Perturbed soliton-like molecular excitations in a deformed DNA chain

We study the nonlinear dynamics of a deformed Deoxyribonucleic acid (DNA) molecular chain which is governed by a perturbed sine-Gordon equation coupled with a linear wave equation representing the lattice deformation. The DNA chain considered here is assumed to be deformed periodically which is the energetically favourable configuration, and the periodic deformation is due to the repulsive force between base pairs, stress in the helical backbones and due to the elastic strain force in both the strands. A multiple scale soliton perturbation analysis is carried out to solve the perturbed sine-Gordon equation and the resultant perturbed kink and antikink solitons represent open state configuration with small fluctuation. The perturbation due to periodic deformation of the lattice changes the velocity of the soliton. However, the width of the soliton remains unchanged.     

Lattice with vacancies: elastic fields and effective properties in frameworks of discrete and continuum models

Linear elastic deformation of the two-dimensional triangular lattice with multiple vacancies is considered. Closed-form analytical expressions for displacement field in the lattice with doubly periodic system of vacancies are derived. Effective elastic moduli are calculated. The results are compared with the ones obtained by molecular dynamics simulations of a lattice with random distribution of vacancies. At low vacancy concentrations, less than 4%, random and periodic distributions of vacancies produce the same effect on elastic moduli. One of the main goals is to examine the possibilities and limitations of modelling of the lattice with vacancies by an elastic continuum with holes. It is found that the effective elastic properties are modelled adequately, provided the shape of the holes is chosen appropriately. On the contrary, the strain field, in particular, strain concentration differs significantly.     

Theoretical Study of Elastic Properties of Tungsten Disilicide

The plane-wave pseudopotential method using the generalized gradient approximation within the framework of density functional theory is applied to analyse the lattice parameters, elastic constants, bulk moduli, shear moduli and Young's moduli of WSi₂. The quasi-harmonic Debye model, using a set of total energy versus cell volume obtained with the plane-wave pseudopotential method, is applied to the study of the elastic properties and vibrational effects. The athermal elastic constants of WSi₂ are calculated as a function of pressure up to 35GPa. The relationship between bulk modulus and temperature up to 1200K is also obtained. Moreover, the Debye temperature is determined from the non-equilibrium Gibbs function. The calculated results are in good agreement with the experimental data.     

Experimental study of lattice distortion in ellipsoid-like nano-crystallites of copper

The elastic state of embedded inclusions is of considerable importance to the properties of materials. The non-uniform lattice distortion in the inclusions in which the interfaces are shaped with variable curvature cannot be measured by usual experimental methods. In this paper, the lattice distortions in an ellipsoid-like nano-crystallite of copper were measured by means of the peak finding method in the central part of the HRTEM image. The effects of contrast delocalization are studied by HRTEM image simulations, which show that the measured spacings of peaks in the middle part of the crystallite can be considered approximately equal to the true spacings of columns. With the HRTEM method, our measured results show that the nano-crystallite is expanded in the short axis direction and compressed in the long axis direction. The results calculated with the elasticity theory incorporating interface tension consist with the experimental results of HRTEM.     

Ground-state energy of dilute neutron matter at next-to-leading order in lattice chiral effective field theory

We present lattice calculations for the ground-state energy of dilute neutron matter at next-to-leading order in chiral effective field theory. This study follows a series of recent papers on low-energy nuclear physics using chiral effective field theory on the lattice. In this work we introduce an improved spin- and isospin-projected leading-order action which allows for a perturbative treatment of corrections at next-to-leading order and smaller estimated errors. Using auxiliary fields and Euclidean-time projection Monte Carlo, we compute the ground state of 8, 12, and 16 neutrons in a periodic cube, covering a density range from 2% to 10% of normal nuclear density.     

