Hirota method for oblique solitons in two-dimensional supersonic nonlinear Schrodinger flow

In a previous work El et al. (2006) [1] exact stable oblique soliton solutions were revealed in two-dimensional nonlinear Schrodinger flow. In this work we show that single soliton solution can be expressed within the Hirota bilinear formalism. An attempt to build two-soliton solutions shows that the system is "close" to integrability provided that the angle between the solitons is small and/or we are in the hypersonic limit. (C) 2012 Elsevier B.V. All rights reserved.

Biometry and fetal weight estimation by two-dimensional and three-dimensional ultrasonography: an intraobserver and interobserver reliability and agreement study

Objective To evaluate and compare the intraobserver and interobserver reliability and agreement for the biparietal diameter (BPD), abdominal circumference (AC), femur length (FL) and estimated fetal weight (EFW) obtained by two-dimensional ultrasound (2D-US) and three-dimensional ultrasound (3D-US). Methods Singleton pregnant women between 24 and 40 weeks were invited to participate in this study. They were examined using 2D-US in a blinded manner, twice by one observer, intercalated by a scan by a second observer, to determine BPD, AC and FL. In each of the three examinations, three 3D-US datasets (head, abdomen and thigh) were acquired for measurements of the same parameters. We determined EFW using Hadlock's formula. Systematic errors between 3D-US and 2D-US were examined using the paired t-test. Reliability and agreement were assessed by intraclass correlation coefficients (ICCs), limits of agreement (LoA), SD of differences and proportion of differences below arbitrary points. Results We evaluated 102 singleton pregnancies. No significant systematic error between 2D-US and 3D-US was observed. The ICC values were higher for 3D-US in both intra- and interobserver evaluations; however, only for FL was there no overlap in the 95% CI. The LoA values were wider for 2D-US, suggesting that random errors were smaller when using 3D-US. Additionally, we observed that the SD values determined from 3D-US differences were smaller than those obtained for 2D-US. Higher proportions of differences were below the arbitrarily defined cut-off points when using 3D-US. Conclusion 3D-US improved the reliability and agreement of fetal measurements and EFW compared with 2D-US.

Computer simulations of two-dimensional colloidal crystals in confinement

Monte Carlo simulations are used to study the effect of confinement on a crystal of point particles interacting with an inverse power law potential in d=2 dimensions. This system can describe colloidal particles at the air-water interface, a model system for experimental study of two-dimensional melting. It is shown that the state of the system (a strip of width D) depends very sensitively on the precise boundary conditions at the two ``walls'' providing the confinement. If one uses a corrugated boundary commensurate with the order of the bulk triangular crystalline structure, both orientational order and positional order is enhanced, and such surface-induced order persists near the boundaries also at temperatures where the system in the bulk is in its fluid state. However, using smooth repulsive boundaries as walls providing the confinement, only the orientational order is enhanced, but positional (quasi-) long range order is destroyed: The mean-square displacement of two particles n lattice parameters apart in the y-direction along the walls then crosses over from the logarithmic increase (characteristic for $d=2$) to a linear increase (characteristic for d=1). The strip then exhibits a vanishing shear modulus. These results are interpreted in terms of a phenomenological harmonic theory. Also the effect of incommensurability of the strip width D with the triangular lattice structure is discussed, and a comparison with surface effects on phase transitions in simple Ising- and XY-models is made

The effect of two-dimensional squat elements on the seismic behavior of building structures

This thesis reports a study on the seismic response of two-dimensional squat elements and their effect on the behavior of building structures. Part A is devoted to the study of unreinforced masonry infills, while part B is focused on reinforced concrete sandwich walls. Part A begins with a comprehensive review of modelling techniques and code provisions for infilled frame structures. Then state-of-the practice techniques are applied for a real case to test the ability of actual modeling techniques to reproduce observed behaviors. The first developments towards a seismic-resistant masonry infill system are presented. Preliminary design recommendations for the seismic design of the seismic-resistant masonry infill are finally provided. Part B is focused on the seismic behavior of a specific reinforced concrete sandwich panel system. First, the results of in-plane psuudostatic cyclic tests are described. Refinements to the conventional modified compression field theory are introduced in order to better simulate the monotonic envelope of the cyclic response. The refinements deal with the constitutive model for the shotcrete in tension and the embedded bars. Then the hysteretic response of the panels is studied according to a continuum damage model. Damage state limits are identified. Design recommendations for the seismic design of the studied reinforced concrete sandwich walls are finally provided.

