Study of intrinsic anchoring in nematic liquid crystals based on modified Gruhn-Hess pair potential

A nematic liquid crystal slab composed of N molecular layers is investigated using a simple cubic lattice model, based upon the molecular pair potential which is spatially anisotropic and dependent on elastic constants of liquid crystals. A perfect nematic order is assumed in the theoretical treatment, which means the orientation of the molecular long axis coincides with the director of liquid crystal and the total free energy equals to the total interaction energy. We present a modified Gruhn-Hess model, which is relative to the splay-bend elastic constant K₁₃. Furthermore, we have studied the free nematic interfacial behavior (intrinsic anchoring) by this model in the assumption of the perfect nematic order. We find that the preferred orientation at the free interface and the intrinsic anchoring strength change with the value of modification, and that the director profile can be determined by the competition of the intrinsic anchoring with external forces present in the system. Also we simulate the intrinsic anchoring at different temperatures using Monte Carlo method and the simulation results show that the intrinsic anchoring favors planar alignment and the free interface is more disordered than the bulk.     

Multilayer relaxation at the Pb(110) surface

A combined experimental and theoretical study of multilayer relaxation at the Pb(110) surface is presented. Ion shadowing and blocking measurements show that the distance d₁₂ between the outermost two atomic layers is smaller than the bulk interlayer distance d by as much as Δd₁₂/d=−15.8±2.5%. For the relaxations of the second and third interlayer distances we find that they satisfy the empirical relation Δd₂₃/d+0.75Δd₃₄/d=+0.5±2.5%. Thermal vibration amplitudes are strongly enhanced at the surface. Our theoretical model, based on energy minimization of the total energy of a semi-infinite simple metal crystal, predicts oscillatory multilayer relaxation with Δd₁₂/d=−15.9%, Δd₂₃/d=+7.9%, Δd₃₄/d=−6.8% and Δd₄₅/d=+0.7%, in agreement with experiment.     

Örtliche Relaxation der Elektronen-Energieverteilung in hohen elektrischen Feldern

The motion of electrons in high electric fields is of particular interest due to its special experimental phenomena and its problems in theoretical treatment. We examine the spatial relaxation of electron energy distributions theoretically and experimentally. In the theory we assume a negligible elastic energy loss and a simple model for the inelastic collisions. The distribution function can be separated in two factors depending either on the kinetic energyε or on the total energyX=g3+Φ (Φ: potential energy). In application to the energy relaxation we calculate the relaxation of a humped initial energy distribution to a smoothed equilibrium distribution. The corresponding experiment was performed in the positive column of an argon plasma at a pressure of 3.6 · 10^?3 Torr. We measured the electron energy distribution as a function of distance from the cathode with a Langmuir probe using the second derivative method. Good agreement was found between the experimental and theoretical distributions.     

Finite element prediction of debonding onset in short fiber reinforced polymers incorporating a hybrid interphase region

A robust finite element procedure for investigating damage evolution in short fiber reinforced polymeric composites under external loads is developed. This procedure is based on an axisymmetric unit cell composed of a fiber, surrounding interphase and bulk matrix. The hybrid interphase concept involves a degraded material phase, the extent of which is material and property dependent. One of the most significant features of the model relies on establishment of variable adhesion conditions between the primary material phases. The unit cell is discretized into linearly elastic elements for the fiber and the matrix and interface elements which allow debonding in the fiber–matrix interface. The interface elements fail according to critical stress and critical energy release rate criteria. The tension and shear aspects of failure are uncoupled, although the resulting nonlinear problem is solved implicitly utilizing quasi-static incremental loading conditions. Final failure resulting from saturation and breakage is modeled by the vanishing interface element technique. Details of the propagation of interface cracks and the initiation of debonds are also observed and discussed for various shapes of fiber end. Numerical results reveal an intense effect of the fiber-end geometry on the initial fiber–matrix de-cohesion. The present finite element procedures can generate meaningful results in the analysis of fiber-reinforced composites.     

