一维短沟槽复合准晶结构减阻效应及模拟分析

本文测试了人工构建的一维短沟槽复合准晶结构对流体的减阻性能,并与一维短沟槽复合周期结构和一维沟槽周期结构的流阻进行了对比.实验结果表明,一维短沟槽复合准晶结构的减阻效果优于一维短沟槽复合周期结构,其中一维短沟槽十二重复合准晶结构的减阻效果最佳,同时与一维沟槽周期结构具有同样的减阻效果.在机理分析方面,建立了二维光栅的夫琅禾费衍射波模型,对通过一维短沟槽复合准晶结构的波谱特征进行模拟分析. 频谱分析表明,经过二维准周期光栅的相干波强度谱具有谱带结构特征,抑制了大角度方向上的强峰形成.这一结果与流体流过一维短沟槽复合准晶结构相对应,展向上的准周期结构在激活边界层微扰动的同时,也使得二次涡分布比较均匀,从而抑制了展向强扰动的形成,所以能够有效减小流阻.     

Electron spectrum and wave functions of icosahedral quasicrystals

Electron spectra and wave functions of icosahedral quasicrystals have been investigated in the tight-binding approximation using the two-fragment structural model (the Amman-MacKay network) with “central” decoration. A quasicrystal has been considered as a limiting structure in a set of optimal cubic approximants with increasing lattice constants. The method of level statistics indicates that the energy spectrum of an icosahedral quasicrystal contains a singular (nonsmooth) component. The density of electron states has been calculated for the first four optimal cubic approximants of the icosahedral quasicrystal, and the respective Lebesgue measures of energy spectra of these approximants have been obtained. Unlike the case of a one-dimensional quasiperiodic structure, the energy spectrum of an icosahedral quasicrystal does not contain a hierarchical gap structure typical of the Cantor set of measure zero in a one-dimensional quasicrystal. Localization of wave functions in an icosahedral quasicrystal has been studied, and their “critical” behavior has been detected. The effect of disorder due to substitutional impurities on electron properties of icosahedral quasicrystals has been investigated. This disorder makes the electron spectrum “smoother” and leads to a tendency to localization of wave functions. Zh. éksp. Teor. Fiz. 113, 1009–1025 (March 1998)     

A possible similarity between lyotropic cubic phases and cholesteric blue phases

Summary The common features in structures and properties of lyotropic cubic phases (LCP) and cholesteric blue phases (BP) are discussed. In both systems the cubic phases have nontrivial structures governed by frustrations. The frustration is connected with the double-twist in BPs and with the layer curvatures in LCPs. The structure of BP can be quantitatively described using the minimization of the Landau free energy with tensor order parameter. The order parameter of LCP is unknown till now; however, some minimization procedure can also be used for the solution of the phase problem. It is noted that in both systems the stable amorphous phases are observed (the fog phase or BPIII in BPs andL ₃ phase in lyotropic crystals). The importance of the observation of ?forbidden? reflections for the unequivocal identification of the space groups is emphasized. Work presented at the second USSR-Italy Bilateral Meeting on Liquid Crystals held in Moscow, September 15–21, 1988.     

Graded photonic quasicrystals

We introduce graded photonic quasicrystals and investigate properties of such structures on the example of a Luneburg lens based on a dodecagonal photonic quasicrystal. It is shown that the graded photonic quasicrystal lens has better focusing properties as compared with the graded photonic crystal lens in a frequency range suitable for experimental realization. The proposed graded photonic quasicrystals can be used in optical systems where compact and powerful focusing elements are required.     

Structure of the AlRhCu decagonal quasicrystal: I. A unit-cell approach

Structure of the Al---Rh---Cu decagonal quasicrystal has been studied by high-resolution electron microscopy. The high-resolution structure image shows an aperiodic tiling composed of three kinds of subunits, namely flattened hexagon, crown and five star. Therefore, a structural model of the Al---Rh---Cu decagonal quasicrystal has been constructed in a unit-cell approach, in which the atom arrangements in the subunits have been proposed. It is known that the phase has two layers in a period of 0.4 nm along the unique tenfold axis according to the previous study by electron diffraction method. The ideal model of the Al---Rh---Cu decagonal quasicrystal is proposed as periodic stacking of the layers with quasiperiodic tessellation of the three kinds of subunits, in each layer the two-colour Penrose tiling is obtained if different atom decorations for the same shape subunits are distinguished by white and black colours. Calculated images reproduces well the contrast features of the observed images, which means that the present model is basically correct. Structural relationship between the Al---Rh---Cu decagonal quasicrystal and the previously reported Al---Ni---Co decagonal quasicrystal, which has also a period of 0.4 nm, has also been discussed.     

