Relaxation procedures for an iterative MFS algorithm for the stable reconstruction of elastic fields from Cauchy data in two-dimensional isotropic linear elasticity

We investigate two numerical procedures for the Cauchy problem in linear elasticity, involving the relaxation of either the given boundary displacements (Dirichlet data) or the prescribed boundary tractions (Neumann data) on the over-specified boundary, in the alternating iterative algorithm of Kozlov et al. (1991). The two mixed direct (well-posed) problems associated with each iteration are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method, while the optimal value of the regularization parameter is chosen via the generalized cross-validation (GCV) criterion. An efficient regularizing stopping criterion which ceases the iterative procedure at the point where the accumulation of noise becomes dominant and the errors in predicting the exact solutions increase, is also presented. The MFS-based iterative algorithms with relaxation are tested for Cauchy problems for isotropic linear elastic materials in various geometries to confirm the numerical convergence, stability, accuracy and computational efficiency of the proposed method.

Information Modelling of Two-Dimensional Optical Parameters Measurement

A method for measurement and visualization of the complex transmission coefficient of 2-D micro- objects is proposed. The method is based on calculation of the transmission coefficient from the diffraction pattern and the illumination aperture function for monochromatic light. A phase-stepping method was used for diffracted light phase determination.

Nonlocal Boundary Value Problems for Two-Dimensional Potential Equation on a Rectangle

Иван Димовски, Юлиан Цанков - Предложено е разширение на принципa на Дюамел. За намиране на явно решение на нелокални гранични задачи от този тип е развито операционно смятане основано върху некласическа двумерна конволюция. Пример от такъв тип е задачата на Бицадзе-Самарски.

Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities

In this paper we consider instabilities of localised solutions in planar neural field firing rate models of Wilson-Cowan or Amari type. Importantly we show that angular perturbations can destabilise spatially localised solutions. For a scalar model with Heaviside firing rate function we calculate symmetric one-bump and ring solutions explicitly and use an Evans function approach to predict the point of instability and the shapes of the dominant growing modes. Our predictions are shown to be in excellent agreement with direct numerical simulations. Moreover, beyond the instability our simulations demonstrate the emergence of multi-bump and labyrinthine patterns. With the addition of spike-frequency adaptation, numerical simulations of the resulting vector model show that it is possible for structures without rotational symmetry, and in particular multi-bumps, to undergo an instability to a rotating wave. We use a general argument, valid for smooth firing rate functions, to establish the conditions necessary to generate such a rotational instability. Numerical continuation of the rotating wave is used to quantify the emergent angular velocity as a bifurcation parameter is varied. Wave stability is found via the numerical evaluation of an associated eigenvalue problem.

Radiation from a D-dimensional collision of shock waves: two-dimensional reduction and Carter–Penrose diagram

We analyze the causal structure of the two-dimensional (2D) reduced background used in the perturbative treatment of a head-on collision of two D-dimensional Aichelburg–Sexl gravitational shock waves. After defining all causal boundaries, namely the future light-cone of the collision and the past light-cone of a future observer, we obtain characteristic coordinates using two independent methods. The first is a geometrical construction of the null rays which define the various light cones, using a parametric representation. The second is a transformation of the 2D reduced wave operator for the problem into a hyperbolic form. The characteristic coordinates are then compactified allowing us to represent all causal light rays in a conformal Carter–Penrose diagram. Our construction holds to all orders in perturbation theory. In particular, we can easily identify the singularities of the source functions and of the Green’s functions appearing in the perturbative expansion, at each order, which is crucial for a successful numerical evaluation of any higher order corrections using this method.

Numerical solution of an elliptic 3-dimensional Cauchy problem by the alternating method and boundary integral equations

We consider the Cauchy problem for the Laplace equation in 3-dimensional doubly-connected domains, that is the reconstruction of a harmonic function from knowledge of the function values and normal derivative on the outer of two closed boundary surfaces. We employ the alternating iterative method, which is a regularizing procedure for the stable determination of the solution. In each iteration step, mixed boundary value problems are solved. The solution to each mixed problem is represented as a sum of two single-layer potentials giving two unknown densities (one for each of the two boundary surfaces) to determine; matching the given boundary data gives a system of boundary integral equations to be solved for the densities. For the discretisation, Weinert's method [24] is employed, which generates a Galerkin-type procedure for the numerical solution via rewriting the boundary integrals over the unit sphere and expanding the densities in terms of spherical harmonics. Numerical results are included as well.

Low-density Three-dimensional Foam Using Self-reinforced Hybrid Two-dimensional Atomic Layers.

