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We provide an overview of current techniques and typical applications of numerical bifurcation analysis in fluid dynamical problems. Many of these problems are characterized by high-dimensional dynamical systems which undergo transitions as parameters are changed. The computation of the critical conditions associated with these transitions, popularly referred to as ‘tipping points’, is important for understanding the transition mechanisms. We describe the two basic classes of methods of numerical bifurcation analysis, which differ in the explicit or implicit use of the Jacobian matrix of the dynamical system. The numerical challenges involved in both methods arementioned and possible solutions to current bottlenecks are given. To demonstrate that numerical bifurcation techniques are not restricted to relatively low-dimensional dynamical systems, we provide several examples of the application of the modern techniques to a diverse set of fluid mechanical problems.
We designed and produced pure cubic zirconia (ZrO2) ceramic1
coatings by an ion beam assisted deposition (IBAD) with nanostructures
comparable to the size of proteins. Our ceramic coatings exhibit high
hardness and a zero contact angle with serum. In contrast to hydroxyapatite
(HA), nano-engineered zirconia films possess excellent adhesion to all
orthopaedic materials. Cell adhesion and proliferation experiments were
performed with a bona fide mesenchymal stromal cell line (OMA-AD). Our
experimental results indicate that the nano-engineered cubic zirconia is
superior in supporting growth, adhesion, and proliferation. Since cell
attachment is mediated by adhesive proteins such as fibronectin (FN), to
elucidate why cells attach more effectively to our nanostructures, we
performed a comparative analysis of adsorption energies of FN fragment using
quantum mechanical calculations and Monte Carlo (MC) simulation both on
smooth and nanostructured surfaces. We have found that a FN fragment adsorbs
significantly stronger on the nanostructured surface than on the smooth
Initial clinical trials using Trichuris suis eggs (TSO) in autoimmune diseases such as inflammatory bowel disease, revealed a striking suppressive effect on the autoimmune response. Here, we analysed the effect of TSO therapy on the course of multiple sclerosis (MS), as a Th1/Th17-associated autoimmune disease. Different immunological parameters in four patients with secondary progressive MS were surveyed during a 6-month therapy with TSO, focusing on the modulation of T-cell Th1–Th2 balance as well as on the innate immune response. We are able to show a slight downregulation of the Th1-associated cytokine pattern, especially relevant in interleukin (IL)-2 (P < 0.05 after 2 months of therapy), with a temporary increase of Th2-associated cytokines such as IL-4. Furthermore, mild eosinophily and changes in CD4+ and CD8+T cells and natural killer (NK) CD56 bright cell numbers were observed. The findings observed in this group of patients suggest that TSO therapy has a moderate immunomodulatory impact in MS.
Five fold i-AlPdMn surface prepared under UHV by ion bombardment and annealing was so far considered to be bulk terminated. This result was substantially based on a quantitative LEED analyses . Analysis of the specular rod in a X ray diffraction experiment at grazing incidence supported this result . We present a new study of this surface by high resolution X ray diffraction at normal incidence. In this Bragg configuration the diffraction peak 18 – 29 for instance is at a photon energy of 2.873keV, the 72 – 116 reflection at 5.725keV. This results in an analyzed thickness of the sample surface of a few micrometers.
The surface was cleaned by ion bombardment. During annealing (T≅880K), we clearly observed the progressive disappearance of the initial Bragg peak characteristic of the as cast bulk sample. Conversely a new Bragg peak grows at an energy position shifted by 1eV compared to the position of the original Bragg peak. This is a clear signature for an irreversible structural transformation which takes place on at least the micron thickness. On the transformed surface, both, a LEED pattern and a RHEED pattern, characteristic for a five fold surface were easily obtained.
This high resolution experiment (the relative Bragg peak shift is 3ׁ10−4) was reproduced on samples from different initial compositions. This shows that five fold i-AlPdMn surface changes after preparation by ion bombardment and annealing at 900K on a micrometer thickness. This is not consistent with the conclusion that the surface is simply terminated by a cut of the original bulk. We conclude that a reorganization process of the quasicrystalline structure during annealing proceeds in the surface vicinity (probed depth is close to a few microns).
We investigated the suitability of powder metallurgy as well as die casting for the fabrication of light-weight Al-based composites with quasicrystalline particles embedded in an aluminum matrix. Al-Mn-Ce and Al-Cu-Fe quasicrystalline powders were synthesized by milling of elemental powder mixtures or arc-melted prealloys using a planetary ball mill. The mixture of the quasicrystalline phase and the Al-matrix phase with an appropriate ratio was realized by an initial aluminum excess or by blending of quasicrystalline powder with pure aluminum. The powders were consolidated by hot extrusion. Bulk samples of Ø3mm diameter and 50mm length were also directly prepared by squeezing the melt into a copper mold. CCRT-compression tests revealed a yield strength of about 400 MPa, an ultimate strength of 565 MPa and a ductility of up to 19 % fracture strain as optimum mechanical properties.