First-principles investigation on the elastic stability and thermodynamic properties of Ti₂SC

Using Vanderbilt-type plane-wave ultrasoft pseudopotentials within the generalized gradient approximation(GGA) in the frame of density functional theory(DFT),we have investigated the crystal structures,elastic,and thermodynamic properties for Ti2SC under high temperature and high pressure.The calculated pressure dependence of the lattice volume is in excellent agreement with the experimental results.The calculated structural parameter of the Ti atom experienced a subtle increase with applied pressures and the increase suspended under higher pressures.The elastic constants calculations demonstrated that the crystal lattice is still stable up to 200 GPa.Investigations on the elastic properties show that the c axis is stiffer than the a axis,which is consistent with the larger longitudinal elastic constants(C 33,C 11) relative to transverse ones(C 44,C 12,C 13).Study on Poisson’s ratio confirmed that the higher ionic or weaker covalent contribution in intra-atomic bonding for Ti2SC should be assumed and the nature of ionic increased with pressure.The ratio(B/G) of bulk(B) and shear(G) moduli as well as B/C 44 demonstrated the brittleness of Ti2SC at ambient conditions and the brittleness decreased with pressure.Moreover,the isothermal and adiabatic bulk moduli displayed opposite temperature dependence under different pressures.Again,we observed that the Debye temperature and Gru¨neisen parameter show weak temperature dependence relative to the thermal expansion coefficient,entropy,and heat capacity,from which the pressure effects are clearly seen.     

Surface shear horizontal waves associated with a periodic array of wires deposited on a substrate

The vibrational and electronic spectra of a semi-infinite crystal with a planar surface are modified by the presence of surface inhomogeneities or roughness such as ridges or grooves, quantum wires or tips. We develop a Green's function formalism to investigate the localized and resonant acoustic modes of shear horizontal polarization associated with the surface of a substrate supporting a single and a periodic array of wires. Each material is assumed to be an isotropic elastic medium. The calculation can be applied to an arbitrary choice of the shape and elastic parameters of the wires. The surface modes are obtained as well-defined peaks of the densities of states (DOS). In this paper, we calculate the variation of the density of states associated with the adsorption of a single wire, and the dispersion curves of the surface modes for a periodic array of wires on the flat surface of a substrate. We discuss their behaviors as a function of the elastic parameters and the relationship between resonant modes of the single wire and dispersion curves of the surface modes for a periodic structure. Received 6 December 2000     

Dislocation energy and calculation from Peierls stress： a rigorous the lattice theory

In the classical Peierls--Nabarro (P-N) theory of dislocation, there is a long-standing contradiction that the stable configuration of dislocation has maximum energy rather than minimum energy. In this paper, the dislocation energy is calculated rigorously in the context of the full lattice theory. It is found that besides the misfit energy considered in the classical P-N theory, there is an extra elastic strain energy that is also associated with the discreteness of lattice. The contradiction can be automatically removed provided that the elastic strain energy associated with the discreteness is taken into account. This elastic strain energy is very important because its magnitude is larger than the misfit energy, its sign is opposite to the misfit energy. Since the elastic strain energy and misfit energy associated with discreteness cancel each other, and the width of dislocation becomes wide in the lattice theory, the Peierls energy, which measures the height of the effective potential barrier, becomes much smaller than that given in the classical P-N theory. The results calculated here agree with experimental data. Furthermore, based on the results obtained, a useful formula of the Peierls stress is proposed to fully include the discreteness effects.     

Computer simulation study of the two-dimensional nematic lattice model based on the modified Gruhn–Hess pair potential model

A modified Gruhn–Hess pair potential model, where the potential parameters related to the elastic constants are different from the original model, was investigated with the aid of Monte Carlo (MC) simulation and Mean Field (MF) theory based upon a two-dimensional nematic lattice model. The model produces a ground state in perfect nematic order, where particles are aligned in the lattice plane. Both the MF predictions and the simulation results for the second-rank ordering tensor show that the system is biaxial in the low-temperature region, with a positive primary order parameter and the main director aligned along the lattice axis. A transition to uniaxial order takes place at higher temperatures with a negative primary order parameter and the director is orthogonal to the lattice plane. This orientational order survives up to temperatures higher than the transition temperature of the three-dimensional lattice model, possibly at all finite temperatures. MF predictions agree qualitatively with simulation but, in quantitative terms, the transition temperature is overestimated by 52%.     

