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In this paper we obtain the Lie derivatives of the scalar parameters in the generalized Euler decomposition with respect to arbitrary axes under left and right deck transformations. This problem can be directly related to the representation of the angular momentum in quantum mechanics. As a particular example, we calculate the angular momentum and the corresponding quantum hamiltonian in the standard Euler and Bryan representations. Similarly, in the hyperbolic case, the Laplace-Beltrami operator is retrieved for the Iwasawa decomposition. The case of two axes is considered as well.
Controlling alloy composition, crystalline quality, and crystal orientation is necessary to achieve high thermoelectric performance in Bi 1-x Sb x thin films. These microstructural attributes are demonstrated in this letter via co-sputter deposition of Bi and Sb metals on Si/SiO 2 substrates followed by ex-situ post anneals ranging from 200 – 300 °C in forming gas with rapid cooling to achieve orientation along the trigonal axis. We show with cross-sectional transmission electron microscopy and energy-dispersive X-ray spectrometry that 50 – 95% of the Sb segregates at the surface upon exposure to air during transfer. This then forms a nanocrystalline Sb 2 O 3 layer upon annealing, leaving the bulk of the film primarily Bi metal which is a poor thermoelectric material. We demonstrate a SiN capping technique to eliminate Sb segregation and preserve a uniform composition throughout the thickness of the film. Given that the Bi 1-x Sb x solid solution melting point depends on the Sb content, the SiN cap allows one to carefully approach but not exceed the melting point during annealing. This leads to the strong orientation along the trigonal axis and high crystalline quality desired for thermoelectric applications.
Motivated by nucleation and molecular aggregation in physical, chemical, and biological settings, we present an extension to a thorough analysis of the stochastic self-assembly of a fixed number of identical particles in a finite volume. We study the statistics of times required for maximal clusters to be completed, starting from a pure-monomeric particle configuration. For finite volumes, we extend previous analytical approaches to the case of arbitrary size-dependent aggregation and fragmentation kinetic rates. For larger volumes, we develop a scaling framework to study the first assembly time behavior as a function of the total quantity of particles. We find that the mean time to first completion of a maximum-sized cluster may have a surprisingly weak dependence on the total number of particles. We highlight how higher statistics (variance, distribution) of the first passage time may nevertheless help to infer key parameters, such as the size of the maximum cluster. Finally, we present a framework to quantify formation of macroscopic sized clusters, which are (asymptotically) very unlikely and occur as a large deviation phenomenon from the mean-field limit. We argue that this framework is suitable to describe phase transition phenomena, as inherent infrequent stochastic processes, in contrast to classical nucleation theory.
We investigated Moran - Ricker model with time lag 1. It is made analytical and numerical study of the model. It is shown there is co-existence of various dynamic regimes under the same values of parameters. The model simultaneously possesses several different limit regimes: stable state, periodic fluctuations, and chaotic attractor. The research results show if present population size substantially depends on population number of previous year then it is observed quasi-periodic oscillations. Fluctuations with period 2 occur when the growth of population size is regulated by density dependence in the current year.
The Monte Carlo simulation of the gamma spectroscopy systems is a common practice in these days. The most popular softwares to do this are MCNP and Geant4 codes. The intrinsic spatial efficiency method is a general and absolute method to determine the absolute efficiency of a spectroscopy system for any extended sources, but this was only demonstrated experimentally for cylindrical sources. Due to the difficulty that the preparation of sources with any shape represents, the simplest way to do this is by the simulation of the spectroscopy system and the source. In this work we present the validation of the intrinsic spatial efficiency method for sources with different geometries and for photons with an energy of 661.65 keV. In the simulation the matrix effects (the auto-attenuation effect) are not considered, therefore these results are only preliminaries. The MC simulation is carried out using the FLUKA code and the absolute efficiency of the detector is determined using two methods: the statistical count of Full Energy Peak (FEP) area (traditional method) and the intrinsic spatial efficiency method. The obtained results show total agreement between the absolute efficiencies determined by the traditional method and the intrinsic spatial efficiency method. The relative bias is lesser than 1% in all cases.
Here, we propose a relationship between the dynamics in the amorphous and crystalline domains during polymer crystallization: the fluctuations of ordering-rate about a material-specific value in the amorphous phase drive those fluctuations associated with the increase in percent crystallinity. This suggests a differential equation that satisfies the three experimentally observed time regimes for the rate of crystal growth. To test this postulated expression, we applied a suite of statistical learning tools to molecular dynamics simulations to extract the relevant phenomenology. This study shows that the proposed relationship holds in the early time regime. It illustrates the effectiveness of soft computing tools in the analysis of coarse-grained simulations in which patterns exist, but may not easily yield to strict quantitative evaluation. This ability assists us in characterizing the critical early time molecular arrangement during the primary nucleation phase of polymer melt crystallization. In addition to supporting the validity of the proposed kinetics expression, the simulations show that (i) the classical nucleation and growth mechanism is active in the early stages of ordering; (ii) the number of nuclei and their masses grow linearly during this early time regime; and (iii) a fixed inter-nuclei distance is established.