Free energy computations by minimization of Kullback–Leibler divergence: An efficient adaptive biasing potential method for sparse representations

The present paper proposes an adaptive biasing potential technique for the computation of free energy landscapes. It is motivated by statistical learning arguments and unifies the tasks of biasing the molecular dynamics to escape free energy wells and estimating the free energy function, under the same objective of minimizing the Kullback–Leibler divergence between appropriately selected densities. It offers rigorous convergence diagnostics even though history dependent, non-Markovian dynamics are employed. It makes use of a greedy optimization scheme in order to obtain sparse representations of the free energy function which can be particularly useful in multidimensional cases. It employs embarrassingly parallelizable sampling schemes that are based on adaptive Sequential Monte Carlo and can be readily coupled with legacy molecular dynamics simulators. The sequential nature of the learning and sampling scheme enables the efficient calculation of free energy functions parametrized by the temperature. The characteristics and capabilities of the proposed method are demonstrated in three numerical examples.     

Morphometric approach to the solvation free energy of complex molecules

We show that the solvation free energy of a complex molecule such as a protein can be calculated using only four geometrical measures of the molecular structure and corresponding thermodynamical coefficients. We compare results from this morphometric approach to those obtained by an elaborate statistical-mechanical theory in liquid state physics for a large variety of different structures of protein G and find excellent agreement. Since the computational time is drastically reduced, the new approach provides a practical and efficient way for calculating the solvation free energy which can be employed when this quantity has to be calculated for a large number of structures, as in a simulation study of protein folding.     

Charge density determination in icosahedral AlPdMn quasicrystal using quantitative convergent beam electron diffraction

Charge density distribution in icosahedral AlPdMn quasicrystal has been studied on a single-crystal specimen by using quantitative convergent beam electron diffraction (QCBED) technique. The QCBED systematic row method was used in the refinement of structure factors. To refine the low-order structure factors, the wave-mechanical formulation of electron diffraction dynamical theory was used in the calculation of electron diffraction intensities for the quasicrystal in fitting the experimental intensity line scan profiles. The shapes of atomic surfaces (occupation domains) were described with symmetry-adapted series of surface harmonics. An iterative procedure was used in determination of structure factors of the quasicrystal. The structure factors of nine strongest symmetry inequivalent reflections according to X-ray diffraction experiment were refined with QCBED technique. The average of refinement results for a given reflection performed on several CBED patterns, which were slightly different in orientation and sample thickness, and on different line scans, was taken as the value of structure factor for the reflection. The obtained structure factors for electrons were transformed into X-ray structure factors with Mott formula. The bonding charge density map for the quasicrystal was constructed with the obtained nine structure factors. Assuming that the atoms are spheres, the gain or loss of electrons for different atoms were calculated. It shows that identical atoms can have different valences at different kinds of positions. The bonding charge is localized along certain directions.     

Ferrielectric smectic phase with a layer-by-layer change of the two-component order parameter

One of the most remarkable properties of smectics is the wide variety of possible equilibrium structures. In this paper, based on the Landau theory of the phase transitions, the transitions between ferroelectric and antiferroelectric phases and the structure formed by smectic layers with different azimuthal and polar orientations of the molecules were calculated. This unique structure has been predicted [P.V. Dolganov et al., JETP Lett. 76, 498 (2002)] using the minimization of the free energy with respect to the phase and modulus of the two-component order parameter, but never before detected. Recently, a nonresonant Bragg reflection, consistent with the predictions of the model, was found [P. Fernandes et al., Eur. Phys. J. E 20, 81 (2006)] in the ferrielectric smectic C* _FI1(SmC* _FI1) phase. In the three-layer ferrielectric structure with a macroscopic helical pitch, the modulus of the order parameter is larger in anticlinic-like layers and smaller in layers with mixed ordering. The values of the interlayer interactions were determined for smectic liquid-crystalline materials forming different polar structures. The text was submitted by the authors in English.     

寻找囚禁在光腔中的玻色-爱因斯坦凝聚体的八重准晶

准晶是一种拥有长程序但不具有周期性结构的一种物质.实验上通过将玻色-爱因斯坦凝聚体(BEC)放置在一个由四个光学腔组成的系统中,通过四个腔中激光照射在凝聚体上从而得到具有八重旋转对称性的准晶.本文结合虚时演化方法和分步傅里叶法从理论上得到了八重准晶体.我们通过这种方法可以实现更为复杂的晶体结构,从而为将来探索新物质提供了可能.     

Free energy reaction root mapping of alanine tripeptide in water

ABSTRACT

We have investigated the free energy surface of alanine tripeptide in water. To elucidate the secondary structure of the amide chain, information on the free energy surface with explicit water at room temperature, and the multidimensional reaction coordinates are required. We studied the minimum free energy paths (MFEPs) connecting reactants, transition structures (TS) and products. To solve this problem, we used the free energy reaction root mapping (FERRMap) method. This is an automated search method to find MFEPs by using umbrella integration and the scaled hypersphere search method. We calculated the four-dimensional free energy surface for alanine tripeptide in water using FERRMap and found 61 equilibrium structures (EQ) connected by 133 TS points. After elucidating the MFEP network, we analysed the structures of the EQ points and the MFEPs connecting beta-sheet structures and beta-turn structures or left-handed helix structures.     

