Finite element modeling of the interaction of laser-generated ultrasound with a surface-breaking notch in an elastic plate

The interaction of surface acoustic waves generated by laser line source in the thermoelastic regime with surface notches are investigated. The finite element method is used to establish the model of the transient displacement field for surface notches with various depths and orientation. The magnitude of the signal enhancement in the near field and the mechanism by which this occurs are explained. The positions of notches were evaluated by the reflected Rayleigh wave. The depths and orientations of the notches were also determined using a shear wave that was generated through mode conversion of a surface acoustic wave at the notch tip. The results agree with previously published experimental measurements.     

Instability of bound states of a nonlinear Schrödinger equation with a Dirac potential

We study analytically and numerically the stability of the standing waves for a nonlinear Schrödinger equation with a point defect and a power type nonlinearity. A major difficulty is to compute the number of negative eigenvalues of the linearized operator around the standing waves. This is overcome by a perturbation method and continuation arguments. Among others, in the case of a repulsive defect, we show that the standing-wave solution is stable in and unstable in under subcritical nonlinearity. Further we investigate the nature of instability: under critical or supercritical nonlinear interaction, we prove the instability by blowup in the repulsive case by showing a virial theorem and using a minimization method involving two constraints. In the subcritical radial case, unstable bound states cannot collapse, but rather narrow down until they reach the stable regime (a finite-width instability). In the nonradial repulsive case, all bound states are unstable, and the instability is manifested by a lateral drift away from the defect, sometimes in combination with a finite-width instability or a blowup instability.     

Diffusion flame instabilities in a 0.75 mm non-premixed microburner

We examine the cellular instabilities of laminar non-premixed diffusion flames that arise in a polycrystalline alumina microburner with a channel wall gap of dimension 0.75 mm. Changes in the flame structure are observed as a function of the fuel type (H₂, CH₄, and C₃H₈) and diluent. The oxidizer is O₂/inert. In contrast to previous observations on laminar diffusion flame instabilities, the current instabilities occur in the direction of flow above the splitter plate, and only occur for the heavier fuel types. They are not observed in a H₂–O₂ mixture, which will only support a continuous laminar flame inside our burner, regardless of the initial mixture strength and whether or not the flame is in near-quenching conditions. The only exception is when helium is added to the H₂–O₂ mixture, raising the effective Lewis numbers of both components.     

On the shock induced instabilities in collisionless plasma

Firehose, mirror and ion-acoustic instabilities behind MHD shock waves are discussed for collisionless anisotropic plasma with heat fluxes. For the parallel shock wave it has been demonstrated that initially stable plasma can be destabilized by the shock which leads to turbulence generation in the downstream flow. Upstream parameter domains are determined where such destabilization occurs.     

Surface-energy-anisotropy-induced orientation effects on Rayleigh instabilities in sapphire

Arrays of controlled-geometry, semi-infinite pore channels of systematically varied crystallographic orientation were introduced into undoped m-plane sapphire substrates using microfabrication techniques and ion-beam etching and subsequently internalized by solid-state diffusion bonding. A series of anneals at 1700 °C caused the breakup of these channels into discrete pores via Rayleigh instabilities. In all cases, channels broke up with a characteristic wavelength larger than that expected for a material with isotropic surface energy, reflecting stabilization effects due to surface-energy anisotropy. The breakup wavelength and the time required for complete breakup varied significantly with channel orientation. For most orientations, the instability wavelength for channels of radius R was in the range of 13.2R-25R, and complete breakup occurred within 2-10 h. To first order, the anneal times for complete breakup scale with the square of the breakup wavelength. Channels oriented along a direction had a wavelength of ≈139R, and required 468 h for complete breakup. Cross-sectional analysis of channels oriented along a direction showed the channel to be completely bounded by stable c(0 0 0 1), , and facets.     

