Search results for "rotational symmetry"
showing 10 items of 58 documents
Mathematical modelling of the feed rod shape in floating zone silicon crystal growth
2017
Abstract A three-dimensional (3D) transient multi-physical model of the feed rod melting in the floating zone (FZ) silicon single-crystal growth process is presented. Coupled temperature, electromagnetic (EM), and melt film simulations are performed for a 4 inch FZ system, and the time evolution of the open melting front is studied. The 3D model uses phase boundaries and parameters from a converged solution of a quasi-stationary axisymmetric (2D) model of the FZ system as initial conditions for the time dependent simulations. A parameter study with different feed rod rotation, crystal pull rates and widths of the inductor main slit is carried out to analyse their influence on the evolution …
Relativistic simulations of rotational core collapse : I. Methods, initial models, and code tests
2002
We describe an axisymmetric general relativistic code for rotational core collapse. The code evolves the coupled system of metric and fluid equations using the ADM 3+1 formalism and a conformally flat metric approximation of the Einstein equations. The relativistic hydrodynamics equations are formulated as a first-order flux-conservative hyperbolic system and are integrated using high-resolution shock-capturing schemes based on Riemann solvers. We assess the quality of the conformally flat metric approximation for relativistic core collapse and present a comprehensive set of tests which the code successfully passed. The tests include relativistic shock tubes, the preservation of the rotatio…
No-core configuration-interaction model for the isospin- and angular-momentum-projected states
2016
[Background] Single-reference density functional theory is very successful in reproducing bulk nuclear properties like binding energies, radii, or quadrupole moments throughout the entire periodic table. Its extension to the multi-reference level allows for restoring symmetries and, in turn, for calculating transition rates. [Purpose] We propose a new no-core-configuration-interaction (NCCI) model treating properly isospin and rotational symmetries. The model is applicable to any nucleus irrespective of its mass and neutron- and proton-number parity. It properly includes polarization effects caused by an interplay between the long- and short-range forces acting in the atomic nucleus. [Metho…
Angular Pseudomomentum Theory for the Generalized Nonlinear Schr\"{o}dinger Equation in Discrete Rotational Symmetry Media
2009
We develop a complete mathematical theory for the symmetrical solutions of the generalized nonlinear Schr\"odinger equation based on the new concept of angular pseudomomentum. We consider the symmetric solitons of a generalized nonlinear Schr\"odinger equation with a nonlinearity depending on the modulus of the field. We provide a rigorous proof of a set of mathematical results justifying that these solitons can be classified according to the irreducible representations of a discrete group. Then we extend this theory to non-stationary solutions and study the relationship between angular momentum and pseudomomentum. We illustrate these theoretical results with numerical examples. Finally, we…
X-ray emission from stellar jets by collision against high-density molecular clouds: an application to HH 248
2015
We investigate the plausibility of detecting X-ray emission from a stellar jet that impacts against a dense molecular cloud. This scenario may be usual for classical T Tauri stars with jets in dense star-forming complexes. We first model the impact of a jet against a dense cloud by 2D axisymmetric hydrodynamic simulations, exploring different configurations of the ambient environment. Then, we compare our results with XMM-Newton observations of the Herbig-Haro object HH 248, where extended X-ray emission aligned with the optical knots is detected at the edge of the nearby IC 434 cloud. Our simulations show that a jet can produce plasma with temperatures up to 10 MK, consistent with producti…
Regularization of spherical and axisymmetric evolution codes in numerical relativity
2007
Several interesting astrophysical phenomena are symmetric with respect to the rotation axis, like the head-on collision of compact bodies, the collapse and/or accretion of fields with a large variety of geometries, or some forms of gravitational waves. Most current numerical relativity codes, however, can not take advantage of these symmetries due to the fact that singularities in the adapted coordinates, either at the origin or at the axis of symmetry, rapidly cause the simulation to crash. Because of this regularity problem it has become common practice to use full-blown Cartesian three-dimensional codes to simulate axi-symmetric systems. In this work we follow a recent idea idea of Rinne…
Modelling the Effects of Internal Textures on Symmetry Detection Using Fuzzy Operators
2009
Symmetry is a crucial dimension which aids the visual system, human as well as artificial, to organize its environment and to recognize forms and objects. In humans, detection of symmetry, especially bilateral and rotational, is considered to be a primary factor for discovering and interacting with the surrounding environment. Rotational symmetry detecting can be affected by less-known factors, such as the stimulus internal texture. This paper explores how fuzzy operators can be usefully employed in modeling the effects of the internal texture on symmetry detection. To this aim, we selected two symmetry detection algorithms, based on different computational models, and compared their output…
Three-Dimensional Core-Collapse Supernova Simulations with Multi-Dimensional Neutrino Transport Compared to the Ray-by-Ray-plus Approximation
2018
Self-consistent, time-dependent supernova (SN) simulations in three spatial dimensions (3D) are conducted with the Aenus-Alcar code, comparing, for the first time, calculations with fully multi-dimensional (FMD) neutrino transport and the ray-by-ray-plus (RbR+) approximation, both based on a two-moment solver with algebraic M1 closure. We find good agreement between 3D results with FMD and RbR+ transport for both tested grid resolutions in the cases of a 20 solar-mass progenitor, which does not explode with the employed simplified set of neutrino opacities, and of an exploding 9 solar-mass model. This is in stark contrast to corresponding axisymmetric (2D) simulations, which confirm previou…
Noise-Assisted Crystallization of Opal Films
2012
International audience; An improvement of the crystal quality of opal fi lms self-assembled from polymer spheres in a moving meniscus using the agitation by white noise acoustic vibrations is demonstrated. A tenfold higher ordering of a hexagonal sphere packing in the (111) plane is achieved. This crystallization method, the mechanism of which is described in terms of the stochastic resonance, is a contrast to the widely used approach based on maintaining equilibrium conditions during the crystallization process. The precise quantifi cation of the incremental lattice order improvement as a function of acoustic noise intensity is achieved by calculating the probability of finding an opposite…
Numerical 2D modelling of turbulent melt flow in CZ system with dynamic magnetic fields
2004
Abstract The paper presents results of 2D axisymmetric mathematical modelling of laboratory CZ model facility that corresponds well to a large industrial silicon CZ growth system. The purpose of the investigation is to examine turbulent melt flow features that develop in the model crucible, when various dynamic magnetic fields (travelling, alternating) are applied, and to test the applicability of the modified low Re k–e turbulence model for the calculation of flows in these cases by extensive comparisons between calculated and measured data. The electromagnetic field is calculated with a self-developed program, and the calculations of the melt motion are carried out with the user modified …