科里奥利力的演示

设计了一演示实验，能力便地对科里奥利力进行课堂演示。     

基于龙基光栅塔尔博特效应的长焦距测量

提出通过对龙基光栅的塔尔博特效应所产生的莫尔条纹角度的计量来测量长焦距的方法。并在此基础上推导了长焦距的计算公式，分析了这种方法的测量误差。这种长焦距测量方法具有实时测量、精度高的特点。     

Measurement of the tau lepton mass and an upper limit on the mass difference between tau+ and tau-

The mass of the tau lepton has been measured in the decay mode tau-->3pinutau using a pseudomass technique. The result obtained from 414 fb-1 of data collected with the Belle detector is Mtau=[1776.61+/-0.13(stat)+/-0.35(sys)] MeV/c2. The upper limit on the relative mass difference between positive and negative tau leptons is |Mtau+-Mtau-|/Mtau<2.8 x 10-4 at 90% confidence level.     

A De Giorgi Type Result to Divergence Degenerate Elliptic Equation with Bounded Coefficients Related To Hörmander's Vector Fields

In this paper, we consider the divergence degenerate elliptic equation with bounded coefficients constructed by Hörmander's vector fields. We prove a De Giorgi type result, i.e., the local Hölder continuity for the weak solutions to the equation by providing a De Giorgi type lemma and extending the Moser iteration to the setting here. As a consequence, the Harnack inequality of weak solutions is also given.     

Effect of Intercalated LiF on Interface Contact Characteristics of MoS2 Field Effect Transistor: A First-Principles Study

Based on the first-principles calculation, the effect of intercalated LiF on the contact characteristics of the interface between Au electrode and MoS₂ layer is studied. It is found that adding LiF film can change the contact type between metal electrode Au and MoS₂ layer from Schottky contact to ohmic contact, which is accompanied by interfacial charge transfer from LiF layer to MoS₂ layer and the downward movement of d (d_xy and d_z2) orbital of Mo atom and p (p_x and p_y) orbital of S atom to Fermi level. And the interlayer spacing between LiF layer and Au electrode has a great impact on the interface contact characteristics. The electric field effect and stress effect of interface contact of Au, LiF and MoS₂ (Au/LiF/MoS₂)is more obvious than that of interface contact of Au and MoS₂ (Au/MoS₂). Au/LiF/MoS₂ shows ohmic contact with the interlayer spacing between Au layer and LiF layer less than 3.05 Å and with the electric field less than 0.15 VÅ⁻¹, respectively, while Au/MoS₂ still shows N-type Schottky contact. These findings are helpful to control the contact resistance and have guiding significance for high performance MoS₂ field effect transistor and other electronic components.     

The effect of axial stretch on cavitation in an elastic cylinder

The phenomenon of cavitation in an elastic cylinder subjected to a combined axial stretch λ_z and radial traction P is examined. One possible response of the cylinder to this loading, for all λ_z; and P, is a pure homogeneous deformation. However, for some materials, the homogeneous deformation becomes unstable at certain critical values of (λ_z, P), and a second deformation bifurcates from the homogeneous one; this latter deformation involves a cylindrical cavity co-axial with the elastic cylinder. We determine the values of (λ_z, P) at which this happens. The results are displayed by constructing a curve in the (λ_z, P)-plane which divides this plane into regions where the homogeneous deformation is stable and unstable.     

On the origin of the hole pressure

Summary One wall of a slit die apparatus contains a slot filled with the test liquid. Photographs of marked streamlines near the slot mouth show a pronounced curvature. A 0.5% aqueous solution of Separan AP 30 and molten polystyrene and polyethylene were investigated at low values of Reynolds number (Re < 1.0). In each case, streamlines are convex towards the slot mouth. This supports the hypothesis ofTanner andPipkin which attributes hole pressures in flowing viscoelastic liquids to the combined effect of holegenerated streamline curvature and shear-generated normal stress differences.

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Zusammenfassung In einer der Wände einer Schlitzdüsenvorrichtung ist eine mit Testflüssigkeit gefüllte Quernut angebracht. Es wurde die Strömung einer 0,5%-igen wässerigen Separan AP 30-Lösung, sowie einer Polystyrol- und einer Polyäthylenschmelze bei kleinen Reynoldszahlen (Re < 1.0) untersucht. In allen Fällen waren die Stromlinien konvex, also zur Schlitzmündung hin gekrümmt. Dadurch wird die Hypothese vonTanner andPipkin unterstützt, wonach die Lochdrücke in strömenden viskoelastischen Flüssigkeiten als Wirkung der durch die Scherung erzeugten Normalspannungsdifferenzen auf die gekrümmten Stromlinien erklärt werden.

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Department of Engineering Mechanics.

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Material Science Program.

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With 4 figures     

A fractional spectral method with applications to some singular problems

In this paper we propose and analyze fractional spectral methods for a class of integro-differential equations and fractional differential equations. The proposed methods make new use of the classical fractional polynomials, also known as Müntz polynomials. We first develop a kind of fractional Jacobi polynomials as the approximating space, and derive basic approximation results for some weighted projection operators defined in suitable weighted Sobolev spaces. We then construct efficient fractional spectral methods for some integro-differential equations which can achieve spectral accuracy for solutions with limited regularity. The main novelty of the proposed methods is that the exponential convergence can be attained for any solution u(x) with u(x ^1/λ ) being smooth, where λ is a real number between 0 and 1 and it is supposed that the problem is defined in the interval (0,1). This covers a large number of problems, including integro-differential equations with weakly singular kernels, fractional differential equations, and so on. A detailed convergence analysis is carried out, and several error estimates are established. Finally a series of numerical examples are provided to verify the efficiency of the methods.