Two-Dimensional Bin Packing Problem with Guillotine Restrictions

This thesis, after presenting recent advances obtained for the two-dimensional bin packing problem, focuses on the case where guillotine restrictions are imposed. A mathematical characterization of non-guillotine patterns is provided and the relation between the solution value of the two-dimensional problem with guillotine restrictions and the two-dimensional problem unrestricted is being studied from a worst-case perspective. Finally it presents a new heuristic algorithm, for the two-dimensional problem with guillotine restrictions, based on partial enumeration, and computationally evaluates its performance on a large set of instances from the literature. Computational experiments show that the algorithm is able to produce proven optimal solutions for a large number of problems, and gives a tight approximation of the optimum in the remaining cases.

Computer simulations of two-dimensional colloidal crystals under confinement and shear

In this thesis we are presenting a broadly based computer simulation study of two-dimensional colloidal crystals under different external conditions. In order to fully understand the phenomena which occur when the system is being compressed or when the walls are being sheared, it proved necessary to study also the basic motion of the particles and the diffusion processes which occur in the case without these external forces. In the first part of this thesis we investigate the structural transition in the number of rows which occurs when the crystal is being compressed by placing the structured walls closer together. Previous attempts to locate this transition were impeded by huge hysteresis effects. We were able to determine the transition point with higher precision by applying both the Schmid-Schilling thermodynamic integration method and the phase switch Monte Carlo method in order to determine the free energies. These simulations showed not only that the phase switch method can successfully be applied to systems with a few thousand particles and a soft crystalline structure with a superimposed pattern of defects, but also that this method is way more efficient than a thermodynamic integration when free energy differences are to be calculated. Additionally, the phase switch method enabled us to distinguish between several energetically very similar structures and to determine which one of them was actually stable. Another aspect considered in the first result chapter of this thesis is the ensemble inequivalence which can be observed when the structural transition is studied in the NpT and in the NVT ensemble. The second part of this work deals with the basic motion occurring in colloidal crystals confined by structured walls. Several cases are compared where the walls are placed in different positions, thereby introducing an incommensurability into the crystalline structure. Also the movement of the solitons, which are created in the course of the structural transition, is investigated. Furthermore, we will present results showing that not only the well-known mechanism of vacancies and interstitial particles leads to diffusion in our model system, but that also cooperative ring rotation phenomena occur. In this part and the following we applied Langevin dynamics simulations. In the last chapter of this work we will present results on the effect of shear on the colloidal crystal. The shear was implemented by moving the walls with constant velocity. We have observed shear banding and, depending on the shear velocity, that the inner part of the crystal breaks into several domains with different orientations. At very high shear velocities holes are created in the structure, which originate close to the walls, but also diffuse into the inner part of the crystal.

Two-dimensional linear-combination model fitting of magnetic resonance spectra to define the macromolecule baseline using FiTAID, a Fitting Tool for Arrays of Interrelated Datasets

To propose the determination of the macromolecular baseline (MMBL) in clinical 1H MR spectra based on T(1) and T(2) differentiation using 2D fitting in FiTAID, a general Fitting Tool for Arrays of Interrelated Datasets.

Surface-acoustic-wave counterflow micropumps for on-chip liquid motion control in two-dimensional microchannel arrays

Fully controlled liquid injection and flow in hydrophobic polydimethylsiloxane (PDMS) two-dimensional microchannel arrays based on on-chip integrated, low-voltage-driven micropumps are demonstrated. Our architecture exploits the surface-acoustic-wave (SAW) induced counterflow mechanism and the effect of nebulization anisotropies at crossing areas owing to lateral propagating SAWs. We show that by selectively exciting single or multiple SAWs, fluids can be drawn from their reservoirs and moved towards selected positions of a microchannel grid. Splitting of the main liquid flow is also demonstrated by exploiting multiple SAW beams. As a demonstrator, we show simultaneous filling of two orthogonal microchannels. The present results show that SAW micropumps are good candidates for truly integrated on-chip fluidic networks allowing liquid control in arbitrarily shaped two-dimensional microchannel arrays.

Two-Dimensional Manganese(II) Coordination Polymer Based on Phthalate and Pyrazine Bridges Exhibiting Antiferromagnetic Porperties

Benzodifuran-functionalised pyrene and anthracene fluorophores 1 and 2 were obtained in reasonable yields. Their single crystal structures, electrochemical, optical absorption, and fluorescence characteristics have been described. They show strong luminescence with high quantum yields of 0.53 for 1 and 0.48 for 2. Magnetic measurements for the 2D coordination polymer [Mn(Pht(Pyz(H2O)2]n (1), in which metal centres are linked together by pyrazine (Pyz) and 1,6-bridging o-phthalate ligand (Pht2-), revealed antiferromagnetic interactions between Mn(II) ions.