Finite size specimens with cracks of icosahedral AI-Pd-Mn quasicrystals

Icosahedral quasicrystals are the most important and thermodynamically stable in all about 200 kinds of quasicrystals currently observed. Beyond the scope of classical elasticity, apart from a phonon displacement field, there is a phason displacement field in the elasticity of the quasicrystal, which induces an important effect on the mechanical properties of the material and makes an analytical solution difficult to obtain. In this paper, a finite element algorithm for the static elasticity of icosahedral quasicrystals is developed by transforming the elastic boundary value problem of the icosahedral quasicrystals into an equivalent variational problem. Analytical and numerical solutions for an icosahedral A1-Pd-Mn quasicrystal cuboid subjected to a uniaxial tension with different phonon-phason coupling parameters are given to verify the validity of the numerical approach. A comparison between the analytical and numerical solutions of the specimen demonstrates the accuracy and efficiency of the present algorithm. Finally, in order to reveal the fracture behavior of the icosahedral A1-Pd-Mn quasicrystal, a cracked specimen with a finite size of matter is investigated, both with and without phonon-phason coupling. Meanwhile, the geometry factors are calculated, including the stress intensity factor and the crack opening displacement for the finite-size specimen. Computational results reveal the importance of pbonon-phason coupling effect on the icosahedral A1-Pd-Mn quasicrystal. Furthermore, the finite element procedure can be used to solve more complicated boundary value problems.     

Survey of Plasmonic Nanoparticles: From Synthesis to Application

The unique properties of plasmonic nanostructures have fuelled research based on the tremendous amount of potential applications. Their tailor‐made assemblies in combination with the tunable size and morphology of the initial building blocks allow for the creation of materials with a desired optical response. In this respect, it is crucial to synthesize nanoparticles with a defined shape that are at the core of such developments. Moreover, the interaction of individual nanoparticles with an incident electromagnetic field cannot only be influenced by their structure, but in fact, also by their spatial arrangement to each other. To harvest such opportunities, a profound theoretical understanding of these interactions is required as well as concise strategies to create such ordered assemblies. A quantitative evaluation of their optical properties can only be conducted when discrete structures of high uniformity can be achieved. As a consequence, separation steps have to be applied in order to obtain materials of high purity and uniformity. This also allows for an easier structural characterization of the nanoparticles and their assembled superstructures. In this progress report, an overview about the current development in this field of research is provided.     

In vitro evaluation of cytotoxic and inflammatory properties of silica nanoparticles of different sizes in murine RAW 264.7 macrophages

The biological response to four well-characterized amorphous silica nanoparticles was investigated in RAW 264.7 macrophages in view of their potential application as drug carriers to sites of inflammation. All silica nanoparticles-induced cell membrane damage, reduced metabolic activity, generated ROS and released various cytokines, but to different extents. Two silica nanoparticles of 34 nm (A and B) with different zetapotentials were more cytotoxic than (aggregated) 11 and 248 nm nanoparticles, while cytokines were mostly induced by the (aggregated) 11 nm and only one of the 34 nm nanoparticles (34A). The results indicate that specific silica nanoparticles may have counterproductive effects, for example when used as carriers of anti-inflammatory drugs. The physicochemical properties determining the response of nanoparticles vary for different responses, implying that a screening approach for the safe development of nanoparticles needs to consider the role of combinations of (dynamic) physicochemical properties and needs to include multiple toxicity endpoints.     

Development of a time-resolved white-light interference microscope for optical phase measurements during fs-laser material processing

A modified Mach–Zehnder interferometer set-up combined with microscope objectives has been developed for the measurement of phase changes in the processed material sample, like modification and melting of glass. The white light is generated by focusing ultrafast laser radiation (t _p=80 fs) in a sapphire crystal using a micro-lens array to minimize temporal and spatial fluctuations in the white-light continuum. Lateral and coaxial pump-probe measurements of the phase changes during material processing are performed using two coupled ultrafast laser sources at different repetition rates (f _rep=1 Hz–1 MHz). The optical phase shift and therefore the refractive index of the material are calculated from the interference images using two approaches. The knowledge of the refractive index during the laser processing with a temporal resolution in the ps-range and a spatial resolution of several microns leads to a better understanding of the initial processes for the permanent material modifications.     