Low-density nanostructured foams are often limited in applications due to their low mechanical and thermal stabilities. Here we report an approach of building the structural units of three-dimensional (3D) foams using hybrid two-dimensional (2D) atomic layers made of stacked graphene oxide layers reinforced with conformal hexagonal boron nitride (h-BN) platelets. The ultra-low density (1/400 times density of graphite) 3D porous structures are scalably synthesized using solution processing method. A layered 3D foam structure forms due to presence of h-BN and significant improvements in the mechanical properties are observed for the hybrid foam structures, over a range of temperatures, compared with pristine graphene oxide or reduced graphene oxide foams. It is found that domains of h-BN layers on the graphene oxide framework help to reinforce the 2D structural units, providing the observed improvement in mechanical integrity of the 3D foam structure.

Assessment Of Robustness On Analysis Using Headspace Solid-phase Microextraction And Comprehensive Two-dimensional Gas Chromatography Through Experimental Designs.

Plackett-Burman experimental design was applied for the robustness assessment of GC×GC-qMS (Comprehensive Two-Dimensional Gas Chromatography with Fast Quadrupolar Mass Spectrometric Detection) in quantitative and qualitative analysis of volatiles compounds from chocolate samples isolated by headspace solid-phase microextraction (HS-SPME). The influence of small changes around the nominal level of six factors deemed as important on peak areas (carrier gas flow rate, modulation period, temperature of ionic source, MS photomultiplier power, injector temperature and interface temperature) and of four factors considered as potentially influential on spectral quality (minimum and maximum limits of the scanned mass ranges, ions source temperature and photomultiplier power). The analytes selected for the study were 2,3,5-trimethylpyrazine, 2-octanone, octanal, 2-pentyl-furan, 2,3,5,6-tetramethylpyrazine, and 2-nonanone e nonanal. The factors pointed out as important on the robustness of the system were photomultiplier power for quantitative analysis and lower limit of mass scanning range for qualitative analysis.

Two-dimensional Ultrasound And Ultrasound Elastography Imaging Of Trigger Points In Women With Myofascial Pain Syndrome Treated By Acupuncture And Electroacupuncture: A Double-blinded Randomized Controlled Pilot Study.

Chronic pain has been often associated with myofascial pain syndrome (MPS), which is determined by myofascial trigger points (MTrP). New features have been tested for MTrP diagnosis. The aim of this study was to evaluate two-dimensional ultrasonography (2D US) and ultrasound elastography (UE) images and elastograms of upper trapezius MTrP during electroacupuncture (EA) and acupuncture (AC) treatment. 24 women participated, aged between 20 and 40 years (M ± SD = 27.33 ± 5.05) with a body mass index ranging from 18.03 to 27.59 kg/m2 (22.59 ± 3.11), a regular menstrual cycle, at least one active MTrP at both right (RTPz) and left trapezius (LTPz) and local or referred pain for up to six months. Subjects were randomized into EA and AC treatment groups and the control sham AC (SHAM) group. Intensity of pain was assessed by visual analogue scale; MTrP mean area and strain ratio (SR) by 2D US and UE. A significant decrease of intensity in general, RTPz, and LTPz pain was observed in the EA group (p = 0.027; p < 0.001; p = 0.005, respectively) and in general pain in the AC group (p < 0.001). Decreased MTrP area in RTPz and LTPz were observed in AC (p < 0.001) and EA groups (RTPz, p = 0.003; LTPz, p = 0.005). Post-treatment SR in RTPz and LTPz was lower than pre-treatment in both treatment groups. 2D US and UE effectively characterized MTrP and surrounding tissue, pointing to the possibility of objective confirmation of subjective EA and AC treatment effects.

In Vivo Determination Of The Volatile Metabolites Of Saprotroph Fungi By Comprehensive Two-dimensional Gas Chromatography.

In this work, we discuss the use of multi-way principal component analysis combined with comprehensive two-dimensional gas chromatography to study the volatile metabolites of the saprophytic fungus Memnoniella sp. isolated in vivo by headspace solid-phase microextraction. This fungus has been identified as having the ability to induce plant resistance against pathogens, possibly through its volatile metabolites. Adequate culture media was inoculated, and its headspace was then sampled with a solid-phase microextraction fiber and chromatographed every 24 h over seven days. The raw chromatogram processing using multi-way principal component analysis allowed the determination of the inoculation period, during which the concentration of volatile metabolites was maximized, as well as the discrimination of the appropriate peaks from the complex culture media background. Several volatile metabolites not previously described in the literature on biocontrol fungi were observed, as well as sesquiterpenes and aliphatic alcohols. These results stress that, due to the complexity of multidimensional chromatographic data, multivariate tools might be mandatory even for apparently trivial tasks, such as the determination of the temporal profile of metabolite production and extinction. However, when compared with conventional gas chromatography, the complex data processing yields a considerable improvement in the information obtained from the samples. This article is protected by copyright. All rights reserved.

