Related papers: Bouncing Jacobi fields and the Allen-Cahn equation…
We investigate the phase diagram and critical behavior of three-dimensional multicomponent Abelian-Higgs models, in which an N-component complex field z_x^a of unit length and charge is coupled to compact quantum electrodynamics in the…
The asymptotic behavior of an anisotropic Cahn-Hilliard functional with prescribed mass and Dirichlet boundary condition is studied when the parameter epsilon that determines the width of the transition layers tends to zero. The double-well…
It follows from the Grothendieck-Ogg-Shafarevich formula that the rank of an abelian variety (with trivial trace) defined over the function field of a curve is bounded by a quantity which depends on the genus of the base curve and on bad…
Phase-field models are a popular choice in computational physics to describe complex dynamics of substances with multiple phases and are widely used in various applications. We present nonlocal non-isothermal phase-field models of…
In this paper, we obtain an explicit formula for the discrepancy between the limit of the second inner variations of $p$-Laplace Allen-Cahn energies and the second inner variation of their $\Gamma$-limit which is the area functional. Our…
We present an alternative derivation of the parity anomaly for a massless Dirac field in 2+1 dimensions coupled to a gauge field. The anomaly functional, a Chern-Simons action for the gauge field, is obtained from the non-trivial Jacobian…
We consider the sharp interface limit for the scalar-valued and vector-valued Allen-Cahn equation with homogeneous Neumann boundary condition in a bounded smooth domain $\Omega$ of arbitrary dimension $N\geq 2$ in the situation when a…
In the light of $\phi$-mapping method and topological current theory, the topological structure and the topological quantization of arbitrary dimensional topological defects are obtained under the condition that the Jacobian $J(\phi/v) \neq…
We consider the inhomogeneous Allen-Cahn equation $$ \epsilon^2\Delta u\,+\,V(y)(1-u^2)\,u\,=\,0\quad \mbox{in}\ \Omega, \qquad \frac {\partial u}{\partial \nu}\,=\,0\quad \mbox{on}\ \partial \Omega, $$ where $\Omega$ is a bounded domain in…
Even dimensional defects and boundaries in conformal field theory support type $a$ anomalies on their world-volume. We show that the one-point functions of marginal operators, in the presence of defects and boundaries, are anomalous, and…
We study numerically the one-dimensional Allen-Cahn equation with the spectral fractional Laplacian $(-\Delta)^{\alpha/2}$ on intervals with homogeneous Neumann boundary conditions. In particular, we are interested in the speed of sharp…
The paper concludes the cycle of investigations on the bifurcation diagrams of the system with three degrees of freedom which describes the motion of an axially symmetric top with the Kowalevski conditions in a double force field. The…
A spherical model of skeleton with junctions is investigated by Monte Carlo simulations. The model is governed by one-dimensional bending energy. The results indicate that the model undergoes a first-order transition separating the smooth…
Given a compact Riemannian manifold with boundary, we prove that the limit of a sequence of embedded, almost properly embedded free boundary minimal hypersurfaces, with uniform area and Morse index upper bound, always inherits a non-trivial…
In this paper we study the Nirenberg problem on standard half spheres $(\mathbb{S}^n_+,g), \, n \geq 5$, which consists of finding conformal metrics of prescribed scalar curvature and zero boundary mean curvature on the boundary. This…
The purpose of this article is to determine explicitly the complete surfaces with parallel mean curvature vector, both in the complex projective plane and the complex hyperbolic plane. The main results are as follows: When the curvature of…
A common paradigm in phase-field models with singular potentials is that global-in-time weak solutions converge to a single equilibrium only after undergoing asymptotic regularization. However, in arXiv:2510.17296 we introduced a novel…
This paper is inspired from the nice result of Andrew Hassell on the eigenfunctions in the stadium billiard. From a classical paper of V. Arnol'd, we know that quasi-modes are not always close to exact modes. We show that, for almost all…
We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills…
We consider the Allen-Cahn equations with memory (a partial integro-differential convolution equation). The prototype kernels are exponentially decreasing functions of time and they reduce the integrodifferential equation to a hyperbolic…