Influences of interfacial damage on the effective wave velocity in composites with reinforced particles

The scattering of elastic waves by a spherical particle with imperfect interface and the multiple scattering by many spherical particles with imperfect interface are studied in this paper. First, the scattering of elastic waves by a spherical particle with imperfect interface, i.e. spring interface model, is studied. Then, the multiple scattering by random distributed particles with interfacial damage in a composite material is investigated. The equations to evaluate velocity and attenuation of effective waves defined by statistic averaging are given. Furthermore, based on the established relation between the effective velocity and interfacial constants, a method to evaluate the interfacial damage nondestructively from the ultrasonic measure data is proposed. The numerical simulation is performed for the Sic-Al composites. The effective velocity is computed to show the influences of interface damage. By using the genetic algorithm, the interfacial damage is evaluated from the synthetic experimental data with various levels of error. The numerical results show the feasibility of the method proposed to approximately evaluate the interfacial damage in a composite material with reinforced particles based on ultrasonic data. Supported by the National Natural Science Foundation of China (Grant Nos. 10672019 and 10272003)     

On dual Schur domain decomposition method for linear first-order transient problems

This paper addresses some numerical and theoretical aspects of dual Schur domain decomposition methods for linear first-order transient partial differential equations. The spatially discrete system of equations resulting from a dual Schur domain decomposition method can be expressed as a system of differential-algebraic equations (DAEs). In this work, we consider the trapezoidal family of schemes for integrating the ordinary differential equations (ODEs) for each subdomain and present four different coupling methods, corresponding to different algebraic constraints, for enforcing kinematic continuity on the interface between the subdomains. Unlike the continuous formulation, the discretized formulation of the transient problem is unable to enforce simultaneously the continuity of both the primary variable and its rate along the subdomain interface (except for the backward Euler method).Method 1 (d-continuity) is based on the conventional approach using continuity of the primary variable and we show that this method is unstable for a lot of commonly used time integrators including the mid-point rule. To alleviate this difficulty, we propose a new Method 2 (modified d-continuity) and prove its stability for coupling all time integrators in the trapezoidal family (except the forward Euler). Method 3 (v-continuity) is based on enforcing the continuity of the time derivative of the primary variable. However, this constraint introduces a drift in the primary variable on the interface. We present Method 4 (Baumgarte stabilized) which uses Baumgarte stabilization to limit this drift and we derive bounds for the stabilization parameter to ensure stability. Our stability analysis is based on the “energy” method, and one of the main contributions of this paper is the extension of the energy method (which was previously introduced in the context of numerical methods for ODEs) to assess the stability of numerical formulations for index-2 differential-algebraic equations (DAEs). Finally, we present numerical examples to corroborate our theoretical predictions.     

Peculiarities of elastic scattering of intermediate-energy electrons related to their capture at quasi-stationary levels of an atom in a continuous spectrum

A theoretical model of electron scattering on an atom is constructed to study elastic atomic scattering of intermediate-energy electrons. The proposed model is based upon the combined Mensing potential with two spheres of atomic electrons, which admits analytical solutions of the radial Schröbinger equation. A procedure for matching the parameters of this scatterer to an approximate electrostatic potential of an atom in the form of a screened Coulomb potential has been determined. The screening radius of the latter potential has been calculated proceeding from the properties corresponding to the Thomas-Fermi method. A model of a scatterer determined according to the aforementioned procedure can be used to calculate the energy dependence of the cross section of elastic electron scattering on some atoms with s, p, and d shells representing elements neighboring zirconium. The main result is the establishment of factors responsible for the appearance of maxima on the energy dependences of the cross section of elastic electron scattering. These maxima are related to the resonant trapping of impinging electrons by quasi-stationary levels in a continuous spectrum.     