Two-dimensional gel electrophoretic protein profile analysis during seed development of Ocotea catharinensis: a recalcitrant seed species

The aim of the present work was to characterize changes in the protein profile throughout seed development in O. catharinensis, a recalcitrant species, by two-dimensional gel electrophoresis. Protein extraction was undertaken by using a thiourea/urea buffer, followed by a precipitation step with 10% TCA. Comparative analysis during seed development showed that a large number of proteins were exclusively detected in each developmental stage. The cotyledonary stage, which represents the transition phase between embryogenesis and the beginning of metabolism related to maturation, presents the highest number of stage-specific spots. Protein identification, through MS/MS analysis, resulted in the identification of proteins mainly related to oxidative metabolism and storage synthesis. These findings contribute to a better understanding of protein metabolism during seed development in recalcitrant seeds, besides providing information on established markers that could be useful in defining and improving somatic embryogenesis protocols, besides monitoring the development of somatic embryos in this species.

HR Del REMNANT ANATOMY USING TWO-DIMENSIONAL SPECTRAL DATA AND THREE-DIMENSIONAL PHOTOIONIZATION SHELL MODELS

The HR Del nova remnant was observed with the IFU-GMOS at Gemini North. The spatially resolved spectral data cube was used in the kinematic, morphological, and abundance analysis of the ejecta. The line maps show a very clumpy shell with two main symmetric structures. The first one is the outer part of the shell seen in H alpha, which forms two rings projected in the sky plane. These ring structures correspond to a closed hourglass shape, first proposed by Harman & O'Brien. The equatorial emission enhancement is caused by the superimposed hourglass structures in the line of sight. The second structure seen only in the [O III] and [N II] maps is located along the polar directions inside the hourglass structure. Abundance gradients between the polar caps and equatorial region were not found. However, the outer part of the shell seems to be less abundant in oxygen and nitrogen than the inner regions. Detailed 2.5-dimensional photoionization modeling of the three-dimensional shell was performed using the mass distribution inferred from the observations and the presence of mass clumps. The resulting model grids are used to constrain the physical properties of the shell as well as the central ionizing source. A sequence of three-dimensional clumpy models including a disk-shaped ionization source is able to reproduce the ionization gradients between polar and equatorial regions of the shell. Differences between shell axial ratios in different lines can also be explained by aspherical illumination. A total shell mass of 9 x 10(-4) M(circle dot) is derived from these models. We estimate that 50%-70% of the shell mass is contained in neutral clumps with density contrast up to a factor of 30.

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.

Electron dephasing scattering rate in two-dimensional GaAs/InGaAs heterostructures with embedded InAs quantum dots

We report a comprehensive study of weak-localization and electron-electron interaction effects in a GaAs/InGaAs two-dimensional electron system with nearby InAs quantum dots, using measurements of the electrical conductivity with and without magnetic field. Although both the effects introduce temperature dependent corrections to the zero magnetic field conductivity at low temperatures, the magnetic field dependence of conductivity is dominated by the weak-localization correction. We observed that the electron dephasing scattering rate tau(-1)(phi), obtained from the magnetoconductivity data, is enhanced by introducing quantum dots in the structure, as expected, and obeys a linear dependence on the temperature and elastic mean free path, which is against the Fermi-liquid model. (c) 2008 American Institute of Physics. [DOI: 10.1063/1.2996034]

Dynamic transitions in a two dimensional associating lattice gas model

Using Monte Carlo simulations we investigate some new aspects of the phase diagram and the behavior of the diffusion coefficient in an associating lattice gas (ALG) model on different regions of the phase diagram. The ALG model combines a two dimensional lattice gas where particles interact through a soft core potential and orientational degrees of freedom. The competition between soft core potential and directional attractive forces results in a high density liquid phase, a low density liquid phase, and a gas phase. Besides anomalies in the behavior of the density with the temperature at constant pressure and of the diffusion coefficient with density at constant temperature are also found. The two liquid phases are separated by a coexistence line that ends in a bicritical point. The low density liquid phase is separated from the gas phase by a coexistence line that ends in tricritical point. The bicritical and tricritical points are linked by a critical lambda-line. The high density liquid phase and the fluid phases are separated by a second critical tau-line. We then investigate how the diffusion coefficient behaves on different regions of the chemical potential-temperature phase diagram. We find that diffusivity undergoes two types of dynamic transitions: a fragile-to-strong transition when the critical lambda-line is crossed by decreasing the temperature at a constant chemical potential; and a strong-to-strong transition when the critical tau-line is crossed by decreasing the temperature at a constant chemical potential.