On the choice of initial approximation in the problem of parameter identification of direct-gap semiconductors by cathodoluminescence microscopy

The problem of the choice of initial approximation has been considered to identify the parameters of direct-gap semiconductors by cathodoluminescence microscopy using the dependence of monochromatic cathodoluminescence intensity on electron beam energy for the case of a low level of signal excitation. It has been shown that the realization of the confluent analysis method can lead to the problem of multidimensional numerical minimization of a quadratic functional, the solution of which depends significantly on the choice of initial approximation. On this basis, some conditions of correct processing of the experimental data have been determined to identify the required parameters for gallium arsenide.     

Hydrogenic impurity ground state in quantum well: the envelope function revisited

We present a new variationnal method for calculating the ground state energy of an electron bound to an impurity located in a quantum well. This method relies on an envelope function which is determined exactly from a formal minimization procedure. The obtained energies are lower by as much as 10% than the ones found by the widely used free electron envelope function. Their large width limits are reached with exponentially small corrections as they should. We also find that, except for narrow wells, the shape of these exact envelope functions strongly depends on the impurity position, being consequently quite different from the usual free electron ones. In order to discuss the improvements brought by our new procedure in the most striking way, we have used a model semiconductor quantum well with infinite barrier height and simplified band structure. Extensions can be made to finite barrier and more realistic band structures, following the same technique. Received 11 December 2000     

Tunable On‐Chip Sources with Aperiodic Metasurface

Surface plasmons show tremendous capability in integrated communication, quantum computing and sensing. Excitations and manipulations of surface plasmons are essential in developing integrated photonic devices. Here, a systematic study of tunable emission of surface plasmons with an eightfold quasicrystal metasurface, which acts as an on‐chip source, is presented. It is shown that the quasicrystal structure can switch on or off the surface plasmons propagation channels in the desired direction. Meanwhile, such a quasicrystal structure can be polarization‐dependent or polarization‐independent based on different constituent slit pairs. The proposed quasicrystal design provides more freedom for steering surface plasmons in the launching process. Thus, it may significantly simplify the design and fabrication of integrated plasmonic devices.     

Study of the magnetic properties of GdZn compound using PAC spectroscopy with 140Ce and 111Cd as probe nuclei

Nanocrystalline Al₆₄Cu₂₃Fe₁₃ icosahedral quasicrystal has been obtained by milling of solid quasicrystal precursors prepared by arc-melt. The local structure around Fe atoms was studied by Mössbauer spectroscopy using a quadrupole splitting distribution method. Mössbauer results of annealed and milled samples show the existence of a broadened distribution of Fe sites which is associated to intrinsic disorder. The structural characterization was determined using x-ray diffraction. The average grain-size of the nanostructured quasicrystal, obtained from the line broadening of the X-ray diffraction peaks, was estimated to be of the order of 10 nm for a sample milled by 5 h.     

The generalized van Laar approximation for free energy

The van Laar equation for the uniform substance phase is analyzed. Based on this, an expression for free energy is found. The structure of the expression allowed us to create a method for determining the free energy in an arbitrary order of the perturbation theory. A generalized equation for free energy is derived based on the using thermodynamic perturbation theory and the accelerated method of convergence of the series of the perturbation theory. This expression agrees well with the asymptotic behavior of the free energy and with the known experimental data. It can be successfully used to describe the behavior of the substance in a super-critical region, as well as to investigate the metastable phase. It is shown that the expression for free energy can be used for a broad class of substances.     

Hydrogen in the approximant <Emphasis Type="Italic">i</Emphasis>-TiZrHf: The energy state,charge, and diffusion

The energy of hydrogen dissolution in different tetrahedral pores of a 1/1 approximant of the icosahedral TiZrHf quasicrystal has been determined in terms of the density functional theory and ab initio pseudopotentials. At low and high degrees of loading of TiZrHf with hydrogen, the charges of atoms involved in the system and the Mayer bond order have been calculated for all possible M-M and M-H pairs. The diffusion coefficient of a single hydrogen atom in the system under study has been estimated numerically.     

十二次对称准周期结构的自相似变换及准晶胞构造

研究十二次对称准晶体模型的几何结构性质.修正了Socolar在正方形-菱形-六边形拼图模型中自相似变换的错误.在Stampfli-Ghler正方形-菱形-三角形拼图模型的基础上,成功地构造出了准晶胞,使得十二次对称准周期结构可以用覆盖理论描述. 关键词： 准晶体 拼图模型 自相似变换 覆盖理论