Surface wave scattering by a nano-object situated on a surface

The scattering of the surface electromagnetic waves by a nano-defect (object) on a surface was calculated. The scattered field has been considered as a field caused by the current generated by the self-consistent local field inside the defect. In turn, the self-consistent local field has been determined as a result of solution of the integral Lippmann-Schwinger equation. The effective susceptibility of the object has been calculated using a self-consistent procedure. The corrections of self-energy part due to direct and indirect electromagnetic interactions, as well as due to interaction with surface wave field are taken into account. The self-energy part is calculated analytically within the framework of the near-field approximation. The scattering indicatrisses in reciprocal space have been computed for different shapes of the scatterer. Strong dependence of the scattered field on geometry of the scatterer has been found and explained.     

The interaction of a screw dislocation with point defects in bcc iron

In this study, we calculate the interaction energy of intrinsic point defects vacancies and interstitials) with screw dislocations in body-centered cubic iron. First (we calculate the dipole tensor of a defect in the bulk crystal using molecular statics. Using a formulation based on linear elasticity theory, we calculate the interaction energy of the defect and the dislocation using both isotropic and anisotropic strain fields. Second, we perform atomistic calculations using molecular statics methods to directly calculate the interaction energy. Results from these two methods are compared. We verify that continuum methods alone are unable to correctly predict the interactions of defects and dislocations near the core. Although anisotropic theory agrees qualitatively with atomistics far from the core, it cannot predict which dumbbell orientations are stable and any continuum calculations must be used with caution. Spontaneous absorption by the core of both vacancies and dumbbells is seen. This paper demonstrates and discusses the differences between continuum and atomistic calculations of interaction energy between a dislocation core and a point defect.     

Ion cyclotron instabilities in a mildly relativistic hydrogen-deuterium fusion plasma

A dispersion relation for the perpendicular propagation of the electromagnetic ion cyclotron wave around the second harmonic of the deuterium ion gyrofrequency in a mildly relativistic, anisotropic Maxwellian plasma with hydrogen as the majority species and deuterium as the minority component has been derived. The work has been carried out in the frame of reference of the majority hydrogen ions; to these ions the waves at 2Θ_D would be at its own gyrofrequency. Using a small quantityɛ to order all relevant parameters of the plasma, it was possible to derive the dispersion relations in a simple form. To the lowest order the relativistic factors do not enter the dispersion relation. The plasma can now support two modes—one above and the other below the hydrogen gyrofrequency in agreement with the assumptions. This was also verified numerically using a standard root solver thereby justifying the correctness of the ordering scheme. In the next higher order, the dispersion relation is a quartic equation and is sensitively dependent on the relativistic factors. The plasma can now support four modes, both above and below the hydrogen gyrofrequency and consistent with the ordering scheme used. However the modes can now coalesce resulting in complex conjugate roots to the dispersion relation thereby indicating an instability. The advantage of such a scheme is that two dispersion relations — one of which is independent of the relativistic factors and the other which is sensitively dependent on them can be separated out.     

Removal mechanisms of micro-scale particles by surface wave in laser cleaning

This paper is to investigate the mechanisms of micro-scale particle removal by surface wave, which was induced by a short pulse laser in a cleaning process. The authors analyzed the adhesive forces of particles on substrate surface and the clearance force produced by surface wave in laser cleaning. The physical model of particle removal by laser-induced surface wave was established to predict the removal area and the processing conditions of laser cleaning. In this research, a KrF excimer laser was applied to irradiate 304 stainless steel specimen distributed with copper particles to generate surface wave for copper particle removal. Considering that a time-varying and uniformly distributed heat source irradiates on material surface with thermao-elastic behavior, the displacement and acceleration of substrate induced by a pulsed laser were solved by an uncoupled thermal–mechanical analysis based on the finite element method. The processing parameters such as laser energy, laser spot size are discussed, respectively. A series of laser cleaning experiments were designed to compare with computation results. The results show that the removal area by surface wave beyond the laser spot increases with the laser energy and that, the surface acceleration decreases with the increase of the laser spot size.     

