The vortex dynamics of a Ginzburg-Landau system under pinning effect

It is proved that the vortices are attracted by impurities or inhomogeities in the superconducting materials. The strong H^1-convergence for the corresponding Ginzburg-Landau system is also proved.Comment: 23page

Development of a Multiphase Photon Monte Carlo Method for Spray Combustion and its Application in High-pressure Conditions

In this work the development of a multiphase photon Monte Carlo (PMC) method with a focus on resolving radiative heat transfer in combustion simulations is presented. The multiphase PMC solver can account for description of participating media in both Lagrangian and Eulerian frameworks. The solver is validated against exact solutions in several one-dimensional configurations. The developed solver is then applied to Diesel spray combustions, where liquid spray droplets are assumed to be cold, nonemitting, large, and isotropically scattering. Several formulations for radiative properties of the Diesel spray are first explored. The PMC solver has then been coupled with the multiphase spray combustion solver in OpenFOAM and the coupled solver is used for simulations of high pressure Diesel spray combustion. It was found that in typical Diesel spray combustion applications, such as in an internal combustion engine, impact of radiation on the evolution of the liquid spray was insignificant. Although the impact of radiation on the spray was minimal, nongray spectral properties and the assumption of semi-transparency for Diesel spray were found to impact the radiative transfer significantly, while impact of scattering was marginal. Spray radiation was also found not to have much effect on global combustion characteristics in high-pressure engine-relevant configurations. However, a small but noticeable effect on minor species distribution relevant to pollutant formation was observed

Searching for Effects of Spatial Noncommutativity via Chern-Simons' Processes

The possibility of testing spatial noncommutativity in the case of both position-position and momentum-momentum noncommuting via a Chern-Simons' process is explored. A Chern-Simons process can be realized by an interaction of a charged particle in special crossed electric and magnetic fields, in which the Chern-Simons term leads to non-trivial dynamics in the limit of vanishing kinetic energy. Spatial noncommutativity leads to the spectrum of the orbital angular momentum possessing fractional values. Furthermore, in both limits of vanishing kinetic energy and subsequent vanishing magnetic field, the Chern-Simons term leads to this system having non-trivial dynamics again, and the dominant value of the lowest orbital angular momentum being $\hbar/4$, which is a clear signal of spatial noncommutativity. An experimental verification of this prediction by a Stern-Gerlach-type experiment is suggested.Comment: 18 page

Distributed Convergence Verification for Gaussian Belief Propagation

Gaussian belief propagation (BP) is a computationally efficient method to approximate the marginal distribution and has been widely used for inference with high dimensional data as well as distributed estimation in large-scale networks. However, the convergence of Gaussian BP is still an open issue. Though sufficient convergence conditions have been studied in the literature, verifying these conditions requires gathering all the information over the whole network, which defeats the main advantage of distributed computing by using Gaussian BP. In this paper, we propose a novel sufficient convergence condition for Gaussian BP that applies to both the pairwise linear Gaussian model and to Gaussian Markov random fields. We show analytically that this sufficient convergence condition can be easily verified in a distributed way that satisfies the network topology constraint.Comment: accepted by Asilomar Conference on Signals, Systems, and Computers, 2017, Asilomar, Pacific Grove, CA. arXiv admin note: text overlap with arXiv:1706.0407

The parity of specular Andreev reflection under mirror operation in zigzag graphene ribbon

It is known that the parity of reflection amplitude can either be even or odd under the mirror operation. Up to now, all the parities of reflection amplitude in the one-mode energy region are even under the mirror operation. In this paper, we give an example of odd parity for Andreev reflection (AR) in a three-terminal graphene-supercondutor hybrid systems. We found that the parity is even for the Andreev retroreflection (ARR) and odd for specular Andreev reflection (SAR). We attribute this remarkable phenomenon to the distinct topology of the band structure of graphene and the specular Andreev reflection involving two energy bands with different parity symmetry. As a result of odd parity of SAR, the SAR probability of a four-terminal system with two superconducting leads (two reflection interfaces) can be zero even when the system is asymmetric due to the quantum interference of two ARs.Comment: 11 pages, 3 figure