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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.
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.
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.
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 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.
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.
Dry sliding friction and wear experiments were performed with pin-on-disc techniques using WC and brass pins in contact with quasicrystalline (Al65Cu23Fe12) and crystalline (Al50Cu35Fe15 and Al70Cu20Fe10) discs, which were prepared by powder metallurgy routes. The contact loads (1, 5 and 10 N) used in this study produced similar coefficients of friction 0.3-0.4 for the Al65Cu23Fe12 and Al50Cu35Fe15 phases. These values are higher than previously reported for quasicrystalline and related crystalline phases. Possible reasons for these differences are presented. The contrasting wear behavior between different pins and discs is discussed in terms of contact area, oxidation, material transfer mechanisms and fracture characteristics.
The nucleation behavior of the 1/1 quasicrystal approximant phase was investigated in Ti-TMSi- O (TM=Mn, Cr, Fe) alloys made near the stoichiometric composition. Containerless solidification studies were performed using electromagnetic (rf) levitation and drop-tube techniques. The solidification microstructures indicate that α-Ti nucleated first in Ti-Cr-Si-O and β-Ti in Ti-Mn-Si-O alloys; the 1/1 phase nucleated and grew on these titanium oxide dendrites. In Ti-Fe-Si-O alloys, the 1/1 phase nucleated and grew directly from the liquid, allowing information on the nucleation rates to be obtained from undercooling data.
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.
Stable quasicrystals exhibit specific and unusual physical properties, such as, diamagnetism, low electrical conductivity, low thermal conductivity, and large themoelectric power at room temperature. These properties can be understood with a Bragg's reflexions scheme due to their dense filled reciprocal space.This leads to small gaps on the Fermi surface (some tenths of eV), much narrower than the usual Hume-Rothery ones (of order of 0.5 eV) which explain their stability. These gaps lead to the existence of quasi Umklapp processes, crucial for the interpretation of thermoelectric power. In some cases, the positive phonon drag contribution due to Umklapp processes, add with the electronic one's and dominates at room temperature with a large positive thermoelectric power. A crude estimate of the figure of merit gives some hope for applications of some quasicrystals and high approximants as new thermoelectric materials.