arXiv subjects

Xiang Qin

Publications and source records attributed to Xiang Qin.

6 recordsLinked to original sources

arXiv2026

Exact Blowup Analysis for the Weak-Advection Hou--Li Model

We study self-similar singularity formation for the one-dimensional weak-advection Hou--Li model, a reduced model motivated by the axisymmetric Euler equations. In the periodic setting, we construct exact finite-time self-similar blowup solutions for $2/3<a<1$, with profiles that are neither focusing nor expanding. In the whole-space setting with a Neumann condition, we construct exact finite-time self-similar blowup solutions for the full range $0<a\leq1$, with profiles of focusing, non-expanding/non-focusing, or expanding form depending on the sign of the self-similar scaling parameter. The construction is based on a fixed-point formulation near the origin, followed by an ODE extension argument. We also establish regularity, asymptotic behavior, monotonicity properties of the profiles, and uniqueness up to the natural scaling invariance.

math.AP↗

arXiv2026

Self-similar blow-up profile for the one-dimensional reduction of generalized SQG with infinite energy

We study the singularity formation mechanisms of the inviscid generalized Surface Quasi-Geostrophic (gSQG) equation on the whole space $\mathbb{R}^2$ and on the upper half-plane $\mathbb{R}^2_+$, allowing infinite energy. In each case, we derive a one-dimensional reduction that captures the leading-order singular behavior of the original 2D system, and use a fixed-point argument to show the existence of finite-time self-similar blow-up solutions for the 1D systems. We also perform numerical simulations for verification and visualization.

math.AP↗

arXiv2024

Multi-scale self-similar finite-time blowups of the Constantin-Lax-Majda model for the 3D Euler equations

We construct a new class of asymptotically self-similar finite-time blowups that have two collapsing spatial scales for the 1D Constantin-Lax-Majda model. The larger spatial scale measures the decreasing distance between the bulk of the solution and the eventual blowup point, while the smaller scale measures the shrinking size of the bulk of the solution. Similar multi-scale blowup phenomena have recently been discovered for many higher dimensional equations. Our study may provide some understanding of the common mechanism behind these multi-scale blowups.

math.AP↗

arXiv2023

Exact self-similar finite-time blowup of the Hou-Luo model with smooth profiles

We show that the 1D Hou-Luo model on the real line admits exact self-similar finite-time blowup solutions with smooth self-similar profiles. The existence of these profiles is established via a fixed-point method that is purely analytic. We also prove that the profiles satisfy some monotonicity and convexity properties that were unknown before, and we give rigorous estimates on the algebraic decay rates of the profiles in the far field. Our result supplements the previous computer-assisted proof of self-similar finite-time blowup for the Hou-Luo model with finer characterizations of the profiles.

math.AP↗

arXiv2023

Self-similar finite-time blowups with smooth profiles of the generalized Constantin-Lax-Majda model

We show that the $a$-parameterized family of the generalized Constantin-Lax-Majda model, also known as the Okamoto-Sakajo-Wunsch model, admits exact self-similar finite-time blowup solutions with interiorly smooth profiles for all $a\leq 1$. Depending on the value of $a$, these self-similar profiles are either smooth on the whole real line or compactly supported and smooth in the interior of their closed supports. The existence of these profiles is proved in a consistent way by considering the fixed-point problem of an $a$-dependent nonlinear map, based on which detailed characterizations of their regularity, monotonicity, and far-field decay rates are established. Our work unifies existing results for some discrete values of $a$ and also explains previous numerical observations for a wide range of $a$.

math.AP↗

arXiv2013

Assemblathon 2: evaluating de novo methods of genome assembly in three vertebrate species

Background - The process of generating raw genome sequence data continues to become cheaper, faster, and more accurate. However, assembly of such data into high-quality, finished genome sequences remains challenging. Many genome assembly tools are available, but they differ greatly in terms of their performance (speed, scalability, hardware requirements, acceptance of newer read technologies) and in their final output (composition of assembled sequence). More importantly, it remains largely unclear how to best assess the quality of assembled genome sequences. The Assemblathon competitions are intended to assess current state-of-the-art methods in genome assembly. Results - In Assemblathon 2, we provided a variety of sequence data to be assembled for three vertebrate species (a bird, a fish, and snake). This resulted in a total of 43 submitted assemblies from 21 participating teams. We evaluated these assemblies using a combination of optical map data, Fosmid sequences, and several statistical methods. From over 100 different metrics, we chose ten key measures by which to assess the overall quality of the assemblies. Conclusions - Many current genome assemblers produced useful assemblies, containing a significant representation of their genes, regulatory sequences, and overall genome structure. However, the high degree of variability between the entries suggests that there is still much room for improvement in the field of genome assembly and that approaches which work well in assembling the genome of one species may not necessarily work well for another.

q-bio.GN↗