Heat Conduction and Characteristic Size of Fractal Porous Media

Based on fractal theory, two types of random Sierpinski carpets （RSCs） and their periodic structures are generated to model the structures of natural porous media, and the heat conduction in these structures is simulated by the finite volume method. The calculated results indicate that in a certain range of length scales, the size and spatial arrangement of pores have significant influence on the effective thermal conductivity, and the heat conduction presents the aeolotropic characteristic. Above the length scale, however, the influence of size and spatial arrangement of pores on the effective thermal conductivity reduces gradually with the increasing characteristic size of porous media, the aeolotropic characteristic is weakened gradually. It is concluded that the periodicity in structures of porous media is not equal to the periodicity in heat conduction.     

Effective field theory for bound state reflection

Elastic quantum bound-state reflection from a hard-wall boundary provides direct information regarding the structure and compressibility of quantum bound states. We discuss elastic quantum bound-state reflection and derive a general theory for elastic reflection of shallow dimers from hard-wall surfaces using effective field theory. We show that there is a small expansion parameter for analytic calculations of the reflection scattering length. We present a calculation up to second order in the effective Hamiltonian in one, two, and three dimensions. We also provide numerical lattice results for all three cases as a comparison with our effective field theory results. Finally, we provide an analysis of the compressibility of the alpha particle confined to a cubic lattice with vanishing Dirichlet boundaries.     

求晶体位错自能的离散弹性方案

考虑到晶体的离散点阵结构,滑移只能在原子之间进行,因此位错中心永远没有原子,位错中心附近分摊到每个原子的离散弹性能量处处有限。在刚性位错假定下,直接应用位错弹性理论解析结果,求出了晶体直奇异位错等效内切半径及其随位错中心位置的周期变化。对于简单四方晶体中奇异螺型位错,一级近似与Peierls模型结果巧合。计算了fcc和bcc两种晶系中各种位错的自能和等效位错内切半径,并初步考虑了各向异性弹性效应。结果表明:位错滑移面不是几何平面,bcc螺型位错滑移面类似于蜂巢结构。指出了用这种离散弹性方法进一步估算各种次级效应的可能。 关键词：     

Flow acoustics in periodic structures

A recent paper [A.A. Krokhin, J. Arriaga, L.N. Gumen, Speed of sound in periodic elastic composites, Phys. Rev. Lett. 91 (2004) 264302-1-4] addresses the speed of sound in periodic elastic composites (phononic crystals) with particular emphasis to the case where air bubbles are present in water and arranged periodically. In such periodically arranged mixtures, the well-known phenomena of the drop of the speed of sound may occur and applications related to, e.g., sound-beam focusing and acoustic surgery are possible [F. Cervera, L. Sanchez, J.V. Sanchez-Perez, R. Martinez-Sala, C. Rubio, F. Meseguer, C. Lopez, D. Caballero, J. Sanchez-Dehesa, Phys. Rev. Lett. 88 (2002) 023902]. In this paper, the analysis is extended theoretically to include cases where a background flow in a periodic structure is maintained. Calculations of dispersion relations and group velocities are presented in cases with one- and two-dimensional material periodicity for background flow values in the range: 0-1m/s. Materials considered in the calculations are periodic water-air mixtures. It is shown that acoustic waves couple to the group velocities only if the (acoustic) wave vector has a component along the background flow velocity direction.     

Structural and elastic properties of LaTiO3 under pressure

We investigate the structural and elastic properties of LaTiO₃ by the plane-wave pseudopotential density functional theory method. The lattice constants, bulk modulus and its pressure derivative are obtained. These properties in the equilibrium phase are well consistent with the available experimental data. The pressure dependence of the elastic constants, ductility, mechanical stabilities, sound velocity and Debye temperatures are investigated for the first time. From the ratio G/B, we conclude that LaTiO₃ is ductile at 0 GPa and becomes more ductile at high pressure. In addition, the anisotropy factors for every symmetry plane and axis as well as linear bulk modulus at diverse pressures have been obtained.     

