Nonlinear Schrödinger equation with a Dirac delta potential: finite difference method*

The nonlinear Schrödinger equation with a Dirac delta potential is considered in this paper. It is noted that the equation can be transformed into an equation with a drift-admitting jump. Then following the procedure proposed in Chen and Deng (2018 Phys. Rev. E 98 033302), a new second-order finite difference scheme is developed, which is justified by numerical examples.     

Cr4Mo4V轴承钢滚动接触疲劳和磨损性能研究

通过球棒滚动接触疲劳(RCF)试验机,研究了Cr4Mo4V轴承钢在4050润滑油润滑和0.18滑滚比条件下的滚动接触疲劳和磨损性能.结果表明:Cr4Mo4V钢的应力-寿命(S-N)曲线数据分散性较大,疲劳寿命随着应力增加呈下降趋势.Cr4Mo4V钢滚动接触磨损主要为磨料磨损,黏着磨损和疲劳磨损,随着应力和时间增加磨损体积增加,滚道凹槽深度达到17μm.通过光学显微镜(OM)和扫描电子显微镜(SEM)观察试样棒剖面与滚道交界处疲劳裂纹,发现疲劳破坏类型主要有两种:起源于表面的剥落(SOF)和起源于白蚀区的剥落(WSF).通过滚道径向切割抛光酸蚀显示Cr4Mo4V钢滚动接触疲劳影响区,随着应力和循环接触次数的增加,在次表层依次发现黑蚀区(DER)、白蚀区(WEA)和蝴蝶组织(BW).表面碳化物的剥落坑,黏着磨损和疲劳磨损的凹坑导致了表面起裂、白蚀区和蝴蝶组织中的碳化物和夹杂导致微裂纹的产生,链状碳化物使裂纹往深处扩展.     

超高效液相色谱-串联质谱法同时测定食用油中痕量的δ-9-四氢大麻酚、大麻酚和大麻二酚

建立了超高效液相色谱-串联质谱(UPLC-MS/MS)同时测定食用油中δ-9-四氢大麻酚(THC)、大麻酚(CBN)和大麻二酚(CBD)的方法。目标分析物经甲醇提取、中性氧化铝固相萃取柱净化后,采用UPLC-MS/MS分离和检测。实验以氘代四氢大麻酚(THC-D3)为内标物,采用同位素内标法定量。在3个添加水平下,目标物的平均回收率为68.0%～101.6%,相对标准偏差为7.0%～20.1%。方法检出限为0.06～0.17 μg/kg,定量限为0.20～0.52 μg/kg。该方法能够满足食用油中痕量四氢大麻酚、大麻酚和大麻二酚检测的需要。     

烷基苯标准生成焓与分子价连接性指数mX*的关系

提出了一个计算不饱和烃分子中碳原子价点价δi^*的新方法，以δi^*为核心建构了分子价连接性指数mx*(M＝0，1)，并研究了烷基苯标推生成焓与mX*指数的相关性。结果表明，mX^*指数对烷基苯的结构选择性和性质相关性均优于mX^*指数和F’指数。以0Xn,1X1和碳原子数N为自变量的三元线性回归方程为：—ΔfHm＝38．079^0X^n 5.0911X^* 954.991N-1501.639,该方程对烷基苯标推生成焓的预测结果相当准确。     

Low temperature electron mobility in Ga0.5In0.5P/GaAs quantum well structures

We analyse the low temperature subband electron mobility in a Ga_0.5In_0.5P/GaAs quantum well structure where the side barriers are delta-doped with layers of Si. The electrons are transferred from both the sides into the well forming two dimensional electron gas (2DEG). We consider the interface roughness scattering in addition to ionised impurity scattering. The effect of screening of the scattering potentials by 2DEG on the electron mobility is analysed by changing well width. Although the ionized impurity scattering is a dominant mechanism, for small well width the interface roughness scattering happens to be appreciable. Our analysis can be utilized for low temperature device applications.      

Numerical investigation of leading edge separated flow over cranked wings using a vortex lattice model

Numerical models based on the vortex lattice concept using free vortex lines have been developed for the calculation of separated flow about cranked wings. Various separated flow models are developed assuming the flow to be separated along the leading edges of (i) the inner wing, (ii) the entire wing and (iii) the inner wing and the outboard part of the outer wing. To illustrate the effects of separation, attached flow solutions are also obtained. Results are compared with available experimental results. Agreement with separated flow solutions is usually good except at very high incidence.     

Solutions of the Schrödinger equation for Dirac delta decorated linear potential

We have studied bound states of the Schrödinger equation for a linear potential together with any finite number (P) of Dirac delta functions. Forx<-0, the potential is given as

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where 0<f; 0<x ₁<x ₂<...<x _P , theσ _i are arbitrary real numbers, and the potential is infinite forx<0.

     

Properties of a pseudo-Hermitian Hamiltonian for harmonic oscillator decorated with Dirac delta interactions

We have investigated bound state solutions of the Schrodinger equation for one-dimensional harmonic oscillator potential together with even number of Dirac delta functions. These point interactions are located at symmetric points x = x _i and x = −x _i (i = 1, 2,..., N) and they have complex conjugate strengths and , respectively. We present explicit forms of eigenfunctions and an algebraic eigenvalue equation and numerical solutions for this -symmetric Hamiltonian. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

Periodic problems and problems with discontinuities for nonlinear parabolic equations

In this paper we study nonlinear parabolic equations using the method of upper and lower solutions. Using truncation and penalization techniques and results from the theory of operators of monotone type, we prove the existence of a periodic solution between an upper and a lower solution. Then with some monotonicity conditions we prove the existence of extremal solutions in the order interval defined by an upper and a lower solution. Finally we consider problems with discontinuities and we show that their solution set is a compact R -set in (CT, L ²(Z)).     

Donsker's Delta Function of Lévy Process

Let X={X(t):tR} be a Lévy process and a non-decreasing, right continuous, bounded function with (–)=0 (((1+u ²)/u ²)d(u) is the Lévy measure). In this paper we define the Donsker delta function (X(t)–a), t>0 and aR, as a generalized Lévy functional under the condition that (0)–(0–)>0. This leads us to define F(X(t)) for any tempered distribution F, and as an application, we derive an Itô formula for F(X(t)) when has jumps at 0 and 1.