Optical emission analysis of solid samples by decoupled sputtering/excitation using a low fluence laser synchronized with a pulsed glow discharge

The use of a microsecond-pulsed glow discharge, synchronized with an ablation laser operating under breakdown fluence, assists in the excitation of the ablated material generated during the analysis. With the glow discharge operating in pulsed mode, it is possible to synchronize accurately both sources to maximize the signal. Additionally, both sources can be independently adjusted to optimize the sample removal and its excitation. By means of the decoupling approach, typical laser energies required for detectable emission signals can effectively be lowered below the excitation and ionization thresholds of the analyte to those required solely for ablation of the sample surface. Under these conditions, the laser represents an advantageous mode to transform solid samples into gas phase that will be efficiently excited by the glow discharge. The advantage of the combination of the techniques has been demonstrated in alloyed samples (Cr/Fe and brass) where a net enhancement in the analytes signals even under sub-threshold and sub-sputtering conditions occur.     

Self-gravito-acoustic waves and their instabilities in a self-gravitating degenerate quantum plasma system

A self-gravitating degenerate quantum plasma (SGDQP) system containing degenerate electron and light nucleus species along with extremely low-dense heavy-nucleus species is considered. The existence of new degenerate pressure-driven self-gravito-acoustic (DPDSGA) waves in this SGDQP system is found, and their dispersion properties along with stable and unstable parametric regimes are identified. The DPDSGA waves emit from this SGDQP system due to the compression and rarefaction (and vice-versa) of the perturbed state of it. Its compression is due to the inward poll of degenerate electron and light nucleus species by the self-gravitational attractive pressures, whereas its rarefaction is due to the outward degenerate pressures exerted by the degenerate electron and light nucleus species. The DPDSGA waves are new because they completely disappear if the electron and light nucleus degeneracies are neglected. The DPDSGA waves exist in the SGDQP system that occurs in astrophysical compact objects like white dwarfs [H. M. Van Horn, Science 252 , 384 (1991); D. Koester, Astron. Astrophys. Rev. 11 , 33 (2002)].     

Localized bifurcations and defect instabilities in the convection of a nematic liquid crystal

The stationary and the time-dependent homogeneous ordered states in convection may both become unstable against localized perturbations. Defects are then created and they may contribute to the disorganization of the homogeneous state. We present an experimental study of defects in some homogeneous stationary structures as well as in the traveling-wave states of convection of a nematic liquid crystal. We show that the core of the defects is a germ of the unstable state and it can become unstable under the external stress. Then, either fully homogeneous states with the symmetry of the core, or complex disordered states can develop from the local instability of defects in processes quite similar to displacive transitions in solids. Some of the main features are qualitatively similar to numerical simulations of an appropriate Landau-Ginzburg equation.     

Temperature effects on capillary instabilities in a thin nematic liquid crystalline fiber embedded in a viscous matrix