Structural, elastic, electronic and optical properties of a new layered-ternary Ta4SiC3 compound

We propose a new layered-ternary Ta₄SiC₃ with two different stacking sequences (α- and β-phases) of the metal atoms along c axis and study their structural stability. The mechanical, electronic and optical properties are then calculated and compared with those of other compounds M₄AX₃ (M=V, Nb, Ta; A=Al, Si and X=C). The predicted compound in the α-phase is found to possess higher bulk modulus than these compounds. The independent elastic constants of the two phases are also evaluated and the results discussed. The electronic band structures for α- and β-Ta₄SiC₃ show metallic conductivity. Ta 5d electrons are mainly contributing to the total density of states (DOS). We see that the hybridization peak of Ta 5d and C 2p lies lower in energy and the Ta 5d-C 2p bond is stronger than Ta 5d-Si 3p bond. Further an analysis of the different optical properties shows the compound to possess improved behavior compared to similar types of compounds.     

Elastic Deuteron Scattering on the <Superscript>12</Superscript>C Nucleus within a Three-Body Model

The formalism developed earlier for elastic pd scattering on the basis of Glauber theory with allowance for a total spin dependence is modified by replacing pN amplitudes by amplitudes for N¹²C scattering and is applied to elastic deuteron scattering on the ¹²C nucleus. The amplitudes for elastic N¹²C scattering are obtained within the optical model. Respective numerical calculations performed at the kinetic deuteron-beam energy of 270 MeV lead to results that agree well with data on the differential cross section for d¹²C scattering into the forward hemisphere, but the calculated spin observable A _y ^d agrees with experimental data only qualitatively.     

Ab initio simulations on the atomic and electronic structure of single-walled BN nanotubes and nanoarches

To simulate the perfect single-walled boron nitride nanotubes and nanoarches with armchair- and zigzag-type chiralities and uniform diameter of ∼5 nm, we have constructed their one-dimensional (1D) periodic models. In this study, we have compared the calculated properties of nanotubes with those for both hexagonal and cubic phases of bulk: bond lengths, binding energies per B-N bond, effective atomic charges as well as parameters of total and projected one-electron densities of states. For both phases of BN bulk, we have additionally verified their lattice constants. In the density functional theory (DFT), calculations performed using formalism of the localized Gaussian-type atomic functions as implemented in the CRYSTAL-06 code we have applied Hamiltonians containing either PWGGA or hybrid (DFT+HF) B3PW exchange-correlation functionals. After calculation of Hessian matrix for the optimized structures of BN bulk (both phases) and nanotubes (both chiralities) using the CRYSTAL code we have estimated their normal phonon modes within the harmonic approximation. Applying both atomistic and continuum models we have calculated the elastic energies and moduli for SW BN nanoarches. Our calculations clearly show a reproducibility of the atomic structure, effective charges and total energy, as well as phonon and elastic properties when using either PWGGA or hybrid B3PW Hamiltonians. On other hand, there is a high sensitivity of the discrete energy spectra parameters (including band gap) to the choice of the first principles approach (the hybrid method reproduce them noticeably better).     

Elestic constants in the interfacial layer at the nematic-liquid-crystal-vapour interface

Summary Close to the interface between a nematic liquid crystal (NLC) and another medium, the elastic constants become functions of distancez from the interface and of angle θ between the directorn and the unit vectork orthogonal to the interface. Furthermore, due to the breaking of the translation symmetry at the interface, a lot of new subsurface elastic contributions can appear. In a previous paper we investigated these subsurface anomalies by using a simple molecular model based on induced-dipole-induced-dipole interactions and by making numerical calculations in the special case of a planar director distortion. In this way, only the numerical values of some effective subsurface elastic constants that characterise planar director distortions could be obtained. In this paper we make a more complete analytical calculation of all the subsurface elastic constants by using a microscopic model and a more general theoretical procedure. The microscopic interaction energy is written in a general form that allows us to investigate different kinds of intermolecular interactions (induced diple-induced dipole, quadrupole-quadrupole and so on). Both thez-dependence and the θ-dependence of the subsurface elastic constants are obtained in a closed analytical form. In the special case of induced-dipole-induced-dipole interactions and for planar director distortions, our analytical results are shown to agree with the previous numerical results. The important macroscopic effect of these elastic subsurface anomalies is discussed.     

