Numerical integrations over an arbitrary quadrilateral region

In this paper, double integrals over an arbitrary quadrilateral are evaluated exploiting finite element method. The physical region is transformed into a standard quadrilateral finite element using the basis functions in local space. Then the standard quadrilateral is subdivided into two triangles, and each triangle is further discretized into 4 × n² right isosceles triangles, with area , and thus composite numerical integration is employed. In addition, the affine transformation over each discretized triangle and the use of linearity property of integrals are applied. Finally, each isosceles triangle is transformed into a 2-square finite element to compute new n² extended symmetric Gauss points and corresponding weight coefficients, where n is the lower order conventional Gauss Legendre quadratures. These new Gauss points and weights are used to compute the double integral. Examples are considered over an arbitrary domain, and rational and irrational integrals which can not be evaluated analytically.     

Smooth maps of a foliated manifold in a symplectic manifold

Let M be a smooth manifold with a regular foliation $ \mathcal{F} $ \mathcal{F} and a 2-form ω which induces closed forms on the leaves of $ \mathcal{F} $ \mathcal{F} in the leaf topology. A smooth map f: (M, $ \mathcal{F} $ \mathcal{F} ) → (N, σ) in a symplectic manifold (N, σ) is called a foliated symplectic immersion if f restricts to an immersion on each leaf of the foliation and further, the restriction of f*σ is the same as the restriction of ω on each leaf of the foliation. If f is a foliated symplectic immersion then the derivative map Df gives rise to a bundle morphism F: TM → T N which restricts to a monomorphism on T $ \mathcal{F} $ \mathcal{F} ⊆ T M and satisfies the condition F*σ = ω on T $ \mathcal{F} $ \mathcal{F} . A natural question is whether the existence of such a bundle map F ensures the existence of a foliated symplectic immersion f. As we shall see in this paper, the obstruction to the existence of such an f is only topological in nature. The result is proved using the h-principle theory of Gromov.     

Zero-field spin splitting in a two-dimensional electron gas with the spin-orbit interaction revisited

We consider a two-dimensional electron gas (2DEG) with the Rashba spin-orbit interaction (SOI) in the presence of a perpendicular magnetic field. We derive analytical expressions of the density of states (DOS) of a 2DEG with the Rashba SOI in the presence of a magnetic field by using the Green's function technique. The DOS allows us to obtain the analytical expressions of the magnetoconductivities for spin-up and spin-down electrons. The conductivities for spin-up and spin-down electrons oscillate with different frequencies and give rise to the beating patterns in the amplitude of the Shubnikov-de Haas (SdH) oscillations. We find a simple equation which determines the zero-field spin splitting energy if the magnetic field corresponding to any beat node is known from the experiment. Our analytical results reproduce well the experimentally observed non-periodic beating patterns, number of oscillations between two successive nodes and the measured zero-field spin splitting energy.     

Sn1−xBixO2 and Sn1−xTaxO2 (0≤x≤0.75): A first-principles study

The structural, elastic, electronic and optical (x=0) properties of doped Sn_1−xBi_xO₂ and Sn_1−xTa_xO₂ (0≤x≤0.75) are studied using the first-principles pseudopotential plane-wave method within the local density approximation. The independent elastic constants C_ij and other elastic parameters of these compounds have been calculated for the first time. The mechanical stability of the compounds with different doping concentrations has also been studied. The electronic band structure and density of states are calculated and the effect of doping on these properties is also analyzed. It is seen that the band gap of the undoped compound narrowed with dopant concentration, which disappeared for x=0.26 for Bi doping and 0.36 for Ta doping. The materials thus become conductive oxides through the change in the electronic properties of the compound for x≤0.75, which may be useful for potential application. The calculated optical properties, e.g. dielectric function, refractive index, absorption spectrum, loss-function, reflectivity and conductivity of the undoped SnO₂ in two polarization directions are compared with both previous calculations and measurements.     