Linear stability analysis of capillary instabilities in a thin nematic liquid crystalline cylindrical fiber embedded in an immiscible viscous matrix is performed by formulating and solving the governing nemato-capillary equations, that include the effect of temperature on the nematic ordering as well as the effect of the nematic orientation. A representative axial nematic orientation texture with the planar easy axis at the fiber surface is studied. The surface disturbance is expressed in normal modes, which include the azimuthal wave number m to take into account non-axisymmetric modes. Capillary instabilities in nematic fibers reflect the anisotropic nature of liquid crystals, such as the ordering and orientation contributions to the surface elasticity and surface normal and bending stresses. Surface gradients of normal and bending stresses provide additional anisotropic contributions to the capillary pressure that may renormalize the classical displacement and curvature forces that exist in any fluid fiber. The exact nature (stabilizing and destabilizing) and magnitude of the renormalization of the displacement and curvature forces depend on the nematic ordering and orientation, i.e. the anisotropic contribution to the surface energy, and accordingly capillary instabilities may be axisymmetric or non-axisymmetric. In addition, when the interface curvature effects are accounted for as contributions of the work of interfacial bending and torsion to the total energy of the system, the higher-order bending moment contribution to the surface stress tensor is critical in stabilizing the fiber instabilities. For the planar easy axis, the nematic ordering contribution to the surface energy, which renormalizes the effect of the fiber shape, plays a crucial role to determine the instability mechanisms. Moreover, the unstable modes, which are most likely observed, can be driven by the dependence of surface energy on the surface area. Low-ordering fibers display the classical axisymmetric mode, since the surface energy decreases by decreasing the surface area. Decreasing temperature gives rise to the encounter with a local maximum or to monotonic increase of the characteristic length of the axisymmetric mode. Meanwhile, in the presence of high surface ordering, non-axisymmetric finite wavelength instabilities emerge, with higher modes growing faster since the surface energy decreases by increasing the surface area. As temperature decreases, the pitches of the chiral microstructures become smaller. However, this non-axisymmetric instability mechanism can be regulated by taking account of the surface bending moment, which contains higher order variations in the interface curvatures. More and more non-axisymmetric modes emerge as temperature decreases, but, at constant temperature, only a finite number of non-axisymmetric modes are unstable and a single fastest growing mode emerges with lower and higher unstable modes growing slower. For nematic fibers, the classical fiber-to-droplet transformation is one of several possible instability pathways, while others include chiral microstructures. The capillary instabilities' growth rate of a thin nematic fiber in a viscous matrix is suppressed by increasing either the fiber or matrix viscosity, but the estimated droplet sizes after fiber breakup in axisymmetric instabilities decrease with increasing the matrix viscosity. Received 15 April 2002 and Received in final form 3 October 2002 RID="a" ID="a"e-mail: alejandro.rey@mcgill.ca     

A 3D dynamic numerical approach for temperature and thermal stress distributions in multilayer laser solid freeform fabrication process

This paper presents a 3D transient numerical approach for modeling the multilayer laser solid freeform fabrication (LSFF) process. Using this modeling approach, the geometry of the deposited material as well as temperature and thermal stress fields across the process domain can be predicted in a dynamic fashion. In the proposed method, coupled thermal and stress domains are numerically obtained assuming a decoupled interaction between the laser beam and powder stream. To predict the time-dependent geometry of the deposited material, once the melt pool boundary is obtained, the process domain is discretized in a cross-sectional fashion based on the powder feed rate, elapsed time, and intersection of the melt pool and powder stream area on the workpiece. Layers of additive material are then added onto the non-planar domain. Main process parameters affected by a multilayer deposition due to the formation of non-planar surfaces, such as powder catchment, are incorporated into the modeling approach to enhance the accuracy of the results. To demonstrate the proposed algorithm, fabrication of a four-layer thin wall of AISI 304 L stainless steel on a workpiece with the same material is modeled. The geometry of the wall, temperature, and stress fields across the modeling domain are dynamically predicted throughout the process. The model is used to investigate the effect of preheating and clamping the workpiece to the positioning table. Results show that preheating improves the process by reducing the thermal stresses as well as the settling time for the formation of a steady-state melt pool in the first layer. In addition, clamping the workpiece can also decrease thermal stresses at its critical locations (i.e. deposition region). In terms of geometrical aspects, the results show that the temperature and the thickness of the deposited layers increase at the end-points of layers 2–4. The reliability and the accuracy of the model are experimentally verified.     

Cavity resonant mode in a metal film perforated with two-dimensional triangular lattice hole arrays

The transmission property of metallic films with two-dimensional hole arrays is studied experimentally and numerically. For a triangular lattice subwavelength hole array in a 150 nm thick Ag film, both cavity resonance and planar surface modes are identified as the sources of enhanced optical transmissions. Semi-analytical models are developed for calculating the dispersion relation of the cavity resonant mode. They agree well with the experimental results and full-wave numerical calculations. Strong interaction between the cavity resonant mode and surface modes is also observed.     

