Potential singularity of the 3D Euler equations in the interior domain

Whether the 3D incompressible Euler equations can develop a finite time singularity from smooth initial data is one of the most challenging problems in nonlinear PDEs. In this paper, we present some new numerical evidence that the 3D axisymmetric incompressible Euler equations with smooth initial data of finite energy develop a potential finite time singularity at the origin. This potential singularity is different from the blow-up scenario revealed by Luo-Hou in \cite{luo2014potentially,luo2014toward}, which occurs on the boundary. Our initial condition has a simple form and shares several attractive features of a more sophisticated initial condition constructed by Hou-Huang in \cite{Hou-Huang-2021,Hou-Huang-2022}. One important difference between these two blow-up scenarios is that the solution for our initial data has a one-scale structure instead of a two-scale structure reported in \cite{Hou-Huang-2021,Hou-Huang-2022}. More importantly, the solution seems to develop nearly self-similar scaling properties that are compatible with those of the 3D Navier-Stokes equations. We will present numerical evidence that the 3D Euler equations seem to develop a potential finite time singularity. Moreover, the nearly self-similar profile seems to be very stable to the small perturbation of the initial data.Comment: 37 pages. This paper has been accepted by Foundation of Computational Mathematics. arXiv admin note: text overlap with arXiv:2102.0666

Dynamics aspect of subbarrier fusion reaction in light heavy ion systems

Subbarrier fusion of the 7Li + 12C reaction is studied using an antisymmetrized molecular dynamics model (AMD) with an after burner, GEMINI. In AMD, 7Li shows an \alpha + t structure at its ground state and it is significantly deformed. Simulations are made near the Coulomb barrier energies, i.e., E_{cm} = 3 - 8 MeV. The total fusion cross section of the AMD + GEMINI calculations as a function of incident energy is compared to the experimental results and both are in good agreement at E_{cm} > 3 MeV. The cross section for the different residue channels of the AMD + GEMINI at E_{cm} = 5 MeV is also compared to the experimental results.Comment: Talk given by Meirong Huang at the 11th International Conference on Nucleus-Nucleus Collisions (NN2012), San Antonio, Texas, USA, May 27-June 1, 2012. To appear in the NN2012 Proceedings in Journal of Physics: Conference Series (JPCS

Dynamical Evolution of Gamma-Ray Burst Remnants with Evolving Radiative Efficiency

In previous works, a generic dynamical model has been suggested by Huang et al., which is shown to be correct for both adiabatic and radiative blastwaves, and in both ultra-relativistic and non-relativistic phases. In deriving their equations, Huang et al. have assumed that the radiative efficiency of the fireball is constant. They then applied their model directly to realistic cases where the radiative efficiency evolves with time. In this paper, we abandon the above assumption and re-derive a more accurate dynamical equation for gamma-ray burst remnants. Numerical results show that Huang et al.'s model is accurate enough in general cases.Comment: 10 pages, 5 embedded eps figures, to appear in: Chin. J. Astron. Astrophys. (2002), Vol

Sergio F. Martínez y Xiang Huang. 2015. Hacia una Filosofía de la Ciencia Centrada en Prácticas

Review of Sergio F. Martínez y Xiang Huang. 2015. Hacia una Filosofía de la Ciencia Centrada en Práctica

Microstructure and mechanical properties of an Mg-3Zn- o.5Zr-5HA nanocomposite processed by ECAE

Mg matrix composites reinforced by natural bone constituent hydroxyapatite (HA) particles have shown promising in-vitro corrosion resistance but are inconsistent in both electrochemical and mechanical performances because of severe particle segregations. The present work was carried out to investigate the feasibility of a novel technology that combines high shear solidification and equal channel angular extrusion (ECAE) for fabricating Mg-HA nanocomposites. Experiments showed that the high shear solidification resulted in a fine and uniform grain structure with a globally uniform HA nanoparticles in fine clusters and the ECAE processing of the as-cast composites resulted in further grain refinement and more importantly the breakdown of nanoparticle aggregates, leading to the formation of a dispersion of true nanoparticles in the Mg alloy matrix with improved mechanical properties. This paper describes mainly the microstructural features and mechanical performance of Mg-3Zn-0.5Zr-xHA (x 1, 3, 5, 10) nanocomposites, in which the HA was in spherical shape with an average diameter of ∼20nm © Published under licence by IOP Publishing Ltd

Elliptical motions of stars in close binary systems

Motions of stars in close binary systems with a conservative mass exchange are examined. It is shown that Paczynski-Huang model widely used now for obtaining the semi-major axis variation of a relative stars orbit is incorrect, because it brings about large mistakes. A new model suitable for elliptical orbits of stars is proposed. Both of reactive and attractive forces between stars and a substance of the flowing jet are taken into account. A possibility of a mass exchange at presence of accretion disk is considere

Hall-Littlewood polynomials and a Hecke action on ordered set partitions

We construct an action of the Hecke algebra $H_n(q)$ on a quotient of the polynomial ring $F[x_1, \dots, x_n]$, where $F = \mathbb{Q}(q)$. The dimension of our quotient ring is the number of $k$-block ordered set partitions of $\{1, 2, \dots, n \}$. This gives a quantum analog of a construction of Haglund-Rhoades-Shimozono and interpolates between their result at $q = 1$ and work of Huang-Rhoades at $q = 0$.Comment: 11 page