Decaying turbulence: What happens when the correlation length varies spatially in two adjacent zones

We have imagined a numerical experiment to explore the onset of turbulent intermittency associated with a spatial perturbation of the correlation length. We place two isotropic regions, with different integral scales, inside a volume where the turbulent kinetic energy is initially uniform and leave them to interact and evolve in time. The different length scales produce different decay rates in the two regions. Since the smaller-scale region decays faster, a transient turbulent energy gradient is generated at the interface between the two regions. The transient is characterized by three phases in which the kinetic energy gradient across the interface grows, peaks and then slowly decays. The transient lifetime is almost proportional to the initial ratio of the correlation lengths. The direct numerical simulations also show that the interface width grows in time. The velocity moments inside this interaction zone are seen to depart from their initial isotropic values and, with a certain lag, the anisotropy is seen to spread to small scales. The longitudinal derivative moments also become anisotropic after a few eddy turnover times. This anisotropic behaviour is different from that observed in sheared homogeneous turbulent flows, where high transverse derivative moments are generated, but longitudinal moments almost maintain the isotropic turbulence values. Apart from the behaviour of the energy gradient transients, the results also show the timescaling of the interface diffusion width, and data on the anisotropy of the large and small scales, observed through one-point statistics determined inside the intermittency sublayer, which is associated with the interaction zone.     

Identification of embedded horizontal cracks in beams using measured mode shapes

Mode shapes (MSs) have been extensively used to detect structural damage. This paper presents two new non-model-based methods that use measured MSs to identify embedded horizontal cracks in beams. The proposed methods do not require any a priori information of associated undamaged beams, if the beams are geometrically smooth and made of materials that have no stiffness discontinuities. Curvatures and continuous wavelet transforms (CWTs) of differences between a measured MS of a damaged beam and that from a polynomial that fits the MS of the damaged beam are processed to yield a curvature damage index (CDI) and a CWT damage index (CWTDI), respectively, at each measurement point. It is shown that the MS from the polynomial fit can well approximate the measured MS and associated curvature MS of the undamaged beam, provided that the measured MS of the damaged beam is extended beyond boundaries of the beam and the order of the polynomial is properly chosen. The proposed CDIs of a measured MS are presented with multiple resolutions to alleviate adverse effects caused by measurement noise, and cracks can be identified by locating their tips near regions with high values of the CDIs. It is shown that the CWT of a measured MS with the n-th-order Gaussian wavelet function has a shape resembling that of the n-th-order derivative of the MS. The crack tips can also be located using the CWTs of the aforementioned MS differences with second- and third-order Gaussian wavelet functions near peaks and valleys of the resulting CWTDIs, respectively, which are presented with multiple scales. A uniform acrylonitrile butadiene styrene (ABS) cantilever beam with an embedded horizontal crack was constructed to experimentally validate the proposed methods. The elastic modulus of the ABS was determined using experimental modal analysis and model updating. Non-contact operational modal analysis using acoustic excitations and measurements by two laser vibrometers was performed to measure the natural frequencies and MSs of the ABS cantilever beam, and the results compare well with those from the finite element method. Numerical and experimental crack identification can successfully identify the crack by locating its tips.     

