从机械能守恒的角度推导单摆简谐振动的周期

本文给出了利用基本的物理原理结合高等数学公式的方法推导单摆做简谐运动的周期公式,可以简明扼要地理解单摆简谐运动的过程.     

On asymptotic elastodynamic homogenization approaches for periodic media

A fairly large family of asymptotic elastodynamic homogenization methods is shown to be derivable from Willis exact elastodynamic homogenization theory for periodic media under appropriate approximation assumptions about, for example, frequencies, wavelengths and phase contrast. In light of this result, two long-wavelength and low-frequency asymptotic elastodynamic approaches are carefully analyzed and compared in connection with higher-order strain-gradient media. In particular, these approaches are proved to be unable to capture, at least in the one-dimensional setting, the optical branches of the dispersion curve. As an example, a two-phase string is thoroughly studied so as to illustrate the main results of the present work.     

Crystal planes and reciprocal space in Clifford geometric algebra

This paper discusses the geometry of kD crystal cells given by (k+ 1) points in a projective space ?^{n+ 1}. We show how the concepts of barycentric and fractional (crystallographic) coordinates, reciprocal vectors and dual representation are related (and geometrically interpreted) in the projective geometric algebra Cl(?^{n+ 1}) (see (Die Ausdehnungslehre von 1844 und die Geom. Anal. Teubner: Leipzig, 1894)) and in the conformal algebra Cl(?^{n+ 1, 1}). The crystallographic notions of d‐spacing, phase angle, structure factors, conditions for Bragg reflections, and the interfacial angles of crystal planes are obtained in the same context. Copyright © 2011 John Wiley & Sons, Ltd.     

Resonant Leading Term Geometric Optics Expansions with Boundary Layers for Quasilinear Hyperbolic Boundary Problems

We construct and justify leading order weakly nonlinear geometric optics expansions for nonlinear hyperbolic initial value problems, including the compressible Euler equations. The technique of simultaneous Picard iteration is employed to show approximate solutions tend to the exact solutions in the small wavelength limit. Recent work [2 Coulombel, J.-F., Gues, O., and Williams, M., 2011. Resonant leading order geometric optics expansions for quasilinear hyperbolic fixed and free boundary problems, Comm. Part. Diff. Eqs. 36 (2011), pp. 1797–1859.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]] by Coulombel et al. studied the case of reflecting wave trains whose expansions involve only real phases. We treat generic boundary frequencies by incorporating into our expansions both real and nonreal phases. Nonreal phases introduce difficulties such as approximately solving complex transport equations and result in the addition of boundary layers with exponential decay. This also prevents us from doing an error analysis based on almost periodic profiles as in [2 Coulombel, J.-F., Gues, O., and Williams, M., 2011. Resonant leading order geometric optics expansions for quasilinear hyperbolic fixed and free boundary problems, Comm. Part. Diff. Eqs. 36 (2011), pp. 1797–1859.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]].     

Application of the multireference equation of motion coupled cluster method,including spin–orbit coupling,to the atomic spectra of Cr,Mn, Fe and Co

The recently introduced multireference equation of motion (MR-EOM) approach is combined with a simple treatment of spin–orbit coupling, as implemented in the ORCA program. The resulting multireference equation of motion spin–orbit coupling (MR-EOM-SOC) approach is applied to the first-row transition metal atoms Cr, Mn, Fe and Co, for which experimental data are readily available. Using the MR-EOM-SOC approach, the splittings in each L-S multiplet can be accurately assessed (root mean square (RMS) errors of about 70 cm^?1). The RMS errors for J-specific excitation energies range from 414 to 783 cm^?1 and are comparable to previously reported J-averaged MR-EOM results using the ACESII program. The MR-EOM approach is highly efficient. A typical MR-EOM calculation of a full spin–orbit spectrum takes about 2 CPU hours on a single processor of a 12-core node, consisting of Intel XEON 2.93 GHz CPUs with 12.3 MB of shared cache memory.     