Effective primality tests for integers of the formsN=k3 n +1 andN=k2 m 3 n +1

Using third roots of unity Proth's theorem for primality testing is generalized to integers of the formN=k3 ⁿ +1, avoiding the use of Lucas sequences which are more suitable ifN+1 is factored instead ofN–1. This approach has the advantage of being easily combined with Proth's test and gives polynomial time algorithms for testing integers of the formN=k2 ^m 3 ⁿ +1.     

Analytic calculation of scaling dimensions: Tricritical hard squares and critical hard hexagons

The finite-size corrections, central chargesc, and scaling dimensionsx of tricritical hard squares and critical hard hexagons are calculated analytically. This is achieved by solving the special functional equation or inversion identity satisfied by the commuting row transfer matrices of these lattice models at criticality. The results are expressed in terms of Rogers dilogarithms. For tricritical hard squares we obtainc=7/10,x=3/40, 1/5, 7/8, 6/5 and for hard hexagons we obtainc=4/5,x=2/15, 4/5, 17/15, 4/3, 9/5, in accord with the predictions of conformal and modular invariance.     

The job-shop problem and immediate selection

The job-shop problem is one of the most difficult NP-hard scheduling problems. A 10×10-problem published in 1963 has been solved only recently by Carlier and Pinson using a branch and bound method. Other branch and bound algorithms have been developed recently. The efficiency of all these branch and bound methods relies on the concept of immediate selection which allows to introduce order relations on the setI of all operations to be processed on the same machine before branching. We present new algorithms for immediate selection. Among them are

1. anO(max {n logn,f})-algorithm for fixing all disjunctions induced by cliques;
2. anO(n ²)-algorithm based on concepts which are different from those used by Carlier and Pinson.

Here,n is the number of operations inI andf is the number of induced order relations.     

Geometric dynamic recrystallization of austenitic stainless steel through linear plane-strain machining

ABSTRACT

Type 316L austenitic stainless steel was severely plastically deformed at room temperature using linear plane-strain machining in a single pass that imparted shear strains up to 2.2 at strain rates up to 2?×?10³ s^?1. The resulting microstructures exhibited significant grain size refinement and improved mechanical strength where geometric dynamic recrystallization was identified as the primary microstructural recrystallization mechanism active at high strain rates. This mechanism is rarely observed in low to medium stacking fault energy materials. The critical stress required for twin initiation is raised by the combined effects of refined grain size and the increase in stacking fault energy due to the adiabatic heating of the chip, thus permitting geometric dynamic recrystallization. The suppression of martensite formation was observed and is correlated to the significant adiabatic heating and mechanical stabilisation of the austenitic stainless steel. A gradient of the amount of strain induced martensite formed from the surface towards the interior of the chip. As the strain rate is increased from 4?×?10² s^?1–2?×?10³ s^?1, a grain morphology change was observed from a population of grains with a high fraction of irregular shaped grains to one dominated by elongated grain shapes with a microstructure characterised by an enhanced density of intragranular sub-cell structure, serrated grain boundaries, and no observable twins. As strain rates were increased, the combination of reduction in strain induced martensite and non-uniform intragranular strain led to grain softening where a Hall-Petch relationship was observed with a negative strengthening coefficient of ?0.08?MPa m^1/2.     

WKB properties of the time-dependent Schrödinger system

It is shown that the time-dependent WKB expansion highlights some of the hidden properties of the Schrödinger equation and forms a natural bridge between that equation and the functional integral formulation of quantum mechanics. In particular it is shown that the leading (zero- and first-order in ) terms in the WKB expansion are essentially classical, and the relationship of this result to the classical nature of the WKB partition function, and of the anomalies in quantum field theory, is discussed.