相关论文: Blow-up Whitney forms, shadow forms, and Poisson p…

Given a real, twisted Dirac structure $L$ on a smooth manifold $M$, and a closed embedded submanifold $N\subseteq M$ of codimension $>1$, we characterise when $L$ lifts to a smooth, twisted Dirac structure on the real projective blowup of…

We define higher quantum Airy structures as generalizations of the Kontsevich-Soibelman quantum Airy structures by allowing differential operators of arbitrary order (instead of only quadratic). We construct many classes of examples of…

We introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The…

The FDA algebras emerging from twisted tori compactifications of M-theory with fluxes are discussed within the general classification scheme provided by Sullivan's theorems and by Chevalley cohomology. It is shown that the generalized…

Topological singularities occur in a broad range of physical systems, including collapsing stars and pinching fluid interfaces. They are important for being able to concentrate energy into a small region. Underwater air bubbles in…

Blow-up solutions to a heat equation with spatial periodicity and a quadratic nonlinearity are studied through asymptotic analyses and a variety of numerical methods. The focus is on the dynamics of the singularities in the complexified…

To investigate the finite time singularity in three-dimensional (3D) Euler flows, the simplified model of 3D axisymmetric incompressible fluids (i.e., two-dimensional Boussinesq approximation equations) is studied numerically. The system…

This paper introduces the basic concepts for physics-compatible discretization techniques. The paper gives a clear distinction between vectors and forms. Based on the difference between forms and pseudo-forms and the $\star$-operator which…

A unified ballooning theory, constructed on the basis of two special theories [Y. Z. Zhang, S. M. Mahajan, X. D. Zhang, Phys. Fluids B4, 2729 (1992); Y. Z. Zhang, T. Xie, Nucl. Fusion & Plasma Phys. 33, 193 (2013)], shows that a weak…

We discuss topological theories, arising from the general $\mathcal{N}=2$ twisted gauge theories. We initiate a program of their study in the Gromov-Witten paradigm. We re-examine the low-energy effective abelian theory in the presence of…

This thesis contains two parts. The first part deals with pion-nucleon/meson-baryon scattering in the Kadyshevsky formalism. This formalism is introduced and discussed. Problems may arise when derivative couplings and/or higher spin fields…

We consider generic 2 x 2 singular Liouville systems on a smooth bounded domain in the plane having some symmetry with respect to the origin. We construct a family of solutions to which blow-up at the origin and whose local mass at the…

We compare heterotic string models on orbifolds with supergravity models on smooth compact spaces, obtained by resolving the orbifold singularities. Our main focus is on heterotic E8xE8 models on the resolution of the compact T^6/Z_3…

The 2d Boussinesq equations model large scale atmospheric and oceanic flows. Whether its solutions develop a singularity in finite-time remains a classical open problem in mathematical fluid dynamics. In this work, blowup from smooth…

A novel thermodynamically consistent diffuse interface model is derived for compressible electrolytes with phase transitions. The fluid mixtures may consist of N constituents with the phases liquid and vapor, where both phases may coexist.…

A general framework is presented for the renormalization of Hamiltonians via a similarity transformation. Divergences in the similarity flow equations may be handled with dimensional regularization in this approach, and the resulting…

Complex tetrahedral surface $\mathcal{T}$ is a non planar projective surface that is generated by four intersecting complex projective planes $CP^{2}$. In this paper, we study the family $\{\mathcal{T}_{m}\} $ of blow ups of $\mathcal{T}$…

We consider the classical problem of the blowing-up of solutions of the nonlinear heat equation. We show that there exist infinitely many profiles around the blow-up point, and for each integer $k$, we construct a set of codimension $2k$ in…

We study $C^1$ blow-up of the compressible fluid model introduced by Gardner and Morikawa, which describes the dynamics of a magnetized cold plasma. We propose sufficient conditions that lead to $C^1$ blow-up. In particular, we find that…

We prove very general formulae for the generating series of (Hodge) genera of symmetric products with coefficients, which hold for complex quasi-projective varieties with any kind of singularities, and which include many of the classical…