Nonlinear phase field theory for fracture and twinning with analysis of simple shear

A phase field theory for coupled twinning and fracture in single crystal domains is developed. Distinct order parameters denote twinned and fractured domains, finite strains are addressed and elastic nonlinearity is included via a neo-Hookean strain energy potential. The governing equations and boundary conditions are derived; an incremental energy minimization approach is advocated for prediction of equilibrium microstructural morphologies under quasi-static loading protocols. Aspects of the theory are analysed in detail for a material element undergoing simple shear deformation. Exact analytical and/or one-dimensional numerical solutions are obtained in dimensionless form for stress states, stability criteria and order parameter profiles at localized fractures or twinning zones. For sufficient applied strain, the relative likelihood of localized twinning vs. localized fracture is found to depend only on the ratio of twin boundary surface energy to fracture surface energy. Predicted criteria for shear stress-driven fracture or twinning are often found to be in closer agreement with test data for several types of real crystals than those based on the concept of theoretical strength.     

Liquid-Vapor Interfaces and Surface Tension in a Mesoscopic Model of Fluid with Nonlocal Interactions

We analyze the problem of phase coexistence, surface tension and the interface patterns between liquid and vapour for the nonlocal free energy functional derived by Lebowitz, Mazel, and Presutti from a system of particles interacting through Kac potentials in the continuum. We study the sharp interface limit in d dimensions and characterize the shape of the interface profiles in the temperature region where a monotonicity property is valid. We further extend our analysis beyond this domain by performing numerical simulations.     

Electron Scattering from Neon Via Effective Range Theory

Elastic cross-sections for electron scattering on neon from 0 energy up to 16 eV are analyzed by an analytical approach to the modified effective range theory (MERT). It is shown that energy and angular variations of elastic differential, integral and momentum transfer cross-sections can be accurately parameterized by six MERT coefficients up to the energy threshold for the first Feshbach resonance. MERT parameters are determined empirically by numerical comparison with large collection of available experimental data of elastic total (integral) cross-sections. The present analysis is validated against numerous electron beams and swarm experiments. The comparison of derived MERT parameters with those found for other noble gases, helium, argon and krypton, is done. The derived scattering length (for the s-partial wave) in neon, 0.227 a ₀, agrees well with recent theories; it is small but, differently from Ar and Kr, still positive. Analogue parameters for the p-wave and the d-wave are negative and positive respectively for all the four gases compared.     

Electrical contact resistance and dynamic contact stiffness for a cluster of microcontacts: cross-property connection in the low-frequency range

An explicit cross-property connection for a rough interface between the electrical contact resistance and dynamic contact stiffness has been established in the low-frequency limit. The present analysis is based on the first-order asymptotic model of multiple dynamic contact between small flat-ended indenters on an elastic half-space, which is a dynamic analogue of the quasi-static Greenwood model. The obtained results can be used in developing a vibration method for measuring the interface contact stiffness in tribological systems, and in estimating the surface-roughness effect in oscillation indentation tests.     

Influence of mesoscale three-phase parameters to the tensile behavior of concrete

In the mesoscopic level, concrete is regarded as three-phase composite material with cement matrix, aggregate, and the interfacial transition zone (ITZ) between them. The mechanical properties of ITZ are regarded weaker than those of the cement matrix and aggregate. In this study, a mesoscale mechanical model based on the interface specimen with a single aggregate is established to study the influence of three-phase parameters on the interface specimen under quasi-static and dynamic direct tensile loading. Besides, the loading rate effect is also considered in this study to further analyze the dynamic performance of ITZ and the whole interface specimen. According to the numerical results, it is indicated that the ITZ properties (elastic modulus and strength) play significant roles in the performance of the interface specimen under quasi-static direct tensile loading. However, the cement matrix is dominant to the mechanical properties of interface specimen under dynamic tensile loading. Moreover, the properties of ITZ (elastic modulus, strength, and DIF values) and the ITZ thickness have some influence on the dynamic performance of ITZ and the whole interface specimen under dynamic tensile loading. In contrast, the Poisson’s ratio and density of ITZ have little influence on the dynamic behavior of the whole interface specimen. Additionally, the aggregate diameter is influential to the time reaching peak stress of ITZ and the whole interface specimen, and the loading rate only influences the time to reach the peak stress of ITZ under dynamic tensile loading.