微液滴在仿蛛丝结构TiO2纤维表面的定向运动与粘附

制备了具有响应性的仿蛛丝周期纺锤节TiO₂纤维。通过改变纤维表面微观结构、紫外光照和超声波等手段,仿蛛丝结构TiO₂纤维表面浸润性会发生响应性变化。纤维表面的这种浸润性变化,不仅实现了水滴从纺锤节两端到中心处的定向运动,而且可以使得水滴被纤维纺锤节粘附。当仿蛛丝结构TiO₂纤维表面为亲水状态时,无论纺锤节光滑还是粗糙,水都是从纺锤节两端向中心方向运动;当仿蛛丝TiO₂纤维表面疏水时,水滴会被具有粗糙表面的纺锤节两端粘附。     

Integrated multidimensional and comprehensive 2D GC analysis of fatty acid methyl esters

Fatty acid methyl ester (FAME) profiling in complex fish oil and milk fat samples was studied using integrated comprehensive 2D GC (GC × GC) and multidimensional GC (MDGC). Using GC × GC, FAME compounds – cis‐ and trans‐isomers, and essential fatty acid isomers – ranging from C18 to C22 in fish oil and C18 in milk fat were clearly displayed in contour plot format according to structural properties and patterns, further identified based on authentic standards. Incompletely resolved regions were subjected to MDGC, with Cn (n = 18, 20) zones transferred to a ²D column. Elution behavior of C18 FAME on various ²D column phases (ionic liquids IL111, IL100, IL76, and modified PEG) was evaluated. Individual isolated Cn zones demonstrated about four‐fold increased peak capacities. The IL100 provided superior separation, good peak shape, and utilization of elution space. For milk fat‐derived FAME, the ²D chromatogram revealed at least three peaks corresponding to C18:1, more than six peaks for cis/trans‐C18:2 isomers, and two peaks for C18:3. More than 17 peaks were obtained for the C20 region of fish oil‐derived FAMEs using MDGC, compared with ten peaks using GC × GC. The MDGC strategy is useful for improved FAME isomer separation and confirmation.     

基底界面效应对聚苯乙烯薄膜分子运动行为的影响

本文研究了Si／Si02、Si／Si—H基底与聚苯乙烯（Ps）之间的界面相互作用对Ps薄膜的玻璃化转变及相关力学性能的影响．结果显示,无论何种基底,Ps薄膜的玻璃化转变温度（L）都随其厚度降低而降低．但相同厚度（〈110nm）下,以Si／Si-H为基底时Ps薄膜的瓦比以Si／Si02为基底的PS薄膜高．Si／Si02表面Ps薄膜疋开始下降的临界厚度为110nm,远高于以Si／Si—H为基底时的40nm．对Ps薄膜的膨胀系数和弹性模量进行研究,也得到相似的临界厚度．另外,与Si／Si02基底相比,在Si／Si-H上的Ps薄膜具有更低的膨胀系数以及较高弹性模量．可能原因是Si／Si-H与Ps具有较强的相互作用,限制了该界面分子的运动能力,导致基底／PS界面效应对薄膜分子运动的影响力增强,造成该薄膜瓦的厚度依赖性下降,并呈现出相对较硬的力学特征．     

Differential geometric analysis of alterations in MH α‐helices

Antigen presenting cells present processed peptides via their major histocompatibility (MH) complex to the T cell receptors (TRs) of T cells. If a peptide is immunogenic, a signaling cascade can be triggered within the T cell. However, the binding of different peptides and/or different TRs to MH is also known to influence the spatial arrangement of the MH α‐helices which could itself be an additional level of T cell regulation. In this study, we introduce a new methodology based on differential geometric parameters to describe MH deformations in a detailed and comparable way. For this purpose, we represent MH α‐helices by curves. On the basis of these curves, we calculate in a first step the curvature and torsion to describe each α‐helix independently. In a second step, we calculate the distribution parameter and the conical curvature of the ruled surface to describe the relative orientation of the two α‐helices. On the basis of four different test sets, we show how these differential geometric parameters can be used to describe changes in the spatial arrangement of the MH α‐helices for different biological challenges. In the first test set, we illustrate on the basis of all available crystal structures for (TR)/pMH complexes how the binding of TRs influences the MH helices. In the second test set, we show a cross evaluation of different MH alleles with the same peptide and the same MH allele with different peptides. In the third test set, we present the spatial effects of different TRs on the same peptide/MH complex. In the fourth test set, we illustrate how a severe conformational change in an α‐helix can be described quantitatively. Taken together, we provide a novel structural methodology to numerically describe subtle and severe alterations in MH α‐helices for a broad range of applications. © 2013 Wiley Periodicals, Inc.