Search results for "Mathematical"
showing 10 items of 7967 documents
Modelling of thermal field and point defect dynamics during silicon single crystal growth using CZ technique
2018
Abstract Silicon single crystal growth by the Czochralski (CZ) technique is studied numerically using non-stationary mathematical models which allow to predict the evolution of the CZ system in time, including Dash neck, cone and cylindrical growth stages. The focus is on the point defect dynamics, also considering the effect of the thermal stresses. During the cylindrical stage, the crystal pull rate is temporarily reduced as in experiments by Abe et al. The crystal radius and heater power change is explicitly considered in the calculations for crystal diameters of 50, 100 and 200 mm and the agreement with experiments is discussed.
On asymmetric periodic solutions in relay feedback systems
2021
Abstract Asymmetric self-excited periodic motions or periodic solutions which are produced by relay feedback systems that have symmetric characteristics are studied in the paper. Two different mechanisms of producing an asymmetric oscillation by a system with symmetric properties are noted and analyzed by the locus of a perturbed relay system (LPRS) method. Bifurcation between the ability to excite symmetric and asymmetric oscillation with variation of system parameters is analyzed. An algorithm of finding asymmetric solutions is proposed.
Reversed polarized emission in highly strained a-plane GaN/AlN multiple quantum wells
2010
The polarization of the emission from a set of highly strained $a$-plane GaN/AlN multiple quantum wells of varying well widths has been studied. A single photoluminescence peak is observed that shifts to higher energies as the quantum well thickness decreases due to quantum confinement. The emitted light is linearly polarized. For the thinnest samples the preferential polarization direction is perpendicular to the wurtzite $c$ axis with a degree of polarization that decreases with increasing well width. However, for the thickest well the preferred polarization direction is parallel to the $c$ axis. Raman scattering, x-ray diffraction, and transmission electron microscopy studies have been p…
Commissioning of the vacuum system of the KATRIN Main Spectrometer
2016
The KATRIN experiment will probe the neutrino mass by measuring the β-electron energy spectrum near the endpoint of tritium β-decay. An integral energy analysis will be performed by an electro-static spectrometer (``Main Spectrometer''), an ultra-high vacuum vessel with a length of 23.2 m, a volume of 1240 m[superscript 3], and a complex inner electrode system with about 120 000 individual parts. The strong magnetic field that guides the β-electrons is provided by super-conducting solenoids at both ends of the spectrometer. Its influence on turbo-molecular pumps and vacuum gauges had to be considered. A system consisting of 6 turbo-molecular pumps and 3 km of non-evaporable getter strips ha…
Description of intermodulation generation of nonlinear responses beyond the validity of the power series expansion
2021
Weakly nonlinear responses are commonly described by a power series expansion. However, intermodulation distortion products that cannot be described by a power series have been observed in a variety of physical systems. As the power series description is only applicable within its radius of convergence, we choose an alternative approach based on Fourier coefficients to describe intermodulation levels beyond the convergence of the power series. The description over a wide power range allows us to make a decision about models and to determine previously inaccessible model parameters. We apply the approach to data obtained from the characterization of the nonlinear dielectric susceptibility of…
Towards Open Domain Chatbots—A GRU Architecture for Data Driven Conversations
2018
Understanding of textual content, such as topic and intent recognition, is a critical part of chatbots, allowing the chatbot to provide relevant responses. Although successful in several narrow domains, the potential diversity of content in broader and more open domains renders traditional pattern recognition techniques inaccurate. In this paper, we propose a novel deep learning architecture for content recognition that consists of multiple levels of gated recurrent units (GRUs). The architecture is designed to capture complex sentence structure at multiple levels of abstraction, seeking content recognition for very wide domains, through a distributed scalable representation of content. To …
Gasdynamic ECR ion source for negative ion production
2018
H− ion sources are needed in various areas of accelerator technology, such as beam injection into cyclotrons and storage rings and as a part of neutral beam injectors for plasma heating in experimental facilities studying thermonuclear fusion. It was recently demonstrated that gasdynamic ion source based on ECR discharge in a simple mirror trap is very efficient for proton beam production [1]. Here we use the gasdynamic plasma source as the first stage driver of volumetric negative ion production through dissociative electron attachment (DEA) [2]. Experiments were performed with a pulsed 37 GHz / up to 100 kW gyrotron radiation in a dual-trap magnetic system, which consists of two identical…
Adaptive Finite Temperature String Method in Collective Variables.
2017
Here we present a modified version of the on-the-fly string method for the localization of the minimum free energy path in a space of arbitrary collective variables. In the proposed approach the shape of the biasing potential is controlled by only two force constants, defining the width of the potential along the string and orthogonal to it. The force constants and the distribution of the string nodes are optimized during the simulation, improving the convergence. The optimized parameters can be used for umbrella sampling with a path CV along the converged string as the reaction coordinate. We test the new method with three fundamentally different processes: chloride attack to chloromethane…
Pressure‐induced widths and shifts for the ν3 band of methane
1994
International audience; Widths and shifts of methane lines perturbed by nitrogen are calculated using a complex-valued implementation of Robert-Bonamy (RB) theory. The static intermolecular potential is described as a sum of electrostatic forces and Lennard-Jones (6-12) atom-atom terms, using literature values for all physical parameters. Vibrational dependence of the isotropic potential is obtained from the polarizability of methane assuming a dispersion interaction. The repulsive part of the Lennard-Jones accounts for the greatest part of widths, while dispersion interactions are largely responsible for shifts. Although the average error between calculated and observed linewidths (up to J…
Theoretical Investigation of the Low-Energy States of CpMoCl(PMe 3 ) 2 and Their Role in the Spin-Forbidden Addition of N 2 and CO
2003
International audience; A recent computational investigation of Jahn−Teller effects in unsaturated 16-electron d4d6 [CpMLn] complexes (Abu-Hasanayn, F.; Cheong, P.; Oliff, M. Angew. Chem.2002, 41, 2120) highlighted the typical presence of two spin-triplet and two singlet states of competing stability in these complexes and pointed out the necessity to account for more than one electronic state in studies thereof. Consequently, we have reinvestigated the addition of N2 to all the four low-energy states of CpMoCl(PH3)2, a reaction for which previously only one singlet and one triplet state have been considered (Keogh, D. W.; Poli, R. J. Am. Chem. Soc.1997, 119, 2516). The present study was pe…