Icosahedral quasicrystals Al71.5Pd20.3Mn8.2, Al70.7Pd21.34Re7.96, Al62.5Cu25.5Fe12.5, and α-Al68.31Mn21.21Si10.48 1/1- approximant were investigated by using a monoenergetic slow positron beam. The structural vacancy densities in the first three samples were determined to be 5.0×1020, 7.7×1020, and 4.7×1020 cm−3, respectively, by analyzing the measured S-parameter.
Thin film coatings of Al-based quasicrystals were deposited by magnetron sputtering. Sputtering targets of Al65Cu23Fe12 and Al65Cu23Fe12+5v/o Fe-Al were prepared with plasma arc spraying by forming thick (∼5mm) coatings onto Cu substrates. By incorporating a controlled fraction of porosity and micro-cracks within the plasma sprayed target, cracking or delamination of the target during magnetron sputtering could be avoided. Compositions of the as-deposited PVD films were close to the sputtering target composition when the bias voltage was kept around –40V; higher bias voltages (e.g., -100 to -200V) lead to coatings that were deficient in Al. As-deposited coatings prepared with the lower bias voltage could be subsequently annealed at 700°C for two hours to yield a nearly single-phase icosahedral structure. After annealing, composite coatings indicate the presence of an Fe-Al phase along with the icosahedral phase.
High pressure X-ray diffraction studies of quasicrystals are presented and discussed for icosahedral Al-Cu-Ru and Ti-Zr-Ni alloys. The results in hydrogenated Ti-Zr-Ni show that Ti- Zr-Ni may be more compressible after hydrogenation.
We have employed molecular beam epitaxy in the growth of InSb on GaAs and InP. The transport, optical and structural properties of the films were investigated by in-situ reflection high energy electron diffraction, Hall effect and temperature dependent Hall effect, photoluminescence, transmission electron microscopy and X-ray diffractometry techniques. We report mobilities of up to 32,000 cm2/volt-sec and free electron concentrations of 3x1016/cm3 at room temperature. We have discovered a new defect state in InSb with an energy position of Ec - 0.05 ± 0.006eV. Optical and structural measurements reveal that the differences in thermal expansion and lattice mismatch between the substrates and films results in the broadening of the X-ray diffraction peaks and the near gap photoluminescence linewidths. Furthermore, we observe band gap shifts to higher energies of 10meV and 20meV for growth on GaAs and InP, respectively.
Expanding interest in large-scale fabrication of electronic and photonic devices and in the scale-up of epitoxial growth reactors is creating the need for high quality large diameter InP substrate material. This paper will discuss the evaluating of three-inch diameter semi-insulating Fe-doped InP substrate material purchased from two commercial suppliers. The results of Photon Back Scatter, Infrared Transmission Microscopy, Hall Effect, and Spatially Resolved Photoluminescence measurements will be presented and evaluated.
Changes in the electronic properties of bulk GaAs crystals, grown from melts of varied As:Ga ratios, and Si-donor concentrations, were investigated by annealing in the temperature range 850°C to 1050°C. We found a gradual reduction of the free carrier concentration, a corresponding decrease in the luminescence spectral intensity, and a suppression of the near band-edge peaks with annealing time at any temperature. Deep level and impurity concentrations remained essentially constant. The magnitude of these changes was found to be determined predominantly by the annealing time and temperature, and the starting composition of the material We argue for a non-radiative native acceptor defect, or defect complex, forming during the annealing cycle. We present here the thermodynamic interpretation for this behavioi in terms of point defect equilibria.
We report the fabrication of modulation doped Si/Gex Si1−x heterostructures by molecular beam epitaxy. The samples are characterized by Rutherford backscattering spectrometry, cross-sectional transmission electron microscopy, electron beam induced current, Hall measurement, and the magnetoresistance (Shubnikov-de Haas) measurements. Threading dislocation densities of = 106cm−2 are observed for relaxed Ge0.3Si0.7 films on Si (100). The modulation doped structures fabricated on these Ge0.3 Si0.7 films contain two-dimensional electron gases with mobilities ranging from 60,000 to 96,000 cm2/V - s at 4.2 K.
We report attaining (3x2) surface reconstruction with streaky reflection high energy electron diffraction (RHEED) patterns on Al0.4Ga0.6As after in-situ Cl2 chemical etch and ultra high vacuum (UHV) anneal. Secondary ion-mass spectrometry (SIMS) analysis at the regrown/etched Al0.4Ga0.6 As interface reveals impurities of O and C in the level of (5±1) × 1012 cm-2 and (3±1) × 1012 cm-2, respectively. These impurity levels are 10 times less than those of Al0.4Ga0.6 As after in-situ electron cyclotron resonance (ECR) plasma etch and UHV anneal without Cl2 chemical etch.