Computer simulation study of a two-dimensional nematogenic lattice model based on a mapping from elastic free-energy density

Over the last few years, it has been recognized that on can construct, in different ways, a nematogenic lattice model with pairwise additive interactions, which approximately reproduce the elastic free energy density, and where the parameters defining the pair potential are expressed in terms of elastic constants. An anisotropic nematogenic pair interaction of this kind, originally proposed by Gruhn and Hess [Z. Naturforsch. A 51 (1996) 1] has been investigated by Monte Carlo simulation, for particle centers of mass associated with both a three- and a two-dimensional lattice. Another approximate procedure for the mapping had also been proposed, and studied by simulation on a three-dimensional lattice (Luckhurst and Romano [Liq. Cryst. 26 (1999) 871]) continuing along this line, we investigate here the 2-dimensional lattice counterpart, by means of Mean Field theory and Monte Carlo simulations. In 2 dimensions, the anisotropic character of these potential models does not preclude the existence of orientational order at finite temperature. The model produces a ground state where particles are aligned in the lattice plane; both Mean Field (MF) predictions and simulation results for the second-rank ordering tensor show a low-temperature régime where the system becomes biaxial, with the main director aligned along a lattice axis; at higher temperature there is a transition to uniaxial order with negative order parameter, and director orthogonal to the lattice plane; this orientational order survives up to temperatures higher than the transition temperature of the 3-dimensional counterpart, possibly at all finite temperatures. MF predictions and simulation results appear to agree qualitatively, but in quantitative terms the MF prediction for the transition temperature is some 56% too high.     

Homogenization theory for designing graded viscoelastic sonic crystals

In this paper,we propose a homogenization theory for designing graded viscoelastic sonic crystals(VSCs) which consist of periodic arrays of elastic scatterers embedded in a viscoelastic host material.We extend an elastic homogenization theory to VSC by using the elastic-viscoelastic correspondence principle and propose an analytical effective loss factor of VSC.The results of VSC and the equivalent structure calculated by using the finite element method are in good agreement.According to the relation of the effective loss factor to the filling fraction,a graded VSC plate is easily and quickly designed.Then,the graded VSC may have potential applications in the vibration absorption and noise reduction fields.     

Dynamic stability of Timoshenko beams resting on an elastic foundation

A finite element model is developed for the stability analysis of a Timoshenko beam resting on an elastic foundation and subjected to periodic axial loads. The effect of an elastic foundation on the natural frequencies and static buckling loads of hinged-hinged and fixed-free Timoshenko beams is investigated. The results obtained for a Bernoulli-Euler beam which is a special case of the present analysis show excellent agreement with the available results obtained by other analytical methods. The regions of dynamic instability are determined for different values of the elastic foundation constant. As the elastic foundation constant increases the regions of dynamic instability are shifted away from the vertical axis and the width of these regions is decreased, thus making the beam less sensitive to periodic forces.     

Bethe ansatz study of two-dimensional soliton lattice melting

We study the melting of incommensurate soliton lattice using the exact Bethe ansatz solution of one-dimensional quantum sine-Gordon Hamiltonian with U(1) coupling. The elastic moduli of soliton lattice are obtained and their asymptotic behaviors are explicitly calculated both at zero and finite temperature. We have obtained the thermodynamic phase boundaries of the soliton lattice and shown that the direct commensurate-incommensurate transitions are intervened by the fluid phase for T>0 as predicted by Coppersmith et al. [Coppersmith et al., Phys. Rev. Lett. 46 (1981) 549. [1]] for n≤2.     

Ab initio calculations of elastic constants and thermodynamic properties of Li2O for high temperatures and pressures

The elastic constants and thermodynamic properties of Li₂O for high temperatures and pressures are calculated by the ab initio unrestricted Hartree-Fock (HF) linear combination of atomic orbital (LCAO) periodic approach. The lattice constant, elastic constants, Debye temperature, and thermal expansion coefficient obtained are in good agreement with the available experimental data and other theoretical results. It is found that at zero pressure the elastic constants C₁₁, C₁₂ and C₄₄, bulk modulus B and Debye temperature Θ_D decrease monotonically over the wide range of temperatures from 0 to 1100 K. When the temperature , C₁₂ approaches zero, consistently with the transition temperature 1200 K. However, with increasing pressure, they all increase monotonically and the anisotropy will weaken.