Calculus of variations as a basic tool for modelling of reaction paths and localisation of stationary points on potential energy surfaces

ABSTRACT

The theory of calculus of variations is a mathematical tool which is widely used in different scientific areas in particular in physics and chemistry. This theory is strongly related with optimisation. In fact the former seeks to optimise an integral related with some physical magnitude over some space to an extremum by varying a function of the coordinates. On the other hand, reaction paths and potential energy surfaces, in particular their stationary points, are the basis of many chemical theories, in particular reactions rate theories. We present a review where it is gathered together the variational nature of many types of reaction paths: steepest descent, Newton trajectories, artificial force induced reaction (AFIR) paths, gradient extremals, and gentlest ascent dynamics (GAD) curves. The variational basis permits to select the best optimisation technique in order to locate important theoretical objects on a potential energy surface.     

The Roper resonance in a finite volume

We calculate the energy levels corresponding to the Roper resonance based on a two-flavor chiral effective Lagrangian for pions, nucleons, deltas, and the Roper resonance at the leading one-loop order. We show that the Roper mass can be extracted from these levels for lattice volumes of moderate size.     

Resistivity exponent of two-dimensional lattice animals

We calculate the average resistanceR(L) of lattice animals spanningL×L cells on the square lattice using exact and Monte Carlo methods. The dynamical resistivity exponent, defined asR(L) L , is found to be =1.36±0.07. This contradicts the Alexander-Orbach conjecture, which predicts 0.8. Our value for differs from earlier measurements of this quantity by other methods yielding =1.17±0.05 and 1.22±0.08 by Havlin et al.On leave from the Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China.     

光声光谱法研究光学薄膜的吸收特性

本文以“一维热流活塞模型”为基础,推导出薄膜光声表达式,光声信号的幅值正比于吸收率.测量了透明基底上光学薄膜的光声吸收谱,实验结果与理论一致.尤其是测量弱吸收薄膜的吸收谱时,具有较高的灵敏度和实用性.     

杨氏双缝干涉实验中的光谱奇异现象

基于部分相干光的传输理论,研究了杨氏双缝干涉实验中的光谱奇异现象。发现在杨氏双缝干涉实验干涉场区中的某个点的光谱奇异现象,它会随着某些参量(如源光谱宽度Γ′,缝宽参量ε,相对空间相干度Δ0)的变化而改变,指出该现象可应用于信息的编码及自由空间的信息传输。     

铝粉点火微观机理的光谱研究

 铝粉是一种含能高的材料,它被广泛地添加到含能材料中。利用3台单色谱仪和OMA谱仪等多种谱仪技术,研究了铝粉在几种不同环境下的快速反应微观特性。研究表明：铝粉冲击波点火的临界条件和铝粉的物理状态相关。微米铝粉点火的临界温度为2 100 K,它接近Al₂O₃的熔化温度。它表明,在空气中容易氧化的微米铝粉点火,必须使铝粉表面的氧化层熔化。在气相反应中,微米铝粉和氧的反应是主要的;和水的反应是次要的。减小微米铝粉的颗粒尺寸,可以明显提高快速反应温度。 含铝复合燃料中的液体燃料反应后的铝粉才能参与反应;铝粉添加至气相反应介质后将明显提高反应温度。     

光谱色散匀滑技术与衍射光学器件联用性能的空间频谱分析

基于空间频谱分析方法,建立了光谱色散匀滑技术(SSD: Smoothing by Spectral Dispersion)与衍射光学器件(DOE: Diffractive Optical Element)联用性能的简化分析模型,为SSD与DOE联用时,SSD参量的优化提供了理论依据.数值模拟了SSD各参量,包括脉冲时间、调制频率、位相调制系数、光栅线色散系数等对束匀滑性能的影响.模拟结果表明,SSD参量经过优化选取,且波前畸变随时间快速变化时,能获得良好的束匀滑性能.     

取压方式对微通道内单相摩擦阻力特性的影响

本文以去离子水和氮气为工质,在水平圆形微通道(dh=0．336 mm)中采用两种直接取压方式-缝隙取压和小孔取压,对单相摩擦阻力特性进行了实验研究,并通过改变缝隙宽度,研究缝隙宽度对压降测量偏差的影响．     

A virtual instrumentation based protocol for the automated implementation of the inner field compensation method

One influential parameter which mediates interactions between many types of molecules and biological membranes stems from the lumped contributions of the transmembrane potential, dipole potential and the difference in the surface potentials on both sides of a membrane. With relevance to cell physiology, such electrical features of a biomembrane are prone to undergoing changes as a result of interactions with the aqueous surrounding. Among the most useful tools devoted to exploring changes of electrical parameters of a lipid membrane induced by certain extracellular ions, lipid composition, and embedded membrane peptides and proteins, are spectroscopic imaging and the inner field compensation (IFC) method. In this work we layout the principles of a fully computerized version of the IFC method, which makes it more readily available to users. As a direct application, we deployed this improved version of the IFC method to time-resolve changes induced by alamethicin monomers upon membrane dipole potential, following their aggregation within an artificial lipid membrane. Intriguingly, even prior crossing the membrane core, the membrane-bound alamethicin monomers are shown to significantly increase the dipole potential of the monolayer they reside in. Such data further emphasize the yet less-explored interplay between membrane-based protein and peptides, and the membrane dipole potential.     

The one-body and two-body density matrices of finite nuclei with an appropriate treatment of the center-of-mass motion⋆

The one-body and two-body density matrices in coordinate space and their Fourier transforms in momentum space are studied for a nucleus (a nonrelativistic, self-bound finite system). Unlike the usual procedure, suitable for infinite or externally bound systems, they are determined as expectation values of appropriate intrinsic operators, dependent on the relative coordinates and momenta (Jacobi variables) and acting on intrinsic wave functions of nuclear states. Thus, translational invariance (TI) is respected. When handling such intrinsic quantities, we use an algebraic technique based upon the Cartesian representation, in which the coordinate and momentum operators are linear combinations of the creation and annihilation operators and for oscillator quanta. Each of the relevant multiplicative operators can then be reduced to the form: one exponential of the set { } times another exponential of the set { }. In the course of such a normal-ordering procedure we offer a fresh look at the appearance of “Tassie-Barker” factors, and point out other model-independent results. The intrinsic wave function of the nucleus in its ground state is constructed from a nontranslationally-invariant (nTI) one via existing projection techniques. As an illustration, the one-body and two-body momentum distributions (MDs) for the ⁴He nucleus are calculated with the Slater determinant of the harmonic-oscillator model as the trial, nTI wave function. We find that the TI introduces quite important effects in the MDs.