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The superfluid phase of helium-4, known as He ii, exhibits extremely small kinematic viscosity and may be a useful tool for economically producing and studying high Reynolds number turbulent flow. Such applications are not currently possible because a comprehensive understanding of the complex two-fluid behavior of He ii is lacking. This situation could be remedied by a systematic investigation of simple, well controlled turbulence that can be directly compared with theoretical models. To this end, we have developed a new apparatus that combines flow visualization with second sound attenuation to study turbulence in the wake of a mesh grid towed through a He ii filled channel. One of three mesh grids (mesh number M = 3, 3.75, or 5 mm) can be pulled at speeds between 0.1 and 60 cm/s through a cast acrylic flow channel which has a 16 mm × 16 mm cross section and measures 330 mm long. The motion of solidified deuterium tracer particles, with diameter of the order 1 μm, in the resulting flow is captured by a high speed camera, and a particle tracking velocimetry algorithm resolves the Lagrangian particle trajectories through the turbulent flow field. A pair of oscillating superleak second sound transducers installed in the channel allows complementary measurement of vortex line density in the superfluid throughout the turbulent decay process. Here, success in early experiments demonstrates the effectiveness of both probes, and preliminary analysis of the data shows that both measurements strongly correlate with each other. Further investigations will provide comprehensive information that can be used to address open questions about turbulence in He ii and move toward the application of this fluid to high Reynolds number fluid research
It is well known that spall failure strongly depends on the microstructure of a material. There have been numerous studies to study the effect of grain size on the overall spall strength and the total amount of damage in single element metals like copper. However, such systematic studies remain rare in two-phase materials and alloys. In this work, two incipient spall experiments were performed on a Cu–1%Pb alloy to understand the effect of grain size on the damage and failure in a two-phase material. Overall, these results showed that even though the spall strength did not change as a function of grain size, there were significant differences in the total amount of damage as a function of grain size. A clear increase in the total damage present in the material was seen as the grain size was increased from 32 to either 70 or 75 μm in either of the experiments. Furthermore, this difference was attributed to variations in the void growth rate as the grain size was increased.
The 5d pyrochlore iridate family (R 2 Ir 2 O 7 , where R is a rare earth ion) has garnered significant attention due to its topological properties, such as Weyl semimetallic phases and axion insulator. However, the investigation of these properties has been impeded by severe iridium loss during growth, which results in the formation of defects and impurities. Herein, we demonstrate a method for controlling impurities and defects in strained Nd 2 Ir 2 O 7 (NIO-227) films by compensating for iridium loss during growth. By increasing the amount of IrO 2 target ablated, we enhance the morphological quality and electrical transport properties of the fabricated films. Furthermore, our results show that the anomalous Hall effects of the films have a strong dependency on the amount of IrO 2 target ablated, which is attributed to the structural inhomogeneity in the NIO-227 films. Our work provides a way to control defects and impurities and would promote the investigation of topological phases in the family R 2 Ir 2 O 7 .
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An experimental sample of a waveguide CO{sub 2} laser with a quasi-uniform profile of the output radiation intensity is designed on the basis of a waveguide quasi-optical cavity of a new type comprising the generic confocal cavity with a nonuniform mirror and the hollow waveguide with the dimensions satisfying the conditions for self-imaging the quasi-uniform field. The surface of the mirror has the discrete large-scale absorbing nonuniformities. Results of theoretical and experimental investigations of spatial-energy characteristics of the laser in using uniform or amplitude-stepped reflecting mirrors are presented. (lasers)
We have proposed an optimal design of five different core structures (St1 – St5) for a seven-core trench-assisted multicore fibre, whose core radius and relative core/cladding refractive index difference Δ{sub 1} are optimal for single-mode propagation. The crosstalk performance and its reduction (in dB) with respect to variations in fibre design parameters, such as cladding/trench (Δ{sub 2}) depth and trench width W{sub t} are investigated. It is shown that some fibre operational parameters, like, fibre bending radius, operating wavelength and fibre length, affect the crosstalk performance. It is found that the crosstalk and its reduction amount are extremely dependent on the values of Δ{sub 1} and Δ{sub 2}. The dispersion characteristics of the cores are investigated for all the proposed core structures and the observed dispersion is found to be about – 6 ps nm{sup −1} km{sup −1} at an operating wavelength of 1550 nm. An ultralow crosstalk (less than –100 dB per 100 km) can be achieved mainly with two proposed core structures (St4 and St5) having a suitably higher values of Δ{sub 1} along with a small core radius for single-mode propagation. The multicore fibre design with many cores (up to 55) is demonstrated to ensure a high transmission capacity. (optical fibres)
We consider differential equations with quadratic right-hand sides that admit two quadratic first integrals, one of which is a positive-definite quadratic form. We indicate conditions of general nature under which a linear change of variables reduces this system to a certain 'canonical' form. Under these conditions, the system turns out to be divergenceless and can be reduced to a Hamiltonian form, but the corresponding linear Lie-Poisson bracket does not always satisfy the Jacobi identity. In the three-dimensional case, the equations can be reduced to the classical equations of the Euler top, and in four-dimensional space, the system turns out to be superintegrable and coincides with the Euler-Poincaré equations on some Lie algebra. In the five-dimensional case we find a reducing multiplier after multiplying by which the Poisson bracket satisfies the Jacobi identity. In the general case for n>5 we prove the absence of a reducing multiplier. As an example we consider a system of Lotka-Volterra type with quadratic right-hand sides that was studied by Kovalevskaya from the viewpoint of conditions of uniqueness of its solutions as functions of complex time. Bibliography: 38 titles.
Significance Formation of quasiparticles, such as excitons, polarons, and trions in semiconductors are the foundation for modern optoelectronics. Unlike the widely investigated exciton and polaron, the trion, a three-body charge-exciton bound state, is less familiar due to its small binding energy in conventional inorganic semiconductors. Here, employing ultrafast spectroscopy and rigorously controlled charge-doping levels, we characterize trion creation and decay in single-walled carbon nanotubes (SWNTs), wherein trions are stable at room temperature. We show that SWNT trions derive exclusively from a precursor exciton state, and importantly, that exciton-to-trion conversion can approach unity under appropriate conditions. Because trions simultaneously carry excitation energy, charge, and spin, our findings may guide design of new SWNT-based optoelectronic devices, including photovoltaics, photodetectors, and spintronics.