Combining a DS-DBR laser with QPM-DFG for mid-infrared spectroscopy

Studies into the suitability of a novel, widely tunable telecom L-band (1563?C1613?nm) digital supermode distributed Bragg reflector (DS-DBR) laser for spectroscopy in the mid-IR are presented. Light from the DS-DBR laser was mixed with 1064?nm radiation in a periodically poled lithium niobate (PPLN) crystal to generate mid-IR light by quasi phase matching difference frequency generation (QPM-DFG). The resultant continuous wave radiation covered the range 3000?C3200?cm^?1 with powers of up to 2.6???W. The use of such laser light for spectroscopic applications was illustrated by performing absorption experiments on both narrow-band and broad-band absorbers, namely methane (CH₄) and methanethiol (CH₃SH). Wavelength modulation spectroscopy (WMS) on CH₄ demonstrated that the modulation characteristics of the DS-DBR laser observed in the near-IR were transposed to the mid-IR and yielded a sensitivity of 3.1×10^?6?cm^?1?Hz^?1/2 over a 47?cm path length. In the CH₃SH spectrum, the absorption feature at 3040?cm^?1 was identified as a potential useful region for monitoring this biomarker in exhaled breath at reduced pressures.     

Rare earth rhodium borides RRh3B (R = Y, Zr, and Nb): mechanical, thermal and optical properties

Conversations allow the quick transfer of short bits of information and it is reasonable to expect that changes in communication medium affect how we converse. Using conversations in works of fiction and in an online social networking platform, we show that the utterance length of conversations is slowly shortening with time but adapts more strongly to the constraints of the communication medium. This indicates that the introduction of any new medium of communication can affect the way natural language evolves.     

Chemoselective synthesis of thieno[3,2‐c][1,8]naphthyridin‐4(5H)‐ones by tandem cyclization

A number of the thieno[3,2‐c][1,8]‐naphthyridin‐4(5H)‐ones are chemoselectively synthesized from 4‐(4′‐aryloxybut‐2′‐ynylthio)‐1‐phenyl‐1,8‐naphthyridin‐2(1H)‐ones in 82–90% yield by the formation of sulfoxide, followed by [2,3] and [3,3]sigmatropic rearrangement and an intramolecular Michael addition. © 2007 Wiley Periodicals, Inc. Heteroatom Chem 18:87–92, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20234     

Metal ion directed synthesis of 14–16 membered tetraimine macrocyclic complexes

A new series of 14–16 membered tetraazatetraimine macrocyclic complexes [ML1X2]-[ML3X2] [M=CoII, NiII and ZnII] and [CuL1]X2-[CuL3]X2 [X=Cl or NO3] have been synthesized by the template condensation of dibenzoylmethane with primary diamines in MeOH. The complexes were characterized by elemental analysis, i.r, 1H-n.m.r., e.p.r. and u.v-vis spectroscopy, as well as by conductivity and magnetic susceptibility measurements. The copper complexes exhibit square planar geometry, whereas an octahedral geometry is suggested for all other complexes.     

沟道长度和宽度对石墨烯场效应晶体管电荷输运的影响

本文基于理论的方法研究了沟道长度和宽度对石墨烯场效应晶体管中大信号和小信号参数的影响. 在快速饱和及高特征频率条件下,石墨烯场效应晶体管均表现出优异的性能. 从传递曲线可以看到,随着沟道长度从440 nm变到20 nm,产生了一个从0.15 V 到0.35 V的狄拉克点正偏移,同时也揭示了石墨烯的双极特性. 而且,由于沟道变宽及漏电流增加,当沟道宽度为2 μm和5 μm时,相应的最大电流为2.4 mA和6 mA. 另外,还在石墨烯场效应晶体管中观察到了几乎对称的电容-电压特性,电容会随着沟道变短而减小,但另一方面电容又可以通过沟道展宽来增加. 最后,在沟道长度为20 nm处获得了一个6.4 mS的高跨导,在沟道宽度为5 μm处获得的跨导值为4.45 mS,特征频率为3.95 THz.     

Core Deformation Impact of One- and Two-Proton Halo $${}^{{27}}$$ S Nucleus

Physics of Atomic Nuclei - The core deformation of a one- and two-proton halo $${}^{27}$$ S nucleus was investigated based on experimental data. The Hamiltonian of the three-body systems and the...