The controled growth of large single grain of quasicrystalline phase in metallic alloys is a difficult task that requires a detailled knowledge of the corresponding phase diagram. We discuss the metallurgical specificities of the ternary systems AlCuFe and AlPdMn with respect to single icosahedral grain elaboration. We show that adding a few percents of Silicon in the AlCuFe system leads to stabilize two low order cubic approximants one, α, based on Bergman clusters with a parent F-type icosahedral phase and the other, α', based on Mackay clusters with a parent P-type icosahedral phase. A section of this quaternary phase diagram at constant Si content shows that these cubic phases have no common stability region but are located on opposite sides of an orthorhombic phase that is expected to be a complex synthetic structure mixing both Mackay and Bergman type atomic clusters.
The dodecagonal (dd) quasicrystalline tantalum telluride dd Ta1.6Te and the crystalline approximant Ta97Te60 have been modified by partly replacing tantalum by vanadium. The impact of the substitution on the structures has been studied by X-ray and electron diffraction and by high-resolution transmission electron microscopy. The layered-type approximant structure of Ta83V14Te60 was determined by single crystal X-ray means. The partitioning of vanadium on 21 out of 29 crystallographically inequivalent metal sites is referred to, but not controlled by the Dirichlet domain volume available at the sites. A HRTEM projection of dd (Ta, V)1.6Te onto the dodecagonal plane is analysed with respect to the arrangement of (Ta, V)151Te74 clusters on the vertices of an irregular aperiodic square-triangle tiling, the edge length of which corresponds to the distance between the centres of two such clusters. The clusters comprise about 1 nm thick corrugated lamellae which are periodically stacked by weak Te-Te interactions.
The first hydrogen absorption pressure-composition isotherms (p-c-T) were measured in quasicrystalline Ti45Zr38Ni17. No evidence for a pressure plateau was found, indicating a distribution of energies for the hydrogen in interstitial sites. Fits to the p-c-T data confirmed this, giving energy peaks at -0.19 eV with a full width at half maximum (half-width) of 0.06 eV, and at -0.09 eV with a half-width of 0.08 eV. This is in contrast with the broad site energy distribution that is characteristic of a metallic glass. In agreement, fits to data taken from amorphous Ti45Zr27Ni20Si8 gave a single broad energy distribution at -0.10 eV with a half-width of 0.35 eV. Based on the weighted averages of the site energies for the pure components, the energies assigned to the tetrahedral sites in the Ti44Zr40Ni16 1/1 approximant phase are in qualitative agreement with the measured data for the quasicrystal, supporting a local structural similarity between these two phases. Almost all of the absorbed hydrogen can be desorbed at 650°C in one hour by pumping, without transforming the quasicrystal phase and without powdering the rapidly-quenched samples.
Biaxially textured yttria stabilized zirconia (YSZ) buffer layers were deposited on long polycrystalline metallic tapes by an ion-beam-assisted deposition process (IBAD) to serve as templates for high-current carrying Y1Ba2Cu3O7-x (YBCO) films. YSZ was deposited by a dualionbeam equipment with two 11 cm Kaufman ion sources. The coating of large-area technical substrates, large in comparison with the ion sources, requires substrate movements to render YSZ films of homogeneous texture quality. These movements can hinder cooling of the metallic tapes in the absence of a thermal contact. Therefore, the temperature of those small-heat-capacity substrates could rise to above 100 °C within minutes, causing a decrease of the in-plane alignment of YSZ. The investigation of the temperature dependence of the IBAD process reveals that the best results of the in-plane alignment could be obtained by room temperature deposition. Applying high tape velocities hinder a rise of the deposition temperature to above 90 °C. Therefore, it is possible to deposit YSZ films on metal tapes (up to 60 mm × 1000 mm) with in-plane textures down to 15° full width at half maximum (FWHM), which allow their coating with highcurrent-carrying YBCO films.
Crystal approximant phases are important because they are believed to have a similar local atomic structure to corresponding quasicrystals. Interstitial hydrogen is used as a probe of the local structures of the Ti-based quasicrystals and crystal approximants. Phase pure samples of ct(TiCrSiO), a Mackay type 1/1 crystal approximant, which were plasma etched and coated with a thin layer of Pd, were loaded with deuterium from the gas phase to a maximum deuterium atom to metal atom ratio (D/M) of 0.26. After deuteration, the sample becomes a fine powder and remains single-phase. A Rietveld structural refinement of powder x-ray and neutron diffraction data was made to determine the location of the interstitial sites. For the fully deuterated sample the deuterium atoms sit at both octahedral and tetrahedral sites. The octahedral sites are formed by six Ti atoms in the first and second shells of the icosahedra. Deuterium atoms are also located at the tetrahedral interstitial sites formed between the clusters along <100> directions. In the partially loaded samples with DiM = 0.11, the deuterium atoms occupy only octahedral sites, demonstrating a preference for these sites.