Calculation of cohesive energy of actinide metals

According to empirical electron theory of solids and molecules (EET), an equation for calculating the cohesive energy of actinide metals is given, the cohesive energy of 9 actinide metals with known crystal structure is calculated, which is identical with the experimental values on the whole, and the cohesive energy of 6 actinide metals with unknown crystal structure is forecast.     

Radiation effects of poly(vinylidene fluoride) II

Seven kinds of poly (vinylidene fluoride) (PMF) specimens with different crystallinity are irradiated with electron beam. The radiation effects on the amorphous and crystal zones and the relationship between the structures of the materials and the radiation effects are discussed. Differential scanning calorimeter (DSC), electron spin resonance (ESR) and X-ray diffraction are used to study the radiation damage of PMF crystal. The zero-entropy-production phase transition temperature, the irradiation damage yield of crystal zone and the destiny of the residual free radical of macromolecules produced by irradiation are all discussed. It is shown that appreciable structural defects and distortions start from both of the deformed points of regularly folded crystalline stems and the irregular loop zone of the crystalline surface layers.     

Orthorhombic distortion energy for monatomic fcc crystals

The potential energy barrier and the geometry of the volume-conserving orthorhombic distortion for monatomic face-centered cubic (fcc) crystals in the absence of thermal motion have been investigated. It is shown that the orthorhombic transformation path can continuously transform a fcc crystal structure into six neighboring fcc crystal structures. Each of the new fcc lattices is equivalent to the original one but has a different orientation. The only difference of the six new fcc monatomic structures is that all the atoms change one pair of twelve atoms in the first coordination sphere into another pair and the structure has finite shear strains. The height of the potential energy barrier between the two neighboring stable fcc structures is calculated with the Morse and Mie two-body potentials under constant volume expansion or contraction. The barrier height is several times less than the energy corresponding to dilatations (the melting energy) where the lattice cohesion is lost. The total energy difference between body- and face-centered cubic crystal structures is equal to the minimum barrier height for large values of the effective radius of interatomic interaction. For small values of the radius, the minimum barrier height is less than this difference. The growth of the effective radius of the interatomic interaction decreases the height of the energy barrier. The height increases greatly with the volume contraction and decreases with the volume expansion of the fcc structures.Department of Mechanics and Mathematics, Moscow State Univesity, Moscow 117234, Russia. Published in Mekhanika Kompozitnykh Materialov, Vol. 34, No. 1, pp. 94–106, January–February, 1998.     

Mathematical analysis of plasmonic resonance for 2-D photonic crystal

In this article, we study the plasmonic resonance of infinite photonic crystal mounted by the double negative nanoparticles in two dimensions. The corresponding physical model is described by the Helmholz equation with so called Bloch wave condition in a periodic domain. By using the quasi-periodic layer potential techniques and the spectral theorem of quasi-periodic Neumann–Poincaré operator, the quasi-static expansion of the near field in the presence of nanoparticles is derived. Furthermore, when the magnetic permeability of nanoparticles satisfies the Drude model, we give the conditions under which the plasmonic resonance occurs, and the rate of blow up of near field energy with respect to nanoparticle's bulk electron relaxation rate and filling factor are also obtained. It indicates that one can appropriately control the bulk electron relaxation rate or filling factor of nanoparticle in photonic crystal structure such that the near field energy attains its maximum, and enhancing the efficiency of energy utilization.     

Magnetic inelastic scattering of neutrons by a ferromagnetic crystal

This paper deals with a theoretical investigation of the energy spectrum of thermal neutrons inelastically scattered by a ferromagnetic crystal. The method of double-time temperature-dependent Green’s functions is used. Formulæ are derived for the line width and for an asymmetry parameter leading to a deviation from the Lorentzian form. The results are discussed and compar d with earlier work. Special attention is paid to the question of the deviation of the energy distribution from the purely Lorentzian form.     

On a general theory for quantum–gravity interaction and an experimental confirmation of heterotic strings

The note gives first a short systematic derivation of the basic topological structure of heterotic string theory using the electromagnetic fine structure constant. Subsequently, we argue that the physical reality of heterotic string theory is confirmed via an indirect comparison between certain theoretical predictions and the experimental results at what are presently accessible energy scales.     

