arXiv subjects

Xiaofeng Yang

Publications and source records attributed to Xiaofeng Yang.

205 records · Page 12Linked to original sources

arXiv2017

Numerical Approximations for a three components Cahn-Hilliard phase-field Model based on the Invariant Energy Quadratization method

How to develop efficient numerical schemes while preserving the energy stability at the discrete level is a challenging issue for the three component Cahn-Hilliard phase-field model. In this paper, we develop first and second order temporal approximation schemes based on the "Invariant Energy Quadratization" approach, where all nonlinear terms are treated semi-explicitly. Consequently, the resulting numerical schemes lead to a well-posed linear system with the symmetric positive definite operator to be solved at each time step. We rigorously prove that the proposed schemes are unconditionally energy stable. Various 2D and 3D numerical simulations are presented to demonstrate the stability and the accuracy of the schemes.

math.NA↗

arXiv2017

Efficient and accurate numerical schemes for a hydrodynamically coupled phase field diblock copolymer model

In this paper, we consider numerical approximations of a hydrodynamically coupled phase field diblock copolymer model, in which the free energy contains a kinetic potential, a gradient entropy, a Ginzburg-Landau double well potential, and a long range nonlocal type potential. We develop a set of second order time marching schemes for this system using the "Invariant Energy Quadratization" approach for the double well potential, the projection method for the Navier-Stokes equation, and a subtle implicit-explicit treatment for the stress and convective term. The resulting schemes are linear and lead to symmetric positive definite systems at each time step, thus they can be efficiently solved. We further prove that these schemes are unconditionally energy stable. Various numerical experiments are performed to validate the accuracy and energy stability of the proposed schemes.

math.NA↗

arXiv2017

Numerical Approximations for a Phase-Field Moving Contact Line Model with Variable Densities and Viscosities

We consider the numerical approximations of a two-phase hydrodynamics coupled phase-field model that incorporates the variable densities, viscosities and moving contact line boundary conditions. The model is a nonlinear, coupled system that consists of incompressible Navier--Stokes equations with the generalized Navier boundary condition, and the Cahn--Hilliard equations with moving contact line boundary conditions. By some subtle explicit--implicit treatments to nonlinear terms, we develop two efficient, unconditionally energy stable numerical schemes, in particular, a linear decoupled energy stable scheme for the system with static contact line condition, and a nonlinear energy stable scheme for the system with dynamic contact line condition. An efficient spectral-Galerkin spatial discretization is implemented to verify the accuracy and efficiency of proposed schemes. Various numerical results show that the proposed schemes are efficient and accurate.

math.NA↗

arXiv2014

Flow-pattern switching in a Motored Spark Ignition Engine

Cyclic-to-cycle variability, CCV, of intake-jet flow in an optical engine was measured using particle image velocimetry (PIV), revealing the possibility of two different flow patterns. A phase-dependent proper orthogonal decomposition (POD) analysis showed that one or the other flow pattern would appear in the average flow, sampled from test to test or sub-sampled within a single test; each data set contained individual cycles showing one flow pattern or the other. Three-dimensional velocity data from a large-eddy simulation (LES) of the engine showed that the PIV plane was cutting through a region of high shear between the intake jet and another large flow structure. Rotating the measurement plane 10° revealed one or the other flow structure observed in the PIV measurements. Thus, it was hypothesized that cycle-to-cycle variations in the swirl ratio result in the two different flow patterns in the PIV plane. Having an unambiguous metric to reveal large-scale flow CCV, causes for this variability were examined within the possible sources present in the available testing. In particular, variations in intake-port and cylinder pressure, lateral valve oscillations, and engine RPM were examined as potential causes for the cycle-to-cycle flow ariations using the phase-dependent POD coefficients. No direct correlation was seen between the intake port pressure, or the pressure drop across the intake valve, and the in-cylinder flow pattern. A correlation was observed between dominant flow pattern and cycle-to-cycle variations in intake valve horizontal position. RPM values and in-cylinder flow patterns did not correlate directly. However, a shift in flow pattern was observed between early and late cycles in a 2900-cycle test after an approximately 5 rpm engine speed perturbation.

physics.flu-dyn↗

arXiv2013

Searching for a preferred direction with Union2.1 data

A cosmological preferred direction was reported from the type Ia supernovae (SNe Ia) data in recent years. We use the Union2.1 data to give a simple classification of such studies for the first time. Because the maximum anisotropic direction is independent of isotropic dark energy models, we adopt two cosmological models ($Λ$CDM, $w$CDM) for the hemisphere comparison analysis and $Λ$CDM model for dipole fit approach. In hemisphere comparison method, the matter density and the equation of state of dark energy are adopted as the diagnostic qualities in the $Λ$CDM model and $w$CDM model, respectively. In dipole fit approach, we fit the fluctuation of distance modulus. We find that there is a null signal for the hemisphere comparison method, while a preferred direction ($b=-14.3^\circ \pm 10.1^\circ, l=307.1^\circ \pm 16.2^\circ$) for the dipole fit method. This result indicates that the dipole fit is more sensitive than the hemisphere comparison method.

astro-ph.CO↗

arXiv2013

Analytical Solutions of Singular Isothermal Quadrupole Lens

Using analytical method, we study the Singular Isothermal Quadrupole (SIQ) lens system, which is the simplest lens model that can produce four images. In this case, the radial mass distribution is in accord with the profile of the Singular Isothermal Sphere (SIS) lens, and the tangential distribution is given by adding a quadrupole on the monopole component. The basic properties of the SIQ lens have been studied in this paper, including deflection potential, deflection angle, magnification, critical curve, caustic, pseudo-caustic and transition locus. Analytical solutions of the image positions and magnifications for the source on axes are derived. As have been found, naked cusps will appear when the relative intensity $k$ of quadrupole to monopole is larger than 0.6. According to the magnification invariant theory of the SIQ lens, the sum of the signed magnifications of the four images should be equal to unity \citep{dal98}. However, if a source lies in the naked cusp, the summed magnification of the left three images is smaller than the invariant 1. With this simple lens system, we study the situations that a point source infinitely approaches a cusp or a fold. The sum of magnifications of cusp image triplet is usually not equal to 0, and it is usually positive for major cusp while negative for minor cusp. Similarly, the sum of magnifications of fold image pair is usually neither equal to 0. Nevertheless, the cusp and fold relations are still equal to 0, in that the sum values are divided by infinite absolute magnifications by definition.

astro-ph.CO↗

arXiv2011

The optimal weighting function for cosmic magnification measurement through foreground galaxy-background galaxy (quasar) cross correlation

Cosmic magnification has been detected through cross correlation between foreground and background populations (galaxies or quasars). It has been shown that weighing each background object by its $α-1$ can significantly improve the cosmic magnification measurement \citep{Menard02,Scranton05}. Here, $α$ is the logarithmic slope of the luminosity function of background populations. However, we find that this weighting function is optimal only for sparse background populations in which intrinsic clustering is negligible with respect to shot noise. We derive the optimal weighting function for general case including scale independent and scale dependent weights. The optimal weighting function improves the S/N (signal to noise ratio) by $\sim 20%$ for a BigBOSS-like survey and the improvement can reach a factor of $\sim 2$ for surveys with much denser background populations.

astro-ph.CO↗