal was effectively improved compared with those of the GO/TiO2 composite film and GO/TiO2 powder.

One-Dimensional Magnetic FeCoNi Alloy Toward Low-Frequency Electromagnetic Wave Absorption

Rational designing of one-dimensional(1D)magnetic alloy to facilitate electromagnetic(EM)wave attenuation capability in low-frequency(2-6 GHz)microwave absorption field is highly desired but remains a significant challenge.In this study,a composite EM wave absorber made of a FeCoNi medium-entropy alloy embedded in a 1D carbon matrix framework is rationally designed through an improved electrospinning method.The 1D-shaped FeCoNi alloy embedded composite demonstrates the high-density and continuous magnetic network using off-axis electronic holography technique,indicating the excellent magnetic loss ability under an external EM field.Then,the in-depth analysis shows that many factors,including 1D anisotropy and intrinsic physical features of the magnetic medium-entropy alloy,primarily contribute to the enhanced EM wave absorption performance.Therefore,the fabricated EM wave absorber shows an increasing effective absorption band of 1.3 GHz in the low-frequency electromagnetic field at an ultrathin thickness of 2 mm.Thus,this study opens up a new method for the design and preparation of high-performance 1D magnetic EM absorbers.