Graded Meshes for Higher Order FEM

A singularly perturbed one-dimensional convection-diffusion problem is solved numerically by the finite element method based on higher order polynomials. Numerical solutions are obtained using S-type meshes with special emphasis on meshes which are graded (based on a mesh generating function) in the fine mesh region. Error estimates in the ε-weighted energy norm are proved. We derive an 'optimal' mesh generating function in order to minimize the constant in the error estimate. Two layer-adapted meshes defined by a recursive formulae in the fine mesh region are also considered and a new technique for proving error estimates for these meshes is presented. The aim of the paper is to emphasize the importance of using optimal meshes for higher order finite element methods. Numerical experiments support all theoretical results.     

Thermodynamic Potential of a System of Electrons and Phonons in a Disordered Alloy

We obtain a cluster expansion for the two-time retarded Green's functions and the thermodynamic potential of a disordered crystal taking the electron–phonon and electron–electron interactions into account. The electron states of the system are described in the framework of a multiband tight-binding model. The calculations are based on the diagram techniques for the temperature Green's functions. The coherent potential approximation is chosen as a zeroth-order one-site approximation in this cluster expansion method. We show that the contributions from the processes of scattering of elementary excitations on clusters decrease as the number of sites in the cluster increases in accordance with certain small parameters. Analytic estimates of the influence of the electron–phonon interaction on the energy spectrum of electrons of an alloy being ordered are obtained in a one-band model. The applicability of these results to describing the influence of strong electron correlations on the electron structure and properties of alloys of transition metals with narrow energy bands is illustrated with the example of the Fe–Ti alloy.     

α-Sn thin film grown on GaAs substrate by MBE and investigation of its multiquantum well structure

α-Sn thin films have been grown on GaAs (001) single crystal substrates by molecular beam epitaxy (MBE). The α-Sn growth process has been characterizedin situ by reflection high energy electron diffraction (RHEED), and the transmission electron microscope (TEM) was used to analyze the interface structures. The measurement results indicate that our metastable a-Sn films have both higher temperature stability which increases by 30°C (from 70 to 100°C) and thickness stability which increases by 200 nm (from 500 to 700 nm) in comparison with previous reports. Other improvements in electrical properties have also been observed. In addition, a new model of multiquantum well structure has been suggested. Project supported by the National Natural Science Foundation of China (Grant No. 69586001).     

On the numerical relaxation of single-slip plasticity in finite strains

The modeling of the elastoplastic behaviour of single crystals with infinite latent hardening leads to a nonconvex energy density, whose minimization produces fine structures. The computation of the quasiconvex envelope of the energy density is faced in this case with huge numerical difficulties caused by the clusters of local minima. By exploiting the structure of the problem, we present a fast and efficient numerical relaxation algorithm as alternative to global optimization techniques usually adopted in literature which are computationally more expensive. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A theoretical model for Reynolds-stress and dissipation-rate budgets in near-wall region

A 3-D wave model for the turbulent coherent structures in near-wall region is proposed. The transport nature of the Reynolds stresses and dissipation rate of the turbulence kinetic energy are shown via computation based on the theoretical model. The mean velocity profile is also computed by using the same theoretical model. The theoretical results are in good agreement with those found from DNS, indicating that the theoretical model proposed can correctly describe the physical mechanism of turbulence in near wall region and it thus possibly opens a new way for turbulence modeling in this region.     

Synchrotron radiation photoemission spectrum study on K3C60 film

K3C60 single crystal film was prepared on the cleaved (111) surface of C60 single crystal. Synchrotron radiation angle-resolved photoemission spectra were measured at normal emission with sample temperature at ～150K. Up to four subpeaks of LUMO-derived band were observed. These sub-peaks exhibit distinct energy dispersions which resemble in general the theoretical ones calculated for K3C60 at low temperature with the so-called one-dimensional disordered structure. But there is large deviation of experimental sub-band intervals from the theoretical values. This result is meaningful for the studies of the physical properties of alkali-doped C60 solids, e.g. the mechanism for superconductivity.     

结构中的离散弹性支承

有几篇文章已经涉及结构的离散弹性支承.它与连续弹性支承有什么关系,两种支承情况对于结构动力特性产生多大差异,这是人们关心的问题.本文通过分析指出,频率是反应系统总能量中动能和势能的比例关系,离散支承和连续支承之间通过某种能量的等效转化,可保证频率不变.并给出了梁的理论推导和旋转壳的的数值结果.     

Smectic A liquid crystal configurations with interface defects

We study planar energy minimizing configurations of smectic A liquid crystal materials and classify the corresponding defect structures. We investigate focal conic configurations in wedge, non‐parallel plates, funnel‐shaped domains, and non‐concentric annuli. The application of the stability condition for focal conics is relevant to the specification of the location of the interfacial defects. Self‐similar structures are discussed for a class of solutions with the same bulk energy. We propose surface energies terms to serve as selection mechanisms of particular self‐similar configurations. We also show how the modelling of chevron texture naturally arises in the present framework. Copyright © 2001 John Wiley & Sons, Ltd.     