Electron-phonon interaction in a free standing beryllium monolayer

We report ab initio study of the electron-phonon coupling in a free standing Beryllium monolayer. The calculations were carried out using a linear-response approach in the plane-wave pseudopotential representation. The Eliashberg spectral function α²F(ω) and the electron-phonon coupling parameter λ are evaluated at the Fermi level. The obtained results show a large contribution to the electron-phonon coupling from the low-energy transverse mode scattering.     

Frequency dependence of images in scanning laser source technique for a plate

Defect imaging using scanning laser source technique has been investigated for a plate with rounded defects and notch-type defects in our previous studies. This paper examines frequency dependence of the defect images with both calculations and experiments in order to acquire clearer images. Both calculation and experimental results for a straight notch revealed that clearer images of notch-type defects can be obtained in the range of low frequency-thickness product below about 200 kHz mm. Moreover, images of the defects of various shapes were obtained by synthesizing images from eight receiving transducers, and similarly to the case of the straight notches, they became more clearly in the low frequency range.     

Surface electromagnetic waves supported by nano conducting layers with inhomogeneities in the conductivity profile

Conducting interfaces and nano conducting layers can support surface electromagnetic waves. Uniform charge layers of non-zero thickness and their asymptotic behavior toward conducting interfaces of infinitely small thicknesses, where the thin charge layer is modeled via a surface conductivity σ _s , are already studied. Here, the possible effects of inhomogeneity in the conductivity profile of the thin conducting layers are investigated for the first time and a new approximate yet accurate enough analytical formulation for mode extraction in such structures is given. In order to rigorously analyze the structure and justify the proposed approximate formulation, the Galerkin’s method with Legendre polynomial basis functions is applied, i.e. the transverse electric field for the TE polarized surface waves and the transverse magnetic field for the TM polarized surface waves are each expanded in terms of Legendre polynomials and then each eigenmode; subjected to appropriate boundary conditions, is sought in the complete space spanned by Legendre basis functions. The proposed approximate solution is then proved to be accurate. In particular, sinusoidal fluctuations are introduced into formerly uniform conductivity profiles and it is numerically demonstrated that surface electromagnetic waves supported by nano conducting layers are not much sensitive to the very shape of conductivity profiles.     

Energetics and electronic structure of a single copper atomic chain wrapped in a carbon nanotube: a first-principles study

In the generalized gradient approximation, the energy and electronic structure are investigated for a single copper atomic chain wrapped in (4, 4), (5, 5) and (6, 6) armchair carbon nanotubes by using the first-principles projector-augmented wave potential within the framework of density functional theory. The results show that the (4, 4) and (5, 5) tubes are too narrow to wrap a Cu chain, but the (6, 6) tube is nearly ideal to wrap a Cu chain on its centre axis. Wider tubes are anticipated to wrap more than one Cu chain spontaneously with forces amounting to a fraction of a nanonewton. Although the tube--chain interaction decreases with the increase of the tube diameter of (4, 4), (5, 5) and (6, 6) successively, the charge density of the Cu@(6, 6) combined system still does not show complete superposition of that of the pristine (6, 6) tube and Cu chain. Successively reducing the restrictions of (4, 4), (5, 5) and (6, 6) tubes on the Cu chain leads to a reduction in shift of the highest peak of the Cu chain towards lower energies, that is from -0.5177~eV of the isolated Cu chain to -1.36785~eV, -0.668~eV and -0.588~eV for the Cu@(4, 4), Cu@(5, 5) and Cu@(6, 6) systems, respectively. In reverse, the strong metallic character of the Cu chain also enhances the metallic character of the combined systems so that the broader pseudogaps of the pristine carbon nanotubes around the Fermi level change into the narrow pseudogaps of the combined systems.