Dispersion relations of elastic waves in three-dimensional cubical piezoelectric phononic crystal with initial stresses and mechanically and dielectrically imperfect interfaces

A three-dimensional cubical piezoelectric phononic crystal is theoretically studied in this paper, formed by pre-stressed piezoelectric rectangular blocks and imperfect interfaces. Firstly, transfer matrices of pre-stressed piezoelectric rectangular blocks and imperfect interfaces are obtained based on the structural characteristics. The Bloch waves consist of three groups of sub-coupled elastic waves corresponding with three orthogonal periodical directions in the three-dimensional periodical structure. Furthermore, based on the transfer matrices of typical single cell and the Bloch theorem, it is established that the theoretical model of above-mentioned three-dimensional cubical piezoelectric phononic crystal to obtain the dispersion relations of Bloch waves. Finally, the influences of non-dimensional geometrical parameters (structural and modal parameters) and physical parameters (initial stress and mechanically and dielectrically imperfect interface parameters) on the dispersion relations are discussed based on the graphically numerical results. Numerical calculation results show that the existences of initial stresses and mechanically and dielectrically imperfect interfaces equivalently lead to the alterations of structural flexibilities or rigidities. The theoretical model and numerical discussions will provide a direct guidance of multi-material additive manufacturing for pre-stressed and inhomogeneous periodic structures with partial and global dispersion properties.     

Synchrotron radiation photoemission spectrum study on K3C60 film

K₃C₆₀, single crystal film was prepared on the cleaved (111) surface of C₆₀, single crystal. Synchrotron radiation angle-resolved photoemission spectra were measured at normal emission with sample temperature at × 150K. Up to four subpeaks of LUMO-derived band were observed. These sub-peaks exhibit distinct energy dispersions which resemble in general the theoretical ones calculated for K₃C₆₀ at low temperature with the so-called one-dimensional disordered structure. But there is large deviation of experimental sub-band intervals from the theoretical values. This result is meaningful for the studies of the physical properties of alkali-doped C₆₀ solids, e.g. the mechanism for superconductivity.     

Application of optimization methods for finding equilibrium states of two-dimensional crystals

A two-dimensional model of a multilayer material and a procedure for simulating its properties based on global optimization methods are proposed. This model is applied for the case of a two-dimensional crystal. Global minima of the interaction energy of the material’s atoms are found, and geometric characteristics of its corresponding equilibrium states are described. The resulting lattices, in particular graphene’s lattices, agree with experimental data, which confirms the validity of the proposed approach. This approach can be extended to a wider class of layered structures, and it can be used for determining the mechanical properties of materials.     

Analytical evaluation of the thermionic emission probability for semiconductor-insulator interfaces using incomplete gamma functions

In this study, a new efficient method for calculation of the charge carrier emission probability over energy barriers in semiconductor devices is presented. As will be seen, the present formulation yields compact closed-form expressions which enable the ready calculation of electron emission function. The results are amenable for use in further theoretical studies of thermionic emission probability for semiconductor-insulator interfaces where analytical methods may be desirable. Finally, the numerical results are presented and compared with results using alternative evaluation schemes.     

Deformation concentration for martensitic microstructures in the limit of low volume fraction

We consider a singularly-perturbed nonconvex energy functional which arises in the study of microstructures in shape memory alloys. The scaling law for the minimal energy predicts a transition from a parameter regime in which uniform structures are favored, to a regime in which the formation of fine patterns is expected. We focus on the transition regime and derive the reduced model in the sense of \(\Gamma \)-convergence. The limit functional turns out to be similar to the Mumford–Shah functional with additional constraints on the jump set of admissible functions. One key ingredient in the proof is an approximation result for \(SBV^p\) functions whose jump sets have a prescribed orientation.     

Metric spaces are universal for bi-interpretation with metric structures

In the context of metric structures introduced by Ben Yaacov, Berenstein, Henson, and Usvyatsov [3], we exhibit an explicit encoding of metric structures in countable signatures as pure metric spaces in the empty signature, showing that such structures are universal for bi-interpretation among metric structures with positive diameter. This is analogous to the classical encoding of arbitrary discrete structures in finite signatures as graphs, but is stronger in certain ways and weaker in others. There are also certain fine grained topological concerns with no analog in the discrete setting.